Some aspects of five-axis machine tool design, assembly, and testing


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Some aspects of five-axis machine tool design, assembly, and testing
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ix, 121 leaves : ill. ; 29 cm.
Bernhard, David Montwid, 1961-
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Mechanical Engineering thesis, Ph.D   ( lcsh )
Dissertations, Academic -- Mechanical Engineering -- UF   ( lcsh )
bibliography   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph.D.)--University of Florida, 1997.
Includes bibliographical references (leaves 117-120).
General Note:
General Note:
Statement of Responsibility:
by David Montwid Bernhard.

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University of Florida
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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
        Page iv
    Table of Contents
        Page v
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        Page vii
        Page viii
        Page ix
    Chapter 1. Introduction
        Page 1
        Page 2
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    Chapter 2. Literature review
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    Chapter 3. Kinematics of five-axis machine toos
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    Chapter 4. Practical aspects of machine tool assembly
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    Chapter 5. Cutting performance testing
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    Appendix. Squareness and straightness errors
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    Biographical sketch
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Full Text







Copyright 1997


David Montwid Bernhard

In memory of Louis Arnold Bernhard and James Jacob Kremer for

inspiring their grandson to use his mind and his hands to dream and build.


The author would like to specially thank Dr. Scott Smith and Dr. Jiri Tlusty

for their guidance and help in pursuing this work. The author would also like to

thank Dr. James Klausner, Dr. Sencer Yeralan, and Dr. John Ziegert for serving

on his supervisory committee.

The author would like to extend special thanks to the members of the

Machine Tool Research Center for helping and for putting up with him over the

past four years. I also wish to thank my good friends Dr. Sinan Badrawy, Dr. Tim

Dalrymple, and Tony Schmidt for being a good sounding board and for

supporting me in this work.

Most of all, the author wishes to thank his best friend Sarah and his

mother for their unconditional support and love.


ACKNOW LEDGM ENTS ..........................................

NO M EN C LA TU R E ..............................................

A B S T R A C T ....... .......... ............ .... .... .............


1 INTR O D U C TIO N ........................................

2 LITERATURE REVIEW ...................................
High Speed M achining ................................
M ulti-A xis C utting ....................................
Testing and Evaluation of Machine Tools ..................

Kinematic Combinations ................
Parameters for the selection of combinations
MTRC's Five-Axis Machine Tool ..........

. . . . . . . . 14
. . . . . . . . 14
. . . . . . . 2 7
. . . . . . . . 3 3

Installation and Leveling of the Machine Bed .........
Mounting of the X-axis Rail Systems ................
X axis Ball Screw Assembly, Mounting and Alignment.
Placement of the Carriages and X-axis Frame ........
Y-axis Rails Mounting and Alignment ................
Installation and Alignment of Y-axis Ball Screw........
Installation of the Y-table .........................
Z-axis Pedestals ...............................
Z-axis Rail Installation and Alignment ...............
Testing of the Motion Errors ......................

...... 40
...... 40
...... 42
...... 47
...... 54
...... 57
...... 60
...... 62
...... 65
...... 67
...... 69

5 CUTTING PERFORMANCE TESTING ....................... 73
C hatte r . . . . . . .. . . . . . . . . . . . . . . 74
Measurement of the Frequency Response Function ......... 78
Spindle Model Analysis .............................. 85
Modal Measurement of Spindle ......................... 86
Examination of Modal Measurements of Spindle Housing ......92
Modal Analysis of Z-axis Table ......................... 94
Discussion of Results ................................. 98
C utting Sim ulation .................................... 99
C utting Tests ....................................... 103
Double Hexagon Test Part ............................ 105
Conclusion and Continuing W ork ....................... 114



R E FE R E N C ES ................................................ 117

BIOGRAPHICAL SKETCH ....................................... 121



Rotary axes in spindle/tool
Rotary axes in table
Radial depth of cut
Axial depth of cut
Axial limit of stable cut
Axial critical limit of stable cut
Feed per tooth
Chatter recognition and control
Computer numerical control
Coordinate System
Cross frequency response function
Direct frequency response function
Degrees of Freedom
Natural frequency
Tooth passing frequency
gravitational acceleration
High Speed Machining
Inches per minute
Specific power
Number of teeth on the cutter
Metal Removal Rate
Machine Tool Research Center
Spindle Speed
Number full waves between teeth
Revolutions per minute
Transfer Function
Linear axes designators in spindle/tool
Linear axes designators in table/work piece
Phase shift between old surface and new surface
Orientation factor

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



David Montwid Bernhard

December 1997

Chairperson: Dr. K. Scott Smith

Major Department: Mechanical Engineering

Five-axis machine tools are gaining broader usage throughout industry.

The aircraft industry has always been a large user of five-axis machine tools for

producing wing and landing gear components. These machine tools are

generally large gantry type machines which operate at conventional feeds and

spindle speeds. New trends in the industry are to use monolithic construction in

the fabrication of aircraft components and to use high speed machining

technology to produce them. The use of high speed machining has shown that

there are significant improvements in the metal removal rates which can

significantly reduce production times.

The following sections will present material to develop designs, point out

many assembly details, and test new machine tools. The thrust of the work is to

combine the technologies of five-axis machine tools with that of high speed

machine. This will be realized in the design and construction of a five-axis

machine tool. The machine tool will incorporates a number of new technologies

in it design. One is the high speed/ high power high stiffness spindle design.

Others include linear motors, open architecture controller, and chatter

recognition and correction system.

This machine tool is to be used as a means to see how far the technology

of producing thin walled and thin webbed structures can be taken. It will also be

used to study tool paths for the cutting of five-axis parts.


It has always been the desire of aircraft manufactures to reduce the time

and cost required to produce their products. This has become of greater

importance with the large reduction in military aircraft orders, which has

occurred since the beginning of the 90's. It pushed the manufacturers of the

defense aircraft sector into examining and using new technologies to improve

their profitability. Competition in the commercial aircraft sector has given a

similar incentive. One of the new technologies which is gaining wide

acceptance in both sectors is high speed machining. High speed machining

(HSM) offers a significant reduction of machining time. It has been found that

implementing HSM in manufacturing of aircraft parts substantially reduces the

production time [MDA94,SCH92].

In aircraft manufacturing it is necessary to produce large, light weight,

integral structures which make up the airframe. At present most of these

structures are fabricated from sheet metal parts which are held together with

rivets. This method of manufacture requires a large quantity of tooling and is

time intensive. The new technology finding wider acceptance as an alternative

means of producing these parts has been the use of monolithic construction.

Here the aircraft structural components, such as bulk heads, arches, doors, and

avionics trays, are cut from solid billets of aluminum. This method of part

manufacture has shown a significant reduction in the tooling and in labor costs,

and production time. An additional benefit is an improved strength to weight ratio

for the parts produced with this method. It is noted that this type of construction

requires large quantities of material to be removed from the billet in production of

the part. The percentage of material removed from the original billet can be as

high as 80-90% in the production of some parts. To remove this quantity of

material efficiently, high metal removal rates are required. This can be achieved

by using high speed machining.

The geometries of these parts often have undercuts on the walls and

floors as well as contoured surfaces. To produce these geometries on a milling

machine would require either special fixturing or rotary axes, which can change

the orientation of the cutter relative to the work piece. Note that special fixturing

for work pieces is an added cost. The use of fixturing would increase the

machine fixing time and the manufacturing costs. Further more, storage for the

fixtures is required. The accuracy of the part is negatively impacted, because of

its repositioning on the machine. These factors have given impetus to

incorporating HSM technology into five-axis machine tools. This combination will

achieve the level of metal removal rates (MRR) needed to produce the thin

walled and floored structures. Additionally, the rotary axes in a five-axis machine

tool will eliminate the need for special fixturing.

Several methodologies required to produce these monolithic structures

have been developed [DV096,RA095,WIN95]. These methodologies make it


possible to produce thin walled and thin floor parts with thicknesses on the order

of 0.5 mm (0.020"). The combining of HSM with five-axis machine tools will

make it possible to have a flexible machine tool which can produce complex

geometries with high MRR.

This work discusses the development, construction, and testing of the

three-axis configuration of the five-axis machine tool. The dissertation is divided

into the following sections: the review of the literature, kinematic combinations

and parameters for design, machine tool assembly, testing and conclusions.

The machine tool was designed and assembled in the Machine Tool Research

Center at the University of Florida. This machine is a test stand for the

combining and testing of machine tool technology and high speed machining



High Speed Machining

High speed machining, often referred to as high speed cutting, has been a

topic of much discussion for many years. The application of HSM is seeing

wider appeal throughout industry. It is being applied to the cutting of cast iron,

hardened steel, titanium and aluminum alloys [TLU93]. HSM is considered as

milling at spindle speeds such that the tooth passing frequency, ft, approaches

the dominant natural frequency, fn, of the system. A general rule to determine

high speed milling is when ft 2! 0.4 fn [SM188]. As an example for a four fluted

end mill with a dominant mode at 1100 Hz, ft = fn means a corresponding spindle

speed of 16,500 rpm. Many of the applications of HSM have an intrinsic lack of

dynamic stiffness in the spindle/tool/work piece system. Examples of this would

be the milling of deep pockets in aircraft structures, milling thin walls, or milling

thin floors using long slender end mills. Thus it is important to have a good

understanding of the dynamics and utilize methods to avoid chatter.

Schulz and Toshimichi indicate that HSM is a broad field. They define it

as cutting at the highest possible speed for a given work piece/cutter material

combination [SCH92]. Further more they point out the advantages of high speed


cutting. Such as increased machining accuracy and surface finish, reduction of

burr formation, larger range of stable cuts, simplified tooling, and an increase of

productivity. They go on to cover many of the requirements needed in modern

machine tools so that the HSM may be fully realized. Research funded by

McDonald Douglas Aircraft Company has show a two fold improvement of

cutting time by utilizing HSM [MDA94]. Tlusty [TLU93] shows general agreement

with Schulz and Toshimichi but makes more of an emphasis on the cutting

dynamics and chatter. Tlusty shows that by using HSM it is possible to find

spindle speeds where the axial depth of cut, bum, can be increased several times

beyond the critical depth of cut. To do this it is necessary to know the dynamic

behavior of the cutting tool. He states that this may not always be practical.

Another method to determine the best speed is to record the sound spectrum of

the chatter when it occurs and then to extract its frequency. This frequency, fn, is

used to avoid chatter by setting the tooth passing frequency, ft, equal to the

chatter frequency or its integer fraction. This generally places the cutting

process in a stable gap in the stability lobe diagram. This method has been fully

realized in the chatter recognition and control system (CRAC) developed by

Manufacturing Laboratories Inc. [ML193]. There can be cases when two or more

modes of similar magnitude exist which could lead to failure of the preceding

method. This is known as competing modes. Smith et al. [SM194] have

developed algorithms which will avoid the problem of competing modes.

