Citation
Improved process control in camshaft grinding through utilization of post process inspection with feedback

Material Information

Title:
Improved process control in camshaft grinding through utilization of post process inspection with feedback
Creator:
Dalrymple, Timothy Mark, 1959- ( Dissertant )
Ziegert, John ( Thesis advisor )
Schueller, John ( Reviewer )
Matthew, Gary K. ( Reviewer )
Phillips, Winfred M. ( Degree grantor )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1993
Language:
English
Physical Description:
x, 117 leaves : ill., photos ; 29 cm.

Subjects

Subjects / Keywords:
Acceleration ( jstor )
Control systems ( jstor )
Error rates ( jstor )
Geometric angles ( jstor )
Geometry ( jstor )
Grinding ( jstor )
Grinding wheels ( jstor )
Machinery ( jstor )
Machining ( jstor )
Parametric models ( jstor )
Dissertations, Academic -- Mechanical Engineering -- UF
Mechanical Engineering thesis M.S
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )
theses ( marcgt )

Notes

Abstract:
In order to take full advantage of the introduction of computer numerical control technology in camshaft grinding and post-process inspection, a closed loop control scheme is proposed. This strategy makes use of post-process inspection results to modify the commanded part geometry used in the grinding program. The commands are modified in order to minimize the lobe contour and relative timing errors. It is shown that using a control strategy comprised of feedforward and feedback elements, substantial improvements in cam contour accuracy can be attained. A system capable of automated reduction of inspection results, application of statistical methods, transformations between different coordinate systems, and production of modified commanded part geometry is presented. This system requires no off-l;ine calibration or learning of grinding machin positioning errors. Additionally, it offers advantages over such techniques, in that it is able to automatically adapt to changing process conditions. the sytem is general in nature and may be used for any camshaft design. Through application of this system, the time required to bring a new part into tolerance is greatly reduced. With such a system used to minimize contour errors, it is no longer necessary to optimize grinding parameters based on these errors. Rather, grinding parameters can be manipulated to optimize other important factors, such as metal removal rates and the corresponding process time. Implementation of this system on existing computer numerically controlled (CNC) equipment is inexpensive. It requires only software necessary to produce the modified part geometry and limited hardware for file transfer. The required hardware is inexpensive and readily available.
Thesis:
Thesis (M.S.)--University of Florida, 1993.
Bibliography:
Includes bibliographical references (leaves 114-116).
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Timothy Mark Dalrymple.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
001892844 ( ALEPH )
29713749 ( OCLC )
AJW8098 ( NOTIS )

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IMPROVED PROCESS CONTROL IN CAMSHAFT GRINDING THROUGH
UTILIZATION OF POST PROCESS INSPECTION WITH FEEDBACK



















By

TIMOTHY MARK DALRYMPLE


A THESIS PRESENTED TO THE GRADUATE SCHOOL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


1993




































Copyright 1993

by

Timothy Mark Dalrymple














To my students at Botswana Polytechnic.



On the nights I remember the incredible gifts you

possess, the diversity of backgrounds and talents you

represent, I sleep well, knowing that Africa, will one day,

be safe in your hands.














ACKNOWLEDGMENTS


Like all human undertakings, this work would not have

been possible without the help of others. I am particularly

grateful to John Andrews and his staff at Andrews Products

for practically unconditional use of his excellent

facilities. At Andrews, I am especially grateful to Scott

Seaman. Also, thanks go to Chuck Dame of Adcole Corporation

for providing essential technical information concerning his

company's products.

I am also pleased to acknowledge the help and

encouragement which my advisor, John Ziegert, provided.

Lastly, I wish to thank my wife, Laura, for her unfailing

confidence, support, and patience.















TABLE OF CONTENTS


ACKNOWLEDGMENTS .. iv

LIST OF FIGURES . vii

ABSTRACT . .ix

CHAPTERS

1 INTRODUCTION .. 1

Scope of the Problem 1
Camshaft Grinding Technology 2
Analysis of Camshaft Geometrical Errors 4
Potential for Improvement 5

2 REVIEW OF THE LITERATURE 6

Compensation Through Positioning Error Modeling 6
Compensation Through In-Process Gauging 8
Compensation Using CMM for Post-Process
Inspection ... 9

3 CAMSHAFT GEOMETRY .. 11

Basic Description and Analysis .. 11
Industrial Convention 15
CCMM Convention 16
Grinding Machine Convention 18
Implications of Machining Techniques ... 18
Calculation of Grinding Wheel Path .. 25
Inspection Techniques for Process Control .. 26
Decomposition of Error Components .. 29
Timing Relative to Keyway/Fixture .. 31
Timing Relative to Lobe 1 .. 33

4 THE STOCHASTIC PROCESS MODEL .. 34

General Linear Least-Squares Estimation .. 34
Identification of Lift Error Model .. 36
Estimation of Model Parameters .. 39
Diagnostic Checking of the Model .. 41
Potential for Model Improvement .. 43


1








5 PROCESS CONTROL STRATEGY


The Control Interface 44
Lift Error Controller Model .. 48
An Interacting Lift Process Model .. 48
Noninteracting Control of Lift .. 50
The Implemented Lift Controller .. 50
Control of Relative Timing .. 55

6 PROCESS NOISE . 58

Statistical Process Control .. 59
Traditional Feedback Control with Filtering 60
Error Repeatability A Preliminary Study .. 63
Process Repeatability of Lift Errors .. 64
Process Repeatability of Timing Error 68

7 EXPERIMENTAL RESULTS .. 71

Results of Lift Error Control .. 74
Results of Timing Error Control .. 81
Control of Timing Relative to Lobe 1 81
Control of Timing Relative to Keyway/Fixture 83

8 CONCLUSIONS AND RECOMMENDATIONS .. 86

Implementation of the Control System .. 86
Further Work . 87


APPENDICES


A GRINDING PARAMETERS .. 90

B CAMSHAFT INSPECTION PARAMETERS .. 107

C SOFTWARE OUTLINES AND CONTROL SYSTEM PARAMETERS 111

REFERENCES . 114

BIOGRAPHICAL SKETCH .. 117


1














LIST OF FIGURES


Figure 3-1 Typical Four Lobe Camshaft .. 12

Figure 3-2 Radial Cam with Roller Type Follower 13

Figure 3-3 CCMM Angle Convention-Clockwise Rotation 17

Figure 3-4 Grinding Machine Angle Convention .. 19

Figure 3-5 Camshaft Axes-of-Rotation .. 22

Figure 3-6 Grinding Between Centers .. 23

Figure 3-7 Centerless Grinding Technique. ... 24

Figure 3-8 Grinding Wheel Path Calculations .. 27

Figure 3-9 Camshaft Inspection on a CCMM .. 28

Figure 3-10 Best Fit of Lift Errors .. 32

Figure 4-1 Lift Acceleration and Measured Lift Error 38

Figure 4-2 Stochastic Model Residual Errors .. 42

Figure 5-1 Typical Workspeed and Lift Acceleration 47

Figure 5-2 Interacting Lift Variables .. 49

Figure 5-3 Noninteracting Lift Control System 51

Figure 5-4 Implemented Lift Control System .. 53

Figure 5-5 Implemented Timing Angle Controller 56

Figure 6-1 Lift Error Process Repeatability 65

Figure 6-2 Lift Error Mean and Standard Deviation 66

Figure 6-3 Lift Error-to-Noise Ratio 67

Figure 6-4 Timing Angle Repeatability Error .. 69

Figure 7-1 Landis 3L Series Cam Grinder .. 72

vii








Figure 7-2

Figure 7-3

Figure 7-4

Figure 7-5

Figure 7-6

Figure 7-7

Figure 7-8

Figure 7-9

Figure 7-10


Adcole Model 911 CCMM ... ...

Lift Error using Control Scheme .

Lift Error using Control Scheme .

Lift Error using Control Scheme .

Lift Error using Control Scheme .

Total Lift Error using Control Scheme .

RMS of Lift Error using Control Scheme

Timing to Lobe 1 using Control Scheme .

Timing to Keyway using Control Scheme


viii














Abstract of Thesis Presented to the Graduate School of the
University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

IMPROVED PROCESS CONTROL IN CAMSHAFT GRINDING THROUGH
UTILIZATION OF POST PROCESS INSPECTION WITH FEEDBACK

By

Timothy Mark Dalrymple

May 1993


Chairman: John Ziegert
Major Department: Mechanical Engineering


In order to take full advantage of the introduction of

computer numerical control technology in camshaft grinding

and post-process inspection, a closed loop control scheme is

proposed. This strategy makes use of post-process

inspection results to modify the commanded part geometry

used in the grinding program. The commands are modified in

order to minimize the lobe contour and relative timing

errors. It is shown that using a control strategy comprised

of feedforward and feedback elements, substantial

improvements in cam contour accuracy can be attained.

A system capable of automated reduction of inspection

results, application of statistical methods, transformations

between different coordinate systems, and production of

modified commanded part geometry is presented. This system








requires no off-line calibration or learning of grinding

machine positioning errors. Additionally, it offers

advantages over such techniques, in that it is able to

automatically adapt to changing process conditions.

The system is general in nature and may be used for any

camshaft design. Through application of this system, the

time required to bring a new part into tolerance is greatly

reduced. With such a system used to minimize contour

errors, it is no longer necessary to optimize grinding

parameters based on these errors. Rather, grinding

parameters can be manipulated to optimize other important

factors, such as metal removal rates and the corresponding

process time.

Implementation of this system on existing computer

numerically controlled (CNC) equipment is inexpensive. It

requires only software necessary to produce the modified

part geometry and limited hardware for file transfer. The

required hardware is inexpensive and readily available.














CHAPTER 1
INTRODUCTION


Scope of the Problem


Camshafts find application in a wide range of consumer

and industrial products. In machine tools, camshafts have

long been used to control precise and high-speed machine

motions. Applications are common in both chip producing

equipment and high-speed dedicated assembly machinery [1].

Additionally, cams are used in fields as diverse as blood

separation and automated laser-scanner checkout systems.

Advances in servo motor and computer numerical control

(CNC) technology have lead to the replacement of cams in

many industrial applications. Still, camshafts will remain

essential for certain applications, such as the internal

combustion engine, for the foreseeable future.

In internal combustion engines, camshafts are used to

mechanically control the opening and closing of intake and

exhaust valves. The shape of the camshaft is critical in

determining the nature of the combustion process. As

pollution emission regulation for internal combustion

engines, particularly automobiles, have become more

stringent, the demands for higher precision camshafts and

better valve and combustion control have increased [2].

1








Z

Improvements in grinding media, machine design, and the

application of CNC provide for better control in camshaft

manufacturing. Yet, achieving high quality results depends

on properly coordinating the setting of a wide range of

grinding variables. These variables include: wheelspeed,

workspeed, dress parameters, grinding wheel quality,

dressing tool quality, temperature, etc. [3]. A change in

any of these parameters can produce deleterious effects on

part quality.


Camshaft Grinding Technology


Dimensional errors occurring in camshaft grinding are

attributable to a wide range of causes. Traditional cam

grinders use master cams to produce relative motion between

the grinding wheel and the workpiece. This relative motion

generates the desired camshaft geometry. Naturally, any

inaccuracies in the master cams produce corresponding errors

in the workpiece. Additionally, machines utilizing master

cams for control produce the optimal shape only for a single

grinding wheel size [3].

Conventional media based grinding wheels, such as

aluminum oxide or silicon carbide, require frequent dressing

to remain sharp and free cutting [4]. This continual

dressing produces a grinding wheel which is constantly

decreasing in diameter. As the wheel size deviates from the

nominal size, the dimensional accuracy of the camshaft








3

deteriorates [3]. While some master cam controlled machines

are able to compensate for wheel size wear through the use

of additional master cams [5,6], this increases the initial

cost, complexity of the machine and set up time. Also, this

improvement in contour requires sacrificing optimal control

over other parameters such as the cutting speed variation.

Additional sources of errors in camshaft grinding can

be traced to the nature of the contact between the grinding

wheel and workpiece. The "footprint," as the area of

contact is known, changes as the grinding wheel encounters

different curvatures on the cam surface. This change in

footprint affects the grinding wheel's cutting ability and

thus impacts the metal removal rate. Changes in grinding

conditions adversely affects workpiece accuracy [3].

The introduction of CNC technology in camshaft grinding

has produced benefits far beyond the flexibility generally

associated with CNC. Using this technology, the tool path

can be continually updated and optimized for any size of

grinding wheel [5,6]. Additionally, using a variable-speed

servo motor to control the headstock rotation, the variation

in footprint speed can be minimized. If the grinding

wheel's speed is constant, then minimizing the footprint

speed variation also minimizes the relative speed variation

between the cutting edges of the grinding wheel and the cam

lobe surface. Finally, the part geometry is specified in

software and can be readily modified.










Analysis of Camshaft Geometrical Errors


Manual techniques of camshaft inspection are generally

based on test fixtures which use dial indicators to measure

dimensional errors. This approach, while sufficient for

determining if functional requirements are satisfied, is

inadequate for quickly identifying machining errors. Using

manual test procedures, it is impossible to analyze all

error components and determine their cause in a timely

manner. Thus, process control based on such inspection

techniques is not feasible.

Computer-controlled cylindrical coordinate measuring

machines (CCMM) capable of fast and accurate camshaft

inspection have been available for two decades. With the

decrease in cost of computer hardware, CCMM have become more

affordable and are currently available in many camshaft

manufacturing facilities. Commercially available software

allows for some flexibility in data reduction [7]. This

flexibility provides for camshaft inspection based on

evaluation of functional criteria or for analysis of the

manufacturing process.

However, until recently, the majority of camshaft

grinders used master cams for control. Since the part

program is essentially ground into the master cam, the

potential for fine adjustments based on inspection results

did not exist. Consequently, the wealth of data derived

from CCMMs was poorly utilized. In most applications CCMMs


I







5

were simply used to identify non-conforming workpieces. In

some cases, CCMMs were effectively used to evaluate the

effects of individual grinding parameters, other than the

commanded geometry, on camshaft geometrical errors.


Potential for Improvement


The widespread introduction of CNC technology in

camshaft grinding provides the opportunity to better utilize

the information derived from CCMMs. Since part programs in

CNC machines can be readily changed, the program can be

modified based on repeatable errors observed in post-process

inspection. CCMMs capable of measuring up to 150 parts per

hour are currently on the market [8]. Camshaft grinders

with CNC produce approximately seven camshafts (12 lobe

shaft) per hour [2]. With the inspection process requiring

less time than the manufacturing process, the opportunity

exists to compensate for errors with a time lag of only one

part. The ability to automatically inspect camshafts and

produce compensated part programs presents great potential

for process improvement with little capital investment or

operator training.















CHAPTER 2
REVIEW OF THE LITERATURE


Most early research concerned with minimizing machining

errors focused on error avoidance. This research lead to

improvements in thermal stability, machine base stiffness,

precision components, and spindle design. These

improvements, while greatly increasing accuracy, did not

come without a cost. As machine tools became ever more

precise and mechanically sophisticated, the cost of these

machines continued to rise.

Much recent research on improving accuracy has focused

on error compensation rather than error avoidance. This

technique provides potential for improved accuracy without

costly mechanical design improvements. A review of the

literature in this area shows major research in three

categories: off-line modeling of positioning errors,

in-process inspection, and post-process inspection with

feedback.


Compensation Through Positioning Error Modeling


The use of a positioning error model has been the focus

of much recent research [9,10,11,12]. Donmez et al. [9]

describe a methodology by which the positioning errors are

6










measured using off-line laser interferometry and electronic

levels. These errors are then decomposed into geometric and

thermally-induced components. The geometric errors are

thermally-invariant and modeled with slide positions as

independent variables. The thermally-induced errors are

modeled using key component temperatures and slide position

as independent variables.

Once the positioning errors have been measured and the

model of the positioning errors established and verified,

error compensation can be applied. Since this method models

the workspace of the machine, and not the errors for a

particular workpiece, it is general in nature and can be

applied to parts not previously produced. However, it is

expected that over time, the machine will wear, the model

will become less accurate, and the machine will require

recalibration.

In certain machining operations, such as single point

turning, a one to one correspondence between machine errors

and workpiece errors can be established. For the single

point turning operation studied, Donmez reports accuracy

improvements of up to 20 times.

This work has been extended by Moon [13] to a system

where the laser measurement system is a integral component

of the machine tool. This system offers the advantage that

it does not require recalibration and is capable of

compensating for the portion of the stochastic error which










is autocorrelated. Such systems, however, greatly increase

the cost and complexity of machine tools.

In camshaft grinding, the relationship between machine

errors and workpiece errors is more complex than for the

case of single point turning. Additionally, the ability to

compensate for thermal errors is not so critical. The lift

of the camshaft is essentially a relative dimension which is

measured from the base circle. Since both the datum (base

circle) and the lift are machined simultaneously, the

accuracy is not greatly affected by thermal effects. A

warm-up period is not generally required.


Compensation Through In-Process Gauging


While many causes of form errors in camshafts have been

understood since the 1930s [14], CCMMs necessary to quickly

and accurately quantify these errors have existed for only

20 years. Additionally, CNC cam grinding machines necessary

for implementation of a compensation scheme, have only come

into widespread use in the past 10 years. Work has been

done in the area of in-process inspection and compensation

on machining centers [15], and the idea of an in-process

compensation scheme was first proposed for cam grinding by

Cooke and Perkins [16].

In their work at Cranfield Institute of Technology,

Cooke and Perkins proposed a prototype CNC camshaft grinding

machine using in-process gauging in 1978. The proposed










system employed a gauge probe located 180 degrees

out-of-phase with the grinding wheel. In the proposed

system, the probe is used to detect any deviation in the

measured workpiece from those commanded. The system

computer takes advantage of the 180 degree phase lag to

produce compensated control commands prior to the next

grinding pass. Through study of available servo drive

mechanisms and linear transducers available at the time, the

researchers expected to realize a machining accuracy on the

order of + 1.5 micrometer. While such systems are not today

in commercial production, this early work realized the

potential benefits of coupling camshaft grinding and

inspection.


Compensation Using CMM for Post-Process Inspection


An extensive review of the literature as well as

personal interviews with CCMM manufacturers revealed no

previous published work dealing with CCMMs and process

control. Much work has, however, been conducted using the

closely related Cartesian coordinate measuring machine (CMM)

for process control [17,18,19].

Yang and Menq [17] describe a scheme using a CMM for

post-process inspection of end-milled sculptured surfaces.

In this approach, 500 measurements are performed on a 55 mm

x 55 mm sculptured surface. The measured errors are then

best fit to a regressive cubic b-spline tensor-product








10

surface model. The results of this best fit are then used

to determine the compensation to be applied. Using this

technique, the researchers reported improvements in maximum

form error of 73%. While this improvement is significant,

CMMs have practical limitations, such as long cycle times,

that make them unsuitable for use in high volume process

control. The method used by Yang and Menq most resembles

the approach taken in this research.















CHAPTER 3
CAMSHAFT GEOMETRY


The material in this chapter is included to review the

nature of camshaft geometry as it relates to this research

project. The mathematical relationships describing cam

contour, the grinding wheel path, and decomposition of

inspection results are presented. Specific aspects of

camshaft geometry are examined for their significance in

developing a control strategy for the manufacturing process.

Lastly, the industrial conventions for specifying camshaft

geometry are introduced.


Basic Description and Analysis


A typical camshaft, as shown in Figure 3-1, consists of

a number of individual cam lobes, journal bearings, and a

timing reference. The geometry of a radial camshaft with a

translating follower is readily described in terms of the

base circle radius rb, the follower radius rf, the follower

lift s as a function of lobe angle 0, and the timing angle (

as shown in Figure 3-2. From this figure, it is evident

that the point-of-contact between the cam surface and the

cam follower does not generally lie along the follower's

line-of-action. This illustrates the difference between cam

11
















Side View


End View


Figure 3-1 Typical Four Lobe Camshaft





























































Figure 3-2 Radial Cam with Roller Type Follower










contour and the follower lift produced. Errors in cam

contour, at the point-of-contact between the follower and

cam profile surface, produce errors in follower lift.

For the radial cam with a roller follower shown in

Figure 3-2, the cam contour can be calculated as [20]


x = r cos + (3-1)
1 (3-1)



ds
x M + r (3-2)
N


where


M = r sin dscos 6 (3-3)
do



N= r cos 6 dsin 0 (3-4)
dO



r = rb + r + S (3-5)


and summarizing notation

s = lift

rb = base circle radius

rf = follower radius

r = the distance between cam and follower centers

0 = lobe angle

All camshaft/follower combinations, such as those with

offset roller followers or flat radial followers, can be

represented as camshafts with radial roller followers. All










camshafts considered in this research are represented in

this manner.


