Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
Vibration and Chatter Analysis Using Third
Wave Systems AdvantEdge
David Singletary
A Seminar submitted to the Faculty of Rensselaer at Hartford in partial fulfillment of the
requirements of the Degree of MASTER of Science
Major Subject: Mechanical Engineering
The original of the Seminar is on file at the Rensselaer at Hartford Library
Approved by Seminar Advisor: Prof. Ernesto Gutierrez – Miravete
Clinical Associate Professor
Department of Engineering and Science
Rensselaer at Hartford, Hartford, CT
April 20 2006
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
2
Abstract:
This paper is concerned with studying vibration and chatter seen during metal cutting
processes. Third Wave Systems AdvantEdge will be used extensively to show how
force/vibration varies when altering criteria like cutting speed, depth of cut and feed
rate. An AdvantEdge standard flat surface work piece will be compared to a custom
made irregular surface work piece and a custom made wavy surface work piece. The
wavy surface work piece has a surface profile that mimics a sine wave. The wavy
surface runs will be performed with and with out tool stiffness and tool dampening.
These test are performed to show how force/vibration oscillations vary with different
system inputs and lead to regenerative chatter. Tables, diagrams and the program
references for solutions obtained are attached in the appendices to the paper or simply
appear within the paper where it is deemed to be relevant.
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
Table of Contents
Abstract------------------------------------------------------------------------------- (2)
Table of contents........................................................................................... (3)
1. Introduction …….…………………………………………………. (4)
2. Methodology.......................................................................................(5)
2.1 Work Piece Surface Description……….….……………….…...(6)
2.2 General types of Machining Vibrations…….….………………(8)
2.3 Stability Lobes…….….………………….…….….……………(10)
2.4 Governing Equations for Tool Cutting and Chatter………….…(11)
2.5 Parametric Cases.……….………….……….……….……….…(13)
3. Analysis..............................................................................................(15)
3.1 Categorizing the vibration/forces into levels….………………...(15)
4. Results and Discussion....................................................................... (16)
4.1 High Force/Vibration Oscillation.….……….……………….......(16)
4.2 Medium Force/Vibration Oscillation………………………….....(18)
4.3 Low Force/Vibration Oscillation…………………………….....(19)
5. Conclusions .........................................................................................(20)
6. Table of Symbols ................................................................................(21)
7. References.......................................................................................... (22)
8. Appendix A .........................................................................................(24)
3
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
4
1. Introduction:
This paper investigates the force/vibration oscilations produced in metal turning
processes that lead to chatter. Chatter has been a long-term problem in metal turning
processes. There is a trend in the machining world to increase part precision and reduce
part tolerances. The increase in part precision and reduction in tolerances cannot occur
while large force/vibration oscillations are present. These oscillations can be directly
related to chatter. Chatter is a result of vibration within the tool and work piece system.
There are three main types of vibrations that may be seen during machining. These
vibrations are free vibration, forced vibration and self-excited vibration. The two main
types of chatter producing vibrations are forced and self-excited vibrations. Self-excited
vibrations are also commonly known as regenerative vibration or regenerative chatter.
Forced vibration is independent of the cutting tool and work piece. Whereas regenerative
chatter usually starts with a slip and slide interaction between the tool and work piece that
leads to increased force oscillations. Chatter is sometimes overlooked when setting up
machining processes, but should not be overlooked if the part being produced should
have good precision and tolerances. If the cutting frequency and natural frequency of the
system become close in magnitude substantial chatter is likely. One way to predict chatter
in metal turning operations is to run finite element software and look for an increase in
vibrations. Third Wave Systems finite element analysis modeling software, AdvantEdge,
was used in this paper to verify the ideal cutting speeds, depth of cuts, and feed rates. By
varying the previously mentioned cutting parameters and surface conditions we are able
to investigate the force/vibration oscilations involved in turning processes that lead to
chatter. The original runs were performed with the parameters shown in table 1.0 below.
Table 1.0 shows all of the default values used with the exception of the work piece
material and cutting tool material. For the runs performed titanium grade 3 was used as
the work piece material and cubic boron nitride as the cutting tool material.