Essentially, they find spindle speeds where the gaps for these competing modes

coincide thus avoiding chatter. This algorithm works well for gaps below the N=O

lobe of the lower frequency mode. There may be problems finding a coincident

gap when looking at speeds in the region above the N=0 lobe for the lower

frequency mode.

To implement HSM into a machine tool, many of the design issues must

be taken into consideration. Tlusty points out a number of tasks which must be

performed to fully to realize HSM in modern machine tool designs [TLU93]. He

listed these tasks as design of high speed spindles, guideways, feed drives,

controls, lightweight structures, and fast NC controllers. Schulz and Toshimichi

listed similar design tasks and add the need to examine new designs for the

tool/spindle interface, fixturing of the work piece, chip removal, and safety

[SCH92]. The first task in both papers is the design of high speed spindles.

They may employ integral motors, and hybrid angular bearing, hydrostatic

bearings, or magnetic bearings. The spindle speeds should be in the range of

20,000 to 50,000 rpm. Available cutting power should be on the order of 1 kW

per 1000 rpm. The spindle design has to be as dynamically stiff as possible. The

dynamic stiffness should be constant over the operating speed range. The

spindle-tool interface must be examined because of the high radial accelerations

seen in the spindle.

The design of the guideways, drives, and structure must be examined

because of the need for high accelerations and velocities in the axes. The CNC

control system needs to meet the high demands imposed by these high feed

rates. Furthermore, the handling of chips and coolant has to be taken into

consideration because of the high MRR. Even safety precautions for protection

from chips, coolant spray, and cutter breakage must also be addressed.

One of the biggest demands of the design are the required velocities and

accelerations. Tlusty [TLU93] and Heisel [HE196] specify velocities in the range

of 10-20 m/min (400 -1000 ipm) and accelerations of 2 g's. This high

acceleration is required to secure the full feed rate in the shortest time. This is of

great importance when producing small pockets. The structure of the machine

must be able to handle velocities and accelerations and maintain its accuracy. It

has been proposed by some authors that the beds of these high speed

machines should be fabricated from polymer concrete because of its good

damping characteristics and good rigidity. The moving structural components

can be manufactured from composites, welded sheet metal, or honeycomb

structures to reduce the weight that must be accelerated by the feed drives. This

make it possible to utilize smaller drives.

Multi-axis Cutting

Many parts in the aircraft structure implement three-dimensional surfaces.

These parts can be cut using three or five-axis cutting operations. Three-axis

cutting of sculpted surfaces requires the use of ball nose end mills. The use of a

ball nose end mills is required to more closely approximate the three-dimensional

surface. By using this type of tooling the surface of the work piece will show

scalloping. These scallops are defined by their width and their depth [BAD94].

The scallop width depends on the step over and the cutter radius. The scallop

depth is determined by the required tolerance. On another hand by five-axis

milling, the cutter can be maintained normal to the surface of the work piece.

This gives a geometric advantage, allowing the use of standard end mills instead

of ball nose end mills. The better geometrical approximation of the cutter to the

surface produces wider scallops with the same tolerance as in three-axis milling,

which improves the overall surface finish. This leads to a higher MRR and

reduces the manufacturing cost.

Five-axis milling could be described as a general milling operation. All

other milling operations are restricted by their lack of motions from the six

degrees of freedom in the Cartesian coordinate system [DAM76]. These five

axes are often realized by three translational and two rotational axes.

Depending on the machine size and the work piece geometrical form, the

rotational axes could be in the tool or in the table, or in both. This variation can

be used to classified the five-axis milling machines by the number of the rotary

axes which are found in the tool or in the work piece [EIS72, ESC72, SPU92].

There are three major groupings based on how the rotary motions are distributed

in the machine. The first group contains machines where the two rotary motions

are in the table. The second contains both rotary motions in the spindle/tool.

The last has the rotary motions split between the table and the spindle. Each of

these groupings has further sub-groupings which contain all the possible


Other possibilities for achieving the linear and rotary motions in the cutting

operation have been shown in the form of hexapods [HE196]. This alternative

design is realized by utilizing struts and gimbal to produce the motions. This type

of machine has a small unconventional work volumes, which limits its

applications when compared to a similarly sized five-axis machines. These

machines are still in their infancy but are gaining wider interest.

The advantages of five-axis machining in cutting three dimensional

surfaces does have an added complication in generating the tool paths. A

number of authors have examined these complications. Most of the literature on

five-axis machine tool kinematics is concerned with the development of the NC

code generation for the cutting of three dimensional surfaces and contours.

Jerard et al. [JER89] have examined methods to determine errors in sculptured

surfaces. The objective of that work was to develop five-axis cutting strategies,

which account for the offset of the tool and step-over size. Their method

attempts to remove the errors due to gouging and undercutting. Rehsteiner

[REH93] examined the milling of twisted ruled surfaces. This type of surface is

well suited for five-axis flank milling. The author was interested in how these

ruled surfaces intersect and how to fully realize the proper motion of the machine

through the NC code. His work, like many of the others, looks at the tool path

and geometry of the work piece. It does not address how the kinematics of the

machine tool plays an important role in the motions of the machine. Takeuchi

and Watanabe [TAK92] examined ways to generate collision-free tool paths for

five axis-cutting. This is of great importance in order to prevent damaging of the

machine tool and the work piece. They used solid models of the tool and the

work piece to determine the interaction between the two during the cutting


All the above literature show the flexibility and benefits of five-axis machine

tools. They also point out that generation of accurate tool paths is not an easy


Testing and Evaluation of Machine Tools

The standard utilized in the United States to evaluated the performance of

machine tools is the ANSI ASME B5.54-1992 (Methods for the Performance

Evaluation of Computer Numerically Controlled Machining Centers) [ASM92].

The Standard establishes requirements and methods for specifying and testing

the performance of CNC machine centers. It is divide into six logical areas:

general definition and machine classification, machine environmental

requirements and responses, machine accuracy performance as a machine tool,

machine performance as a measuring machine, machine cutting performance,

and machining of test parts. This standard is used by manufacturers and end

users as an acceptance test for machine tools.

Generally, acceptance tests of machine tools can be classified in two

major groups. One of these groups is the direct evaluations of the machine

accuracy. This evaluation test determines the systematic and random errors of

the machine tool by using direct methods to determine the static, dynamic, and

thermal behavior, the geometric accuracy of the axes and there positioning

accuracy. The other group is the indirect evaluation of the machine accuracy.

This group produces standardized test parts which are measured to determine

the errors and general performance of the machine. These parts include the

errors which are caused by the machine, the cutting process, and the

environment. These parts can determine the positioning accuracy, parallelism

and orthogonality of the machine axes, linear interpolation behavior, circular

interpolation behavior, and the thermal drift. Besides the parts proposed in the

B5.54 there are other national and international recommended standard parts

like the NAS 930 [NAS91], the German VDI 2851 Blatt 3 [VD186], and the

Russian GOST 26016-83 [EN183]. All these standardized test parts may

determine, more or less, the same performance criteria as the B5.54. They are

useful for testing a machine with linear and incremental rotary axes, but they can

not be used to determine the behavior of the continuous motion rotary axes as

founded in a five-axis machine.

The foundations of the evaluation and acceptance testing starts with the

work of Schlesinger [SCL27]. He developed methods to determine the

geometric accuracy of machine tools. Tlusty [TLU59] advanced methods to

quantify the abilities of machine tools. He lists five main qualities which

characterize a machine tool. These are accuracy, output, life, convenience,

safety, and economy. Each of these represents a complex list of information

about the machine tool's performance. He points out that often manufacturers

disperse a limited amount of information on their machines. Generally this

information is in regard to the dimensions, weight, speeds, feeds, and power.

Much of the information related to actual 'qualities' of the machine is not

presented and for that matter is often not known by the manufacturers. He

points out the importance of testing the machine tool to see how its abilities

compare to others which have been similarly tested. The paper goes on to

present a number of methods to be followed to test machine tools. Tlusty and

Koenigsberger [TLU70] presented a very comprehensive report which covers the

preceding material in much more detail. The UMIST report covers all the

previously discussed categories explaining their importance and how to make the

measurements in complete detail. Much of the material making up the testing

methods can be found in the Technology of Machine Tools Report and

supplements present by the Machine Tool Task Force [MTT80] as well as the

UMIST report. These standardized tests give the manufacture and the end user

a means to compare various machines in a given class.

The literature reviewed shows that many of the areas for implementing

HSM into five-axis cutting have yet to be covered. This is especially true for the

testing of five-axis machine tool performance. Further more in all the machine

performance tests, no material was found to test and evaluate five-axis machine

tools. Particularly, this is true for determining the accuracy of the machine's

rotary axes. The influences of five-axis kinematics on the dynamic behavior of

the cutting process and the work piece accuracy also needs to be researched.

The literature points out that there is a large need to develop interactive CAM

systems to produce tool paths that incorporate collision avoidance and allow for

dynamic feed control and technological issues. There has been work examining

the accuracy of the NC codes but little or no cutting of test parts has been

performed to determine which of these techniques provides the best solution.

The machine tool described here will provide a test stand to examine how these

technologies work together and provide a means to develop the new

technologies required to fully realize a production machine tool incorporating

these technologies. The work presented in the following pages covers the

development and construction of such a test machine.


Kinematic Combinations

A machine tool is an assemblage of prismatic and revolute joints which

move in concert to bring the cutting tool to a desired location within the work

volume. This is true for the smallest, manually controlled, bench top mill as well

as the largest, computer numerically controlled (CNC), milling machine. A

grouping of these kinematic elements form the machine tool kinematic loop.

Actuation of these joints produces the machine motions. The kinematic loop is

often described by the kinematic elements from the work piece moving along the

structure and joints towards the cutting tool. The loop is closed by the cutting

tool/work piece interface. The arrangement, type, and number of these joint

elements has a significant impact on the types of parts which can be machined

on a given machine tool.

This section focuses on the kinematics of five-axis machine tools. For the

purpose of this chapter, a five degree of freedom (DOF) machine tool is a

system having five single DOF joints connected in a serial chain. A serial linkage

machine contains joint elements that are connected in a linear fashion where the

end of one joint is connected to the start of the next in the chain. In this


configuration each of the individual joints produces a motion in its specific single

DOF without any movement of the other joints. This differs from a parallel

linkage machine which requires multiple joints elements to be actuated for

motion in one DOF. A good example of a parallel machine tool is the Hexapod

milling center being developed at Ingersoll Milling Machine Company, Rockford

Illinois. This section focuses on serial rather then parallel machines.