Industrial Convention


Both the CCMM and the CNC camshaft grinder used in this

research project adopt the same basic convention for

describing camshaft geometry. This convention is the de

facto industry standard and is used for programming CNC

machines and for reporting error results. These conventions

are adopted in this research to simplify the control

interface.

While both machines employ the same general convention,

the details of the implementation differ with regard to sign

convention and measurement datums. On both machines, the

follower lift is specified as a function of the lobe angle 6

as shown in Figure 3-2. The lobe angle is measured relative

to a coordinate system attached to the cam lobe and oriented

relative to a given geometrical lobe feature. The timing

angle 0 of the individual lobes is then specified relative

to some camshaft feature. Typical camshaft timing

references are eccentrics, lobe 1, dowel pins, or keyways as

illustrated in Figure 3-2. The base circle radius is the

datum for measurement of lift values. The positive

rotational direction is specified as counterclockwise when

viewed from the non-driven end of the camshaft, looking


I










towards the driven end. The details of the implementation

are described in the following two sections.


CCMM Convention


The convention illustrated in Figure 3-3 shows the

convention use by the Adcole 911 CCMM. This convention is

dependent on the camshaft direction-of-rotation. That is,

the CCMM direction-of-rotation is programmable and is

selected as the application direction-of-rotation. The

convention shown is for a camshaft which rotates in a

clockwise direction. In this convention, the lift s is

specified relative to the lobe angle 8. The lift values for

the opening side (the side of the lobe which produces

follower motion away from the camshaft axis-of-rotation)

precede the lift values for the closing side.

The timing angles are measured in the same direction as

the lift specification angle, but to a different datum.

Figure 3-3 shows the lobe timing angles measured from the

timing reference to the lobe nose. Again, the convention

shown is for a camshaft which rotates in a clockwise

direction. For a camshaft which rotates in a

counterclockwise direction, the lobe and timing angles are

measured in the opposite direction.










View Looking from Non-driven End to Driven End

















Opening
N N Side /
Se / Closing

Side





















Direction of
Rotation


Figure 3-3 CCMM Angle Convention-Clockwise Rotation










Grinding Machine Convention


The convention used on the CNC grinding machine does

not consider the camshaft functional direction-of-rotation.

Rather, the camshaft geometry is specified in a format which

reflects the direction-of-rotation of the grinding machine.

This convention is shown in Figure 3-4.


Implications of Machining Techniques


In analyzing camshaft geometry, it is necessary to

carefully consider the axis-of-rotation. For effective

process control, machining and inspection must be performed

with respect to the same axis. To facilitate a discussion

of the different axes used for camshaft machining and

inspection, it is helpful to introduce terminology for the

different axes. This terminology is defined as it is

introduced and summarized in Table 3-1.



Table 3-1 Camshaft Axes-of-Rotation

MAOR Axis-of-Rotation for Machining

IAOR Axis-of-Rotation for Inspection/Decomposition

CAOR Camshaft Axis-of-Rotation defined by Centers

JAOR Camshaft Axis-of-Rotation defined by Journals










View Looking from Non-driven End to Driven End












I






















4 Direction of
Rotation


Figure 3-4 Grinding Machine Angle Convention










The first two axes are the machining axis-of-rotation

(MAOR) and the inspection axis-of-rotation (IAOR). These

two axes do not refer to the actual camshaft axis-of-

rotation, but rather to the axis-of-rotation of the process.

The MAOR is defined as the axis about which the camshaft

rotates during the machining process. The IAOR is the axis,

with respect to which, the inspection results are

decomposed. The IAOR need not necessarily be the axis about

which the part rotates during the inspection process, since

it is possible to mathematically transform the inspection

results to other axes.

As stated previously, the MAOR and the IAOR must agree

for effective process control. If the two axes do not

agree, an error component, which is random in phase and

skew-symmetrically distributed in magnitude, is introduced

into the inspection results and therefore into the process

control signal. This error component is due to the

eccentricity of the journal bearings to the MAOR. This

component occurs only in cases where the journals are not

ground on the cam grinder. This error component will be

demonstrated through the introduction of the two additional

axes-of-rotation as described below.

First, the journal axis-of-rotation (JAOR) is defined

as the axis about which the camshaft rotates when the

camshaft journals are mated with ideal journal bearings.

The JAOR is determined in the inspection process.










To determine the JAOR, a best fit of a circle to the

inspection data for each journal is performed. The JAOR is

then established as the axis which passes through the

centers of these circles. In the case where more than two

journal bearings exist, a segmented JAOR can be used.

Second, the center axis-of-rotation (CAOR) is defined

as the axis about which the camshaft rotates, when the

female camshaft centers are mated with ideal male centers.

The JAOR and the CAOR, as shown in Figure 3-5, represent the

physical axes-of-rotation of the camshaft. In this figure,

the eccentricity of the journal surface is greatly

exaggerated to clearly illustrate the different axes.

The MAOR is dependent on the work holding method used

in the machining process. In this research, the camshaft is

held between centers. When using this method, the MAOR is

defined to be the CAOR. Camshaft grinding between centers

is shown in Figure 3-6. This arrangement uses a live

workhead center and a dead tailstock center.

Alternatively, camshafts can be ground using a

centerless grinding technique as shown in Figure 3-7. In

this approach, the camshaft is supported by fixtures and a

three jaw chuck. Here, the bearing journals must be ground

prior to grinding the cam contours, since these surfaces are

used to locate the camshaft during the grinding process.

The fixtures have hardened bearing surfaces which

effectively simulate the camshaft operating conditions. For


























JAOR


CAOR


Figure 3-5 Camshaft Axes-of-Rotation





































































Figure 2-6


indinc Between Centers



























































Figure 3-7 Centerless Grinding Technique

Source: "State-of-the-Art 3L Series CNC Cam Grinding
Systems," Litton Industrial Automation Systems, Pub. No.
3L-88 FR 3M, 1988. Used with permission.










centerless grinding approaches, the MAOR is defined as the

JAOR.

During inspection, measurement data must be decomposed

relative to a specific axis-of-rotation. The IAOR is

programmable. While the actual inspection is performed

between centers and therefore with respect to the CAOR, the

inspection results can be mathematically transformed from

the CAOR to the JAOR. Again, the IAOR must agree with the

MAOR to avoid the introduction of additional noise into the

process control signal.


Calculation of Grinding Wheel Path


The Cartesian coordinates, xc and y, of the path

traced by the grinding wheel axis-of-rotation are readily

calculated [20] as


x = x + (r cos 8 x) (3-6)



yc = y + (r sin y) (3-7)
if


where r, is the radius of the grinding wheel. The path can

be expressed in polar coordinates [20], which are suitable

for programming the CNC grinding machine, as

1
S (x + -) (3-8)



4 =arctan ye (3-9)
X 0








26

where p is the distance from the MAOR to the grinding wheel

axis-of-rotation, and y is the corresponding lobe angle for

the grinding process. The cam grinding operation is

illustrated in Figure 3-8.

From these equations, a table of p versus \ can be

constructed for any useful grinding wheel size. This table

corresponds to the positioning commands used internally in a

CNC grinding machine. The commands must frequently be

recalculated depending on grinding wheel size and

potentially even after each increment of in-feed if the

metal removal rate is to be closely controlled. The reason

for this can be seen from Figure 3-2. As discussed

previously, it is evident that the point-of-contact between

the cam surface and follower does not generally lie along

the follower's line-of-action. Consequently, an in-feed of

the grinding wheel does not have the effect of removing the

same amount of material from all portions of the cam lobe

surface since the point-or-contact will vary.


Inspection Techniques for Process Control


Camshaft inspection on CCMMs is accomplished using a

precision follower, of the diameter to be used in the

camshaft application, attached to a spring-loaded sliding

gauge head as shown in Figure 3-9. The movement of the

gauge head is measured using either precision scales or a

laser interferometer. This approach allows direct






























Grinding Wheel
Axis-of-Rotation


Figure 3-8 Grinding Wheel Path Calculations


MAOR










































































Figure 3-9 Camshaft Inspection on a CCMM


1.* I W- -










evaluation of camshaft lift errors and eliminates the need

to mathematically transform results from a non-conforming

follower to the actual follower diameter. When necessary,

this conversion can be performed using equations (3-6) and

(3-7) where the radius of the non-conforming follower is

substituted for the radius of the cutter. Numerical methods

must again be used to solve for the measured lift of the

application follower.

Using CCMMs it is possible to evaluate a range of

camshaft attributes. In addition to lift and timing errors,

most CCMMs are capable of measuring the following

parameters: eccentricity, roundness, taper, lift velocity,

and diameter. Camshaft inspection can be performed with

regard to either manufacturing or functional considerations.

These two approaches can differ depending on the technique

used to hold the work during grinding.


Decomposition of Error Components


Once the appropriate IAOR is selected, the CCMM is used

to decompose measurement results into components which can

be directly used to modify the commanded input to CNC cam

grinding machines. For the CCMM used in this study, the

method of decomposition is programmable. In this section,

the various available methods of decomposition are discussed

and the methods selected for this research are justified.








30

In order to explain the decomposition, a description of

the nature of CCMMs is required. These gauges collect data

on camshaft geometry by rotating the part about the CAOR as

shown in Figure 3-9. The camshaft drives the precision

follower and the measured lift is recorded, generally at one

degree increments. This process allows for rapid data

collection for the entire cam contour.

CCMMs are relative measurement devices and as such they

are ideally suited for inspecting camshafts which are used

with translational followers. The lift of the follower is

both defined and measured relative to the base circle. This

ensures exceptional accuracy for measuring lift errors by

eliminating any d.c. error component. The measurements of

absolute dimensions such as size, may or may not be

particularly accurate, depending on the configuration of the

individual CCMM.

When inspecting a cam lobe, data are first gathered for

the entire 360 degrees of rotation. Next, the d.c.

component or size error of the cam lobe is removed from the

data. This is accomplished by setting the average lift of

the base circle equal to zero and adjusting the data

accordingly. The data are then corrected for the

appropriate axis-of-rotation. As discussed in the previous

section, this selection depends on the machining work

holding method as well as whether the results are for use in










cam grinding process control or overall functional

evaluation.

The timing error and lift errors are next separated

using various programmable approaches. In the method used

in this research, the measured cam lift is rotated about the

selected IAOR until the root mean square value of the

difference between the nominal and measured lifts are

minimized. This is illustrated in Figure 3-10. Once the

orientation with the minimum error is determined, the lift

error is reported as the difference between the rotated

measured lift and the nominal lift. The timing error is

reported as the difference between the measured timing,

derived from the best fit process, and the nominal timing.


Timing Relative to Keyway/Fixture


Once the best fit of the lift values is performed, the

timing angle error can be evaluated. For lobe 1 the timing

must be specified relative to some reference such as a

keyway/fixture combination, an eccentric or a dowel. The

repeatability of these different references is highly

variable. Consequently, angles measured relative to such a

reference can have a high stochastic component.

For the case studied, the reference during inspection

is established using a key, a keyway and a mating fixture.

The fixture is fitted with an external timing pin as shown

in Figure 3-9. The CCMM determines the location of the


























Measured
Lift





















Nominal
Lift


Figure 3-10 Best Fit of Lift Errors










timing reference based on this pin. The grinding fixture,

shown in Figure 3-6, uses the same keyway/fixture

arrangement and includes a slot for the grinding drive pin.

Again, the grinding machine uses this slot as the timing

reference. This arrangement produces a highly non-

repeatable reference as will be discussed in more detail in

Chapter 6. Due to this stochastic component, it is

necessary to separate the lift error from the timing error

in order to more tightly control the repeatable lift errors.


Timing Relative to Lobe 1


The timing of all cam lobes except lobe 1 can be

measured relative to lobe 1. Since all stochastic

components due to fixture errors are removed, the lobe-to-

lobe 1 timing is repeatable and can be tightly controlled.

While timing angles for CNC camshaft grinding machines are

specified relative to a reference other than lobe 1, this

presents no problem as the absolute angle is readily

calculated from the relative angle measurement.














CHAPTER 4
THE STOCHASTIC PROCESS MODEL


Process modeling is used to establish the relationship

between the measured and commanded lift for any given cam

lobe. A stochastic process model of the combined cam

grinding machine and the existing CNC controller can be

developed using established modeling techniques. These

techniques best fit dimensionally homogeneous experimental

data to nominal data and produce an empirical relationship

between process input and output. To develop such a model,

it is advantageous to have a general idea of the causes of

process errors. If the source of errors can be identified,

then the selection of the form of the model does not need to

be made blindly, and the number of models tested can usually

be reduced.


General Linear Least-Squares Estimation


The technique of linear least-squares estimation is

used for the model developed [21,22]. In this technique,

the input to the system is manipulated and the output is

recorded. These data are collected and a linear algebra

based minimization technique is then used to best fit model

coefficients based on the experimental data. The model








35

obtained must then be examined for its ability to correctly

predict the behavior of the process.

In general, a process can be estimated by the discrete

model

Cn = so cn-1 + al cn-2" +a,- n-1 p (4-1)
+ 0P mn-d + P1 m-1-d + + Ps-1 mn-q-d+ + n


where

cn = controlled variable

mn = manipulated variable

p = order of model in controlled variable

q = order of model in manipulated variable

Ci = coefficient of controlled variable (i=0,1,2,...,p-l)

pj = coefficient of manipulated variable (j=0,l,2,...,q-l)

d = delay

n = residual error

The controlled and manipulated variables can be measured for

any number of observations N. The resulting N equations can

then be written in matrix form where n = 0, 1, 2,..., N-l as

c = xb + (4-2)


where


C-1 C-2 ... Cp mo-d m-1-d ... ml-q-d
Cg ... C-Ip ml-d md m2-q-d

x. (4-3)


CN-2 CN-3 CN-p MN-l-d mN-2-d .. mN-q-d











and where


Co
c !
C2




C- 1


I eN-I


ao
01





Pp-1
Po



Pi


(4-4)


The residuals of the model are


E = c xb


(4-5)


If the square of the residual errors is minimized then the

model coefficient matrix can be solved for as


(4-6)


.8 =[XT-1 X] C


where b contains the estimates of the model parameters.


Identification of Lift Error Model


The process model was employed to develop an

understanding of the interaction of lift error at different

lobe angles. The actual control scheme implemented controls

the lift at each of 360 points on the cam surface as if they

were separate variables. This means that there are

essentially 360 control systems for each cam lobe. The

process model developed here does not attempt to model the

control of the lift over a series of parts, but rather it










examines the relationship of the lift errors, and

consequently the 360 control systems, for individual cam

lobes.

As stated previously, it is useful to understand the

lift error source when developing the process model.

Figure 4-1 shows the lift error and lift acceleration for

the process studied. The use of the term acceleration here

is imprecise, since the workspeed is not constant during one

rotation. Therefore, the effective lift acceleration during

machining is somewhat different. To avoid confusion, the

acceleration shown in Figure 4-1 will be referred to as the

geometric acceleration. As suggested by Figure 4-1, a

strong correlation between the observed lift error and

geometric acceleration exists. The form of the interaction

model is suggested by examination of the mathematical

relationship between follower lift and acceleration.

The geometric acceleration can be expressed using the

backward-difference expression [23] as

A2m im 2 mg _+ m' (4-7)
A62 h2

where m. represents the manipulated variable which is the

commanded lift in this case. Assuming that the correlation

between lift error and acceleration suggested by Figure 4-1

is correct, then from equation (4-7) it can been seen that

the lift error at a given lobe angle is related to lift

commanded at that angle as well as lift commanded at the two




















Lift Acceleration and Error
1 -!


0.6' \ l !
0 ----- ---- ----------------------------. ....... ............... ............-..............................................
S0.6- 1 ----- -- --- -- *..........i......... ----------- -------- --*--*-......--*-- -'--- --- ------ -------------- ** ...........
........ ..... ....... .... .. .... ......... .....
0o. ---- ------ -----J
> I






-0.8 r
0. 2 ----- -- .. ......... ......................................................
.04-.. ... ......../............. ---....--

-- .... ------------------- ... ... .................... .................................-

-0.6.... ... .. ........................... ......... ............. ------------....-
-0.8-1---------------------------------------
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


S-- Acceleration .... Error


Figure 4-1 Lift Acceleration and Measured Lift Error










preceding angles. This relationship suggests that these

terms should be included in the model.

It is noted that this model includes no terms of the

controlled variable co, which represents the measured lift

at lobe angle 0. This is necessary, since with post-process

inspection, the value of the controlled variable is not

available until after the process is completed. Therefore,

it is not useful to include these components in a model

designed for process control based on post-process

inspection. The process model selected must be a purely

regressive model, where the process output is expressed in

terms of the commanded input.


Estimation of Model Parameters


Based on the correlation between lift error and the

geometric lift acceleration developed in the previous

section, the form of the stochastic interaction model is

selected. The model is given as equation (4-8) and models

the measured lift co using two unknown parameters.


CE = p m + 3 P'[ me 2 rp-i + m-2j (4-8)

The first term in the model is the product of model

parameter 3 and the commanded lift. The second term is the

product of parameter V3 and the commanded geometric

acceleration of the lift.

The actual correlation between commanded lift values

and inspection results were developed using a generalized










form of (4-8). The general second order regressive model,

assuming no delay, is given as

C = P0 m + Pi nm-1 + 2 me-2 (4-9)

The coefficients 0,fP, and $2 were found to be 1.84934,

-1.69993, and 0.85091 respectively.

A detailed comparison of these three coefficients with

those from equation (4-8), demonstrates a compelling

confirmation of the form of the model given in equation

(4-8). Equating coefficients of equation (4-8) and equation

(4-9) for mc_- gives

S- _P -1.69993 0.84997 (4-10)
1 2 2

Equating coefficients of m_-2 gives


P:= 2 (4-11)

Substituting in the value of PI from equation (4-10) and the

value of 0, from the regression analysis into equation

(4-11) gives

0.84997 = 0.85091 (4-12)

These values for P2 differ by less than 0.12%. Finally

equating coefficients of me and substituting in the value of

P0 and using the average value of p, gives

0 = po = 1.84934 0.85044 = 0.99890 = 1 (4-13)

Again this result is consistent with the proposed model.










Diagnostic Checking of the Model


This model can be examined for its ability to

accurately predict the process errors through examination of

the residuals as defined by equation (4-5). These

residuals, shown in Figure 4-2, indicate good agreement

between the model and actual process results. The residual

errors are an order of magnitude smaller than the measured

lift errors. While these errors are small, they are clearly

deterministic. This indicates that the model fails to

account for all deterministic components of the process

error. Yet, in spite of testing many models, this small

deterministic component in the residuals proved difficult to

eliminate using a simple form of model.

Two possible sources of the deterministic component

seen in the residuals are discussed for the purpose of

future model refinement. The first source is the workspeed

generation method. This source is suggested since the

relationship between lift errors and geometric acceleration

used in this analysis is based on constant rotational speed.

However, the workspeed varies within a rotation during the

grinding operation. The workspeed generation method is

discussed in more detail in Chapter 5.

The second possible source of the deterministic

component is the difference between reference follower

diameter and the changing grinding wheel diameter. This

factor is considered for two reasons. First, the change in





















Residuals of Lift Error
Second order regressive model
0.0008
S 0.00 0 .... .........6-.....--7..-- ..- .-- ... ...- ......'.. .... .... J
o 0.0005 --. --...... ... .....-...... --. ---.. .........
" -.0 --03 ..................... .......... ........... .... ............... ....... ...................

- 0.00031 i
% 0 0 ..... ...... .. -.... ..--- ------- ------- .. ...... ... .. ... ..... .................... ........
- 0 .00 0 2 -4-- ------- ------------ --- ----------------- --- ------------..
" 0 .0 0 0 1 -- -- -- -- --.. .............................................. ..................................... ................ :

-0 .0 0 0 1 ........... .... ........ .. ............ ...
-0.00012- ---------------- --------------------------------------....-
-0.0002 1
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


Figure 4-2 Stochastic Model Residual Errors








43

grinding wheel size produces a change in the grinding wheel

footprint and consequently its cutting ability. Second,

changes in the wheel size alter the commands which the

grinding machine controller generates for controlling the

individual machine axes. As these commands change, the

commanded movements of the machine axes are altered and the

process dynamics change accordingly. The change in process

dynamics affects the geometric errors produced in the part.