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
-- PROJECT --
5
-- PROCESS --
Project / Job Name = Chatter1
Project / Job Description = Chatter in Turning
Units = SI
Process Type = turning
WorkPiece Type = STANDARD
Tool Type = STANDARD
Tool Material Type = STANDARD
Depth of cut = 1.0 mm
Length of cut = 3.0 mm
Feed = 0.15 mm
Cutting speed = 3000.0 m/min
Initial temperature = 20.0 degC
Friction coefficient = Default
Cutting mode = General
Coolant = OFF
-- CUSTOM WORKPIECE --- SIMULATION -Material = CPTitaniumGrade3
-- STANDARD TOOL -Tool File = Chatter1.twt
Rake angle = 5.0 deg
Rake length = 2.0 mm
Relief angle = 10.0 deg
Relief length = 2.0 mm
Cutting edge radius = 0.02 mm
Tool Material = Cubic-Boron-Nitride
Coating Layer No. = 0
Simulation Mode = Rapid
Steady State Analysis = 0
Avg Length Of Cut = 10.0
Chip Breakage = 0
Max. number of nodes = 12000
Max Element Size = 0.1 mm
Min Element Size = 0.02 mm
Fraction of Radius = 0.6
Fraction of Feed = 0.1
Mesh Refine = 2
Mesh Coarse = 6
Output Frame = 30
Table 1.0 Default AdvantEdge Settings
Chatter is usually the deciding factor when it comes to the productivity of metal turning
processes. The presence of chatter can greatly reduced the cutting tool life, decrease
work piece tolerances or even make it impossible to turn the work piece within desired
specifications. Reducing chatter does not always mean that one should increase or
decrease the cutting speed, but altering the speed is usually one of the easier parameters
to adjust. Sometimes the depth of cut or feed rate can be decreased in order to avoid
chatter. Altering the turning speed, depth of cut, and feed rate may increse the time that it
takes to produce a part, but it is a small price to pay for the increased precision and
tolerances that can be seen when chatter is not present. In order to decrease or eliminate
the presence of chatter the entire turning system must be studied. The turning system
may be very dynamic and therefore it may be difficult to study all aspects of it. One way
to study the dynamic system is to simplify it. A simplified system includes the actual
turning machine, machining tool, work piece, and parameters like stiffness and
dampening that link these items together and can be seen in figure 2.11. Once a
symplified dynamic system is available one can use stability lobe diagrams in order to
gather more information concerning the correct machine parameters in order to avoid
chatter. Stability lobe diagrams plot the spindle speed verses depth of cut. In order to
properly use stability lobe diagrams one must stay below the unstable region on the
diagram. Stability lobes will be discussed further in the next section.
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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2. Methodology
2.1 Work Piece Surface Description
Three different work piece surfaces are studied in this paper. The first surface is a
standard flat top work piece that is provided by Third Wave Systems AdvantEdge
software package. The second and third work pieces were produced by using the custom
tool feature in Third Wave Systems AdvantEdge. The second surface has an irregular
profile pattern with an approximate average wavelength of 0.5 mm. Wavelength refers to
the repeated length of a periodic function like a sign wave. It is noted in the plot below
as Lambda (). Wavelength is the distance between similar points of a repeating, periodic
signal. A real surface profile is a sum of many different individual functions, each with
its own wavelength. The next surface descriptive factor that is used is the profile peak.

Mean Line
Figure 2.0 Wavelength ()
Profile Peak
The profile peak is the region of the profile that is above the mean line and intersects the
mean line at each end. In figure 2.1 below, each shaded region is a profile peak. The
height of a peak is defined to be the point of maximum height within the region noted.
The next surface descriptive factor that is used is the profile valley.
Mean Line
Figure 2.1 Profile Peak
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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Profile Valley
The profile valley is the same as the peak but it is below the mean line instead of above it.
In figure 2.2 below, each shaded region is a profile valley. In this study the irregular
surface pattern that was produced has a profile peak and profile valley that are
approximately the same, with a length of 0.1 mm. This gives a total average valley to
peak length of 0.2 mm for the irregular surface work piece.
Mean Line
Figure 2.2 Profile Valley
The wavy surface work piece in this study has a larger wavelength than the irregular
surface, with an average wavelength of approximately 1mm. The wavy surface has
profile peaks and profile valleys that are approximately the same in length. These lengths
are approximately 0.055 mm each. This gives a total average valley to peak length of
0.11 mm for the wavy surface work piece. The standard flat work piece surface provided
in Third Wave Systems AdvantEdge software package can be seen below in figure 2.3.
The custom-made irregular surface work piece and wavy surface work piece are also
shown below in figures 2.4 and 2.5 respectively.