On machine tools, a systematic method to label the direction and

orientation is required in order to standardize programing of NC machines. To

distinguish one axis of motion from another an internationally standardized

system of letter addresses is employed. The letter address system which is

used can found in the three following standards: EIA RE-267-B, issued by the

Electronics Industries Association; the AIA NAS-938, issued by the Aerospace

Industries Association; and the ISO/R 841, issued by the International

Organization for Standards [MEC92]. Each of these three standards is in full

agreement with the others.

The lettering system used for machine tools is an orthogonal "right-hand"

Cartesian coordinate system (CS). This coordinate system describes the

orientation as well as the direction of motion. The coordinate system could be

attached at various points on the machine tool, such as the tool point or the

work piece. The translation motions generally produced by prismatic joints, are

designated as X, Y, and Z. Figure 3-1 shows the orientation of a Cartesian

coordinate system which is attached to a typical table or pallet. The Z' axis is

oriented such that it points normal to the plane formed by the surface of the

table. The X' and Y' are orthogonal to each other and are in the plane of the

table. The arrows point in the positive direction of motion. The primes indicate

that these letter addresses are attached to a coordinate system on the

table/work piece. A coordinate system attached to the spindle/tool would not

have these prime marks. The rotary motions are designated as A, B, and C.

The rotary motions are orientated with respect to the translation axes of motions.

The A rotary axis is about the X axis; the B rotary axis is about the Y axis; and

the C rotary axis is about the Z axis. The positive direction of rotation follows

the right-hand rule.

The three translation and the three rotation axes form the six degrees of

freedom which can fully describe all motions of any rigid body. A five-axis

machine tool utilizes five of these six DOF to position the tool relative to the work

piece to obtain the desired geometry during the cutting operations. A base

reference coordinate system can be located anywhere on the machine tool or in

space in order to analyze the motions on the machine. Since the motion of the

work piece with respect to the tool or vice versa is the concern here, reference

coordinate systems are attached to the table/work piece and the spindle/tool.

Either of these coordinate systems can be used to fully characterize the motion

of the machine tool. It will be noted that the coordinate system attached to the

table/work piece is used as the reference system for NC code generation. The

two coordinate systems are ideally oriented so that the axes are parallel to each

other. Figure 3-2 shows the general arrangement of these two coordinate

systems. These two six DOF coordinate systems will be used to examine the

various possible kinematic configurations that can be incorporated into the

design of a five-axis machine tool. The combinations of motions for a five-axis

machine tool examined here will be limited to combinations with three prismatic

joints and two revolute joints, since this is common arrangement for a five-axis

machine tool.

It will first be necessary to determine the total possible number of

combinations for a five-axis machine tool given the three prismatic and two

revolute joints. It should be noted that the motion axes could be attached to the

spindle/tool system or to the table/work piece system or divided between the two

systems. The number of combinations which can be found in the most general

terms is determined using basic combination mathematics. The fundamental

equation is

n n(3-1)
k!(n -k)!

where n is the number of items in the group to be selected from, and k is the

number of items to be selected each a time. It can be shown that the total

number of kinematic combinations is made up of a product of the minor

combinational groups. These minor groups are the number of combinations for

the two revolute joints, the number of combinations on how the revolute joints

are distributed between the two coordinate systems, and the number of

combinations of the three translation motions divided between the two

coordinate systems.






Figure 3-1 Right hand cartesian coordinate system











7 7



Figure 3-2 General arrangement of the two coordinate

The first minor group of combinations is the number of revolute joint

combinations that can be selected from the three possible axes of rotation. This

one is simple to see by inspection, but will be a good example to see how the

above equation is applied. The number of items, n, in the group is 3. The

number of items, k, to be selected from the group is 2. The equation for the

possible revolute joint combinations is thus

C 3! (3-2)
RI -- (2 2!1!

The three possible rotary combinations are AB, AC, and BC. These three

possible combinations of rotary axes can be in either of the two coordinate

systems. The two rotations can be in the spindle/tool system or the table/work

piece system or split between the two coordinate systems. Thus the minor group

of combinations which is related to how the rotational axes are distributed

between the two coordinate systems is the sum of possible combinations divided

between the two coordinate systems. The size of the group is 2. The number of

items to be selected varies from 0 to 2. This variation comes from distribution of

the rotations from all the rotations are in one coordinate system; split between

the two systems; and all rotations are in the other coordinate system. The

resultant summation is

CR2 E Q = 4 (3-3)

Now the combinations of the translation motions can be determined. Since all

three translation motions will be selected, there is only one combination of the

translation joints, X, Y, and Z. Next, the number of combinations due to

distribution between the two coordinate systems needs to be determined. The

same method is applied as was used to determine the number of combinations

of the revolute joints distributed between the two coordinate systems. The group

size is n = 3 and the number of items to be selected varies from k = 0 to 3. The

resultant summation is
CT E Q 3 = 8 (3-4)

The total number of possible combinations is determined by taking the product of

the three combinational groups. The equation for the total is

C = CRICR2CT = 96 (3-5)

These are the 96 combinations which are possible in the most general terms.

The next level analysis will show that 50% of the total number of combinations is

either redundant or not functional for application in a machine tool.

The first examination will be for any similarities in the motions. Looking at

the combined rotary motions AC and BC or A'C' and B'C' shows that they

produce the same motions. This motion combination is often called a nutating

motion. The A and B axes of rotation are in the same plane. The only difference

is that these two axes of rotation are orthogonal. Though the orientation of the

tilting motions differs by 90' the resultant motion is the same. Figure 3-3 and

3-4 show how the motions in the two configurations are similar. This

observation removes 32 combinations from the total number of theoretical

possibilities. The next rotational combination to be checked is the AB rotary joint

combinations where the two rotations are divided into each of the coordinate

systems. This would be AB' or A'B rotary combinations.Similar motions can be

produced if the A is in the tool/spindle system and the B is in the workpiece/table

system or vice versa. Figure 3-5 shows how the two rotations distributed

between the two coordinate systems produced the same resultant motions. This

removes an additional eight combinations from the total. Next the case was

examined where the C axis of rotation was the lone rotation on the tool/spindle

side. This rotational motion has no net resultant effect to the tool orientation.

This case simply rotates the spindle in the same axis of rotation as the tool. This

removes an additional eight combinations from the total. Thus the total number

of combinations which can practically be selected from are reduced from 96 to

48. Table 3-1 lists the possible rotational and translation combinations.

The combinations in Table 3-1 is in agreement with the generalized

kinematic model presented by Ruegg [RUE92]. The work of Takeuchi and

Watanabe is also in agreement with the above number of feasible structural

arrangements for five axis machining centers. That paper goes on to further

subdivide five axis machine tool configurations into three subdivisions.


I 1





Figure 3-3 AC & BC head configurations


j zl





V )




Figure 3-4 A'C' & B'C' Rotating and Tilting table combinations






Figure 3-5 AB' & A'B Tilting spindle and Tilting Table Combinations





xyz IxYz I xYz I xY, z I x Yz, I xYz

The three subdivisions are broken down according to how the 2 DOF of rotation

distributed between the 2 CS. The first subdivision has both rotary motions in

the table CS. There are two possible arrangements for this subdivision. Type 1

is an arrangement where a tilting table has a rotary table attached to it. Type 2 is

a rotary table arrangement with a attached tilting table. Figure 3-6 shows these

two types of table arrangements for this subdivision. Similarly, the second

subdivision, having both rotary motions in the spindle CS, has two types of

arrangements. Type 1 has two tilting axes, and is often called an AB head.

Type 2 has one tilting axis and one rotating axis and is often called an AC head

or nutating head. Figure 3-7 shows these two rotary head configurations. The

third subdivision has the rotational motions divided between the 2 CS. There

are two types in this subdivision as well. Type 1 is a tilting head spindle

arrangement with a rotary table. Type 2 is a tilting spindle with a tilting table. It

should be noted that the rotational joints are commonly located at the beginning

or end of the kinematic loop.


The placement of the rotary motion in between translation joints would make the

kinematic solution significantly more difficult to solve when developing the post-

processor to control the machine motions.

Parameters for the Selection of Combinations

The 48 combinations can all be used for the layout of a five-axis machine

tool. To select an appropriate kinematic configuration, a number of different

parameters need to be examined. These parameters will dictate which of the

combinations is more practical to use than the others for a given application.

These parameters were divided into four main groups. These groups are the

work piece specifications, the types of cutting operations, the machine

performance specifications, and the productivity of the machine tool


The first parameter to evaluate in the work piece specification group is the

size of a typical work piece to be cut on the machine tool. The characteristic

length, height, and width of typical parts to be cut on the machine are needed.

For example, tilting and rotating table machines may not be practical for work

pieces with large characteristic lengths and widths. It may be more practical to

have the spindle move around the work piece. The next parameter, of equal

importance, is the geometry of the work piece. The work piece geometry may be

classified as either prismatic or rotary. An example of a prismatic work piece is

an engine block.







Figure 3-6 Tilting table with rotary top and Rotating table with tilting top







\ ,


(7j\ ~


Figure 3-7 AB Tilting Head and AC Nutating Head

Examples of a rotary work piece are turbine buckets or ship's propeller. A

tilting table and tilting spindle arrangements are good for prismatic geometries.

These motions can be used effectively on the planar surfaces seen in such

parts. A rotary table configuration is better for rotary geometries where an axis

curvature of the part could easily correspond to an axis of rotation on the

machine. The form and the shape of the whole work piece will affect the size

and shape of the work volume. Another geometric concern is that of the greatest

angle of the under cut required in the work piece and the largest angle in

contours. This will dictate the range of angular motion required in the rotary

axes. The next parameter is the cutting strategies to be employed in the cutting

operation. This is a function of cutter orientation and the type of tooling to be

used. A parameter which is often not considered is the material of the work

piece. The weight of the work piece is a vital parameter that has an effect on the

design of the machine tool and must be considered.

The cutting operations of the machine tool are the next group of

parameters to examine. The first parameter in this group is the desired power of

the spindle. The power requirements of the spindle will govern the size of the

drive and the type of drive to be used. The spindle may be of an integral motor

design or utilize a drive train with any type of prime mover. The size of the drive

and spindle will affect how it will be incorporated into the machine's structure

and affect selection of a tilting head or tilting table configuration. The next sub-

group is the types of cutting operations to be performed on the work piece.

These cutting operations generally are milling, drilling, boring, tapping, and

grinding. This could affect the power requirements of the axes. The type of

cutting technology to be employed by the machine also needs to be considered.

The two technologies are high speed milling and conventional milling. This will

dictate spindle configuration and dynamic stability considerations. The type of

cutting tools to be employed and their geometry should be considered. The final

parameter to be considered in this group is the type of cooling to be employed.