Further testing would be required to determine if either of

these factors produce effects large enough to be measured.


Potential for Model Improvement


If the method of workspeed generation is known, the

form of regressive model can be modified to account for this

component. Error components correlated to grinding wheel

size cannot be handled directly in the planned

implementation because direct access to wheel size is not

available in the interface used in this research. If the

current wheel size were available, a disturbance feedforward

controller could be implemented to compensate for errors due

to a changing wheel size.














CHAPTER 5
PROCESS CONTROL STRATEGY


The Control Interface


The control approach taken in this project is to modify

camshaft program data based on the post-process inspection

results. This approach, known as command feedforward

control, allows for a software implementation and

demonstration of the effectiveness of the system. All the

necessary control parameters are manipulated using the

existing control interface. This approach follows industry

standards in describing camshaft geometry and is easily

adapted to cam grinders from different manufacturers.

Part programs for CNC camshaft grinders typically

consist of several main types of commands which will be

referred to as fields. The first field is the lift field.

The lift field contains the 360 commanded lift values for a

cam lobe, the base circle radius and the follower diameter.

The lift values are specified as a function of the lobe

angle. Since the individual lobes of a camshaft may have

different contours, multiple lift fields may exist for a

given camshaft. The second type of field is the timing

field. This field is used to specify the timing angle of

the individual lobes relative to a timing reference. The










third field is the workspeed field and is used to specify

the workspeed (camshaft rotational speed during machining)

as a function of the lobe angle. The fourth field, the lobe

position field, specifies the position of the lobes along

the camshaft axis.

In the implemented process control scheme, the lift and

timing fields will be directly manipulated to control the

lift and timing errors respectively. The workspeeed field

is considered in this discussion, but it is not modified.

The lobe position field is not a concern.

From these four fields, the machine controller

calculates the command signals for the individual machine

axes-of-motion. In the compensation control scheme

implemented in this work, the internal command generation

scheme is unaltered. Rather the lift and timing fields,

from which the internal commands are generated, are modified

based on the inspection results. These modified fields

effect the generation of corrected control commands for the

machine axes-of-motion.

The workspeed field is generated off-line using a

proprietary algorithm. Investigation of this field

indicates that the workspeed is a normalized parameter based

on the demanded acceleration of the wheelhead, including

non-linearities due to servo demand limiters and the

commanded lift acceleration. Comparisons of the workspeed

field and corresponding lift acceleration indicate that










workspeed is roughly inversely proportional to lift

acceleration as shown in Figure 5-1.

Since the workspeed field is based on the commanded

lift, it changes as the commanded lift field changes.

However, this field is developed off-line and can therefore,

be held constant if desired. This is advantageous since

modifying the workspeed field, based on the compensated lift

field, would amplify the effects of the compensations made

to the lift field. This is readily demonstrated by

observing that when the commanded lift, and consequently the

commanded lift acceleration, for a region of the cam is

increased, the commanded workspeed for this region would be

decreased when recalculated. As shown in Chapter 4, lift

errors are correlated to lift acceleration and therefore are

essentially dynamic positioning errors. Consequently, a

decrease in workspeed would decrease the dynamic positioning

error of the machine-axes-of motion and decrease the lift

error relative to the commanded lift field. This decrease

in error would occur in addition to the decrease effected by

the modification of the commanded lift field. Thus the

system would tend to overcompensate and might exhibit

oscillatory behavior.





















Lift Acceleration and Workspeed


0 .8 .................... I, ............. .. .............. .......... .. ................

0 ...... .................... ... ...... ........... ................ ..... ..... ................... :.......... .........................
,, / /
0 .4 ------- ---------- .. ... ..--... .. ................ .................. .................. ..................................
S 0 .2 ----------------- --.. -- ---....... ................ ..........................
N
= 0 A --
S-0.2....... ....................... ............... ..........
E
| -0 .2 -. -.--.-.........I..-....------- --------------------------------
0
Z: 0 1


3 100 150 200 250 300
Lobe Angle (degrees) CCMM Convention



SAcceleration ..... Workspeed


Figure 5-1 Typical Workspeed and Lift Acceleration










Lift Error Controller Model


An Interacting Lift Process Model

As shown in Chapter 4, interaction exists between the

lift commanded at different lobe angles. Therefore, the

process can be described as a system which has 360

interacting variables [21]. The form of the regressive

model developed in Chapter 4 suggests the nature of the

interaction between variables. A block diagram for this

interacting system is shown in Figure 5-2. This figure

shows that the lift produced is a function of the lift

commanded for the given lobe angle and the lift commanded

for the two preceding lobe angles, where

n = Part sample number

0 = Lobe angle

so'n = Desired lift

co,n = Measured lift

fen = Feedforward desired lift

eon = Measured lift error

mOn = Commanded lift

Am ,n = Lift compensation

wen = Disturbances

Additionally the lift controllers are given as:

Gf(B) = Feedforward controller

Gc(B) = Process controller for feedback

Gmc(B) = Cam grinder internal controller









49





-- ----- --- ------- ,


Controller for s,_,


m-
i--_ _-l.n -2,n
-------------- -


Sg,n


m6 m0
| m.n m -l.n


Controller for seI


Figure 5-2 Interacting Lift Variables


S-l,n I
------


I

S+l.,n
I
-4]


L,,,,
-L-~C -- -










The lift transfer functions are given as

G (B) = CCMM

G (B) = Machining Process

G, (B) = Lumped G (B) and G_(B)

G,, (B) = interaction between m, and c,

Ge (B) = interaction between m, and c,


Noninteractinq Control of Lift


From a theoretical control perspective, it is possible

to design a noninteracting control system which eliminates

the interaction of the 360 lift variables [21]. Figure 5-3

shows the block diagram for such a control system. The

controllers required to eliminate interaction are given as:

De-1 = Controller between m.,_ and c,

Do-2 = Controller between m-2 and c,

While this control strategy has potential for excellent

control, it is complex. Fortunately, if interactions

between variables are small, as will be shown to be the case

for the lift variables, the process model can be simplified.


The Implemented Lift Controller


While the interaction between lift values commanded at

different lobe angles has been established as a source of

lift error, this interaction will be neglected in the

implemented control model. This may be justified by

examining equation (4-8) which is repeated here as (5-1).



















Sg 1,n Controller for s,_i
----~-^ L-




Ime-1,n m -2,n
-----_-n ---- "","


G-_ Gp (B)
G e2 ((B

D -i(B) +

+ G---- (B)

Gf (B) WO,n

SO,.n ee,n m.n + men + --

G, (B) G,, (B) Gm (B
Gp (B) (+


Gi (B)


r"- ~ ------ ----------- --j---c
Me, n Me-l,n



S6+l,n I Controller for s, I

F 1 IC






Figure 5-3 Noninteracting Lift Control System------


Figure 5-3 Noninteracting Lift Control System










Ca = .99890 mn + 0.84997 [m0 2 m0_ %_,2] (5-1)

The first term of this equation is the contribution of

the commanded lift to the total lift predicted by the model.

The second term is the contribution of the geometric

acceleration to the total lift predicted. The geometric

acceleration term represents the interaction of commanded

lift values at adjacent lobe angles. If the geometric

acceleration and lift terms are evaluated separately, the

geometric acceleration term is found to be three orders of

magnitude smaller than the lift term in critical regions of

the cam. For example, at a lobe angle of 340 (convention

Figure 3-4), the geometric acceleration and lift terms are

0.0001 and 0.2218 respectively. Therefore, due to the

dominance of the lift term on the predicted lift, it is

possible, in a closed loop control strategy, to neglect the

acceleration term and consequently the interaction of lift

variables.

The block diagram for the implemented command-

feedforward/feedback strategy is shown in Figure 5-4. The

control system calculates the 360 individual lift commands

me, needed to update the commanded lift field. That is, the

control system shown in Figure 5-4 is invoked 360 times for

each cam lobe. An integral controller of the form


(B) KB (5-2)
G(B) s

is selected where K is the integral control gain.












































fe,n


Ir -


S.,n


Implemented Lift Control System


en


--7


Figure 5-4










To further simplify the control model, ideal transfer

functions are assumed. Thus G,(B) = 1 and G,(B) = 1. The

solution for the feedforward controller is

1 1
Gf(B) 1 =1 (5-3)
Gp(B) 1

The control equation can then be written as

KB
mn = Sn+ 1- B (Sn ,n) (5-4)


The process equation is


en = Wen+ n en (5-5)

From these two equations, the closed loop control can be

solved for as

-B W (5-6)
C.= 1 ( K)B w, + (5-6)


Even while individual lobes on a camshaft often have

the same desired lift, the measured error results are not

identical. Therefore, the control system is applied to each

lobe independently. This requires a separate lift command

field for each lobe which creates a slight practical

problem. The CNC controller of the cam grinder used in this

study is not designed to handle high data transfer rates.

Hence, excessive time is required to read in the modified

lift field. This tends to reduce productivity, since the

machine is out of service during data transfer.










Control of Relative Timing


The control of lobe timing is a much simpler system to

model. Unfortunately, it is complicated by practical

matters for the systems used in this work. In the existing

process, different timing fixtures are used during the

grinding and inspection processes. These fixtures establish

the timing datum for their respective operations. The

repeatability of these fixtures is an important

consideration. Poor repeatability introduces a large

stochastic component into the data which negatively affects

the ability of the control system to effectively control

lobe timing.

Based on these considerations, the timing of lobe 1 is

controlled relative to the keyway/fixture reference, while

the control of all other lobes is performed relative to lobe

1. The timing relative to lobe 1 is highly repeatable and

therefore allows for aggressive control of timing relative

lobe 1. The block diagram for the implemented timing

control system is shown in Figure 5-5, where

e,n = Desired timing angle

cen = Measured timing angle

fon = Feedforward desired timing angle

e0,n = Measured timing angle error

men = Commanded timing angle

AmOn = Timing angle compensation

wen = Disturbances





































fen


Wen


+ me,


Implemented Timing Angle Controller


Figure 5-5










Additionally the timing controllers are given as

Gf(B) = Feedforward controller

G((B) = Process controller for feedback

Gmc(B) = Cam grinder internal controller

The timing transfer functions are given as:

G (B) = CCMM

Gm(B) = Machining Process

Gp ) (B) = Lumped Gm (B) and Gm(B)

Much of the notation introduced for the lift controller is

reused here. However, no confusion should result as the

meaning of the symbols will be clear from the context in

which they are used.

Again if an integral controller is selected and the

same simplifying assumptions are made concerning the

transfer functions, the timing control equation becomes

K ( ,n Cn) (5-7)
mOn : + i nn B On


This equation is implemented to control the timing of lobe 1

relative to the keyway/fixture and to control the timing of

all other lobes relative to lobe 1.















CHAPTER 6
PROCESS NOISE


From a practical standpoint, all production and

inspection processes have stochastic and repeatable

components. The stochastic component, also referred to as

the repeatability error or signal noise, is defined as six

standard deviations (60) of the process output. The noise

in the control system has components due to both the

manufacturing and inspection processes.

The inspection process noise can be directly evaluated

and expressed as the standard deviation of multiple

inspections of the same workpiece. Process noise is

evaluated based on the measured variability of the parts

produced. Since the actual values of the controlled

variables differ from the measured values of these

variables, the inspection process noise is superimposed on

the manufacturing process noise. However, if the inspection

process is highly repeatable, relative to the manufacturing

process, it is not necessary to separate the noise from the

two sources, and a good estimate of the process

repeatability is obtained from the measured values of the

controlled variables. For the machines studied, the

repeatability of the inspection process is more than ten

58










times better than the repeatability of the manufacturing

process [24,5].

Even with a highly repeatable inspection process, the

lack of repeatability in the machining process can present

problems for control based on post-process inspection. It

is not possible to correct for process noise using post-

process inspection. In fact, control strategies which are

overaggressive will actually worsen the situation through

increasing the process variability [25,26]. Therefore, a

strategy designed to attenuate the deleterious effects of

process noise is desired. Two different approaches are

considered.

First, Statistical Process Control (SPC), a type of

dead-band control, historically favored by industrial

engineers and statisticians [25] is considered for its

suitability. Second, traditional feedback control with the

addition of a discrete first order filter, as favored by

control engineers [22,26], is discussed and justified for

use in this problem.


Statistical Process Control


SPC typically refers to the use of Shewhart control

charts and WECO run rules as defined in the text by the

Western Electric Staff [27]. These rules are based on

comparing current inspection results with the mean and

standard deviation of parts previously produced. The WECO










rules suggest that an out-of-control condition (shift in

process mean value or increase in process variability)

should be suspected if one or more of the following occurs:

1. An instance of the controlled variable deviates from

the nominal by more than three standard deviations.

2. Two out of three instances deviate from the nominal by

more than two standard deviations.

3. Four out of five instances deviate from the nominal by

more than one standard deviation.

4. Eight consecutive instances with all positive or all

negative deviations occur.

While these rules are useful for detecting shifts in the

mean of the controlled variable, they do not indicate the

size of the shift. Additionally, Shewhart and other SPC

charts require storing past inspection results in order to

evaluate the WECO rules. For a camshaft with eight lobes, a

run of 25 parts requires storing, recalling and evaluating

72,000 floating point numbers. This represents significant

overhead in terms of storage and execution time.


Traditional Feedback Control with Filtering


It has been shown by Koenig [26] that feedback process

controllers amplify non-repeatability error, also called

pure white noise, for processes with short time constants.

The idea of a time constant for a discrete manufacturing

process is different in nature from the time constant of a










continuous process which is sampled at discrete points in

time. For discrete processes, the full effects of applied

compensation are realized in the very next part. The

amplification of process noise is a problem as it means an

increase in the variability of the parts produced. To

reduce the effects of process noise on the controlled

variables, a discrete first order filter of the form

Cf (n)= C, + (1 a) c~ (n- (6-1)

can be applied, where

a = filter constant (between 0 and 1)

cn = measured value of controlled variable for part n

c,(n, = filtered value of controlled variable for part n

cfn-_) = filtered value of controlled variable for part n-1

For white noise, the standard deviation of the filter

input 7, is related to the standard deviation of the filter

output c, by


0= (6-2)
ao V 2 -a

By inspection of equation (6-2), it is apparent that To is

less than (. for all values of a less than one. For a equal

to 0.15 (filter coefficient used for lift data in trials)

the standard deviation of filter output to the input can be








62

calculated from equation (6-2) as


o 0. 15 0.285 (6-3)
o V 2 0.15

The use of this filter effectively introduces a time

constant and corresponding time lag to the system while

reducing the standard deviation of the process noise. For

such a filter the effective time constant of the filter Tf

is


T = h (6-4)
S lIn(1 a)


where h is the sample period.

Using equation (6-4), an effective time constant can be

calculated in terms of the number of parts as


T, = 6.15 parts (6-5)
In(1 0.15)


A discrete filter for the lift requires the introduction of

the lobe angle subscript 0 and is given as


Cf (,n) = a C6,n + (1 a) Cf (,n-1) (6-6)

where c0, is the measured value of the lift s at lobe angle

0 for part n. Equation (6-1) can be directly implemented as

a filter for the timing angle 0, where cn is the measured

value of the timing angle for part n.

Unfortunately, the introduction of such a substantial

time constant can cause overshoot in integral only control.

This overshoot can be greatly reduced by including a

proportional term in the control equation. This








63

proportional term was not included at the time of trials and

the filtering technique was therefore modified at high

error-to-noise ratios. For the trials conducted in this

work, the filtered value was reinitialized after each

adjustment to the manipulated variables. This effectively

eliminated any overshoot but reduced the effectiveness of

the filter to limit noise. As implemented, the filtering

process effectively became a weighted average of parts

inspected between adjustments. With this modification the

process noise reduction can be approximated as [25]


o i (6-7)



where N is the number of parts inspected to calculate the

compensation.

The use of discrete filters reduces data storage

requirements and calculations as compared with SPC.

Discrete filters can be applied to allow compensation based

on the first part produced, where the error-to-noise ratio

is generally high. The compensation frequency can be

reduced as the error-to-noise ratio decreases. SPC

generally lacks this flexibility and requires the inspection

of many parts prior to initial compensation.


Error Repeatability A Preliminary Study


A preliminary study was done to determine the size of

the repeatable process errors relative to the stochastic










process errors. The tests were performed as described in

Appendix A. For this study, 11 camshafts were ground. The

camshaft geometry and grinding parameters were similar those

used in the control system experiments described in Chapter

7. The only adjustments made to the process were to correct

for base circle size error.1


Process Repeatability of Lift Errors


Lobe 1 lift error is shown in Figure 6-1 for selected

camshafts. Clearly, the general pattern of lobe error

repeats from part to part. Figure 6-2 shows the mean and

the standard deviation for all 360 measured lift error

values of lobe 1 for the 11 parts. This figure clearly

indicates the high value of the mean process error as

compared to the process noise.

Figure 6-3 shows the 360 discrete error-to-noise ratios

for the grinding process. For lobe angles where high errors

are measured, correspondingly high error-to-noise ratios are

obtained. The ratios here might even suggest that with such

high error-to-noise ratios, effective process control could

be achieved with no special considerations taken for process

noise. In fact, this will work quite well in eliminating the

larger lift errors. However, as the lift errors decrease,

the process noise will remain unchanged and the error-to-



1 Size has little effect on our problem; no attempt to
control it is made.
















Lift Error for Lobe 1
Six selected runs


0.0008
0.0007-
0.0006---- ----- ---- ---- -------------------- -----
0 .0 0 05ooo --- ....... --- ..... .....................
0o .o o o0 5 T. ...... .... ... .- .. ........ .............. .. ........................................................
0 .0 00 4 ----------- ---------------.. -- ..... .. ------ ............ ..................................................
0 .0 0 02o 3 ------------------------------- .......... ............. .... .... ........................... ......................
0 .0 0 0 12 ---- ----- --- ---- .--... -.- ........... .............. ...... ............... ....
0 .0 0O0 1 I I ...... .... ..... .... ...... ......... ......... ...... .......
-0.0001 *** ...-t^ .. .....
-0.0002 -----.--.------ ^-----------------
-0.0002
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


-- run 1 ---- run 3 ---- run 5
----- run 7 -- run 9 .....-.... run 11


Figure 6-1 Lift Error Process Repeatability.


















Lift Error for Lobe 1
Mean and Standard Deviation
0.0008
0.0007-----?----------------------------- --------------------------------------
- 0.0006- .
0.000
0.000 5 1--- -------- ----- --- -- --- -- ------- ----- -- ---- -------------------------
0 .0 0 0 ..................................... ................. .............. .........................--------
2 0.0004-
S 0 .0 0 0 3 .... ........... .. ........................................
S0 .0 0 0 5 ... ..... ... ............. ....... ....I..: ...............................................................
E 0.0001
,,-,_ r------"-- ~ '- -

-0 .0 0 0 1 ......... ................... .... ..... ...... ................ ... ...............
-0.0002--
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


....... Mean Error -- Standard Deviation


Figure 6-2 Lift Error Mean and Standard Deviation




















Error to Noise Ratio for Lobe 1


6.0-


5.0--


4.0


3.01--


2.0-


.................... ...... .......... .


1.01- .. ---


0.0 .
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


Lift Error-to-Noise Ratio


1




i \


1


...... ... .


Figure 6-3








68

noise ratio will decrease dramatically. It is in this area

that the filtering technique becomes useful. The results

shown for lobe 1 are typical of results for all four lobes.


Process Repeatability of Timing Error


As shown in Figure 6-4, the lobe timing measured

relative to the keyway/fixture reference is far less

repeatable than the timing measured relative to lobe 1. In

the existing process, different timing fixtures are used in

grinding and inspection processes. These fixtures establish

the timing datum for their respective operations. The

repeatability of these fixtures is an important

consideration as it greatly affects the ability of the

control system to effectively control lobe timing.

Based on these results, the expected process variation

for the 11 parts is calculated to be 1.2 degrees. If

instead, the timing is measured using one of the cam lobes

as a reference, a large reduction in process noise is

effected. By convention, lobe 1 is selected as the

reference. If the process variation is now evaluated

relative to lobe 1, a variation of 0.126 degrees is obtained

for the same 11 parts. This represents an order of magnitude

improvement over the timing repeatability measured relative

to the keyway/fixture reference. Clearly, different degrees







69













Lobe Timing Error
no compensation applied

0.5
2 0.4 Lobe 1 relative to keyway


0 0 .2 .................................................................. .. .......... .. -......................... ......................................... i
c 0.3 *


o 0.21- .......... --- ----. .-.