Figure 2.3 Standard Advantage Work piece Surface
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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Figure 2.4 Custom Irregular Work piece Surface
Figure 2.5 Custom Wavy Work Piece Surface
2.2 General Types of Machining Vibrations
There are three general types of machining vibrations. These are forced vibration, free
vibration, and self-excited vibration also know as regenerative chatter, which is the most
common. Forced vibration usually has frequency of the force applied and is dependent on
the ratio of the force frequency to the systems natural frequency. An example of forced
vibration is an unbalanced rotor or shaft, which inputs an exciting force into the system.
Figure 2.6 below shows an example of a forced vibration case.
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
9
Figure 2.6 Forced Vibration [7]
The next vibration is free vibration. Free vibration involves a characteristic natural
vibration that reveals the damping and natural frequency of the system. When dealing
with free vibrations external forces do not act on the system and the amplitude and
natural frequency decay over time. Free vibrations need an initial impact to get them
started, but the vibrations die out over a period of time. Strumming of a guitar string is an
example of a free vibration. Below in figure 2.7 is an example of free vibration.
Figure 2.7 Free Vibration [7]
The last vibration to be looked at is self-excited vibration, otherwise known as
regenerative vibration or regenerative chatter. It is regenerative because it feeds upon
itself and regenerates. When dealing with wavy surfaces the wave of current surface
causes the newly cut surface to produce increased waviness that grows on each pass.
Regenerative vibration usually starts as a slip-slide interaction between the tool and work
piece and grows into wavy surfaces. An example of an exaggerated wavy surface can be
seen below in figure 2.8. In this example the first wavy surface causes a build up of
forces for the proceeding cut and therefore makes the following cut become just as wavy
if not wavier than the previous cut. As this continues and the amplitudes of waviness
increase so does the likely hood of an increase in force/vibration oscillations and
therefore chatter.
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
10
Figure 2.8 Regenerative Vibration (chatter) [8]
2.3 Stability Lobes
There are known stability lobes that can be used in order to prevent chatter during turning
processes. Stability lobes allow for the selection of different axial depths of cut and
spindle speeds in order to avoid high force/vibrations and chatter. The stability lobes
have large gaps where the system can perform with out chatter. Selecting a turning
process below the unstable region can greatly increase the likely hood of producing a part
with out chatter. Figure 2.9 below is an example of a stability lobe diagram used in
turning. The stability zone is the area beneath the curve. This diagram points out that if
chatter is seen, the depth of cut and or spindle speeds can be changed in order to avoid
chatter.
Figure 2.9 Stability Lobes for the Prevention of Chatter [8]
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
11
Self-excited vibrations cause a constant input of energy into machining systems. This
creates vibrations at the cutting edge and therefore produces a regenerative wavy like
surface. When self-excited vibration is present the tool makes a pass over the work piece
and leaves a wavy surface behind, then when the next pass is made the tool is now
removing built up material from the previous pass while at the same time it is leaving
behind another wavy surface. This process is a continuous one that feeds upon itself and
can grow unstable with time. The work piece chip that is removed carries both the
waviness of the previous pass and that of the current pass. If this new cut produces chips
of variable thickness that would translate into variable forces on the tool and eventually
as undesired force/vibration oscillations and chatter. If the chip is in phase with the
previous cut it may cause a somewhat stable cut, but the force will vary through the cut
and will cause other undesirable effects. Below in figure 2.10 are cartoon examples of in
phase and out of phase cuts. Obviously the out of phase cutting process is the worse of
the two cases because it can be directly associated with chatter.
In Phase
Out of Phase
Figure 2.10 In Phase and Out of Phase Waviness
2.4 Governing Equations for Tool Cutting and Chatter.
Merchant in the middle 1940’s performed much of the most influential work on the
dynamics of metal cutting processes. In the 1950’s and 1960’s the Russians conducted
most of the cutting dynamic studies namely Zorev and Kudinov. There are theories that
the cutting process (feed rate, DOC etc) play a major role in tool cutting process stability,
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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but on the other hand there is a large amount of research that points to the machine tool
itself being the most important factor in creating dynamic instabilities. In this paper we
will only concentrate on the work piece surface and the tool cutting process. Below in
figure 2.11 is a complete tool and work piece system that gives a good pictorial
description of a dynamic tool and the results on the work piece.