These could vary from dry, mist spray, flood, or high pressure cooling. This will

affect the amount of coolant that will be required and how the coolant and chips

from the cutting process will be handled. The incorporation of the coolant and

chip handling systems can affect kinematic selection.

The third group is that of the machine performance specifications. This

general group covers the parameters desired in the machine tool motions and

structure. The first parameter is the desire acceleration and velocities. The

desire for higher production rates has pushed accelerations and velocities in the

axes of motion higher. Higher accelerations require that the machine have high

static and dynamic stiffness. The selection of the proper configuration to obtain

the highest dynamic stiffness for the high speed, high acceleration cutting is a

trade off. In general to achieve the high stiffness massive structures are

required, but that gives rise to the obvious problem of having to accelerate these

massive structures. Extensive analysis of the structures using finite element

analysis is needed to obtain the optimal design. The last parameter in this group

is the material to be used in the construction of the structural components

making up the machine tool. Material such as cast iron and welded steel are

conventional materials used in many of today's machine tools. Other materials

which are finding more usage are epoxy concrete, granite, and composites

materials such as carbon fiber. Cast iron is strong and has good inherent

damping but requires large cross sections to obtain the same strength as steel.

Granite is a good foundation material, but care must be taken to keep it in a dry

environment. Moisture is absorbed into the granite causing it to swell which

could cause distortion in the machine structure. Epoxy concrete is also a stiff

material with good damping characteristics yet requires large sections to achieve

the needed strength. Composites have high strength to weight ratios but there

are may complications due to problems of creep and fiber orientation. The cost

of composites is also high.

The last group relates to the productivity of the machine. The parameters

in this group deal with how the machine tool would be integrated into production

of the typical workpiece. The first parameter is the machine's integration in the

manufacturing facility. The machine tool could be part of a production line or it

could be part of a flexible machining cell. The integration into the factory floor

depends on the volume of parts to be produced and the desired duty cycle of the

machine. The amount of automation incorporated into the machine may include

an automatic tool changer or pallet changer. This will affect the layout of the

machine and its structure so that these subsystems can be incorporated into the

structure of the machine tool. The number of simultaneously operating axes

should be considered. Some of the axes on the machine tool maybe strictly for

positioning while others will be active during machining. This could require


braking or position locking devices to be incorporated. The number of spindles

incorporated into the machine's design for cutting operations. Some machine

tools utilize interchangeable spindles to obtain the best characteristics for

different speed ranges. While others utilize multiple spindles in the cutting


An example of how parameters are weighed and used in the selection of

the most applicable kinematic arrangement of the machine motions will be

shown in the next section.

The example will be for the design of the five axis machine tool recently

constructed in the machine tool laboratory.

MTRC's Five-Axis Machine Tool

The five-axis machine tool to be constructed in the laboratory is primarily

a research machine. This machine will be used to test new technologies and

new methods in high speed machining. It is noted that the analysis presented

here is after the fact. The machine was well into its design at this writing. It is

used as an example to show how these parameters may be used in the design

process. The four groups of parameters were weighed given the primary

purpose of the machine tool. Since the machine tool was not a production

machine the group of parameters concerned with production was given

secondary status to other design considerations. The work piece specifications

were examined first. The work pieces to be cut on this machine tool are primarily


monolithic aircraft components milled from 4-6 inch thick aluminum billets. The

parts will have a number of pockets with thin walls, and thin floors. The

thicknesses of the thin walls and floors cut will be 0.5 mm (0.020 in). A high

metal removal rates is of great importance because up to 80% of the billet will be

removed in the production of these parts. The characteristic length of the work

piece, height or width is generally up to five times or greater then the depth.

Table 3-2 shows a listing of some typical aircraft parts used to select the

machine configuration.


Part Material Dimension Max. Depth Method Tool

Slide 7050-T7 45xl 7x3.5 1.5 5-axis 0.75xl.5
Housing 7050-T7 40x37x3.2 3.06 5-axis 0.5x2
Housing 7050-T7 40x40x3 1.55 5-axis 0.5x2
Rib 7050-T7 13x9.5x2.2 1.32 5-axis 0.75x1.5
Rib 7050-T7 24x.3x4 1.84 5-axis 0.75xl .5
Floor 7050-T7 33.5x30x2 1.81 5-axis 0.75xl.5
Gear flap 7050-T7 29x17x2.5 1.4 3-axis 0.75xl.5
Door 7050-T7 34x29x4.5 1.73 5-axis 0.75x2.25
Door 7050-T7 30xlOxl.2 1.08 5-axis 0.75xl.5
Guide 2219-T8 42x23x4 1.85 5-axis 1x2
Note: All dimensions are in inches.

These characteristic lengths make it desirable to have large ranges of motions in

the X and Y axes. The geometry of the work pieces is prismatic. Some of the

thin walls are angled requiring under cuts. Thus it will be possible to use either

tilting table or tilting spindles type configuration. The angular motion

requirements are less then T45' from the normal. The materials of the work

pieces will mostly be 7050-T7 and 7075-T6 aluminum, although consideration for

the cutting hardened steel and titanium has been discussed. No geometric

variations should be necessary to cut these two hard materials.

The cutting operations to be performed on the machine tool will be milling.

The spindle to be employed is designed for milling operations only. The spindle

is of a compact design with an integrated motor. A number of attachments for

compressed air, lubrication, coolant, and power must be incorporated into the

design. These many connections would add significant complexity to an AC type

head design configuration. The spindle is designed for high power/high speed

milling. The spindle is rated at 37 kW at 36,000 RPM. The design of the spindle

supporting structure will require high dynamic stiffness. The cutting tools to be

used on the machine will be primarily carbide end mills. Table 3-2 shows some

of the tool diameters and lengths to be used in the milling of the work pieces.

Due to the use of a high speed spindle, face mills will see very limited use. Due

to the high metal removal rates to be achieved by the machine tool, an important

design concern will be the removal of the hot chips from the work piece. High

speed milling produces a large quantity of chips in a short period of time. The

metal removal rates will be on the order of 200 cubic inches per minute,

assuming 80% of full spindle power is utilized. The orientation of the table is an

important consideration for the removal from the work piece. A horizontal table

will have the problem that the chips will accumulate on the work piece. To

alleviate this problem a vertical orientation of the table is used. This allows

gravity to remove the bulk of the chips from the work piece. Accommodations

will needed to remove the high volume of chips from below the vertical table.

The machine tool will utilize mist, flood and possible high pressure cooling

systems. This will give the machine the added flexibility for performing various

research projects.

The third group of parameters had a strong influence on the kinematics of

the machine. The machine was to have linear accelerations on the order of 2 g's

(19.62 m/s2) and linear cutting velocity of 25.4 m/min (1000 ipm). The high

acceleration and velocity are needed to best utilize the positive aspects of high

speed milling. Most of the parts have a large number of pockets requiring a

large number of accelerations in and out of the corners of the pockets. The high

linear acceleration will significantly reduce the time required for decelerate and

accelerate in and out of the corners. Typical production machines on the market

today have accelerations on the order of 0.5 g's (4.9 m/s2 ). The axes will

achieve full speed in one quarter of the time. This enables the cutting operation

to have a higher overall average feed rate and thus reduces the machining time.

The higher accelerations seen in this machine required high-power servo drives.

The X and Y motions are compounded and will be operated at high velocities

and accelerations. The moving structural components were designed with the

thought to minimizing the mass to minimize power requirements, and yet having

sufficient stiffness to meet dynamic stiffness needs. The acceleration

requirements made having a rotary or tilting table attached to the X and Y

motions less desirable due to the large mass associated with the components

which make up the rotary axes. Attachment of the spindle to the X-Y motion was

not desirable due to the weight of the spindle. The spindles mass was greater

then that of a typical workpiece. This lead to the attachment of the work piece to

the X and Y motions. This compounded axes arrangement minimized the mass

to be accelerated, thus reducing the size of the drives and associated equipment

required. This leaves the configuration of the rotary motions. Two possible

designs were considered. One was a nutating head design and the other was a

tilting head design. The tilting head design was selected for it could more readily

be fitted with the high speed spindle. The many complexities of getting the

existing spindle to fit into a nutating head made this design less attractive. The

tilting head also had the added benefit of having a smaller foot print. The two

rotary motions are attached to the Z axis. This makes the mass to be moved by

the Z large. This is not a concern for the motions of the Z-axis do not require the

same kind of performance needed in the X and Y axes. This comes from the

fact that the work pieces are generally flat having a characteristic length of less

then 102 mm (4").

The materials for the structure of the machine tool are limited to cast iron,

steel and composites. The use of granite or epoxy concrete was considered. It

would have been possible to use it for the bed of the machine, but facilities to

handle the epoxy concrete and granite where not available. There where also

structural limitation of the building which had to be considered. The moving

structural components require dynamic high stiffness and low mass to minimize

power requirements in the drives. This would make for composites the first

chose in materials for the machine tools structural running gear. The cost

associated with composites made use of these materials prohibitive. Estimates

where that cost would be more then two times greater then conventional

materials. This left cast iron and steel. Cast iron parts and castings would be

difficult to obtain at a reasonable cost and had a higher mass the strength ratio

then steel. The use of welded steel construction was decide upon because of

the good stiffness characteristics and ease of manufacture.

The final configuration of the machine tool is seen in the figure 3-8. The

machine has a compound translation X-Y axis. Each having 28 inches of

motion. The table is mounted in a vertical position to use gravity to help remove

the chips and coolant from the work piece during cutting operations. The Z-axis

carries the tilting AB head spindle assembly. The AB head has angular motions

of 450 in both directions of rotation. The X and Y axes are driven by brush-less

DC servo motors attached to ball screws. It should be noted that the X-axis has

two drive assemblies associated with it. The Z-axis has two linear servo drives.

The A and B rotary motions are performed by split-worm gear arrangements

driven with brushed DC servo motors. The structural components are of welded

steel. The bed is a 9 % ton weldment forming a rigid base for the machine. The

moving structural components use tubular construction to reduce mass in the

moving X-frame and the Y-table.








Figure 3-8 Final machine tool configuration


The assembly of machine tools is a trade which has traditionally been

handled by craftsmen. Engineers are involved with the design but often have

little contact with the machine during the assembly stage except when problems

arise. From a technical writing point there is very little material discussing many

of the practical aspects concerning the assembly of a machine tool. Much of that

which is written is not in the public domain. The work presented in this chapter

shows some of the practical points of the assembly process used in assembling

the five axis machine tool. Note that it only goes through the assembly of the

three translational axes because the design and manufacture of the AB head

was not completed at this writing.