0. ... ... ........ .......... .............-. ............ ...... --- ----- ---

O
c -0.3+ 1 Lobes 2. 3 & 4 relative to lobe 1 ........................... ..... .. .. .. ..... ..
-0.4 1 ,
0 5 10 15 20 25
Sample Number


Figure 6-4 Timing Angle Repeatability Error










of control are possible depending on the timing reference

selected.

For the cases studied, the timing variation relative to

the keyway/fixture exceeds the total timing tolerance. This

means that the existing process is not capable of producing

all parts to specification and no post-process gauging with

feedback strategy will change this. As a practical matter,

this situation can be improved upon. The timing errors

relative to keyway/fixture can be corrected during the

mating of the camshaft and drive gear. Additionally the

problem is related to the quality of fixtures which can also

be improved.

Still, this presents a problem in demonstrating the

control system with limited parts available for trials. For

processes with greater variability, more samples are

required to separate the mean error signal from the process

noise for a given error size of interest. Correcting for

timing errors relative to lobe 1 and lift errors requires

many fewer samples than does the correction of timing errors

relative to the keyway/fixture.














CHAPTER 7
EXPERIMENTAL RESULTS


The trials performed in this study were performed at

Andrews Products in Rosemont Illinois, using a Landis 3L

series cam grinder as shown in Figure 7-1. An Adcole Model

911 CCMM, shown in Figure 7-2, was used for camshaft

inspection. The grinding parameters, including lift and

timing specifications for the trial part, are given in

appendix A. The camshaft inspection parameters are given in

Appendix B. The control system parameters and a functional

diagram of the control software are included in Appendix C.

During the trials, the only changes made to process

parameters were those made to the lift and timing command

fields.

The trials were carried out in a production environment

over a run of approximately 100 pieces. The parts were

milled from stock to within 0.01 inches of finished

dimensions. Camshafts were case hardened prior to grinding.

The camshafts were ground, inspected, and compensation

applied according to the schedule shown in Table 7-1. This

schedule represents an attempt to balance the demands of

production needs with experimental technique.



























































Figure 7-1 Landis 3L Series Cam Grinder

Source: "State-of-the-Art 3L Series CNC Cam Grinding
Systems," Litton Industrial Automation Systems, Pub. No
3L-88 FR 3M, 1988. Used with permission.









































































Figure 7-2 Adcole Model 911 CCMM


----P-~-~---~~-----------








74
Table 7-1 Grinding, Inspection, and Compensation Schedule

Compensation Part(s) Compensation Notes
Number Ground Based on Part(s)

0 1 nominal part data

1 2 1

2 3-13 2

3 14-28 3-13 Parts
14-93
4 29-82 14-28 made
two
5 83-88 79-82 days
after
6 89-93 83-88 1-13




Results of Lift Error Control


The reduction in lift error is shown in three different

ways. First, the measured lift error for lobe 2, after each

application of compensation is shown in Figure 7-3,

Figure 7-4, Figure 7-5, and Figure 7-6. Second, the total

lift error, that is the maximum positive minus the maximum

negative lift error, is shown for all four lobes in

Figure 7-7. Third, the root mean square (RMS) of all 360

individual lift measurements for all four lobes is shown in

Figure 7-8. Clearly, all three measures show improvement in

the lift error. The data for lobe 2 show an order of

magnitude reduction in the measured lift error with other

lobes showing smaller reductions, depending primarily on the

initial value of the lift error. Both the RMS and total

lift error data give some indication of the effects of the





















Measured Lift Error Lobe 2


2.0E-04--

1.OE-041

O. OE + 00-


, / i
.. Comp. #0

Comp. #1


........... ................ ....... j
.....................................
corn0.,,--- -------


0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


Lift Error using Control Scheme


-1.OE-04-

-2.0E-04 ...

-3.0E-04- ....

-4.OE-04- -

-5.0E-04-


-6.OE


Figure 7-3























Measured Lift Error Lobe 2
2.0E-04 ,


1. OE-04 ..

O.OE +00-. --- -- --*.. ---

-1.0E -04 ......................

-2.0 E -0 4 i .- ............. ..............

-3 .0 E -041-- ..---- -------- -.- ----------------------
i


-4.0E-04--

-5.OE-04-t

-6.OE-04+-
0


50 100 150 200 250
Lobe Angle (degrees) CCMM


300 350 400
Convention


Lift Error using Control Scheme


SComp. #2

Comp. #3


Figure 7-4


























Measured Lift Error Lobe 2
2.0E-04 ,

1.0E-04 Comp. #4


o.OE00 A Comp. #5


-20E-04--.

-3.0E-04 --

-4.OE-04- .

-5.0E-04-

-6.OE-04 -
0


50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


Figure 7-5 Lift Error using Control Scheme


...........................................................................................

.......................................... I ......... I ......................................

-------------------------------------------------------------------------------------------






















Measured Lift Error Lobe 2
2.OE-04

1.0E -0 4 .. ......... ... .. .

O.OE+00

-1.OE-04i--------------

-2.O E-041 -- --------.........

-3.0E -04 .. .... --... ..- ...----.---- -----....................-----

-4.0E -04 -- --- -- ------------------------. --- --------

-5.OE-04--- -- -------- ------ -------- ---- -

-6.0E-04 1
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention


Figure 7-6 Lift Error using Control Scheme


Comp. #6



























Total Lift Error
average for all parts inspected


7.0E-04-

6.OE-04


5.OE-04---

4.OE-04 --

3.0E-041

20E-04 ----

1.OE-041--

O.OE 00--
0


lobe 1


lobe 2


lobe 3

lobe 4


...... ..... ..... ..... ....-- -- --- --------------- --I. .. -

----- ---- --------- -- -- -- .. .. .



-- '_- -r _~--- -------- -- ----------------


-------------
I








..-- ---




1 2 3 4 5 6
Compensation Number


Figure 7-7 Total Lift Error using Control Scheme






















RMS of Lift Error
average values for all parts inspected
2.OE-04
l.E-04----------------------------------------------- -----
i lobe 1
1.6E-041----------- -


1.2E -04 4 ... ............ ... .......
1 .O E -0 4 .. ........... ... ..............'.. ....... lo b e 3
8 .O E -0 5 ..- .... .. .................................................... -
Slobe 4
6. OE-05 -- --- ---
.0E -05- .......... ... .. ................
4.0E-051- ..
2.0E-05-i
O.OE-O 00
0 1 2 3 4 5 6
Compensation Number


Figure 7-8 RMS of Lift Error using Control Scheme








81

two day interruption in the trials. This indication appears

in the form of modest reductions and even slight increases

in form error between compensation number 2 and 3. When the

camshafts used to calculate the compensated command number 3

were ground, the machine had been operating for eight hours.

Compensation number three was then applied when the machine

was re-started two days later. Thus, the increase in lift

error associated with this delay, combined with the further

reduction in lift error when compensation is applied in a

timely manner, suggests that thermal effects account for a

small but nevertheless measurable component of lift error.

Additionally, mixed results are obtained between

compensation numbers three and four. Fifty parts were

ground between the inspected parts and the application of

compensation. These results may indicate a lift error

component due to the changing wheel size (0.2 inch for 50

parts). Results after compensation numbers four, five and

six, where no parts were ground between the inspected parts

and the application of compensation, demonstrate that more

frequent compensation further reduces errors.


Results of Timing Error Control


Control of Timing Relative to Lobe 1


The results of the timing control relative to lobe one

are shown in Figure 7-9. Small initial timing errors, as

compared with the results of the preliminary repeatability
























Timing Error Relative to Lobe 1
0.10,

0.05-- ------- ----- ---- --------------- ------..---- ------ -----

0.00 .
- 0 .0 5 .. ..... ........ .. ............ ..... ....... ...... .. .. ... ... --........ ... .... .. ...
-0.05--;- ---
-0.1 0 --- ---- --- -------- ---------- ----- ---- -----'-------- ------- --- --------- ----


s~-- ------ --------- --- --- ------ --- ---- ---------
-0.10i1- '-.'; -- ..----------
-0.1 5

-0.201--- ----- -- ----- ------------------------------------ ----------
-0. 0--............... -----.........----------------.---- ---........... .................... ...............................



-0.25-

-0.30-
I -0.35




-0 3 510 .. .... ..... ........ .... .... ..... ... .....
-0. 40 1 T I T I


5 10 15 20 25
Part Number


80 85 90


Lobe 2


Lobe 3

Lobe 4


Figure 7-9 Timing to Lobe 1 using Control Scheme










study, existed for the camshaft used in the control trials.

While the initial values were small, it is significant to

note that no timing errors developed during the control

period and the timing angle remained within the noise levels

established in the preliminary trials.

This is especially significant considering that the

timing angle is decomposed from the measured lift data.

Since compensation is applied to the lift field, the lift

data are altered. Nevertheless, the results show that it is

possible to control these parameters separately. This

ability to control these coupled parameters as if they were

separate, has great practical benefits and greatly

simplifies the control system.


Control of Timing Relative to Keyway/Fixture


The control of timing of lobe 1 relative to the

keyway/fixture was less successful as shown in Figure 7-10.

While the process is approximately centered about zero

error, the timing of lobe 1 to the keyway/fixture

demonstrated a greater variability than the uncontrolled

timing measured in the preliminary repeatability studies.

This result is not surprising considering the low error-to-

noise ratio which exists for this parameter and the short

effective time constant of the process. It was anticipated

that this control might prove overaggressive. However, to

avoid introducing additional complexity for these initial

























Timing Error Relative to Keyway
1.00


0.801
i I


0.40-

0.20

0.00-


I I /


-0.40-


, \


10 15 20 25
Part Number


80 85 90


Timing to Keyway using Control Scheme


S. Lobe 1


-0.604

-0.801-


. .. I


; I
I..ii.


Figure 7-10








85

trials, this was accepted. Recommendations for improving

the effective control over timing relative to the

keyway/fixture are discussed in Chapter 8.














CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS


It has been shown that significant improvements in

camshaft lift error can be realized through feedback of

post-process inspection results. It was shown that even

while the lift errors at nearby lobe angles interact, good

results are obtained when this interaction is neglected.

The use of discrete filtering prevents an increase in the

variability of a process about a mean operating point.


Implementation of the Control System


The strategy employed relies on the use of standard CNC

industrial camshaft inspection and production equipment.

Many camshaft production facilities currently use equipment

suitable for implementation of this control strategy. These

facilities could realize significant quality control

improvements by better utilizing existing production

equipment.

Prior to introduction into a manufacturing environment,

the control system requires the development of a user

interface and further investigation of factors discussed in

the next section. Minor modification of the grinding

machine controller software would allow for seamless










operation and higher data transfer rates. Additionally,

minor modifications to the CCMM's software are required for

a high quality implementation of the control system. As a

practical matter, production and inspection equipment need

to be located together. In the ideal implementation,

camshafts are ground and automatically transferred, in

sequence, to the CCMM. The feedback of inspection data and

compensated command fields occurs automatically.


Further Work


While the effectiveness of such a control system has

been clearly demonstrated, much interesting work remains in

this area. For a full implementation of discrete filtering,

a proportional term needs to be added to the controller and

the parameters of the model should be optimized through the

use of the regressive model and verified in the actual

implementation. With regard to control of the timing of

lobe 1 to the keyway/fixture, production implementations

would need to be less aggressive. This could be readily

accomplished through the use of greater filtering and the

addition of a proportional term in the controller. As

before, the controller parameters would need to be selected

through simulation and verified experimentally.

Additionally, a non-interacting control system could be

investigated for lift errors. This system should be










investigated for its ability to improve control system

convergence rate.

The long term stability of the control system should be

investigated with particular attention to the emergence of

high frequency components in the lift command field. While

the high frequency components of the commanded lift field

are effectively filtered by the limited bandwidth of the

grinding machine, these high frequency components produce

large internal following errors and consequently excessive

demand on the servo motors. Over time, these high frequency

components may lead to increased lift error and a

degradation of control.

Finally, additional trials should be conducted

investigating the effectiveness of different control gains.

Specifically the effectiveness of a control system using

control gain of unity for the lift error should be compared

with the results obtained in this study.















APPENDIX A

GRINDING PARAMETERS








The trials used a Ramron 1-A-90-O-B-7 grinding wheel.

The wheel was dressed using a Norton LL-271B Sequential

Cluster.



The lift and timing fields, given in the following pages,

are specified according to the cam grinding machine

convention described in Chapter 3.




Full Text
IMPROVED PROCESS CONTROL IN CAMSHAFT GRINDING THROUGH
UTILIZATION OF POST PROCESS INSPECTION WITH FEEDBACK
By
TIMOTHY MARK DALRYMPLE
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR
THE DEGREE OF MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
1993

Copyright 1993
by
Timothy Mark Dalrymple

To my students at Botswana Polytechnic.
On the nights I remember the incredible gifts you
possess, the diversity of backgrounds and talents you
represent, I sleep well, knowing that Africa, will one day,
be safe in your hands.

ACKNOWLEDGMENTS
Like all human undertakings, this work would not have
been possible without the help of others. I am particularly
grateful to John Andrews and his staff at Andrews Products
for practically unconditional use of his excellent
facilities. At Andrews, I am especially grateful to Scott
Seaman. Also, thanks go to Chuck Dame of Adcole Corporation
for providing essential technical information concerning his
company's products.
I am also pleased to acknowledge the help and
encouragement which my advisor, John Ziegert, provided.
Lastly, I wish to thank my wife, Laura, for her unfailing
confidence, support, and patience.
IV

TABLE OF CONTENTS
ACKNOWLEDGMENTS iv
LIST OF FIGURES vii
ABSTRACT ix
CHAPTERS
1 INTRODUCTION • 1
Scope of the Problem 1
Camshaft Grinding Technology 2
Analysis of Camshaft Geometrical Errors 4
Potential for Improvement 5
2 REVIEW OF THE LITERATURE 6
Compensation Through Positioning Error Modeling . 6
Compensation Through In-Process Gauging 8
Compensation Using CMM for Post-Process
Inspection 9
3 CAMSHAFT GEOMETRY 11
Basic Description and Analysis 11
Industrial Convention 15
CCMM Convention 16
Grinding Machine Convention 18
Implications of Machining Techniques 18
Calculation of Grinding Wheel Path 25
Inspection Techniques for Process Control .... 26
Decomposition of Error Components 29
Timing Relative to Keyway/Fixture 31
Timing Relative to Lobe 1 33
4 THE STOCHASTIC PROCESS MODEL 34
General Linear Least-Squares Estimation 34
Identification of Lift Error Model 36
Estimation of Model Parameters 39
Diagnostic Checking of the Model 41
Potential for Model Improvement 43
v

5 PROCESS CONTROL STRATEGY 4 4
The Control Interface 44
Lift Error Controller Model 48
An Interacting Lift Process Model 48
Noninteracting Control of Lift 50
The Implemented Lift Controller 50
Control of Relative Timing 55
6 PROCESS NOISE 58
Statistical Process Control 59
Traditional Feedback Control with Filtering ... 60
Error Repeatability - A Preliminary Study .... 63
Process Repeatability of Lift Errors .... 64
Process Repeatability of Timing Error .... 68
7 EXPERIMENTAL RESULTS 71
Results of Lift Error Control 74
Results of Timing Error Control 81
Control of Timing Relative to Lobe 1 .... 81
Control of Timing Relative to Keyway/Fixture 83
8 CONCLUSIONS AND RECOMMENDATIONS 86
Implementation of the Control System 86
Further Work 8 7
APPENDICES
A GRINDING PARAMETERS 90
B CAMSHAFT INSPECTION PARAMETERS 107
C SOFTWARE OUTLINES AND CONTROL SYSTEM PARAMETERS . Ill
REFERENCES 114
BIOGRAPHICAL SKETCH 117
vi

LIST OF FIGURES
Figure 3-1 Typical Four Lobe Camshaft 12
Figure 3-2 Radial Cam with Roller Type Follower ... 13
Figure 3-3 CCMM Angle Convention-Clockwise Rotation 17
Figure 3-4 Grinding Machine Angle Convention 19
Figure 3-5 Camshaft Axes-of-Rotation 22
Figure 3-6 Grinding Between Centers 23
Figure 3-7 Centerless Grinding Technique 24
Figure 3-8 Grinding Wheel Path Calculations 27
Figure 3-9 Camshaft Inspection on a CCMM 2 8
Figure 3-10 Best Fit of Lift Errors 32
Figure 4-1 Lift Acceleration and Measured Lift Error . 38
Figure 4-2 Stochastic Model Residual Errors 42
Figure 5-1 Typical Workspeed and Lift Acceleration . . 47
Figure 5-2 Interacting Lift Variables 49
Figure 5-3 Noninteracting Lift Control System .... 51
Figure 5-4 Implemented Lift Control System 53
Figure 5-5 Implemented Timing Angle Controller .... 56
Figure 6-1 Lift Error - Process Repeatability 65
Figure 6-2 Lift Error Mean and Standard Deviation . . 66
Figure 6-3 Lift Error-to-Noise Ratio 67
Figure 6-4 Timing Angle Repeatability Error 69
Figure 7-1 Landis 3L Series Cam Grinder 72
vii

Figure 7-2 Adcole Model 911 CCMM 73
Figure 7-3 Lift Error using Control Scheme 75
Figure 7-4 Lift Error using Control Scheme 76
Figure 7-5 Lift Error using Control Scheme 77
Figure 7-6 Lift Error using Control Scheme 78
Figure 7-7 Total Lift Error using Control Scheme ... 79
Figure 7-8 RMS of Lift Error using Control Scheme . . 80
Figure 7-9 Timing to Lobe 1 using Control Scheme ... 82
Figure 7-10 Timing to Keyway using Control Scheme . . 84
viii

Abstract of Thesis Presented to the Graduate School of the
University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
IMPROVED PROCESS CONTROL IN CAMSHAFT GRINDING THROUGH
UTILIZATION OF POST PROCESS INSPECTION WITH FEEDBACK
By
Timothy Mark Dalrymple
May 1993
Chairman: John Ziegert
Major Department: Mechanical Engineering
In order to take full advantage of the introduction of
computer numerical control technology in camshaft grinding
and post-process inspection, a closed loop control scheme is
proposed. This strategy makes use of post-process
inspection results to modify the commanded part geometry
used in the grinding program. The commands are modified in
order to minimize the lobe contour and relative timing
errors. It is shown that using a control strategy comprised
of feedforward and feedback elements, substantial
improvements in cam contour accuracy can be attained.
A system capable of automated reduction of inspection
results, application of statistical methods, transformations
between different coordinate systems, and production of
modified commanded part geometry is presented. This system
IX

requires no off-line calibration or learning of grinding
machine positioning errors. Additionally, it offers
advantages over such techniques, in that it is able to
automatically adapt to changing process conditions.
The system is general in nature and may be used for any
camshaft design. Through application of this system, the
time required to bring a new part into tolerance is greatly
reduced. With such a system used to minimize contour
errors, it is no longer necessary to optimize grinding
parameters based on these errors. Rather, grinding
parameters can be manipulated to optimize other important
factors, such as metal removal rates and the corresponding
process time.
Implementation of this system on existing computer
numerically controlled (CNC) equipment is inexpensive. It
requires only software necessary to produce the modified
part geometry and limited hardware for file transfer. The
required hardware is inexpensive and readily available.
x

CHAPTER 1
INTRODUCTION
Scope of the Problem
Camshafts find application in a wide range of consumer
and industrial products. In machine tools, camshafts have
long been used to control precise and high-speed machine
motions. Applications are common in both chip producing
equipment and high-speed dedicated assembly machinery [1].
Additionally, cams are used in fields as diverse as blood
separation and automated laser-scanner checkout systems.
Advances in servo motor and computer numerical control
(CNC) technology have lead to the replacement of cams in
many industrial applications. Still, camshafts will remain
essential for certain applications, such as the internal
combustion engine, for the foreseeable future.
In internal combustion engines, camshafts are used to
mechanically control the opening and closing of intake and
exhaust valves. The shape of the camshaft is critical in
determining the nature of the combustion process. As
pollution emission regulation for internal combustion
engines, particularly automobiles, have become more
stringent, the demands for higher precision camshafts and
better valve and combustion control have increased [2].
1

2
Improvements in grinding media, machine design, and the
application of CNC provide for better control in camshaft
manufacturing. Yet, achieving high quality results depends
on properly coordinating the setting of a wide range of
grinding variables. These variables include: wheelspeed,
workspeed, dress parameters, grinding wheel quality,
dressing tool quality, temperature, etc. [3]. A change in
any of these parameters can produce deleterious effects on
part quality.
Camshaft Grinding Technology
Dimensional errors occurring in camshaft grinding are
attributable to a wide range of causes. Traditional cam
grinders use master cams to produce relative motion between
the grinding wheel and the workpiece. This relative motion
generates the desired camshaft geometry. Naturally, any
inaccuracies in the master cams produce corresponding errors
in the workpiece. Additionally, machines utilizing master
cams for control produce the optimal shape only for a single
grinding wheel size [3].
Conventional media based grinding wheels, such as
aluminum oxide or silicon carbide, require frequent dressing
to remain sharp and free cutting [4]. This continual
dressing produces a grinding wheel which is constantly
decreasing in diameter. As the wheel size deviates from the
nominal size, the dimensional accuracy of the camshaft

3
deteriorates [3]. While some master cam controlled machines
are able to compensate for wheel size wear through the use
of additional master cams [5,6], this increases the initial
cost, complexity of the machine and set up time. Also, this
improvement in contour requires sacrificing optimal control
over other parameters such as the cutting speed variation.
Additional sources of errors in camshaft grinding can
be traced to the nature of the contact between the grinding
wheel and workpiece. The "footprint," as the area of
contact is known, changes as the grinding wheel encounters
different curvatures on the cam surface. This change in
footprint affects the grinding wheel's cutting ability and
thus impacts the metal removal rate. Changes in grinding
conditions adversely affects workpiece accuracy [3].
The introduction of CNC technology in camshaft grinding
has produced benefits far beyond the flexibility generally
associated with CNC. Using this technology, the tool path
can be continually updated and optimized for any size of
grinding wheel [5,6]. Additionally, using a variable-speed
servo motor to control the headstock rotation, the variation
in footprint speed can be minimized. If the grinding
wheel's speed is constant, then minimizing the footprint
speed variation also minimizes the relative speed variation
between the cutting edges of the grinding wheel and the cam
lobe surface. Finally, the part geometry is specified in
software and can be readily modified.