Figure 2.11 Reference [5]
If the tool is flexible in the Y-direction only, the uncut chip thickness h(t) at any instant in
time is given by,
h(t) = ho+y(t-T)-y
Where h(t) is the uncut chip thickness ho is the initial chip thickness, y(t) and y(t-T) is
respectively the current and previous relative displacement between tool and work piece.
In order to calculate the cutting force assuming that the cutting forces is proportional to
the frontal area of the chip we have the cutting force in the Y direction as follows,
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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Fc(t) = Kf * a*[ho+y(t-T)-y]
Where Fc is the cutting force, kf is the work piece material cutting stiffness, and a is the
cutting depth.
The dynamic equation for motion in the Y direction for an orthogonal cutting system
considering regenerative chatter is given below.
my(t )  cy (t )  ky(t )  k f  a  [ho  y (t  T )  y (t )]
Where m is the mass of the system, y(t) and y(t-T) is respectively the current and previous
relative displacement between tool and work piece, a is the cutting depth, ho
Is the nominal undeformed chip thickness, T is the time delay (T=60/spindle speed in
rpm), kf is the work piece material cutting stiffness, with k being the effective stiffness.
2.5 Parametric Cases
Multiple AdvantEdge runs were performed with variances to the work piece surface,
depth of cut, feed rate, length of cut, cutting speed and tool dampening and stiffness
parameters. The different combinations of cases performed are summarized in table 2.1
below. In this table and throughout the rest of this paper, anything that has a numeric
value only i.e. 1, 2, 5 without a following alphabetic letter is the original run that had the
standard AdvantEdge flat surface work piece and original tool properties that are listed in
table 1.0. Runs that contain an alpha numeric value i.e. 1a, 2b, 5c ran with different work
piece materials and tool properties as described in table 2.1. That is any item with a
trailing “A” i.e. 1A, is a case with a irregular surface as shown in figure 2.4 and in
appendix A, all other tool and work piece properties remain the same as the original case.
Any item with a trailing “B” is the same as the original case but has a wavy surface as
can be seen in figure 2.5 and in appendix A. The last case, case “C” is the same as case
“B”, but with added tool stiffness in the Y direction of 9.6E8 N/m and damping in the Y
direction of 7000 N*sec/m. The actual plots of the runs listed in table 2.1 can be found in
Appendix A, using the same number and letter convention that has been defined here.
`
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
Runs
Original Case Had High Vibes
Original Case
Cutting Speed
(m/min)
Chatter2
Chatter8
Chatter18
Chatter23
100
200
100
100
Original Case Had Medium Vibes
Cutting Speed
Original Case
(m/min)
Chatter5
1,500
Chatter11
600
Original Case Had Low Vibes
Cutting Speed
Original Case
(m/min)
Chatter1
3,000
Chatter15
15,000
Chatter22
10,000
Chatter30
1,000
Chatter14
1,000
Initial
Depth of Cut Length of
Feed (mm)
Temperature
(mm)
Cut (mm)
0.15
0.15
0.5
1
Feed (mm)
0.15
0.15
Feed (mm)
0.15
0.15
0.5
1
1
20oC
20oC
20oC
o
20 C
1
2
1
1
2-4
4
2-4
2-4
Initial
Depth of Cut Length of
Temperature
(mm)
Cut (mm)
o
20 C
1
4
o
20 C
1
4
Initial
Depth of Cut Length of
Temperature
(mm)
Cut (mm)
20oC
1
2-4
o
20 C
1.5
2-4
o
20 C
1
4
o
20 C
1
2-4
o
20 C
1
2-4
Table 2.1 Parametric Cases
2
8
18
23
2A
8A
18A
23A
2B
8B
18B
23B
Wavy Surface
with Tool
Vibration in Y
direction (C)
2C
8C
18C
23C
Original
Surface A
Surface B
Surface C
5
11
5A
11A
5B
11B
Original
Surface A
Surface B
Surface C
1
15
22
30
14
1A
15A
22A
30A
14A
1B
15B
22B
30B
14B
1C
15C
22C
30C
14C
Original Case Irregular Wavy Surface
(flat surface) Surface (A)
(B)
2C5C
11C
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
3. Analysis:
3.1 Categorizing Vibrations/Forces into Levels
In table 2.1 force oscillations are divided into three different categories. These categories
are high force/vibration oscillations, medium force/vibration oscillations and low
force/vibration oscillations. An example of high force/vibration oscillations is shown
below in figure 3.1. It is categorized as high force/vibration oscillations due to the large
number of oscillations that occur in a short amount of time.