Installation and Leveling of the Machine Bed

The assembly of the machine tool began with the preparation of the

machine bed. The bed arrived from the manufacture with dirt and rust on many

of the ground surfaces. The bed was cleaned and painted. All of the rust and

dirt was removed from the ground mating surfaces and a protective layer of

grease was applied. The bed was moved into position, using a set of rollers,

called tanks. Once the bed was in position, the rollers were removed and the

bed was placed on six Unisorb Model LL-7 resilient mounts. Each mount has a

load-bearing capacity of 3175 kg (7000 lbs.). The resilient mounts are

sandwiched between TitanTM shock pads fitted between the foundation and the

bed. These pads are a textile based laminated neoprene material which isolates

the machine bed from the foundation. These pads were selected to give the

machine sufficient support and to provide a means to absorb the energy

produced during the high accelerations and deceleration of the axes and

minimize its transmission into the foundation.

The leveling of the bed was done using a hydraulic jack and a set of

Federal electronic levels to measure angular displacement. The angular

measurements and profiling of the bed base was performed following the

procedure laid out in the handbook supplied by the electronic level manufacture

[FED01]. The angular measurements determine the angle the bed sits relative

to the gravitation normal. The profiling of the bed determines if there is sagging,

twisting, or other deformation of the machine bed. The bed was brought into

level using the hydraulic jack and adjustment of the resilient mounts. The

leveling of the bed was to minimize the amount of pitch and roll from the

gravitational norm. This helps distribute the weight of the machine over the six

resilient mounts and the foundation. The profiling measurements looked for any

twisting or sagging of the bed. The measurements were made on the ground

mating surfaces where the pedestals would be placed. No significant twist or

sag was measured in the structure. Measured value of twisting was 0.0005 mm

(0.00002") variation in the longitudinal direction, and 0.0013 mm (0.00005") in

the transverse direction. Similar magnitude of values was measured for the sag.

These may not be sag or twist of the bed, but could also be attributed to minor

errors in the final grinding of the mating surfaces. Since the values measure

were so small it was considered unnecessary to look any further into their cause.

Once the bed was set and leveled, the rail systems and moving components

were attached.

Mounting of the X-Axis Rail Systems

The first components to be attached to the bed were the X-axis rails. The

machine tool uses the AccuMax 55 rail-carriage system manufactured by

Thomson for the X-axis. These rail systems were selected due to their high load

carrying capability, high life cycle rating and compact size [TH095]. Three rails,

each with two carriages, were used on the X-axis. The mounting of the rails, on

the vertical wall of the bed, began with preparing the ground surfaces on the bed

and the rails. All the protective coatings, dirt, and grease were removed to

permit uniform contact between the two mating surfaces. The order of the

installation of the rails began with the bottom rail, and moved up the bed's

vertical wall. All the threaded holes for fastening the rails to the bed where

chased with a M14x2 tap to remove any burrs and debris. The tapped holes

were blown clean of any debris. This helps in obtaining a uniform pre load on

each of the fasteners when they are tightened to their final torque. The fasteners

used to mount the rails are M14x2 class 12.9 metric socket head cap screws.

When mounting the rails care was taken to protect the precision surfaces against

inadvertent impacts which could have damaged them. Note that the individual

rails each weigh over 36 kilograms (80 lbs.). Sufficient manpower was used to

safely handle the rails as they were attached to the bed wall. The socket head

screws threads were given a coating of a nickel-based anti seize paste before

being threaded into place. The anti seize was used to help prevent the

possibility of the machine screws becoming seized in place with time due to

corrosion or any galvanic action. This will make any disassembly in the future

easier and will improve the uniformity of the pre load. The cap screws have

been put in place and tightened until they were finger tight. They were left finger

tight until after the initial alignment of the rail was performed.

The primary concern during the alignment of the rails was to get the rails

parallel to a reference edge, minimizing any bending or curvature. The reference

edge was utilized as the datum for all the components on the X-axis. The

reference edges used were the alignment edges machined into the bed wall for

the alignment of ball screw bearing housings and pillow blocks. A precision

beam was suspended on these alignment edges and the secured to the

structure. This beam was used as the reference artifact for the alignment of the

rail. Figure 4-1 shows the arrangement of the precision beam set on the

alignment edges above the rail. Precision gage blocks are used to set the

distance from the rail to the precision beam. The distance between the flank of

the rail and the beam was 49.53 mm (1.950"). A stack of precision gage blocks

was used to produce the desired spacer. The blocks were wrung together to

form the measuring stack. The rail was adjusted up or down to obtain the proper

distance using a wood lever. The rail was considered to be in position when the

stack of precision gage blocks fitted snugly between the precision beam and the

rail. Note that the stack of blocks could still be moved freely yet some resistance

could be felt. This was important point. To prevent any deformation or

misalignment it was important not to apply so much force to the rail, that the

gage blocks became pinched and could not be moved. The alignment

procedure was started at one end of the rail. The stack of blocks was placed,

and the rail is moved into position. The stack of blocks was moved regularly to

check that they had not become bound between the rail and beam. Once the

proper gap was set, the adjacent cap screw was tightened to hold the rail in

position. The stack of blocks was then moved along the rail to a position two cap

screws down from the preceding position. The rail was again moved into

position until the stack was snug and the cap screw was tightened. This

procedure was followed along the total length of the rail. Once this was

completed, the direction was reversed and the rail was aligned as before at

those locations which had been skipped. Once the rail was initially aligned, the

first time, the stack of gage blocks was moved along the rail to check for any

needed adjustments of the rail alignment. This procedure was repeated until the

rail had obtained a nominal alignment.






Figure 4-1 X-axis rail alignment

The nominal alignment being that the gage block stack had a uniform snugness

between the rail and the beam along the full length. Upon completing the

alignment of the rail all of the socket head cap screws were torqued to 100 Nm.

The cap screws were tightened starting from the middle of the rail, and working

out to the ends alternating left to right. Every other cap screw was skipped.

Once the ends where reached the direction was reversed and the cap screws

which had been skipped where tightened to their proper torque. This method of

tightening the socket cap screws was intended to give the rail/wall joint a uniform

and balanced pre load along its length.

A final check was made of the alignment to make sure no movement occurred

during the final tightening.

Once the bottom rail had been attached and aligned, the next two rails

were attached and aligned. The same procedure was used to attach the two

other rails, but the alignment procedure was different due to the distance

between the rails and the desire to use the bottom rail as the datum. The

selection of using the bottom rail as the datum would mean that each of the three

rails would be parallel to the others. To align the upper two rails, a measuring

jig was constructed. The jig consisted of a 25.4 mm (1") square rod 609 mm

(24") in length attached to a 165.1 mm (6.5") by 139.7 mm (5.5") by 25.4 mm (1")

block. This assembly was attached to one of the rail carriages which rides on

the bottom rail. This jig gave a stiff attachment point to which a dial indicator with

a 0.0127 mm (0.0005") resolution was attached. The same procedure was

followed to align the middle rail to the bottom rail. The only difference was that

the measuring jig and dial indicator was used instead of the precision beam and

the precision gage blocks. Figure 4-2 shows the arrangement of the jig and dial

indicator on the bottom rail carriage. Once the alignment and final tightening of

the cap screws was completed the measuring jig was moved to the middle rail so

that the top rail could be attached and aligned using the same procedure.

Upon completion of the alignment of the rails a set of final measurements

was made to examine the variation of the parallelism of the rails to each other. It

was found that the largest overall variation between the rails was less than 0.05

mm (0.002") over the 2 m (78.74") run of the rails. The carriages were placed on

the rails. To protect the rails and carriages a layer of oil was applied and a

protective covering was placed over the rails and carriages to protect against

corrosion and accidental impacts.

X Axis Ball Screw Assembly, Mounting and Alignment.

The X-axis has two ball screws to drive the axis. The screws are situated

between the three X-axis rails. The ball screws are 60 mm diameter with 20 mm

pitch and were manufactured by Thomson Saginaw. The screws were removed

from the shipping crate and all protective plastic and coatings were removed.

Care was taken to protect the screw from any possible damage during assembly

procedure. The installation of the ball screws began with the assembling the

bearings and the housing on the driven end of the ball screw. The roller element

bearings, seals, and spacers where all installed on the ball screw.






Figure 4-2 Alignment of middle X-axis rail

Note that the tapered-roller bearings are arranged to produce a cross to reduce

axial displacement due to thrust loading. Figure 4-3 shows a cross section of the

bearing housing displaying the component arrangement. A backing spacer was

pressed into place by a bearing nut until the bearing assembly was snugly

together. The nut was then tightened until 0.001" axial displacement was

obtained. This applied the desired pre load to the taper-roller bearings of 1000

lbf. This pre load setting is equivalent to a bearing rolling torque of 58 in-lbf at

3.5 RPM. A locking nut was then spun up against the previous nut and

tightened to prevent the pre load from backing off. The tapered-roller bearings

were hand packed with an EP-I grease. The ball screw's bearing assembly was

then slid into the bearing housing. The grease port was aligned and the

compression plate was set in place. The six socket head cap screws were taken

up evenly around the compression plate to prevent any misalignment of the

assembly in the housing. The cap screws were then tightened to a torque of 70

Nm. A feeler gauge was used to check the gap between the face of the housing

and the compression plate to check for any misalignment. The ball screw

housing assembly was now ready to be placed on the machine.

The screw assembly was lifted into place using a chain hoist. The

assembly weighs approximately 90 kg. A lifting sling was placed around the

screw where it exits the bearing housing. This was near the center of gravity

allowing the assembly to be positioned horizontal with relative ease. The

assembly was moved into position on the wall and the 5/8" fasteners were put in

place to secure the assembly to the wall.





Figure 4-3 X-axis bearing housing assembly

The flank of the housing was placed against the alignment edge on the bed's

mounting pad. The socket head cap screws were only tightened finger tight at

this point. The pillow block was put in place at the free end. The alignment of

the ball screw was begun now that all the components were in place.

To align the screw it was necessary to ascertain the longitudinal stiffness

of the ball screw assembly. This information was needed to calculate the

amount of sag at the free end, so the final placement of the pillow block could be

established. This value was determined experimentally. The ball screw was

modeled as a cantilevered beam which was fixed at one end and free at the

other end and a point load applied at the free end. The equation for the

displacement at the free end of this model is

PL 3
)point E3 (4-1)

where point is the displacement at the free end, P is the point load at the free

end, L is the distance from the fixed end to the point load, E is the modulus of

elasticity, I is the mass moment of inertia. An experiment was performed to

determine the unknown value of the product of the modulus of elasticity and the

mass moment of inertia (El). This was be found using the equation (1) and a

simple displacement test. A dial indicator on a magnetic base was attached bed

wall. The stylus of the dial indicator was set on the free end of the ball screw. A

known mass was attached to the free end of the ball screw and the deflection

due to its weight was measured. The amount of the deflection was used to


calculate the product El. To calculate the sag the ball screw is now modeled as

a cantilever beam with a distributed load. The equation for the calculation of the

deflection is

dist wL4 (4-2)
dit 8E1

where w is the distributed load. The distributed load (w) was the weight per unit

length of the ball screw. Note that the ball nut was moved to the fixed end so

that its impact on the deflection would be minimal. The diameter of the ball

screw and the density steel were used to calculate distributed load. This value

and the calculated value of El were used to find the sag. The value of the

deflection was calculated to be 0.6604 mm (0.026") and was the amount which

the center of the bore of the pillow block was offset from the center of the ball

screw. The screw center was set low in the bore of the pillow block.