4
Analysis of Camshaft Geometrical Errors
Manual techniques of camshaft inspection are generally
based on test fixtures which use dial indicators to measure
dimensional errors. This approach, while sufficient for
determining if functional requirements are satisfied, is
inadequate for quickly identifying machining errors. Using
manual test procedures, it is impossible to analyze all
error components and determine their cause in a timely
manner. Thus, process control based on such inspection
techniques is not feasible.
Computer-controlled cylindrical coordinate measuring
machines (CCMM) capable of fast and accurate camshaft
inspection have been available for two decades. With the
decrease in cost of computer hardware, CCMM have become more
affordable and are currently available in many camshaft
manufacturing facilities. Commercially available software
allows for some flexibility in data reduction [7]. This
flexibility provides for camshaft inspection based on
evaluation of functional criteria or for analysis of the
manufacturing process.
However, until recently, the majority of camshaft
grinders used master cams for control. Since the part
program is essentially ground into the master cam, the
potential for fine adjustments based on inspection results
did not exist. Consequently, the wealth of data derived
from CCMMs was poorly utilized. In most applications CCMMs

5
were simply used to identify non-conforming workpieces. In
some cases, CCMMs were effectively used to evaluate the
effects of individual grinding parameters, other than the
commanded geometry, on camshaft geometrical errors.
Potential for Improvement
The widespread introduction of CNC technology in
camshaft grinding provides the opportunity to better utilize
the information derived from CCMMs. Since part programs in
CNC machines can be readily changed, the program can be
modified based on repeatable errors observed in post-process
inspection. CCMMs capable of measuring up to 150 parts per
hour are currently on the market [8]. Camshaft grinders
with CNC produce approximately seven camshafts (12 lobe
shaft) per hour [2]. With the inspection process requiring
less time than the manufacturing process, the opportunity
exists to compensate for errors with a time lag of only one
part. The ability to automatically inspect camshafts and
produce compensated part programs presents great potential
for process improvement with little capital investment or
operator training.

CHAPTER 2
REVIEW OF THE LITERATURE
Most early research concerned with minimizing machining
errors focused on error avoidance. This research lead to
improvements in thermal stability, machine base stiffness,
precision components, and spindle design. These
improvements, while greatly increasing accuracy, did not
come without a cost. As machine tools became ever more
precise and mechanically sophisticated, the cost of these
machines continued to rise.
Much recent research on improving accuracy has focused
on error compensation rather than error avoidance. This
technigue provides potential for improved accuracy without
costly mechanical design improvements. A review of the
literature in this area shows major research in three
categories: off-line modeling of positioning errors,
in-process inspection, and post-process inspection with
feedback.
Compensation Through Positioning Error Modeling
The use of a positioning error model has been the focus
of much recent research [9,10,11,12]. Donmez et al. [9]
describe a methodology by which the positioning errors are
6

7
measured using off-line laser interferometry and electronic
levels. These errors are then decomposed into geometric and
thermally-induced components. The geometric errors are
thermally-invariant and modeled with slide positions as
independent variables. The thermally-induced errors are
modeled using key component temperatures and slide position
as independent variables.
Once the positioning errors have been measured and the
model of the positioning errors established and verified,
error compensation can be applied. Since this method models
the workspace of the machine, and not the errors for a
particular workpiece, it is general in nature and can be
applied to parts not previously produced. However, it is
expected that over time, the machine will wear, the model
will become less accurate, and the machine will require
recalibration.
In certain machining operations, such as single point
turning, a one to one correspondence between machine errors
and workpiece errors can be established. For the single
point turning operation studied, Donmez reports accuracy
improvements of up to 20 times.
This work has been extended by Moon [13] to a system
where the laser measurement system is a integral component
of the machine tool. This system offers the advantage that
it does not require recalibration and is capable of
compensating for the portion of the stochastic error which

8
is autocorrelated. Such systems, however, greatly increase
the cost and complexity of machine tools.
In camshaft grinding, the relationship between machine
errors and workpiece errors is more complex than for the
case of single point turning. Additionally, the ability to
compensate for thermal errors is not so critical. The lift
of the camshaft is essentially a relative dimension which is
measured from the base circle. Since both the datum (base
circle) and the lift are machined simultaneously, the
accuracy is not greatly affected by thermal effects. A
warm-up period is not generally required.
Compensation Through In-Process Gauging
While many causes of form errors in camshafts have been
understood since the 1930s [14], CCMMs necessary to quickly
and accurately quantify these errors have existed for only
20 years. Additionally, CNC cam grinding machines necessary
for implementation of a compensation scheme, have only come
into widespread use in the past 10 years. Work has been
done in the area of in-process inspection and compensation
on machining centers [15], and the idea of an in-process
compensation scheme was first proposed for cam grinding by
Cooke and Perkins [16] .
In their work at Cranfield Institute of Technology,
Cooke and Perkins proposed a prototype CNC camshaft grinding
machine using in-process gauging in 1978. The proposed

9
system employed a gauge probe located 180 degrees
out-of-phase with the grinding wheel. In the proposed
system, the probe is used to detect any deviation in the
measured workpiece from those commanded. The system
computer takes advantage of the 180 degree phase lag to
produce compensated control commands prior to the next
grinding pass. Through study of available servo drive
mechanisms and linear transducers available at the time, the
researchers expected to realize a machining accuracy on the
order of +_ 1.5 micrometer. While such systems are not today
in commercial production, this early work realized the
potential benefits of coupling camshaft grinding and
inspection.
Compensation Using CMM for Post-Process Inspection
An extensive review of the literature as well as
personal interviews with CCMM manufacturers revealed no
previous published work dealing with CCMMs and process
control. Much work has, however, been conducted using the
closely related Cartesian coordinate measuring machine (CMM)
for process control [17,18,19].
Yang and Menq [17] describe a scheme using a CMM for
post-process inspection of end-milled sculptured surfaces.
In this approach, 500 measurements are performed on a 55 mm
x 55 mm sculptured surface. The measured errors are then
best fit to a regressive cubic b-spline tensor-product

10
surface model. The results of this best fit are then used
to determine the compensation to be applied. Using this
technique, the researchers reported improvements in maximum
form error of 73%. While this improvement is significant,
CMMs have practical limitations, such as long cycle times,
that make them unsuitable for use in high volume process
control. The method used by Yang and Menq most resembles
the approach taken in this research.

CHAPTER 3
CAMSHAFT GEOMETRY
The material in this chapter is included to review the
nature of camshaft geometry as it relates to this research
project. The mathematical relationships describing cam
contour, the grinding wheel path, and decomposition of
inspection results are presented. Specific aspects of
camshaft geometry are examined for their significance in
developing a control strategy for the manufacturing process.
Lastly, the industrial conventions for specifying camshaft
geometry are introduced.
Basic Description and Analysis
A typical camshaft, as shown in Figure 3-1, consists of
a number of individual cam lobes, journal bearings, and a
timing reference. The geometry of a radial camshaft with a
translating follower is readily described in terms of the
base circle radius rb, the follower radius rf, the follower
lift s as a function of lobe angle 0, and the timing angle (j)
as shown in Figure 3-2. From this figure, it is evident
that the point-of-contact between the cam surface and the
cam follower does not generally lie along the follower's
line-of-action. This illustrates the difference between cam
11

12
Side View
End View
Figure 3-1
Typical Four Lobe Camshaft

Figure 3-2 Radial Cam with Roller Type Follower

14
contour and the follower lift produced. Errors in cam
contour, at the point-of-contact between the follower and
cam profile surface, produce errors in follower lift.
For the radial cam with a roller follower shown in
Figure 3-2, the cam contour can be calculated as [20]
x = r cos 0
y =
X M +
r
ds
c/0
N
where
M = r sin 0
ds
d0
cos 0
(3-1)
(3-2)
(3-3)
N
r cos
0 - ^fsin 0
cro
(3-4)
r = rb + rf + s (3-5)
and summarizing notation
s = lift
rb = base circle radius
r£ = follower radius
r = the distance between cam and follower centers
0 = lobe angle
All camshaft/follower combinations, such as those with
offset roller followers or flat radial followers, can be
represented as camshafts with radial roller followers. All

15
camshafts considered in this research are represented in
this manner.
Industrial Convention
Both the CCMM and the CNC camshaft grinder used in this
research project adopt the same basic convention for
describing camshaft geometry. This convention is the de
facto industry standard and is used for programming CNC
machines and for reporting error results. These conventions
are adopted in this research to simplify the control
interface.
While both machines employ the same general convention,
the details of the implementation differ with regard to sign
convention and measurement datums. On both machines, the
follower lift is specified as a function of the lobe angle 9
as shown in Figure 3-2. The lobe angle is measured relative
to a coordinate system attached to the cam lobe and oriented
relative to a given geometrical lobe feature. The timing
angle ()) of the individual lobes is then specified relative
to some camshaft feature. Typical camshaft timing
references are eccentrics, lobe 1, dowel pins, or keyways as
illustrated in Figure 3-2. The base circle radius is the
datum for measurement of lift values. The positive
rotational direction is specified as counterclockwise when
viewed from the non-driven end of the camshaft, looking

16
towards the driven end. The details of the implementation
are described in the following two sections.
CCMM Convention
The convention illustrated in Figure 3-3 shows the
convention use by the Adcole 911 CCMM. This convention is
dependent on the camshaft direction-of-rotation. That is,
the CCMM direction-of-rotation is programmable and is
selected as the application direction-of-rotation. The
convention shown is for a camshaft which rotates in a
clockwise direction. In this convention, the lift s is
specified relative to the lobe angle 0. The lift values for
the opening side (the side of the lobe which produces
follower motion away from the camshaft axis-of-rotation)
precede the lift values for the closing side.
The timing angles are measured in the same direction as
the lift specification angle, but to a different datum.
Figure 3-3 shows the lobe timing angles measured from the
timing reference to the lobe nose. Again, the convention
shown is for a camshaft which rotates in a clockwise
direction. For a camshaft which rotates in a
counterclockwise direction, the lobe and timing angles are
measured in the opposite direction.

17
View Looking from Non-driven End to Driven End
Figure 3-3 CCMM Angle Convention-Clockwise Rotation

18
Grinding Machine Convention
The convention used on the CNC grinding machine does
not consider the camshaft functional direction-of-rotation.
Rather, the camshaft geometry is specified in a format which
reflects the direction-of-rotation of the grinding machine.
This convention is shown in Figure 3-4.
Implications of Machining Techniques
In analyzing camshaft geometry, it is necessary to
carefully consider the axis-of-rotation. For effective
process control, machining and inspection must be performed
with respect to the same axis. To facilitate a discussion
of the different axes used for camshaft machining and
inspection, it is helpful to introduce terminology for the
different axes. This terminology is defined as it is
introduced and summarized in Table 3-1.
Table 3-1 Camshaft Axes-of-Rotation
MAOR Axis-of-Rotation for Machining
IAOR Axis-of-Rotation for Inspection/Decomposition
CAOR Camshaft Axis-of-Rotation defined by Centers
Camshaft Axis-of-Rotation defined by Journals
JAOR

19
View Looking from Non-driven End to Driven End
Figure 3-4 Grinding Machine Angle Convention

20
The first two axes are the machining axis-of-rotation
(MAOR) and the inspection axis-of-rotation (IAOR). These
two axes do not refer to the actual camshaft axis-of-
rotation, but rather to the axis-of-rotation of the process.
The MAOR is defined as the axis about which the camshaft
rotates during the machining process. The IAOR is the axis,
with respect to which, the inspection results are
decomposed. The IAOR need not necessarily be the axis about
which the part rotates during the inspection process, since
it is possible to mathematically transform the inspection
results to other axes.
As stated previously, the MAOR and the IAOR must agree
for effective process control. If the two axes do not
agree, an error component, which is random in phase and
skew-symmetrically distributed in magnitude, is introduced
into the inspection results and therefore into the process
control signal. This error component is due to the
eccentricity of the journal bearings to the MAOR. This
component occurs only in cases where the journals are not
ground on the cam grinder. This error component will be
demonstrated through the introduction of the two additional
axes-of-rotation as described below.
First, the journal axis-of-rotation (JAOR) is defined
as the axis about which the camshaft rotates when the
camshaft journals are mated with ideal journal bearings.
The JAOR is determined in the inspection process.

21
To determine the JAOR, a best fit of a circle to the
inspection data for each journal is performed. The JAOR is
then established as the axis which passes through the
centers of these circles. In the case where more than two
journal bearings exist, a segmented JAOR can be used.
Second, the center axis-of-rotation (CAOR) is defined
as the axis about which the camshaft rotates, when the
female camshaft centers are mated with ideal male centers.
The JAOR and the CAOR, as shown in Figure 3-5, represent the
physical axes-of-rotation of the camshaft. In this figure,
the eccentricity of the journal surface is greatly
exaggerated to clearly illustrate the different axes.
The MAOR is dependent on the work holding method used
in the machining process. In this research, the camshaft is
held between centers. When using this method, the MAOR is
defined to be the CAOR. Camshaft grinding between centers
is shown in Figure 3-6. This arrangement uses a live
workhead center and a dead tailstock center.
Alternatively, camshafts can be ground using a
centerless grinding technique as shown in Figure 3-7. In
this approach, the camshaft is supported by fixtures and a
three jaw chuck. Here, the bearing journals must be ground
prior to grinding the cam contours, since these surfaces are
used to locate the camshaft during the grinding process.
The fixtures have hardened bearing surfaces which
effectively simulate the camshaft operating conditions. For

22
Figure 3-5 Camshaft Axes-of-Rotation

23
Figure 3-6
Grinding Between Centers

24
Figure 3-7 Centerless Grinding Technique
Source: "State-of-the-Art 3L Series CNC Cam Grinding
Systems," Litton Industrial Automation Systems, Pub. No.
3L-88 FR 3M, 1988. Used with permission.

25
centerless grinding approaches, the MAOR is defined as the
JAOR.
During inspection, measurement data must be decomposed
relative to a specific axis-of-rotation. The IAOR is
programmable. While the actual inspection is performed
between centers and therefore with respect to the CAOR, the
inspection results can be mathematically transformed from
the CAOR to the JAOR. Again, the IAOR must agree with the
MAOR to avoid the introduction of additional noise into the
process control signal.
Calculation of Grinding Wheel Path
The Cartesian coordinates, xc and yc, of the path
traced by the grinding wheel axis-of-rotation are readily
calculated [20] as
x_ = x + — (r cos 0 - x) (3-6)
C T
yc = y + — (r sin 0 - y) (3-7)
rf
where r„ is the radius of the grinding wheel. The path can
be expressed in polar coordinates [20], which are suitable
for programming the CNC grinding machine, as
iJj = arctan
y,
x,
(3-9)

26
where p is the distance from the MAOR to the grinding wheel
axis-of-rotation, and \\i is the corresponding lobe angle for
the grinding process. The cam grinding operation is
illustrated in Figure 3-8.
From these equations, a table of p versus \]/ can be
constructed for any useful grinding wheel size. This table
corresponds to the positioning commands used internally in a
CNC grinding machine. The commands must frequently be
recalculated depending on grinding wheel size and
potentially even after each increment of in-feed if the
metal removal rate is to be closely controlled. The reason
for this can be seen from Figure 3-2. As discussed
previously, it is evident that the point-of-contact between
the cam surface and follower does not generally lie along
the follower's line-of-action. Consequently, an in-feed of
the grinding wheel does not have the effect of removing the
same amount of material from all portions of the cam lobe
surface since the point-or-contact will vary.
Inspection Techniques for Process Control
Camshaft inspection on CCMMs is accomplished using a
precision follower, of the diameter to be used in the
camshaft application, attached to a spring-loaded sliding
gauge head as shown in Figure 3-9. The movement of the
gauge head is measured using either precision scales or a
laser interferometer. This approach allows direct

27
Figure 3-8 Grinding Wheel Path Calculations

28
Figure 3-9
Camshaft Inspection on a CCMM

29
evaluation of camshaft lift errors and eliminates the need
to mathematically transform results from a non-conforming
follower to the actual follower diameter. When necessary,
this conversion can be performed using equations (3-6) and
(3-7) where the radius of the non-conforming follower is
substituted for the radius of the cutter. Numerical methods
must again be used to solve for the measured lift of the
application follower.
Using CCMMs it is possible to evaluate a range of
camshaft attributes. In addition to lift and timing errors,
most CCMMs are capable of measuring the following
parameters: eccentricity, roundness, taper, lift velocity,
and diameter. Camshaft inspection can be performed with
regard to either manufacturing or functional considerations.
These two approaches can differ depending on the technique
used to hold the work during grinding.
Decomposition of Error Components
Once the appropriate IAOR is selected, the CCMM is used
to decompose measurement results into components which can
be directly used to modify the commanded input to CNC cam
grinding machines. For the CCMM used in this study, the
method of decomposition is programmable. In this section,
the various available methods of decomposition are discussed
and the methods selected for this research are justified.

30
In order to explain the decomposition, a description of
the nature of CCMMs is required. These gauges collect data
on camshaft geometry by rotating the part about the CAOR as
shown in Figure 3-9. The camshaft drives the precision
follower and the measured lift is recorded, generally at one
degree increments. This process allows for rapid data
collection for the entire cam contour.
CCMMs are relative measurement devices and as such they
are ideally suited for inspecting camshafts which are used
with translational followers. The lift of the follower is
both defined and measured relative to the base circle. This
ensures exceptional accuracy for measuring lift errors by
eliminating any d.c. error component. The measurements of
absolute dimensions such as size, may or may not be
particularly accurate, depending on the configuration of the
individual CCMM.
When inspecting a cam lobe, data are first gathered for
the entire 360 degrees of rotation. Next, the d.c.
component or size error of the cam lobe is removed from the
data. This is accomplished by setting the average lift of
the base circle equal to zero and adjusting the data
accordingly. The data are then corrected for the
appropriate axis-of-rotation. As discussed in the previous
section, this selection depends on the machining work
holding method as well as whether the results are for use in

31
cam grinding process control or overall functional
evaluation.
The timing error and lift errors are next separated
using various programmable approaches. In the method used
in this research, the measured cam lift is rotated about the
selected IAOR until the root mean square value of the
difference between the nominal and measured lifts are
minimized. This is illustrated in Figure 3-10. Once the
orientation with the minimum error is determined, the lift
error is reported as the difference between the rotated
measured lift and the nominal lift. The timing error is
reported as the difference between the measured timing,
derived from the best fit process, and the nominal timing.
Timing Relative to Keyway/Fixture
Once the best fit of the lift values is performed, the
timing angle error can be evaluated. For lobe 1 the timing
must be specified relative to some reference such as a
keyway/fixture combination, an eccentric or a dowel. The
repeatability of these different references is highly
variable. Consequently, angles measured relative to such a
reference can have a high stochastic component.
For the case studied, the reference during inspection
is established using a key, a keyway and a mating fixture.
The fixture is fitted with an external timing pin as shown
in Figure 3-9. The CCMM determines the location of the

Measured
Lift
Nominal
Lift
Figure 3-10 Best Fit of Lift Errors

timing reference based on this pin. The grinding fixture,
shown in Figure 3-6, uses the same keyway/fixture
arrangement and includes a slot for the grinding drive pin.
Again, the grinding machine uses this slot as the timing
reference. This arrangement produces a highly non-
repeatable reference as will be discussed in more detail in
Chapter 6. Due to this stochastic component, it is
necessary to separate the lift error from the timing error
in order to more tightly control the repeatable lift errors.
Timing Relative to Lobe 1
The timing of all cam lobes except lobe 1 can be
measured relative to lobe 1. Since all stochastic
components due to fixture errors are removed, the lobe-to-
lobe 1 timing is repeatable and can be tightly controlled.
While timing angles for CNC camshaft grinding machines are
specified relative to a reference other than lobe 1, this
presents no problem as the absolute angle is readily
calculated from the relative angle measurement.

