|Table of Contents|
Table of Contents
Chapter 1. Introduction
Chapter 2. Literature review
Chapter 3. Kinematics of five-axis machine toos
Chapter 4. Practical aspects of machine tool assembly
Chapter 5. Cutting performance testing
Appendix. Squareness and straightness errors
SOME ASPECTS OF FIVE-AXIS MACHINE TOOL
DESIGN, ASSEMBLY, AND TESTING
DAVID MONTWID BERNHARD
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
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.
TABLE OF CONTENTS
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 ..................
3 KINEMATICS OF FIVE-AXIS MACHINE TOOLS
Kinematic Combinations ................
Parameters for the selection of combinations
MTRC's Five-Axis Machine Tool ..........
. . . . . . . . 14
. . . . . . . . 14
. . . . . . . 2 7
. . . . . . . . 3 3
4 PRACTICAL ASPECTS OF MACHINE TOOL ASSEMBLY .
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 ......................
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
SQUARENESS AND STRAIGHTNESS ERRORS ............... 115
R E FE R E N C ES ................................................ 117
BIOGRAPHICAL SKETCH ....................................... 121
CNC or NC
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
Cross frequency response function
Direct frequency response function
Degrees of Freedom
Tooth passing frequency
High Speed Machining
Inches per minute
Number of teeth on the cutter
Metal Removal Rate
Machine Tool Research Center
Number full waves between teeth
Revolutions per minute
Linear axes designators in spindle/tool
Linear axes designators in table/work piece
Phase shift between old surface and new surface
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
SOME ASPECTS OF FIVE-AXIS MACHINE TOOL
DESIGN, ASSEMBLY, AND TESTING
David Montwid Bernhard
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
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.
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.
KINEMATICS OF FIVE AXIS MACHINE TOOLS
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
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
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
Figure 3-1 Right hand cartesian coordinate system
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.
AC NUTATING HEAD
XY TABLE SLIDE
Figure 3-3 AC & BC head configurations
ROTATING & TILTING
Figure 3-4 A'C' & B'C' Rotating and Tilting table combinations
Figure 3-5 AB' & A'B Tilting spindle and Tilting Table Combinations
TABLE 3-1 MACHINE KINEMATIC 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
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
Table 3-2 TYPICAL AIRCRAFT PARTS:
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
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
PRACTICAL ASPECTS OF MACHINE TOOL ASSEMBLY
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
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.
ACCU-MAX 55 RAIL
-j- RESILIENT MOUNTS
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.
- ALIGNMENT JIG
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.
\ X-AXIS HOUSING
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
)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
dist wL4 (4-2)
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.
DIAL INDICATOR SET
IN PILLOW BLOCK BORE
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
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).
PRECISION GRANITE SQUARE
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
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.
111111 II' 1
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.
Y-AXIS BALL SCREW
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.
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-
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
CUTTING PERFORMANCE TESTING
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)
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
MAG N TUDE
FP E (I.1E N C
iH T F 'LE
FE G I10 1
T, PIL I "
:PF] DLE I FEEL
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.
- - - - - - - -
Figure 5-2 Lobing diagram for simple single degree of freedom system
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.
I MIF HAMIEF
:HAPGE AMP LFILF
Figure 5-3 Diagram of impulse excitation measurements
FREQUENCY RESPONCE FUNCTIONS
4 FLUTE CARBIDE END MILL
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
MEASURED MODAL DATA
4 FLUTED CARBIDE END MILL
44 mm OVERHANG
MODAL DATA X-DIRECTION
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
MODAL DATA Y-DIRECTION
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
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.
OF HIGH SPEED SPINDLE
FITTED WITH CARBIDE END MILLS
PA 1 4LY HOLE :HAR'E
1': M M I:AF':TTE El 9 HILL
',4 MM ]'v/EP'H, Hl
F-' kIJALL"-l' NODE -H FP
I9 rl IAP I E El] I LL
I,-: MH 1'iEPHA1.1
6084e+ 07 N,,
1 3>7'.. HZ
L 7 7 H
8636c 007 N/p
- : r-, H -
2,768e '008 N/m
,- -I 1 ,
7, -q H Z
4 410t+009 N/r
4 221e+007 N/rvi
W8 08+008 N/r,/
4 U H
I 8jte+OCH N/v
5 ,41}J0 H/r
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
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
EXTRACTED FROM MODAL MEASUREMENTS OF THE
HIGH SPEED SPINDLE FITTED WITH A 4 FLUTED
CARBIDE END MILL
19 mm DIA 54 mm OVERHANG
ID HDE SH PE-
:AFBIDE END HILL
IFE,_T IOI J
H EA-UPEl HODE S IAF'ES
F 19 CAPPIE DID MIHLL
4 ri OVFPHA 3
- - - --- t
9 -1:4 K1
, 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
I 4 I 1
S 71-Ie+0 7 IJ
+ D 0 7 H/
: 7, +11 1 rI ,)/1,,
Figure 5-6 Measured mode shapes of 54 mm length end mill
M EA -- 11 E
OZF 1 r' I:
1 3 f,
EXTRACTED FROM MODAL MEASUREMENTS OF THE
HIGH SPEED SPINDLE FITTED WITH A 2 FLUTED
CARBIDE END MILL
19 mm DIA 123 mm OVERHANG
dlASU E MODE SH APL-H HME A rJEI} MODLE -HAPE
IF 19 I-ARBIDE LIZ HILL IF .9 mr B APLDE ELI HILL
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
6.'66e+1006 II 1
L- 4 H -
- :00E+008 N P,
&6, 2 H z
4l ~ 00 .
4.24"-e +0306 J,,I'
I F] -74 H-
I.-S + 0
1,3$e 1 -4 7 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