A post was screwed into the free end of the ball screw and a dial indicator

was attached to the post so that the distance between the bore of the pillow

block and the center of the screw could be measured. Figure 4-4 shows the post

and dial indicator arrangement at the free end of the ball screw. This

arrangement allowed for measurement of the vertical and horizontal offsets of

the free end of the ball screw. The initial measurement of the bore position

showed it to be 1.397 mm (0.055") offset in the horizontal and 1.346 mm (0.053")

offset in the vertical. The horizontal offset was removed by placing steel shims

between the pillow block and the wall.







Figure 4-4 X-axis ball screw alignment

The vertical was removed by adjusting the bearing housing's vertical position

until the proper amount of vertical offset was read at the dial indicator. The

vertical alignment of the pillow block was maintained using the ground locating

edge on the mounting pad. When the pillow block was aligned and secured the

ball bearing to support the free end was put into place. The backing ring was

secured into position with the six cap screws. The bearing was then packed with

grease. The ball screw assembly was rotated to check that it rotated freely.

The above procedure was repeated for the installation of the second X-

axis ball screw. Both of the ball nuts were then given an initial charge of grease

and spun back and forth along the length of the screws. This gave the screws a

protective cover of grease and distributed the grease throughout the ball nuts.

The couplings and servo motors where then attached.

Placement of the Carriages and X-Axis Frame

The X-axis frame is the structural component carried on the X-axis

carriages which carries the running gear for the Y-axis. The X-axis frame is a

weldment composed square tubes and plates. The X-axis frame was cleaned

and painted in preparation for installation. The threaded holes on the mounting

pads on the frame for connecting the X-axis carriages and Y-axis rails where

chased and cleaned to remove any debris in the threads. The X-axis carriages

and the mounting pads were wiped to remove any debris from the joint surfaces.

The X-axis frame was hoisted into place using a chain hoist. The X-frame

weighs approximately 450 kg. (1000 lbs.). The structure was hoisted along the

line of the center of gravity. Care was taken to prevent any damage to those

components which were already attached to the structure. The X-axis frame was

slowly moved toward the bed's vertical wall and the carriages were positioned

behind the mounting pads on the X-axis frame. Figure 4-5 shows the X-axis

frame being hoisted into place. Once the X-axis frame was up against the

carriages it was lowered down onto the alignment edges on the top set of

mounting pads coming to rest on the top flanks of the top two carriages.

M12x1.5 class 12.9 socket head cap screws were placed through the carriages

into the X-axis frame mounting pads and tightened finger tight. The chain hoist

was removed. A feeler gage was used to check that the alignment edges on the

X-axis frame were up against the carriage flank faces. Then the cap screws

were tightened starting from the top moving to the bottom. The X-axis carriages

were given their initial charge of grease. The X-axis frame was then moved

along the X-axis rails to see that there was no binding or areas of rough motion.

The ball nuts were connected to the X-axis frame at this point. A nut

bracket serves as the intermediate piece between the X-axis frame and the ball

screw's nut. The brackets are attached to the flanges of the ball nuts. Care was

taken to make sure that the attachment surfaces where clean of any debris.

Spacer plates were fitted between the nut brackets and the mounting pads to fill

the gap between the mounting pad and the bracket. This prevents any

horizontal deflection of the screw.



Figure 4-5 Positioning the X-axis frame on to the X-axis carriages



, j-

The assembled X-axis frame, carriages and ball screws were moved back and

forth along the length of travel by hand driving the ball screws. This was to

check for any binding or misalignment of the assembly as it was moved through

its range of travel. This completed assembly of the X-axis running gear.

Y-Axis Rails Mounting and Alignment.

The Y-axis is fitted with Accumax 45 rails and carriages. These carriage

are similar to the ones used on the X-axis except they are of a smaller size. The

rails were cleaned and prepared for mounting. A similar procedure was followed

as was performed with the mounting of the X-axis rails. The rails were hung on

the surfaces provided on the X-axis frame with socket head cap screws. The

cap screws were tightened finger tight. The right-hand mounting pad on the X-

axis frame has an alignment edge for positioning the rail. The flank of the rail

was pressed firmly against this alignment edge using a clamp. Once the flank of

the rail was snugly against the alignment edge the adjacent cap screw was

tightened to hold the rail in place. This process was repeated moving down the

rail until all the cap screws were tightened. The cap screw threads had been

coated with anti seizing paste before being threaded. The cap screws were

torqued to 100 Nm using the procedure as presented previously. The

straightness of the rail was checked using a granite straight edge. No

straightness errors could be seen. Once the rail was secured to the X-axis frame

the squareness of the Y-axis to the X-axis rails was measured.

To make this squareness measurement a jig holding a precision granite

square was placed the X-axis to act as the reference artifact. A dial indicator

riding on a y-axis carriage was used to make the measurement. Figure 4-6

shows the arrangement of the square and the dial indicator on the X-axis frame.

The square was positioned on the edge surface of middle rail's right-hand

carriage. The alignment surface on the carriage is approximately parallel to the

X-axis rail. An adjustment screw, with a ball end, supports the square

kinematically. This prevents any misalignment of the base of the square with the

flank surface of the carriage. The dial indicator's position was adjusted to bring

the stylus into contact with the vertical surface of the precision granite square.

The Y-axis carriage was moved along the Y-axis to check the squareness. The

initial measurement showed a significant yaw, relative to a line perpendicular X-

axis. The measurement showed a yaw of 0.00204 rads (7 arcmin). To remove

this yaw the X-axis frame's position was adjusted with shims placed between the

alignment edges on the top mounting pads and the flanks of the two top X-axis

carriages. This required that all of the cap screws securing the X-axis carriages

and nut brackets be loosened to prevent any distortions or misalignments to the

running gear. The amount of shim to be place was approximated by performing

a simple trigonometric calculation of the rise over the run. The X-axis frame was

lifted off the alignment edges using a hydraulic jack placed at its base and the

shims were put in place. The hydraulic jack was then lowered and the bolts to

the carriages were re-secured. The squareness was measured again. The

process was repeated until the error was less then 3.57e-5 rads (0.123 arcmin).






Figure 4-6 Alignment of Y-axis rail and squaring to X-axis


This procedure brought the X and Y axis into the range of perpendicularity which

could be measured with the equipment used.

The second Y-axis rail was mounted following the same procedure. The

alignment of the second Y-axis rail to the preceding rail was accomplished using

the same procedure as was used to align the upper two rails on the X-axis.

Figure 4-7 shows the arrangement of the jig and the dial indicator. The

measurement jig is placed on the Y-axis carriage of the aligned rail and the dial

indicator stylus was brought into contact with the flank of the unaligned rail.

Starting from the top the rail was moved into position and the adjacent socket

screw was secured. The procedure was repeated moving down the Y-rail

following the procedure used on the X-axis rails. Once the alignment was

completed, a final check was made and then the fasteners were torqued to the

proper level.

Installation and Alignment of Y-Axis Ball Screw.

The Y-axis ball screw is of similar design to the X-axis ball screws. A

difference in the assembly of this ball screw is that it is unsupported away from

the driven end. Since the Y-axis ball screw is in a vertical orientation there was

no concern about any sag. The installation of the ball screw was straight

forward. The bearing, ball screw, and housing were assembled in the same

manner as the X-axis ball screws. Once assembled and greased the assembly

was lifted into place with a chain hoist.



1 ...1:

111111 II' 1

Ii-__-~ _

Figure 4-7 Alignment of the second Y-axis rail


Cap screws secured the bearing housing to the mounting pads on the X-axis

frame. The ball screw was aligned to the rails using jig and a dial indicator.

Figure 4-8 shows the arrangement of the jig and dial indicator. The screw's

parallelism to the rails was checked by measuring the distance between the rail

and the ball screw by moving the jig and indicator down the rail. The lack of

parallelism showed up as a yaw in the ball screw relative to the rails. To remove

the yaw the bearing housing's position was adjusted. This process was repeated

until the yaw was removed. A gross check for pitch relative to the face of the X-

axis frame was made on the ball screw. It was not possible to make a fine

measurement due to the lack of a uniform surface to make measurements

against. When the ball screw had been aligned, the free rotation was checked

and the ball nut was charged with grease.

Installation of the Y-Table

The Y-table is the structure to which the work piece is attached. The table

is a robust structure with a approximate mass of 700 kg. (1500 lbs.). Provisions

were made in the Y-table for lifting eye bolts to be attached to the top edge which

was close to the line of action for the center of gravity. The Y-axis ball screw nut

bracket was fastened to the ball nut flange and the four Y-axis carriages were

positioned on the rails. The table was hoisted and moved into position. Figure

4-9 shows the Y-table suspend in position.






j I

Figure 4-8 alignment of the Y-axis ball screw





Figure 4-9 Positioning of the Y-axis table

The alignment edges on the Y-table's carriage mounting pad were brought up

against the flank surfaces on the carriages. The bolt holes on the carriages and

pads were aligned and the socket head cap screws were put in place. The cap

screws were tightened. The ball screw was turned by hand to bring the nut

bracket into position aligning the bolt holes. The fasteners were threaded and

tightened. Wood blocks were positioned under the Y-table and the table was

lowered onto the blocks. These blocks prevented the table from moving off the

end of the rails and the ball screw until the servo motor and the coupling were

connected. The servo motor lifted the Y-table off the blocks and the wood blocks

were removed. This completed assembly of the Y-axis running gear.

Z-Axis Pedestals

The Z-axis motion is set on two pedestals. Each of these pedestals are

large steel weldments which have been machined to accept the drive gear for

the Z-axis and support the AB rotary head. The weldments each have a mass of

900 kg. (2000 lbs.). To handle these pedestals, a lifting beam was fabricated. It

was designed to span the length of the pedestals and attach to lifting bolts via

wire slings. The lifting bolts were placed along the longitudinal line of action of

the center of gravity. The chain hoist attached to the lifting beam at mid length.

Each of the pedestals was lifted onto the bed and secured in place with socket

head cap screws. Figure 4-10 shows the left pedestal being lifted into place.