CHAPTER 4
THE STOCHASTIC PROCESS MODEL
Process modeling is used to establish the relationship
between the measured and commanded lift for any given cam
lobe. A stochastic process model of the combined cam
grinding machine and the existing CNC controller can be
developed using established modeling techniques. These
techniques best fit dimensionally homogeneous experimental
data to nominal data and produce an empirical relationship
between process input and output. To develop such a model,
it is advantageous to have a general idea of the causes of
process errors. If the source of errors can be identified,
then the selection of the form of the model does not need to
be made blindly, and the number of models tested can usually
be reduced.
General Linear Least-Squares Estimation
The technique of linear least-squares estimation is
used for the model developed [21,22]. In this technique,
the input to the system is manipulated and the output is
recorded. These data are collected and a linear algebra
based minimization technique is then used to best fit model
coefficients based on the experimental data. The model
34

35
obtained must then be examined for its ability to correctly
predict the behavior of the process.
In general, a process can be estimated by the discrete
model
+
«0 Cn-1 + “l Cn-2- ■ ■ +“r-l cn-p
+ Pi mn- i-d + - • • + P,-1 mn-q-d+ 1
+
(4-1)
where
cn = controlled variable
nijj = manipulated variable
p = order of model in controlled variable
q = order of model in manipulated variable
(Xi = coefficient of controlled variable (i = 0,1,2 , . . . , p-1)
Pj = coefficient of manipulated variable (j=0,1,2,...,q-1)
d = delay
en = residual error
The controlled and manipulated variables can be measured for
any number of observations N. The resulting N equations can
then be written in matrix form where n = 0, 1, 2,, N-l as
c - x b + e (4-2)
where
C-1
C-2
... C.p
m0-d
m-l-d â– 
â–  mi-q-d
Co
.
C-1
■ • •
mi-d
M-d â– 
â–  m2-q -d
.
CN-Z
CN- 3
• ’ ' CN-p
mN- l-d
mN- 2-d ‘
• mN-q-d

36
and where
co
60
C1
61
C2
€2
/ G =
CN-1
6W-1 .
The residuals of the model are
e = c - x b
(4-4)
(4-5)
If the square of the residual errors is minimized then the
model coefficient matrix can be solved for as
£ = (4-6)
where b contains the estimates of the model parameters.
Identification of Lift Error Model
The process model was employed to develop an
understanding of the interaction of lift error at different
lobe angles. The actual control scheme implemented controls
the lift at each of 360 points on the cam surface as if they
were separate variables. This means that there are
essentially 360 control systems for each cam lobe. The
process model developed here does not attempt to model the
control of the lift over a series of parts, but rather it

37
examines the relationship of the lift errors, and
consequently the 360 control systems, for individual cam
lobes.
As stated previously, it is useful to understand the
lift error source when developing the process model.
Figure 4-1 shows the lift error and lift acceleration for
the process studied. The use of the term acceleration here
is imprecise, since the workspeed is not constant during one
rotation. Therefore, the effective lift acceleration during
machining is somewhat different. To avoid confusion, the
acceleration shown in Figure 4-1 will be referred to as the
geometric acceleration. As suggested by Figure 4-1, a
strong correlation between the observed lift error and
geometric acceleration exists. The form of the interaction
model is suggested by examination of the mathematical
relationship between follower lift and acceleration.
The geometric acceleration can be expressed using the
backward-difference expression [23] as
A2/7? _ me ~ 2 + m9.2 (4-7)
A02 h2
where me represents the manipulated variable which is the
commanded lift in this case. Assuming that the correlation
between lift error and acceleration suggested by Figure 4-1
is correct, then from equation (4-7) it can been seen that
the lift error at a given lobe angle is related to lift
commanded at that angle as well as lift commanded at the two

Normalized Values
38
Lift Acceleration and Error
-0.6-f
.0.8+- T T
0 50 100 150 200 250 300 350 400
Lobe Angie (degrees) CCMM Convention
Acceleration Error
Figure 4-1 Lift Acceleration and Measured Lift Error

39
preceding angles. This relationship suggests that these
terms should be included in the model.
It is noted that this model includes no terms of the
controlled variable ce, which represents the measured lift
at lobe angle 0. This is necessary, since with post-process
inspection, the value of the controlled variable is not
available until after the process is completed. Therefore,
it is not useful to include these components in a model
designed for process control based on post-process
inspection. The process model selected must be a purely
regressive model, where the process output is expressed in
terms of the commanded input.
Estimation of Model Parameters
Based on the correlation between lift error and the
geometric lift acceleration developed in the previous
section, the form of the stochastic interaction model is
selected. The model is given as equation (4-8) and models
the measured lift cfl using two unknown parameters.
C6 = Po mg + Pi [ mg - 2 mg., + me_2] (4-8)
The first term in the model is the product of model
parameter [3 '0 and the commanded lift. The second term is the
product of parameter pi and the commanded geometric
acceleration of the lift.
The actual correlation between commanded lift values
and inspection results were developed using a generalized

40
form of (4-8) . The general second order regressive model,
assuming no delay, is given as
CB = Po + Pi me-i + P2 me-2 (4-9)
The coefficients P0,P1( and (32 were found to be 1.84934,
-1.69993, and 0.85091 respectively.
A detailed comparison of these three coefficients with
those from equation (4-8), demonstrates a compelling
confirmation of the form of the model given in equation
(4-8). Equating coefficients of equation (4-8) and equation
(4-9) for mg.! gives
o/ _ _ Pi -1.69993
2 2
Equating coefficients of m9_2 gives
0.84997
(4-10)
Pi = P2 i4'11*
Substituting in the value of Pi from equation (4-10) and the
value of P2 from the regression analysis into equation
(4-11) gives
0.84997 ~ 0.85091 (4-12)
These values for P2 differ by less than 0.12%. Finally
equating coefficients of me and substituting in the value of
p0 and using the average value of Px gives
Po = Po “ Pi = 1-84934 - 0.85044 = 0.99890 * 1 (4-13 )
Again this result is consistent with the proposed model.

41
Diagnostic Checking of the Model
This model can be examined for its ability to
accurately predict the process errors through examination of
the residuals as defined by equation (4-5). These
residuals, shown in Figure 4-2, indicate good agreement
between the model and actual process results. The residual
errors are an order of magnitude smaller than the measured
lift errors. While these errors are small, they are clearly
deterministic. This indicates that the model fails to
account for all deterministic components of the process
error. Yet, in spite of testing many models, this small
deterministic component in the residuals proved difficult to
eliminate using a simple form of model.
Two possible sources of the deterministic component
seen in the residuals are discussed for the purpose of
future model refinement. The first source is the workspeed
generation method. This source is suggested since the
relationship between lift errors and geometric acceleration
used in this analysis is based on constant rotational speed.
However, the workspeed varies within a rotation during the
grinding operation. The workspeed generation method is
discussed in more detail in Chapter 5.
The second possible source of the deterministic
component is the difference between reference follower
diameter and the changing grinding wheel diameter. This
factor is considered for two reasons. First, the change in

Residual Error (inches)
42
Residuals of Lift Error
Second order regressive model
0.0008a-
0.0007+
0.0006+
0.0005 -i
0.0004 •
0.0003-
0.0002 •
0.0001 -t
I
-0.0001 1
-'v
'•'WV
,-.w:
-0.0002
0 50 100 150 200 250 300 350
Lobe Angle (degrees) CCMM Convention
400
Figure 4-2 Stochastic Model Residual Errors

43
grinding wheel size produces a change in the grinding wheel
footprint and consequently its cutting ability. Second,
changes in the wheel size alter the commands which the
grinding machine controller generates for controlling the
individual machine axes. As these commands change, the
commanded movements of the machine axes are altered and the
process dynamics change accordingly. The change in process
dynamics affects the geometric errors produced in the part.
Further testing would be required to determine if either of
these factors produce effects large enough to be measured.
Potential for Model Improvement
If the method of workspeed generation is known, the
form of regressive model can be modified to account for this
component. Error components correlated to grinding wheel
size cannot be handled directly in the planned
implementation because direct access to wheel size is not
available in the interface used in this research. If the
current wheel size were available, a disturbance feedforward
controller could be implemented to compensate for errors due
to a changing wheel size.

CHAPTER 5
PROCESS CONTROL STRATEGY
The Control Interface
The control approach taken in this project is to modify
camshaft program data based on the post-process inspection
results. This approach, known as command feedforward
control, allows for a software implementation and
demonstration of the effectiveness of the system. All the
necessary control parameters are manipulated using the
existing control interface. This approach follows industry
standards in describing camshaft geometry and is easily
adapted to cam grinders from different manufacturers.
Part programs for CNC camshaft grinders typically
consist of several main types of commands which will be
referred to as fields. The first field is the lift field.
The lift field contains the 360 commanded lift values for a
cam lobe, the base circle radius and the follower diameter.
The lift values are specified as a function of the lobe
angle. Since the individual lobes of a camshaft may have
different contours, multiple lift fields may exist for a
given camshaft. The second type of field is the timing
field. This field is used to specify the timing angle of
the individual lobes relative to a timing reference. The
44

45
third field is the workspeed field and is used to specify
the workspeed (camshaft rotational speed during machining)
as a function of the lobe angle. The fourth field, the lobe
position field, specifies the position of the lobes along
the camshaft axis.
In the implemented process control scheme, the lift and
timing fields will be directly manipulated to control the
lift and timing errors respectively. The workspeeed field
is considered in this discussion, but it is not modified.
The lobe position field is not a concern.
From these four fields, the machine controller
calculates the command signals for the individual machine
axes-of-motion. In the compensation control scheme
implemented in this work, the internal command generation
scheme is unaltered. Rather the lift and timing fields,
from which the internal commands are generated, are modified
based on the inspection results. These modified fields
effect the generation of corrected control commands for the
machine axes-of-motion.
The workspeed field is generated off-line using a
proprietary algorithm. Investigation of this field
indicates that the workspeed is a normalized parameter based
on the demanded acceleration of the wheelhead, including
non-linearities due to servo demand limiters and the
commanded lift acceleration. Comparisons of the workspeed
field and corresponding lift acceleration indicate that

46
workspeed is roughly inversely proportional to lift
acceleration as shown in Figure 5-1.
Since the workspeed field is based on the commanded
lift, it changes as the commanded lift field changes.
However, this field is developed off-line and can therefore,
be held constant if desired. This is advantageous since
modifying the workspeed field, based on the compensated lift
field, would amplify the effects of the compensations made
to the lift field. This is readily demonstrated by
observing that when the commanded lift, and consequently the
commanded lift acceleration, for a region of the cam is
increased, the commanded workspeed for this region would be
decreased when recalculated. As shown in Chapter 4, lift
errors are correlated to lift acceleration and therefore are
essentially dynamic positioning errors. Consequently, a
decrease in workspeed would decrease the dynamic positioning
error of the machine-axes-of motion and decrease the lift
error relative to the commanded lift field. This decrease
in error would occur in addition to the decrease effected by
the modification of the commanded lift field. Thus the
system would tend to overcompensate and might exhibit
oscillatory behavior.

Lift Acceleration and Workspeed
Acceleration Workspeed
Figure 5-1 Typical Workspeed and Lift Acceleration

48
Lift Error Controller Model
An Interacting Lift Process Model
As shown in Chapter 4, interaction exists between the
lift commanded at different lobe angles. Therefore, the
process can be described as a system which has 360
interacting variables [21]. The form of the regressive
model developed in Chapter 4 suggests the nature of the
interaction between variables. A block diagram for this
interacting system is shown in Figure 5-2. This figure
shows that the lift produced is a function of the lift
commanded for the given lobe angle and the lift commanded
for the two preceding lobe angles, where
n = Part sample number
9 = Lobe angle
s0n = Desired lift
c0n = Measured lift
f0 n = Feedforward desired lift
e0n = Measured lift error
m0 n - Commanded lift
Am0n = Lift compensation
w0n = Disturbances
Additionally the lift controllers are given as:
Gf(B) = Feedforward controller
GC(B) = Process controller for feedback
Gmc (B) = Cam grinder internal controller

49
r
i
â– i
i
i
S0-l,n
I
*4
Controller for
I
1
I
I
1
s9+li„ I Controller for s0+1
I
I
Figure 5-2 Interacting Lift Variables

50
The lift transfer functions are given as
G.: (B)
= CCMM
GJB)
= Machining Process
Gp(#, (B)
= Lumped Gmc(B)
and G„,(B)
Gp(8-D (B)
= interaction
between m^
and c
Gp (9-2) ( B )
= interaction
between m9_2
and c
Noninteracting Control of Lift
From a theoretical control perspective, it is possible
to design a noninteracting control system which eliminates
the interaction of the 360 lift variables [21]. Figure 5-3
shows the block diagram for such a control system. The
controllers required to eliminate interaction are given as:
= Controller between m^ and cg
D9_2 = Controller between m9_2 and ce
While this control strategy has potential for excellent
control, it is complex. Fortunately, if interactions
between variables are small, as will be shown to be the case
for the lift variables, the process model can be simplified.
The Implemented Lift Controller
While the interaction between lift values commanded at
different lobe angles has been established as a source of
lift error, this interaction will be neglected in the
implemented control model. This may be justified by
examining equation (4-8) which is repeated here as (5-1).

51
r
T
*T
I
I
S8-l,n 1
Controller for
m8,n m8-l,n
’8 + 1, n
Controller for s
8 + 1
u
TT
Figure 5-3 Noninteracting Lift Control System

52
C0 = .99890 /Hg + 0.84997 [n^ - 2 Wq^ + m$_2] (5-1)
The first term of this equation is the contribution of
the commanded lift to the total lift predicted by the model.
The second term is the contribution of the geometric
acceleration to the total lift predicted. The geometric
acceleration term represents the interaction of commanded
lift values at adjacent lobe angles. If the geometric
acceleration and lift terms are evaluated separately, the
geometric acceleration term is found to be three orders of
magnitude smaller than the lift term in critical regions of
the cam. For example, at a lobe angle of 34° (convention
Figure 3-4), the geometric acceleration and lift terms are
0.0001 and 0.2218 respectively. Therefore, due to the
dominance of the lift term on the predicted lift, it is
possible, in a closed loop control strategy, to neglect the
acceleration term and consequently the interaction of lift
variables.
The block diagram for the implemented command-
feedforward/ feedback strategy is shown in Figure 5-4. The
control system calculates the 360 individual lift commands
m0n needed to update the commanded lift field. That is, the
control system shown in Figure 5-4 is invoked 360 times for
each cam lobe. An integral controller of the form
GC(B) = (5-2)
1 - B
is selected where K is the integral control gain.

'0,n
Am
¿OH
G (B)
6, n
+
¿•O
^ ,n |
\ 1
+ _
) T
i
Gmc(B)
n
p(9)
(B)
Gm(B)
Gi(B)
Figure 5-4 Implemented Lift Control System

54
To further simplify the control model, ideal transfer
functions are assumed. Thus GP(B) = 1 and Gi(B) = 1. The
solution for the feedforward controller is
GAB) =
= l=i
Gp(B) 1
(5-3)
The control equation can then be written as
Me.n ~ SB,n +
K 3
1-3
(s0,„ - q»,„)
(5-4:
The process equation is
Ce.n = we.n + â„¢B.n (5-5)
From these two equations, the closed loop control can be
solved for as
c
0, n
1
1 - B
(1 - K)B
"0,n
°B,n
(5-6)
Even while individual lobes on a camshaft often have
the same desired lift, the measured error results are not
identical. Therefore, the control system is applied to each
lobe independently. This requires a separate lift command
field for each lobe which creates a slight practical
problem. The CNC controller of the cam grinder used in this
study is not designed to handle high data transfer rates.
Hence, excessive time is required to read in the modified
lift field. This tends to reduce productivity, since the
machine is out of service during data transfer.

55
Control of Relative Timing
The control of lobe timing is a much simpler system to
model. Unfortunately, it is complicated by practical
matters for the systems used in this work. In the existing
process, different timing fixtures are used during the
grinding and inspection processes. These fixtures establish
the timing datum for their respective operations. The
repeatability of these fixtures is an important
consideration. Poor repeatability introduces a large
stochastic component into the data which negatively affects
the ability of the control system to effectively control
lobe timing.
Based on these considerations, the timing of lobe 1 is
controlled relative to the keyway/fixture reference, while
the control of all other lobes is performed relative to lobe
1. The timing relative to lobe 1 is highly repeatable and
therefore allows for aggressive control of timing relative
lobe 1. The block diagram for the implemented timing
control system is shown in Figure 5-5, where
<})e n = Desired timing angle
c0 n = Measured timing angle
f0n = Feedforward desired timing angle
e0 n = Measured timing angle error
m0n = Commanded timing angle
Am0 n = Timing angle compensation
we,n
Disturbances

56
Figure 5-5 Implemented Timing Angle Controller

57
Additionally the timing controllers are given as
Gf(B) = Feedforward controller
GC(B) = Process controller for feedback
Gmc (B) = Cam grinder internal controller
The timing transfer functions are given as:
Gi(B) = CCMM
Gm(B) = Machining Process
Gp(fl) (B) = Lumped Gmc (B) and Gm(B)
Much of the notation introduced for the lift controller is
reused here. However, no confusion should result as the
meaning of the symbols will be clear from the context in
which they are used.
Again if an integral controller is selected and the
same simplifying assumptions are made concerning the
transfer functions, the timing control equation becomes
= This equation is implemented to control the timing of lobe 1
relative to the keyway/fixture and to control the timing of
all other lobes relative to lobe 1.

CHAPTER 6
PROCESS NOISE
From a practical standpoint, all production and
inspection processes have stochastic and repeatable
components. The stochastic component, also referred to as
the repeatability error or signal noise, is defined as six
standard deviations (6a) of the process output. The noise
in the control system has components due to both the
manufacturing and inspection processes.
The inspection process noise can be directly evaluated
and expressed as the standard deviation of multiple
inspections of the same workpiece. Process noise is
evaluated based on the measured variability of the parts
produced. Since the actual values of the controlled
variables differ from the measured values of these
variables, the inspection process noise is superimposed on
the manufacturing process noise. However, if the inspection
process is highly repeatable, relative to the manufacturing
process, it is not necessary to separate the noise from the
two sources, and a good estimate of the process
repeatability is obtained from the measured values of the
controlled variables. For the machines studied, the
repeatability of the inspection process is more than ten
58

59
times better than the repeatability of the manufacturing
process [24,5] .
Even with a highly repeatable inspection process, the
lack of repeatability in the machining process can present
problems for control based on post-process inspection. It
is not possible to correct for process noise using post¬
process inspection. In fact, control strategies which are
overaggressive will actually worsen the situation through
increasing the process variability [25,26]. Therefore, a
strategy designed to attenuate the deleterious effects of
process noise is desired. Two different approaches are
considered.
First, Statistical Process Control (SPC), a type of
dead-band control, historically favored by industrial
engineers and statisticians [25] is considered for its
suitability. Second, traditional feedback control with the
addition of a discrete first order filter, as favored by
control engineers [22,26], is discussed and justified for
use in this problem.
Statistical Process Control
SPC typically refers to the use of Shewhart control
charts and WECO run rules as defined in the text by the
Western Electric Staff [27]. These rules are based on
comparing current inspection results with the mean and
standard deviation of parts previously produced. The WECO

60
rules suggest that an out-of-control condition (shift in
process mean value or increase in process variability)
should be suspected if one or more of the following occurs:
1. An instance of the controlled variable deviates from
the nominal by more than three standard deviations.
2. Two out of three instances deviate from the nominal by
more than two standard deviations.
3. Four out of five instances deviate from the nominal by
more than one standard deviation.
4. Eight consecutive instances with all positive or all
negative deviations occur.
While these rules are useful for detecting shifts in the
mean of the controlled variable, they do not indicate the
size of the shift. Additionally, Shewhart and other SPC
charts require storing past inspection results in order to
evaluate the WECO rules. For a camshaft with eight lobes, a
run of 25 parts requires storing, recalling and evaluating
72,000 floating point numbers. This represents significant
overhead in terms of storage and execution time.
Traditional Feedback Control with Filtering
It has been shown by Koenig [26] that feedback process
controllers amplify non-repeatability error, also called
pure white noise, for processes with short time constants.
The idea of a time constant for a discrete manufacturing
process is different in nature from the time constant of a

61
continuous process which is sampled at discrete points in
time. For discrete processes, the full effects of applied
compensation are realized in the very next part. The
amplification of process noise is a problem as it means an
increase in the variability of the parts produced. To
reduce the effects of process noise on the controlled
variables, a discrete first order filter of the form
Cf <„)=« Cn + (1 - “> Cf in - 1) (6-1)
can be applied, where
a = filter constant (between 0 and 1)
cn = measured value of controlled variable for part n
cf(n) = filtered value of controlled variable for part n
Cf(n-i) = filtered value of controlled variable for part n-1
For white noise, the standard deviation of the filter
input <3l is related to the standard deviation of the filter
output a0 by
By inspection of equation (6-2), it is apparent that CT0 is
less than ct for all values of a less than one. For a equal
to 0.15 (filter coefficient used for lift data in trials)
the standard deviation of filter output to the input can be

62
calculated from equation (6-2) as
°o
a
0.15
-0.15
0.285
(6-3)
The use of this filter effectively introduces a time
constant and corresponding time lag to the system while
reducing the standard deviation of the process noise. For
such a filter the effective time constant of the filter Tf
is
Tf
h
In(1 - a)
(6-4)
where h is the sample period.
Using equation (6-4), an effective time constant can be
calculated in terms of the number of parts as
T f
- 1
In(1 - 0.15)
=6.15 parts
(6-5)
A discrete filter for the lift requires the introduction of
the lobe angle subscript 0 and is given as
Cf (0,n) = « C0,n + (1 " «) Cf (0,^-d (6-6)
where ce_n is the measured value of the lift s at lobe angle
0 for part n. Equation (6-1) can be directly implemented as
a filter for the timing angle (}), where cn is the measured
value of the timing angle for part n.
Unfortunately, the introduction of such a substantial
time constant can cause overshoot in integral only control.
This overshoot can be greatly reduced by including a
proportional term in the control equation. This

63
proportional term was not included at the time of trials and
the filtering technique was therefore modified at high
error-to-noise ratios. For the trials conducted in this
work, the filtered value was reinitialized after each
adjustment to the manipulated variables. This effectively-
eliminated any overshoot but reduced the effectiveness of
the filter to limit noise. As implemented, the filtering
process effectively became a weighted average of parts
inspected between adjustments. With this modification the
process noise reduction can be approximated as [25]
where N is the number of parts inspected to calculate the
compensation.
The use of discrete filters reduces data storage
requirements and calculations as compared with SPC.
Discrete filters can be applied to allow compensation based
on the first part produced, where the error-to-noise ratio
is generally high. The compensation frequency can be
reduced as the error-to-noise ratio decreases. SPC
generally lacks this flexibility and requires the inspection
of many parts prior to initial compensation.
Error Repeatability - A Preliminary Study
A preliminary study was done to determine the size of
the repeatable process errors relative to the stochastic

64
process errors. The tests were performed as described in
Appendix A. For this study, 11 camshafts were ground. The
camshaft geometry and grinding parameters were similar those
used in the control system experiments described in Chapter
7. The only adjustments made to the process were to correct
for base circle size error.1
Process Repeatability of Lift Errors
Lobe 1 lift error is shown in Figure 6-1 for selected
camshafts. Clearly, the general pattern of lobe error
repeats from part to part. Figure 6-2 shows the mean and
the standard deviation for all 360 measured lift error
values of lobe 1 for the 11 parts. This figure clearly
indicates the high value of the mean process error as
compared to the process noise.
Figure 6-3 shows the 360 discrete error-to-noise ratios
for the grinding process. For lobe angles where high errors
are measured, correspondingly high error-to-noise ratios are
obtained. The ratios here might even suggest that with such
high error-to-noise ratios, effective process control could
be achieved with no special considerations taken for process
noise. In fact, this will work quite well in eliminating the
larger lift errors. However, as the lift errors decrease,
the process noise will remain unchanged and the error-to-
1 Size has little effect on our problem; no attempt to
control it is made.

Lift Error (inches)
65
Lift Error for Lobe 1
Six selected runs
0.0008-r
0.0007 -j-
0.0006+
0.0005 +
0.0004-J
0.0003 +
0.0002-
0.0001 +
of
-0.0001 +
-0.0002-
" " \
i: ??1
wrr.
50 100 150 200 250 300 350
Lobe Angle (degrees) CCMM Convention
400
run 1 run 3 run 5
run 7 run 9 run 11
Figure 6-1 Lift Error - Process Repeatability.

Lift Error (inches)
66
Lift Error for Lobe 1
Mean and Standard Deviation
0.0008^
0.0007-j-
0.0006-j
0.0005-j-
0.0004Í
0.0003-}
0.0002i
0.0001 J
Of
-o.ooon-
-0.0002-i : t t 7 ;
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention
| Mean Error Standard Deviation
l
Figure 6-2 Lift Error Mean and Standard Deviation

Lift Error to Noise Ratio
67
Error to Noise Ratio for Lobe 1
6.0-
1
A
1 r\
1
|
|
j
1
1 1
f 1
1
i I
Í
' i
j
A
l\
: \ )
7 i - .,
i ¡ A ',
II f A !
] \ / )
/\ ! \ / 1 ;
4.0
3.0
2.0-t
1.0-f
o.o-
i /
,i \ >\/
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention
Figure 6-3 Lift Error-to-Noise Ratio

68
noise ratio will decrease dramatically. It is in this area
that the filtering technique becomes useful. The results
shown for lobe 1 are typical of results for all four lobes.
Process Repeatability of Timing Error
As shown in Figure 6-4, the lobe timing measured
relative to the keyway/fixture reference is far less
repeatable than the timing measured relative to lobe 1. In
the existing process, different timing fixtures are used in
grinding and inspection processes. These fixtures establish
the timing datum for their respective operations. The
repeatability of these fixtures is an important
consideration as it greatly affects the ability of the
control system to effectively control lobe timing.
Based on these results, the expected process variation
for the 11 parts is calculated to be 1.2 degrees. If
instead, the timing is measured using one of the cam lobes
as a reference, a large reduction in process noise is
effected. By convention, lobe 1 is selected as the
reference. If the process variation is now evaluated
relative to lobe 1, a variation of 0.126 degrees is obtained
for the same 11 parts. This represents an order of magnitude
improvement over the timing repeatability measured relative
to the keyway/fixture reference. Clearly, different degrees

Random Error Component (deg)
69
Lobe Timing Error
no compensation applied
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
II I !
-0.34'i Lobes 2. 3 8» 4 relative to lobe 1 ~ * ]
-0.4 I - ■ = ’ t i
0 5 10 15 20 25
Sample Number
Lobe 1 relative to keyway
\ \
Figure 6-4 Timing Angle Repeatability Error

70
of control are possible depending on the timing reference
selected.
For the cases studied, the timing variation relative to
the keyway/fixture exceeds the total timing tolerance. This
means that the existing process is not capable of producing
all parts to specification and no post-process gauging with
feedback strategy will change this. As a practical matter,
this situation can be improved upon. The timing errors
relative to keyway/fixture can be corrected during the
mating of the camshaft and drive gear. Additionally the
problem is related to the quality of fixtures which can also
be improved.
Still, this presents a problem in demonstrating the
control system with limited parts available for trials. For
processes with greater variability, more samples are
required to separate the mean error signal from the process
noise for a given error size of interest. Correcting for
timing errors relative to lobe 1 and lift errors requires
many fewer samples than does the correction of timing errors
relative to the keyway/fixture.

CHAPTER 7
EXPERIMENTAL RESULTS
The trials performed in this study were performed at
Andrews Products in Rosemont Illinois, using a Landis 3L
series cam grinder as shown in Figure 7-1. An Adcole Model
911 CCMM, shown in Figure 7-2, was used for camshaft
inspection. The grinding parameters, including lift and
timing specifications for the trial part, are given in
appendix A. The camshaft inspection parameters are given in
Appendix B. The control system parameters and a functional
diagram of the control software are included in Appendix C.
During the trials, the only changes made to process
parameters were those made to the lift and timing command
fields.
The trials were carried out in a production environment
over a run of approximately 100 pieces. The parts were
milled from stock to within 0.01 inches of finished
dimensions. Camshafts were case hardened prior to grinding.
The camshafts were ground, inspected, and compensation
applied according to the schedule shown in Table 7-1. This
schedule represents an attempt to balance the demands of
production needs with experimental technique.
71

72
Figure 7-1 Landis 3L Series Cam Grinder
Source: "State-of-the-Art 3L Series CNC Cam Grinding
Systems," Litton Industrial Automation Systems, Pub. No.
3L-88 FR 3M, 1988. Used with permission.

Figure
H
73
7-2 Adcoie Model 911 CCMM

74
Table 7-1 Grinding, Inspection, and Compensation Schedule
Compensation
Number
Part(s)
Ground
Compensation
Based on Part(s)
Notes
0
1
nominal part data
1
2
1
2
3-13
2
3
14-28
3-13
Parts
14-93
4
29-82
14-28
made
two
5
83-88
79-82
days
after
6
89-93
83-88
1-13
Results of Lift Error Control
The reduction in lift error is shown in three different
ways. First, the measured lift error for lobe 2, after each
application of compensation is shown in Figure 7-3,
Figure 7-4, Figure 7-5, and Figure 7-6. Second, the total
lift error, that is the maximum positive minus the maximum
negative lift error, is shown for all four lobes in
Figure 7-7. Third, the root mean square (RMS) of all 360
individual lift measurements for all four lobes is shown in
Figure 7-8. Clearly, all three measures show improvement in
the lift error. The data for lobe 2 show an order of
magnitude reduction in the measured lift error with other
lobes showing smaller reductions, depending primarily on the
initial value of the lift error. Both the RMS and total
lift error data give some indication of the effects of the

Lift Error (inches)
75
Measured Lift Error - Lobe 2
Figure 7-3 Lift Error using Control Scheme

Lift Error (inches)
76
Measured Lift Error - Lobe 2
2.0E-04t
-4.0E-041
-5.0E-041
¡ Comp. #2 I
Comp. #3 I
-6.0E-04H i i : ’ •
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention
Figure 7-4 Lift Error using Control Scheme

Lift Error (inches)
77
Measured Lift Error - Lobe 2
2.0E-04t
-4.0E-044
Comp. #4 !
Comp. #5 i
-5.0E-041
-6.0E-04H t t i——t ■
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention
Figure 7-5 Lift Error using Control Scheme

Lift Error (inches)
78
Measured Lift Error - Lobe 2
2.0E-04i i -
1.0E-04-)
O.OE^OO
I
-1 .OE-04-í-
j
-2.0E-04+
I
-3.0E-04j
-4.0E-04+
-o.0E-04i
-6.0E-04-
Comp. rr6
0 50 100 150 200 250 300 350 400
Lobe Angle (degrees) CCMM Convention
Figure 7-6 Lift Error using Control Scheme

Total Lift Error (in.)
79
Total Lift Error
average for all parts inspected
7.0E-041
L
6.0E-041 V
5.0E-04 • -V
\
4.0E-04Í
3.0E-04-)
ZOE-04-t
1.0E-041 "
i
0.0E + 00H i t t
0 1 2 3 4 5
Compensation Number
lobe 1
lobe 2
lobe 3
lobe 4
6
Figure 7-7
Total Lift Error using Control Scheme

RMS Lift Error (in.)
80
RMS of Lift Error
average vaiues for ail parts inspected
2.0E -041
1.8E-04-:
1.6E-04 I
1.4E-04-»
1.2E-04-
1.0E-04--
8.0E-054
6.0E-05j
4.0E-05Í
2.0E-05Í
0.0E-^00^ t i
0 1 2 3 4 5
Compensation Number
i
i
i
i
6
Figure 7-8 RMS of Lift Error using Control Scheme
lobe 1
lobe 2 !
lobe 3 I
I
j lobe 4

81
two day interruption in the trials. This indication appears
in the form of modest reductions and even slight increases
in form error between compensation number 2 and 3. When the
camshafts used to calculate the compensated command number 3
were ground, the machine had been operating for eight hours.
Compensation number three was then applied when the machine
was re-started two days later. Thus, the increase in lift
error associated with this delay, combined with the further
reduction in lift error when compensation is applied in a
timely manner, suggests that thermal effects account for a
small but nevertheless measurable component of lift error.
Additionally, mixed results are obtained between
compensation numbers three and four. Fifty parts were
ground between the inspected parts and the application of
compensation. These results may indicate a lift error
component due to the changing wheel size (0.2 inch for 50
parts). Results after compensation numbers four, five and
six, where no parts were ground between the inspected parts
and the application of compensation, demonstrate that more
frequent compensation further reduces errors.
Results of Timing Error Control
Control of Timing Relative to Lobe 1
The results of the timing control relative to lobe one
are shown in Figure 7-9. Small initial timing errors, as
compared with the results of the preliminary repeatability

82
Timing Error Relative to Lobe 1
0.10-r
0.054
I
O.OCH-
co
a>
O)
v
~o
LU
U)
c
-0.054 â– 
I ;
•0.10:
-0.151
-0.20 j
-0.254
I
-0.301
-0.354
I
-Q.40Jr-r-
1
—t—i i—i—i—i—i—i—i—i—r—n—tth—i—i—tt—i—rn—rr-'—1—i—i—i i—n r—r
5 10 15 20 25 80 85 90
Part Number
â–  Lobe 2
Lobe 3
Lobe 4
Figure 7-9 Timing to Lobe 1 using Control Scheme

83
study, existed for the camshaft used in the control trials.
While the initial values were small, it is significant to
note that no timing errors developed during the control
period and the timing angle remained within the noise levels
established in the preliminary trials.
This is especially significant considering that the
timing angle is decomposed from the measured lift data.
Since compensation is applied to the lift field, the lift
data are altered. Nevertheless, the results show that it is
possible to control these parameters separately. This
ability to control these coupled parameters as if they were
separate, has great practical benefits and greatly
simplifies the control system.
Control of Timing Relative to Keywav/Fixture
The control of timing of lobe 1 relative to the
keyway/fixture was less successful as shown in Figure 7-10.
While the process is approximately centered about zero
error, the timing of lobe 1 to the keyway/fixture
demonstrated a greater variability than the uncontrolled
timing measured in the preliminary repeatability studies.
This result is not surprising considering the low error-to-
noise ratio which exists for this parameter and the short
effective time constant of the process. It was anticipated
that this control might prove overaggressive. However, to
avoid introducing additional complexity for these initial

Timing Error (degrees)
84
Timing Error Relative to Keyway
1.00-
J Lobe 1
5 10 15 20 25 80 85 90
Pan Number
Figure 7-10 Timing to Keyway using Control Scheme

85
trials, this was accepted. Recommendations for improving
the effective control over timing relative to the
keyway/fixture are discussed in Chapter 8.

CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS
It has been shown that significant improvements in
camshaft lift error can be realized through feedback of
post-process inspection results. It was shown that even
while the lift errors at nearby lobe angles interact, good
results are obtained when this interaction is neglected.
The use of discrete filtering prevents an increase in the
variability of a process about a mean operating point.
Implementation of the Control System
The strategy employed relies on the use of standard CNC
industrial camshaft inspection and production equipment.
Many camshaft production facilities currently use equipment
suitable for implementation of this control strategy. These
facilities could realize significant quality control
improvements by better utilizing existing production
equipment.
Prior to introduction into a manufacturing environment,
the control system requires the development of a user
interface and further investigation of factors discussed in
the next section. Minor modification of the grinding
machine controller software would allow for seamless
86

87
operation and higher data transfer rates. Additionally,
minor modifications to the CCMM's software are required for
a high quality implementation of the control system. As a
practical matter, production and inspection equipment need
to be located together. In the ideal implementation,
camshafts are ground and automatically transferred, in
sequence, to the CCMM. The feedback of inspection data and
compensated command fields occurs automatically.
Further Work
While the effectiveness of such a control system has
been clearly demonstrated, much interesting work remains in
this area. For a full implementation of discrete filtering,
a proportional term needs to be added to the controller and
the parameters of the model should be optimized through the
use of the regressive model and verified in the actual
implementation. With regard to control of the timing of
lobe 1 to the keyway/fixture, production implementations
would need to be less aggressive. This could be readily
accomplished through the use of greater filtering and the
addition of a proportional term in the controller. As
before, the controller parameters would need to be selected
through simulation and verified experimentally.
Additionally, a non-interacting control system could be
investigated for lift errors. This system should be

88
investigated for its ability to improve control system
convergence rate.
The long term stability of the control system should be
investigated with particular attention to the emergence of
high frequency components in the lift command field. While
the high frequency components of the commanded lift field
are effectively filtered by the limited bandwidth of the
grinding machine, these high frequency components produce
large internal following errors and consequently excessive
demand on the servo motors. Over time, these high frequency
components may lead to increased lift error and a
degradation of control.
Finally, additional trials should be conducted
investigating the effectiveness of different control gains.
Specifically the effectiveness of a control system using
control gain of unity for the lift error should be compared
with the results obtained in this study.