Figure 4-10 Placement of Z-axis pedestal on to machine bed

Note that the mating surfaces were cleaned of any dirt or debris prior to

assembly. Only a gross alignment was preformed at this point of the Z-axis


Z-Axis Rail Installation and Alignment

The Z-axis rails are THK HSR-45 series linear ball guideways. One rail

system was attached to each of the pedestals. The left pedestal has an

alignment edge for the alignment of the rail. The flank of the rail was pressed

against the alignment edge and the cap screws secured in the same fashion as

the Y-axis rail, on the right side, was placed and aligned. The rail on the right

pedestal was put in place and the cap screws were tightened. The straitness of

the rails was checked using a granite strait edge. Due to the large span between

the two rails it was not possible to use a jig riding on a z-axis carriage to measure

the alignment between the two rails.

Rather the left pedestal was secured the right pedestal was allowed to be

moved. The Z-axis table was set on the carriages. Figure 4-11 shows the Z-axis

table being move into place to be set on the carriages. The Z-axis table has

alignment edges to milled into the underside of the table. These two edges were

used to align the Z-axis carriages on the two rails with one another. This would

result in the two Z-axis rails being parallel to each other. The Z-axis table was

positioned so the left alignment edge was pressed up against the flanks of the

two carriages on the left rail. The Z-axis table was then secured to left rail's

carriages with socket head cap screws.


Figure 4-11 Positioning of the Z-axis table

The right pedestal position was adjusted so that the right-hand alignment edge

was brought up against the flanks of the carriages on the right pedestal's rail.

The pedestal was moved into position using a hydraulic jack. Care was taken

not to jam or distort the carriages or rails. Once the pedestal was in place the

carriages were fastened to the table and the pedestal was fastened to the bed.

The Z-axis table was tested for freedom of motion. The Z-axis running gear

assembly was completed with the attachment of the linear drives. The stationary

magnets were attached to the pedestals and the coils where attached to the Z-

axis table.

Testing of the Motion Errors

To check the accuracy of the assembly of the machine tool's three linear

axes squareness and straightness error were measured. The squareness and

the straightness of the three axes were measured using the laser ball bar. The

measurements showed that the assembly of the machine tool had been

successful. The largest squareness error was between the X-Y axis. It was

measured at 1.3245 mrad. The squareness errors for X-Z and Y-Z were both

less then 1 mrad. The straightness errors on all the axes were less then 0.008

mm (0.0003"). A complete set of the measurements of the squareness errors

and plots of the straightness errors is presented in the Appendix.

This completed the assembly of the three translational axes of motion.

The next stage of assembly would be the two rotary axes of motion. Due to the


need to test the machine in its present configuration, the machine tool was set

up as a three-axis machine tool. The spindle was attached to the Z-axis table on

a stationary saddle. Figure 4-12 shows the spindle be put into position. Figure

4-13 displays a photograph of the machine tool in its three axis configuration as

of January 1996. Presentation of the dynamic testing and cutting test is

presented in the next section.




Figure 4-12 Placement of the Phase II high speed spindle

Figure 4-13 Photograph of the three axis configuration of the machine tool


This section will cover the testing and evaluation of the cutting

performance of the three axis configuration of the high speed machine tool. The

cutting performance testing will follow procedures similar to those presented in

Section 7 and appendix A of the ASME B5.54 [ASM92]. The spindle idle run

losses test, the chatter limit tests, and full torque testing were performed. The

testing of cutting force induced errors was not performed. The data found in

these tests can be used to compare this machine tool with others in its class.

The fundamental concept of this high speed machine tool, from its initial

inception, was to have high metal removal rates for the cutting of aluminum

aircraft components. This requires that a majority of the available spindle power

be utilized in the cutting the material. The power consumed in the cutting

process can be determined from the following equation.

P = Ksabcmn (5-1)

where K. is the specific power of the material, a is the radial depth of cut, b is the

axial depth of cut, c is the feed per tooth, m is the number of teeth on the cutter,

and n is the spindle speed. Ks is a property of the material being cut. The value


of K. for aluminum is about 750 N/mm2 The values of c, m, and n are limited by

cutter material, cutter geometry, and the maximum speed of the spindle. The

axial and radial immersions are limited by the tool path and the dynamic stability

of the tool/spindle/work piece system.

The MRR in HSM of aluminum is typically limited by the available torque

of the spindle for cutting the material or by the onset of chatter. It would be ideal

to reach the spindle's torque limit at top spindle before the onset of chatter. This

would mean that the cutting process is stable and drawing upon all the available

power of the spindle, thus maximizing the metal removal rate (MRR). If on the

other hand the limit of stability is reached first, the total available power cannot

be used. This has the effect of reducing the maximum possible MRR.

The occurrence of chatter is due to insufficient dynamic stiffness of the

tool/holder/spindle system and the supporting structure. Thus, the cutting

performance is directly coupled to the dynamic stiffness of the spindle and the

machine tool's structure. To see how chatter is related to the lack of dynamic

stiffness, a short discussion on chatter is presented in the following section. It

will cover the fundamentals of chatter and the lobing diagram.


Chatter arises from the regeneration of the waviness on the surface being

cut. Each cutting edge removes material from the work piece producing a

surface. Any vibration, at the time that the surface is being cut, generates a

wavy surface. This wavy surface leads to variable chip thickness, which

produces unsteady cutting forces. The magnitude of the cutting force is

proportional to the thickness of the chip. Depending on the conditions of the

cutting process, the vibration of the tool either grows or diminishes. If the

vibration diminishes, the cutting process is stable. If the vibration grows, the

cutting process is unstable and chatter occurs. Chatter produces a rough

surface on the work piece. Chatter is detrimental not only to the surface of the

work piece, but also to the cutting tool and the spindle. The high dynamic forces

due to chatter can break the cutter and damage the spindle.

The onset of chatter, as stated previously, limits the amount of power that

can be utilized in the cutting process. The maximum axial and/or radial

immersions become limited with chatter. This reduces the MRR causing and

increase in the machining time for a given part. A complete discussion on

Chatter is presented in the original work by Tlusty [TLU85]. The worst case for

the onset of chatter is the cutting of a slot, 100% radial immersion. This case

leaves only the axial depth of cut as the dominant variable for the onset of

chatter. The chip load can also be varied but only affects the magnitude of the

chatter. It does not affect the onset of chatter. The equation for determining the

limit of the axial depth of cut is
blim [ G1 (5-2)
2 Ks (p, Re[Gx] + py Re[ Gy])mavg

where bim is axial depth of cut, K, is specific power of the material being cut, p is

the directional orientation factor, mavg is the average number of teeth in the cut.

The orientation factor is a function of the radial immersion. It relates how the

cutting force causes deflection in the direction of the measured FRF and how

that deflection affects chip thickness. Re1[Gi] is the negative real part of the FRF

for each of the orthogonal directions in the plane of the cut. Figure 5-1 shows

the relationship between the FRF of a cutter and axial limit of stability. There are

two additional equations used to obtain the stability lobe diagram. These

equations relate the calculated axial depth of the cut, bim, to the spindle speed.

Equation 5-3 relates the ratio of the frequency of chatter, f,, and the tooth

passing frequency, ft = nm, to the number of waves and phase shift between the

previous surface and the new surface being cut. The equation is

= N + (5-3)
nm 2n

where f is the frequency of chatter, n is the spindle speed, m is the number of

teeth on the cutter, e is the phase shift between the vibration of the cutter tooth

and the wavy surface left by the previous tooth, N is an integer such that /2-r <

1. Equation 5-4 determines the phase shift between the vibration of the cutter

tooth and the surface left by the previous tooth as

e = 2 2tan- pxRe[Gx]+pyRe[GY] (54)
pxlm[G] +pylm[G1 y](54



FP E (I.1E N C

iH T F 'LE
FE G I10 1

T, PIL I "


Figure 5-1 Relationship between frequency responce function
and stability lobes


The preceding equations define the relationship between the spindle speed and

the permissible depth of cut which is commonly referred to as the "stability lobe

diagram." Figure 5-2 shows the stability lobe diagram for a simple single DOF


To calculate the stability lobe diagrams for a given cutting tool/machine

tool configuration, the FRF of the cutting tool relative to the work piece must be

measured. The modal parameters can them be extracted and used to produce

the stability lobe diagrams. These diagrams can be used to determine the

maximum stable depth of cut for a given spindle speed. Stability lobe diagrams

for varying radial immersions can also be produced. It is noted again that the

feed per tooth is not a contributing factor to the onset of chatter. It will only affect

the magnitude of the forces.

Measurement of the Frequency Response Functions

The modal parameters of the cutting tools were extracted from

measurements made using the impulse excitation method. Direct frequency

response functions (DFRF) were measured between the tool and the workpiece

in the X and Y directions perpendicular to the axis of rotation of the spindle. The

FRF's, Gx and GY are the ratios X(o)/Flc(w) and Y(co)/F2 (w). F, (w) and F2 (w) are

the variable forces acting in the two axes, respectively. The DFRFs are obtained

using an instrumented hammer, accelerometer and a dynamic analyzer.

/[1 1

- - - - - - - -

I 11111

Figure 5-2 Lobing diagram for simple single degree of freedom system

0 F


The hammer used was a PCB model 086C80 micro impulse hammer, and the

accelerometer is a PCB model U352A1 0 micro accelerometer. The dynamic

analyzer and software used in the measurements were developed by

Manufacturing Laboratories Inc. The measurement of the DFRF was made at

the free end of the cutting tool. The micro accelerometer was attached to the tip

of the end mills using a petroleum-based wax. The end mill/spindle was rotated

to bring the accelerometer into alignment with the direction that is being

measured. Figure 5-3 shows a diagram of the accelerometer positioned at the

tip of the end mill, and the location where the impulse was applied. The impulse

is applied to the tool tip on the opposite side from the accelerometer. The

analyzer measures and records the accelerometer's response and the

magnitude of the impulse and performs the fourier transform by by dividing the

former by the latter. Five measurements were taken and averaged in the X and

Y directions. Figure 5-4 shows the frequency response function of a 19 mm

(0.75") diameter carbide end mill with 44 mm (1.73") overhang from the end of

the tool holder installed in the spindle. The tool was held by a shrink fit 40 taper

type holder. Examination of the FRF's shows that there is a significant difference

between the two directions. In the X-direction it can be seen that there are four

significant modes, while in the Y-direction there are six significant modes. Table

5-1 presents the modal data extracted from the 2 FRFs. It can be seen that

there are modes at 747 Hz, 944 Hz, 1075 Hz and 1693 Hz in both the X and Y

direction. The Y-direction has two additional modes at 875 Hz and 1149 Hz.