APPENDIX A
GRINDING PARAMETERS

The trials used a Ramron 1-A-90-O-B-7 grinding wheel.
The wheel was dressed using a Norton LL-271B Sequential
Cluster.
The lift and timing fields, given in the following pages,
are specified according to the cam grinding machine
convention described in Chapter 3.
90

91
THE COMMANDED TIMING AND LOBE POSITION FIELDS (0 & Z)
I
S
FLAALL
0
4
FLAALL,39.8400000,96.733,9
FLAALL,0.4949996,213.763,9
FLAALL,0.4949996,208.654,9
FLAALL,0.5250000,304.,9
THE COMMANDED LIFT FIELD (S)
I
P
FLAALL
0.4275000
0.5150000
0.0000000,116.0000000, 1.000
0.0000000, .0000000
0.31600000
0.31591250
0.31565000
0.31521250
0.31459990
0.31381220
0.31284940
0.31171130
0.31039810
0.30890970
0.30724600
0.30540700
0.30339300
0.30120400
0.29884020
0.29630180
0.29358940
0.29070330
0.28764410
0.28441270
0.28100990
0.27743700
0.27369520
0.26978610
0.26571150
0.26147350
0.25707450
0.25251730
0.24780490
0.24294080
0.23792900

O . 23277360
0.22747960
0.22205210
0.21649700
0.21082050
0.20502970
0.19913200
0.19313550
0.18704890
0.18088180
0.17464410
0.16834650
0.16200060
0.15561840
0.14921280
0.14279720
0.13638570
0.12999320
0.12363500
0.11732690
0.11108540
0.10492740
0.09886978
0.09293015
0.08712596
0.08147468
0.07599366
0.07069986
0.06560974
0.06073898
0.05610230
0.05171318
0.04758355
0.04372355
0.04014116
0.03684193
0.03382865
0.03110100
0.02865526
0.02648411
0.02457631
0.02291664
0.02148587
0.02026088
0.01921501
0.01831868
0.01754032
0.01684775
0.01621014
0.01560068
0.01500000
0.01440000

O.01380000
0.01320000
0.01260000
0.01200000
0.01140000
0.01080000
0.01020000
0.00960000
0.00900000
0.00840000
0.00780000
0.00720000
0.00660000
0.00600000
0.00540000
0.00480000
0.00420000
0.00360050
0.00300732
0.00243371
0.00189653
0.00141266
0.00099616
0.00065625
0.00039616
0.00021266
0.00009653
0.00003371
0.00000732
0.00000050
0.00000000
0.00000000
0.00000000
0.00000000
117.0000000,242.0000000, 1.000
0.0000000, .0000000
0.0000000R
243.0000000,359.0000000, 1.000
0.0000000, .0000000
O . 00000000
O.00000000
O . 00000000
O.00000000
O . 00000000
O.00000050
O.00000732
O.00003371
O . 00009653
O . 00021266
O . 00039616
O.00065625
O.00099616

O . 00141266
0.00189653
0.00243371
0.00300732
0.00360050
0.00420000
0.00480000
0.00540000
0.00600000
0.00660000
0.00720000
0.00780000
0.00840000
0.00900000
0.00960000
0.01020000
0.01080000
0.01140000
0.01200000
0.01260000
0.01320000
0.01380000
0.01440000
0.01500000
0.01560068
0.01621014
0.01684775
0.01754032
0.01831868
0.01921501
0.02026088
0.02148587
0.02291664
0.02457631
0.02648411
0.02865526
0.03110100
0.03382865
0.03684193
0.04014116
0.04372355
0.04758355
0.05171318
0.05610230
0.06073898
0.06560974
0.07069986
0.07599366
0.08147468
0.08712596
0.09293015
0.09886978

O . 10492740
0.11108540
0.11732690
0.12363500
0.12999320
0.13638570
0.14279720
0.14921280
0.15561840
0.16200060
0.16834650
0.17464410
0.18088180
0.18704890
0.19313550
0.19913200
0.20502970
0.21082050
0.21649700
0.22205210
0.22747960
0.23277360
0.23792900
0.24294080
0.24780490
0.25251730
0.25707450
0.26147350
0.26571150
0.26978610
0.27369520
0.27743700
0.28100990
0.28441270
0.28764410
0.29070330
0.29358940
0.29630180
0.29884020
0.30120400
0.30339300
0.30540700
0.30724600
0.30890970
0.31039810
0.31171130
0.31284940
0.31381220
0.31459990
0.31521250
0.31565000
0.31591250

THE COMMANDED WORKSPEED FIELD (W)
I
W
FLAALL
1.122494
98.000000
0.000000,359.000000,1.000000
0.000000,0.000000
0.763663
0.772310
0.780876
0.780812
0.780620
0.780299
0.779851
0.779277
0.778578
0.777756
0.776811
0.775747
0.774565
0.773269
0.771860
0.770342
0.768717
0.766991
0.765165
0.763245
0.761234
0.759136
0.756956
0.754699
0.752369
0.749971
0.747511
0.744994
0.742425
0.739809
0.737153
0.734461
0.733883
0.732152
0.729277
0.725276
0.720169
0.713986
0.706762
0.698536
0.689355
0.679270

O.668337
O.656618
O.644178
O.631086
0.617417
0.603245
0.588652
0.573717
0.558526
0.543162
0.527711
0.512261
0.496897
0.481705
0.466771
0.452177
0.438006
0.424337
0.411245
0.398805
0.387086
0.376153
0.366068
0.356887
0.348661
0.341437
0.335254
0.330147
0.326146
0.323271
0.321540
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.321084
0.321452
0.322063
0.322919
0.324017
0.325359
0.326942
0.328765
0.330828
0.333128
0.335664
0.338435

O.341438
O.344670
0.348131
0.351816
0.355724
0.359852
0.364196
0.368755
0.373523
0.378498
0.383677
0.389055
0.394629
0.400395
0.406348
0.412484
0.418799
0.425288
0.431947
0.438771
0.445754
0.452892
0.460180
0.467612
0.475184
0.482889
0.490722
0.498677
0.506749
0.514932
0.523220
0.531606
0.540086
0.548653
0.557300
0.566021
0.574811
0.583662
0.592569
0.601524
0.610523
0.619557
0.628620
0.637707
0.646810
0.655923
0.665039
0.674152
0.683255
0.692342
0.701406
0.710440

O . 719438
O . 728394
O.737301
0.746152
0.754941
0.763663
0.772310
0.780876
0.789356
0.797743
0.806031
0.814213
0.822285
0.830241
0.838074
0.845779
0.853350
0.860782
0.868070
0.875208
0.882192
0.889016
0.895674
0.902164
0.908479
0.914615
0.920568
0.926333
0.931907
0.937285
0.942464
0.947439
0.952208
0.956766
0.961110
0.965238
0.969146
0.972832
0.976292
0.979525
0.982527
0.985298
0.987834
0.990134
0.992197
0.994020
0.995603
0.996945
0.998044
0.998899
0.999511
0.999878

100
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
0.999819
0.999276
0.998372
0.997110
0.995491
0.993520
0.991200
0.988537
0.985535
0.982203
0.978546
0.974573
0.970292
0.965711
0.960842
0.955694
0.950279
0.944607
0.938691
0.932543
0.926178
0.919607
0.912846
0.905909
0.898810
0.891565
0.884189
0.876697
0.869107
0.861434
0.860601
0.858107
0.853967
0.848207
0.840863
0.831980
0.821612

O . 809823
0.796687
0.782283
0.766702
0.750038
0.732396
0.713882
0.694613
0.674705
0.654283
0.633472
0.612400
0.591198
0.569995
0.548923
0.528112
0.507690
0.487783
0.468513
0.450000
0.432357
0.415694
0.400112
0.385709
0.372572
0.360784
0.350416
0.341532
0.334188
0.328429
0.324289
0.321795
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.320962
0.321084
0.321452
0.322063
0.322919
0.324017
0.325359
0.326942
0.328765
0.330828
0.333128
0.335664

O . 338435
O . 341438
O . 344670
0.348131
0.351816
0.355724
0.359852
0.364196
0.368755
0.373523
0.378498
0.383677
0.389055
0.394629
0.400395
0.406348
0.412484
0.418799
0.425288
0.431947
0.438771
0.445754
0.452892
0.460180
0.467612
0.475184
0.482889
0.490722
0.498677
0.506749
0.514932
0.523220
0.531606
0.540086
0.548653
0.557300
0.566021
0.574811
0.583662
0.592569
0.601524
0.610523
0.619557
0.628620
0.637707
0.646810
0.655923
0.665039
0.674152
0.683255
0.692342
0.701406

103
0.710440
0.719438
0.728394
0.737301
0.746152
0.754941
E

GRINDING PARAMETERS
LANDIS CNC CAM GRINDER
SERIAL
NO. 902-56
SHAFT NAME
FLAALL
PART CLEARANCE RADIUS
(in)
1.5
FIRST CAM WAIT ANGLE
(deg)
170
BETWEEN CAM WAIT ANGLE
(deg)
290
RAPID FEED RATE
(in/sec.)
2
WORKSPEED DURING DRESS
(RPM)
25
FEED BACKOFF DURING DRESS
(in)
0.002
FEED DURING ROUGH DRESSING
1 =
ZES;0=NO :
0
INFEED PARAMETER SET 1
TO
12
11
ROUGH TOTAL FEED
(in)
0.0075
ROUGH INCREMENTS
3
ROUGH INCREMENT 1
(in)
0.003
ROUGH INCREMENT 2
(in)
0.0025
ROUGH INCREMENT 3
(in)
0.002
ROUGH INCREMENT RATE
(in/deg)
0.02
ROUGH INCREMENT ANGLE
(deg)
330
ROUGH WORK RPM
98
ROUGH SIZE DWELL
(seconds)
0.4
FINISH TOTAL FEED
(in)
0.0025
FINISH INCREMENTS
2
FINISH INCREMENT 1
(in)
0.0015
FINISH INCREMENT 2
(in)
0.001
FINISH INCREMENT RATE
(in/sec)
0.02
FINISH INCREMENT ANGLE
(deg)
330
FINISH WORK RPM
25
V.S.WORK IN FINISH 1=YES;0
=NO
1
WHEEL BALANCE INTERVAL
(shafts)
25
FINISH SIZE DWELL
(seconds)
0.4
FEED RESET ANGLE
(deg)
10
CARRIAGE RECIP. SPEED
(
HZ
0=OFF) :
0
ECCENTRIC LOBE 1=YES;0=
NO
0
SIZE ADJUST CURRENT SET
(in)
0
PHASE ADJUST CURRENT SET
(deg)
0

105
DRESSING PARAMETERS
LANDIS CNC CAM GRINDER SERIAL NO. 902-56
DRESSER ENABLED l=CONB.FRONT;2=CBN.FRONT;3=REAR
ROUGH LOBES/DRESS
FINISH LOBES/DRESS
WORKSPEED DURING DRESS
FEED BACK OFF DURING DRESS
FEED DURING ROUGH DRESSING
SINGLE PASS DRESS
ROUGH DEPTH OF CUT
FINISH DEPTH OF CUT
ROUGH TRAVERSE RATE
FINISH TRAVERSE RATE
;0=OFF) : 8
;0=OFF) : 0
(RPM): 25
(in): 0.002
1=YES;0=No : 0
1=YES;0=NO
(in)
(in)
(in/sec)
(in/sec)
1
0.0003
0.007
0.215
0.215
COMPENSATION CORRECTION (PERCENT) : 0
CONTINUOUS DRESS CYCLES : 10

APPENDIX B
CAMSHAFT
INSPECTION PARAMETERS

CAMSHAFT INSPECTION INITIALIZATION ROUTINE
1
52
0.000000
2
54
1.000000
3
83
4
17
9250.000000
5
16
100.000000
6
34
1.000000
7
91
1.000000
HARV3A.DAT
8
36
1.000000
HARLEY.PL1
Complete check.
9
36
2.000000
HARLEY.SP1
No ecc corr or jnls
10
36
3.000000
HARLEY.NT1
One cut. No taper.
11
36
5.000000
HARNEW.PL1
Control Inspection
Rout.
12
36
7.000000
DRIVAN.TST
Checks Drive Key To
Cam 1
13
36
8.000000
HEDSTK.CAL
Head cal.
14
36
9.000000
HARLEY.HTC
Head/tail cal.
15
111
1.000000
1.001150
.000150 -.000150
16
111
2.000000
.812250
.000250 -.000250
17
112
99.000000
. 000300
.000300 1.000000 2.
000000
18
113
99.000000
1.064500
.002500 .000500
000500
19
114
99.00000
104.0000
255.0000 0.00050
001000
20
115
53.330000
53 . 830000
.500000 1.00000 99
. 0000
21
116
0.000000
0.000000
0.000000 0.00000 1
. 0000
22
117
99.000000
0.000100
0.000100 1.00000 0.
000100
23
122
0.250000
0.000000
0.000500 0.000100 -
0.0001
24
150
25
26
36
4.000000
HARLEY.NPL 1
Ho plot. Taper. Storage.
107

108
CAMSHAFT INSPECTION ROUTINE FOR PROCESS CONTROL
1
83
2
11
250.000000
3
23
4
14
0.000000
5
81
1.000000
1.000000
0.000000
6
48
0.750000
7
21
8
12
2.000000
0.000000
9
23
10
14
1.000000
11
13
1.000000
12
15
1.000000
1.000000
.000000
13
22
14
84
1.000000
15
81
1.000000
0.000000
0.000000
16
48
0.500000
17
21
18
12
2.000000
0.000000
19
23
20
14
1.000000
21
13
1.000000
22
15
1.000000
1.000000
.000000
23
22
24
11
50.000000
25
27
2.650000
0.000000
0.000000
26
48
1.500000
27
21
28
12
2.000000
0.000000
29
23
30
14
1.000000
31
38
0.700000
.300000 1.
.000000 30
32
48
1.500000
33
11
150.000000
34
82
1.000000
0.000000
0.000000
35
48
0.850000
36
21
37
12
2.000000
1.000000
38
23
39
14
1.000000
40
123
1.000000
1.000000
41
82
0.000000
0.000000
1.000000
42
12
2.000000
1.000000
43
23
44
14
1.000000
45
123
1.000000
1.000000
46
35
1.000000
1.000000
3.000000
47
15
1.000000
1.000000
.000000
48
85
1.000000
49
85
-1.000000
1.000000
1.000000

109
50
49
51
118
52
119
53
82
0.000000
0.000000
2.000000
54
12
2.000000
0.000000
55
23
56
14
1.000000
57
123
1.000000
1.000000
58
48
0.850000
59
85
1.000000
60
32
34.000000
3.000000
61
22
62
27
.500000
.000000
. 000000
63
23
64
14
0.000000
65
150
1.000000
INITIALIZATION PARAMETERS
2 52 0.000000
3 83
4 17 9540.000000
5 11 150.000000
6 34 1.000000
7 16 100.000000
10 150
11
12 *** Routine 33 and 95 are in STEPOl.FOR
8 36 13.000000 9.000000 frdgrn.pll
9 36 9.000000 13.000000 frdgrn.pll

APPENDIX C
SOFTWARE OUTLINES AND CONTROL SYSTEM PARAMETERS

SOFTWARE OUTLINE FOR LIFT CONTROLLER
Read Lift Inspection Data
Read Filtered Lift Data
Filter Lift Inspection Data
Store Filtered Lift Data
Read Desired Lift
Calculate Lift Error
Transform Lift Data to Grinder
Coordinate System
Calculate Lift Compensation
Read Commanded Lift
Calculate New Commanded Lift
Output New Commanded Lift
c«,
cf(
cf (
cf<
se
ee,
ee,
Am
m9,
n
d,n-1)
d,n)
d, n)
n
n
0, n
n
n+1
n+1
in

SOFTWARE OUTLINE FOR TIMING CONTROLLER
Read Timing Inspection Data
Read Filtered Timing Data
Filter Timing Inspection Data
Store Filtered Data
Read Desired Timing
Calculate Timing Error
Transform Data to Grinder
Coordinate System
Calculate Compensation
Read Commanded Timing
Calculate New Commanded Timing
Output New Commanded Timing
Cf (n-l)
Gf Cf (n)
00
e
n
e
n
Atip
m
n+1

CONTROL SYSTEM PARAMETERS
#define
#define
#define
#define
#define
#define
#define
#define
#define
ALPHA_LIFT 0.15
ALPHA__KEY 0.15
ALPHA_L1 0.15
PROPORTI ONAL__L I FT__GAIN 0.0
INTE GRAL__LIFT_GAIN 0.7
PRO_TIMING_GAIN_REL_REF 0.0
INTEGRAL_TIMING_GAIN_REL_REF 0.7
PR0_TIMING_GAIN_REL_L1 0.0
INTEGRAL TIMING GAIN REL L1 0.7

REFERENCES
[1] Jensen, P. W., Cam Design and Manufacture, New York:
Marcel Deckker, 1987.
[2] "CNC Cam Grinding Complex Contours," Manufacturing
Engineering, Vol. 103, No. 6, Dec. 1989, p.32.
[3] King, R. I., Hahn, R. S., Handbook of Modern Grinding
Technology, New York: Chapman and Hall, 1986,
[4] Malkin, S., Crinding Technology, Chichester, U.K.: Ellis
Horwood, 1989.
[5] "State-of-the-Art 3L Series CNC Cam Grinding Systems,"
Litton Industrial Automation Systems, Pub. No. 3L-88 FR 3M,
Waynesboro, PA, 1988.
[6] "The Bryant Lectraline LL2 CNC Grinding Machine," Bryant
Grinder Corporation, Pub. No. LL2f ADB 5M, Springfield, VT,
August 1984.
[7] "Adcole Model 911 - Computer Aided Camshaft and Piston
Inspection Gage," Adcole Corporation, Pub. No. 911 2M,
Marlborough, MA, Feb. 1990.
[8] Adcole Model 1310 - High Speed Computer Aided Camshaft
Inspection Gage," Adcole Corporation, Marlborough, MA, n.d.
[9] Donmez, M. A., Blomguist, D. S., Hocken, R. J., Liu, C.
R. and Barash, M. M., "A General Methodology for Machine
Tool Accuracy Enhancement by Error Compensation," Precision
Engineering, Vol. 8, No. 4, 1986, pp. 187-196.
[10] Hocken, R. J., "Quasistatic Machine Tool Errors,"
Machine Tool Task Force Report, Lawrence Livermore National
Laboratory, Livermore, CA, 1980.
[11] Ernán, K. F., Wu, B. T. and DeVries, M. F., "A
Generalized Geometric Model for Multi-Axis Machines,"
Annuals of the CIRP, Vol. 36, No. 1, 1987, pp. 253-256.
114

115
[12] Ziegert, J. C. and Smith, S. K., "Neural Network Error
Compensation of Machine Tools and Coordinate Measuring
Machines," Proposal to NSF, University of Florida,
Gainesville, May 1990.
[13] Moon, E. J. "Forecasting Compensatory Control for
Machining Straightness," Ph. D. Thesis, University of
Wisconsin-Madison, 1984.
[14] Jacobs, F. B., Automotive Grinding, Cleveland, OH:
Penton, 1928.
[15] Fan, K. C., Chen, L. C. and Lu, S. S., "A CAD-Directed
in-Cycle Gaging System with Accuracy Enhancement by Error
Compensation Scheme," Proceedings of the Japan/USA Symposium
of Flexible Automation. ASME, Vol. 2, San Francisco, 1992,
pp. 1015-1021.
[16] Cooke, P. and Perkins, D. R., "A Computer Controlled
Cam Grinding Machine," Cams and Cam Mechanisms, Ed. J. R.
Jones, London: Mechanical Engineering Publications, 1978.
[17] Yang, B. D. and Menq, C. H., Compensation for Form
Error of End-Milled Sculptured Surfaces Using Discrete
Measurement Data," Proceedings of the Japan/USA Symposium of
Flexible Automation, ASME, Vol. 1, San Francisco, 1992, 385-
392 .
[18] Roblee, J. W., Chen, Y. L., Becker, K. B. and Fiedler,
K. H., "Refinements in Postprocess Gaging with Feedback in
the Production of Diamond Turned Optics," Proceeding of
Laser Interferometry and Computer Aided Interferometry IV,
SPIE, Vol. 1553, The Hague, Netherlands, 1991, pp. 187-191.
[19] Eversheim, V. W., Kónig, W., Week, M., and Pfeifer, T.,
"Productiontechnik auf dem Weg zu Integrierten Systemen,"
UPI-Z, Nr. 6, June 1987, pp. 61-65.
[20] Chen, F. Y., Mechanics and Design of Cam Mechanisms,
New York: Pergamon, 1982.
[21] Bollinger, G. B. and Duffie, N. A., Computer Control of
Machines and Processes, Reading, MA: Addison-Wesley, 1988.
[22] Box, G. E. P. and Jenkins, G. M., Time Series Analysis:
Forecasting and Control, San Francisco: Holden-Day, 1976.
[23] James, M. L., Smith, G. M. and Wolford, J. C., Applied
Numerical Methods for Digital Computation with Fortran and
CSMP, New York: Harper and Row, 1977.

116
[24] Dalrymple, T. M., "Adcole 910 Machine Acceptance
Report," Bosch Corporation Internal Report, Charleston, SC,
May 1985.
[25] Grant, E. L. and Levenworth, R. S., Statistical Quality
Control. New York: McGraw-Hill, 1988.
[26] Koenig, D. M., Control and Analysis of Noisy Processes,
Englewood Cliffs, NJ: Prentice-Hall, 1991.
[27] Statistical Quality Control Handbook. Western Electric
Corporation, New York, 1956.

BIOGRAPHICAL SKETCH
The author was born on 24 February 1959, in Langdale,
Alabama. He grew up in the eastern United States where he
attended public schools. In 1981, he received his B. S.
from Auburn University, Auburn, Alabama. After graduation,
he worked for Robert Bosch in the U.S. and Munich, Germany,
where he married his wife, Laura. In 1988, he and his wife
became U.S. Peace Corps volunteers and were posted to the
southern African republic of Botswana. While there, the
author served as a Lecturer of Mechanical Engineering at
Botswana Polytechnic. In 1991, he returned to the U.S. and
to graduate school at the University of Florida. After
graduation, he plans to pursue a career in manufacturing.
117

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a thesis for the degree of Master of Science.
J.
lirman
k
John Ziegert,
Assistant Profesor
of Mechanical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a thesis for the degree of Master of Science.
líohn Schueller
Associate Professor
of Mechanical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a thesis for the degree of Master of Science.
of 'Mechanical Engineering
This thesis was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
Madelyn M. Lockhart
Dean, Graduate School

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aforementioned dissertation, hereby grant specific and limited archive and distribution
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