Figure 5-3 Diagram of impulse excitation measurements

19 mm DIA. 44 mm OVERHANG


/ '.. .......... ', i / ... ...................................... ....... ..

0 50 1000 1500 200D 2500


0 500 100o 1500 2000 2500

0 .......... .. . . . . . .. .. .: :" .. ..... ".. . .. ..... ... ........

0 a0 1000 150 2000 25M

..... ... ......i '

0 500 1000 1500 2000 250

Figure 5-4 Frequency responce functions of carbide end mill


No fn H Rel Reu M K Zeta 1/H
1 747.7 0.0000 727.8 758.4 0.961 21210 0.0204 86550
2 944.5 0.0000 906.4 976.6 1.276 44930 0.0372 33390
3 1075.7 0.0000 1052.9 1092.5 0.347 15860 0.0184 58490
4 1693.7 0.0000 1641.8 1734.9 0.352 39810 0.0275 21880

No fn H Rel Reu M K Zeta 1/H
1 724.8 0.0000 711.1 732.4 2.016 41820 0.0147 12330
2 875.9 0.0000 848.4 914 0.788 23870 0.0375 17890
3 944.5 0.0000 933.8 959.8 1.264 44520 0.0137 12230
4 1081.8 0.0000 1057.4 1100.2 0.723 33390 0.0197 13190
5 1149 0.0000 1138.3 1162.7 2.227 11610 0.0106 24660
6 1702.9 0.0000 1635.7 1760.9 0.24 27530 0.0367 20230

Table 5-1 Modal data of carbide end mill

It can also be observed that there is a difference in the magnitudes of the

modes. Examining the most compliant modes in the two directions also shows

an interesting difference. In the X-direction the most flexible mode is at 1075 Hz

with a modal stiffness is 1.586e+7 N/m. The corresponding mode in the Y-

direction is two times as stiff. The most flexible mode in the Y-direction is at 944

Hz. It has a modal stiffness of 4.452e+7 N/m. The corresponding modal

stiffness in the X-direction differs by less then 1%. A calculation of the critical

depth of cut, blimcrit can be made for the most flexible modes in both directions.

The smaller of the two values will be a stable depth of cut for any spindle speeds

(safe side estimate). It will be calculated for the cutting of a slot in each of the

directions, maximizing the radial immersion. The equation for this calculation is

1~ 1
bim cr1H m (5-5)

where blimcrit is the maximum axial depth of cut, Ks is the specific power of the

material being cut, p is the orientation factor, H is the magnitude of the mode, m

is the number cutting edges on the end mill. Taking the most flexible modes

from Table 5-1 for the two directions, the blimcrit is calculated as 1.114 mm

(0.044") for the X-direction and 2.329 mm (0.092") for the Y-direction. This

calculation shows a two fold greater depth of cut is possible in the Y-direction

then in theX-direction. It is noted that this calculation only gives an estimate of

the difference in the depth of cut. It assumes that the modal stiffnesses in the

two directions act independently of each other which is not the case.

This lack of symmetry between the 2 DFRFs was found with all the end

mills tested. It is believed that this variation in the FRF's for these two directions

is due to the structural arrangement of the Z-axis. The structure supporting the

spindle consists of the spindle housing, saddle, Z-axis table, and the two

pedestals. The pedestals were placed wide apart to make room for the AB

head's drive components. To examine the difference between the two

directions' DFRFs, a systematic analysis was performed. The analysis consists

of dynamic modeling of the spindle and taking modal measurements of the

spindle and the structure.

Spindle Model Analysis

The spindle model analysis was performed using a spindle analysis

program called SPA. This program was developed by Manufacturing

Laboratories Inc. The program utilizes 4 DOF beam elements to build a spindle

model. The four DOF for these elements are divided into one translational DOF

and one rotational DOF at each end of the beam element. The model is

assumed to be symmetric about the axis of spindle rotation. The stiffnesses will

be considered to be equal in all planes passing through this axis. Spring and

mass elements are added to the model to account for the bearings, tool holder,

motor elements, and other components. Listings of the two spindle models used

are presented in the appendices. The two spindle models incorporate a shrink fit

tool holder and carbide end mills with overhangs of 54 mm and 123 mm. Plots

of the mode shapes with their corresponding natural frequencies, and modal

stiffnesses at the tool tip are presented in figure 5-5.

Examination of the model modes shapes and stiffnesses shows that the

tool length has a strong effect on the mode shapes and the stiffness at the tool

tip. This is consistent with what has been seen by others [TLU96, WIN95]. The

short tool model shows that the most flexible modes are the first, second, and

third modes of the spindle. The stiffness at the tool tip is approximately 6e+7

N/m at 826 Hz, 1042 Hz, and 1373 Hz. The tool mode is stiffer, having an

approximate stiffness of 8.6e+7 N/m at a frequency of 3568 Hz. Note that all

four of these modes have a similar magnitude of stiffness. The second model

with the long tool shows the tool mode to be the most flexible. It has a modal

stiffness of 3.4e+6 N/in at a frequency of 648 Hz. The spindle modes are all at

least an order of magnitude greater in stiffness. The comparison of the mode

shapes and stiffness from the model to experimental data will be conducted in

the next section.

Modal Measurements of the Spindle

A modal analysis of the spindle was performed examining the direct and

cross FRF's of the spindle in two perpendicular directions. These measurements

were made on two tool/spindle combinations. Two micro-grain carbide end mills

were used. Both end mills are 19 mm (0.75") in diameter.


1': M M I:AF':TTE El 9 HILL
',4 MM ]'v/EP'H, Hl



4~j-~ -~

I9 rl IAP I E El] I LL
I,-: MH 1'iEPHA1.1

826 Hz
6.059e+007 N/m

1042' Hz
6084e+ 07 N,,
1 3>7'.. HZ
;(j08e+007 N,'rl
L 7 7 H
2.506e+0083 N/m
3'- 7
8636c 007 N/p

- : r-, H -

2,768e '008 N/m
,- -I 1 ,
9,73te+008 N/mn
7, -q H Z
1,693e+009 NM

4 410t+009 N/r

9E98 Hz
2,406e+O09 N/m



443e+006 H/r


115J H-
4 221e+007 N/rvi

W8 08+008 N/r,/
4 H

44 H


4 U H

I 8jte+OCH N/v

7 H
442+008 WI/

5 ,41}J0 H/r
2.8ef@ N/


I: '4 I H --
' 4 ? (I(l J? H, I

Figure 5-5 Spindle model analysis of mode shapes

One was a four fluted end mill with an overall length of 101.6 mm (4 inches).

The other was a two fluted end mill with an overall length 152.4 mm (6 inches).

Both tools were held by shrink fit tool holders manufactured by Tooling

Innovations. The tool holder has a standard 40 taper tool holder, for the

spindle/tool interface.

The measurements made are a combination of one DFRF taken at the

tool tip and a number of cross transfer functions (CFRF's) measured along the

tool/holder/spindle system.The frequency range measured was 5000 Hz.

Figures 5-6 and 5-7 show the placement of the accelerometer for the

measurements. The impulse excitation was always applied at location #1, the

tool tip. The measurements were made in two perpendicular directions. These

where made along the lines formed by the XZ and the YZ planes as it passes

through the rotational axis of the spindle. The line formed by the XZ plane is

parallel to X-axis of motion of the machine and is considered the X-direction.

Similarly the line formed by the YZ plane is parallel to the Y-axis of motion and is

considered the Y-direction. It is noted that any orientation of the two

perpendicular directions could be used as long as they remain perpendicular to

each other and the Z axis. Figure 5-6 and 5-7 shows the resultant mode shapes,

natural frequencies, and stiffnesses at the tool tip, which has been extracted

from the measured DFRF's. It can be readily seen from the mode shapes that

there is a difference in the two directions. There are more significant modes in

the Y-direction for both cases. This is consistent with the initial tool


19 mm DIA 54 mm OVERHANG


4 ri OVFPHA 3

- - - --- t

9 -1:4 K1

!2'44 H

, 1[4 + (I (7 N'1 ,

:4 4 8.H
5,8 3_ + 00I7 N/rm

3-2 l H Hz
E',512e+007 N, m

8 C~ 4 6,07 1 ,p

J-ni H

ii0 H

I 4 I 1
lI19i Hz
S 71-Ie+0 7 IJ

+ D 0 7 H/
: 7, +11 1 rI ,)/1,,

'-44 -7

Figure 5-6 Measured mode shapes of 54 mm length end mill

M EA -- 11 E
OZF 1 r' I:
X -I

4 H:


1 3 f,

19 mm DIA 123 mm OVERHANG

1 I F E ll! JZ2 I' E1 E HIJ
I P E C T 1]I 1>-LJl I PE : T 111

5) 7, 3 5

7 H
.,442e+006. NII

96E6 H7
1.228e+007 N/r,

10'% Hz
6.'66e+1006 II 1

I Hz

L- 4 H -
- :00E+008 N P,
&6, 2 H z

_*111 H

4l ~ 00 .
4-0 .


H -~-+~-l



73-: Hz

4.24"-e +0306 J,,I'

r ,-
1 IN

I F] -74 H-
I.-S + 0

1,3$e 1 -4 7 H/'
114 H

jE::k4 Hz

154(-1 H
I125e+007 H

S 'I H Z

I4 +, D 8 j

Figure 5-7 Measured mode shapes of 123 mm length end mill

Closer examination of the mode shapes shows that there are corresponding

modes in the two directions for both tools. There are some differences in the

frequencies. This maybe due to the failure of capturing the peak values of the

FRF, because of the discrete data acquisition and non-linearities of the system.

Comparison of the mode shapes and stiffnesses measured on the 54 mm tool

and those of the 54 mm model shows reasonable agreement. The frequency

variation is less the 10% at its greatest variance. The stiffnesses are of the same

magnitude. It can be seen that there are three individual modes which show up

in the Y-direction that are not found in the model or measured in the X-direction.

These modes occur at 443 Hz, 1001 Hz, and 1122 Hz. There is also a mode at

2270 Hz that shows up in both X and Y directions, but is not found in the spindle

model. Similarly, examination of the measured values of the 123 mm tool show

good correspondence in the two directions and with the model. However, there

are modes in the Y-direction which do not correspond to the X-direction or to the

model. These modes are at 439 Hz, 858 Hz, 1147 Hz and 1227 Hz. There is a

mode at 3111 Hz in the X-direction which does not match up with model or the

Y-direction measurements. It is noted that the models assumed a value of 3%

for the damping ratio. Measured values of the damping ratio varied from less

than 1 % to more than 7%. The stiffnesses found at the tool tips for both cases

shows that the X-direction is always more compliant.

The difference in the number of significant modes between the two

directions is probably a result of the influence of the structure supporting the

spindle. The supporting structure consists of the spindle housing, spindle