Figure 3.1 High Force/Vibration Oscillations
Figure 3.2 shows a medium force/vibration oscillation case. Medium force/vibration
oscillations are categorized, as medium because of the number of oscillations that occur
are less than the high force/vibration cases but less than the low force/vibration
oscillation cases.
Figure 3.2 Medium Force/Vibration Oscillations
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
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Figure 3.3 shows an example of the low force/vibration oscillation case. This is
categorized as low due to the very infrequent oscillations. The force/vibration oscillations
almost seem to be steady with very small variations through out the entire material
cutting process.
Figure 3.3 Low Force/Vibration Oscillations
4. Results and Discussion:
4.1 High Force/Vibration Oscillations
The first cases to be discussed are the high force/vibration cases. They were categorized
as high force/vibration cases during the original runs. The original runs have a standard
AdvantEdge flat work piece and do not include tool stiffness or dampening. The original
runs are designated with numeric values only (i.e. 2, 8, 18, 23). Case 2 had
force/vibration oscillation in the X and Y direction from approximately 400 N to –100 N.
Case 2A, which had an irregular work piece surface, had force oscillations similar to case
2 but at one point the oscillations increased to approximately 600 N then decreased to
approximately –400 N. As time progressed the force oscillations slowly decreased. Case
2A had a substantial increase in force oscillations from the original flat work piece. The
increase in force oscillations can be directly related to the irregular surface that was
present in 2A. Looking at case 2A’s force oscillations it is noted that there seems to be a
correspondence between the peaks and valleys of the work piece surface and the
force/vibration oscillations seen. Case 2B had similar oscillations to 2A, but 2B started
off with higher oscillations and slowly decreased to be similar to the original case 2 run.
The maximum force values seen in 2B were approximately 600 N to –400 N, much
higher than case 2, but approximately the same as 2A. The last case, 2C, had the same
setup as 2B but it had a tool with stiffness and dampening added to the Y direction. The
X direction did not have stiffness and dampening, which is a default values in
AdvantEdge. The force in the X direction mimicked case 2B, but in the Y direction the
force oscillations were much smaller. The reduction in force oscillations does not mean
lower displacement oscillations in fact C cases actually experienced much larger
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
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increases in displacement oscillations while the tool force seen were much smaller. C
cases included tool stiffness and dampening parameters, which allowed the tool to react
as it would in the real world. The tool would have displacement oscillations as the forces
increased or decreased. The displacement oscillations caused a much wavier surface than
the cases with out tool dynamics and therefore would be much more suseptable to
displacement oscillations the next time the tool passes over its surface. The increase in
displacement oscillations lead to increased likely hood chatter with each pass of the tool.
In figure 4.1 below it can be seen that case 2C has a surface waviness that is much greater
than previous work piece surfaces and other cases. Figure 4.2 is an example of a work
piece surface that was produced with out using stiffness and dampening in the Y direction
and therefor sees very little waviness. Figure 4.2 is case 2B with all parameter being the
same as 2C except for the added stiffness and dampening values in the Y direction.
Increased Waviness
Figure 4.1 Case 2C Increased Surface Waviness
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Less Waviness
Figure 4.2 Case 2B with Low Post Cut Surface Waviness
The next high force/vibration oscillation case to be studied is case 8. Case 8 had results
that were similar to Case 2 except that case 8 has a higher oscillation frequency. The
wavy surface cases 8B and 8C had a greater number of increasing and decreasing force
patterns over the cutting time. This is most likely a result of the increased cutting speed
used in case 8. Case 8 had a cutting speed that was twice as fast as case 2, but it was still
fairly slow at 200 m/min. Case 18 had the same setup as case 2, except its feed rate that
was set to 0.5 mm instead of the 0.15 mm. It is interesting to note that the force/vibration
oscillations were smaller when using an increased feed rate, but the overall force was
greater. The maximum and minimum force values for case 18 were approximately 700 N
to 200 N respectively, where the valley to max peak was approximately the same as case
2, but the overall magnitude of force was higher in case 18. This was expected since the
feed rate was much greater and greater feed rates cause an increase in the cutting force
because of the increase in the amount of material that has to be removed. 18A had very
large initial oscillations and at one point increased to approximately 850 N at the
maximum peak and -200 N at the valley. 18B had very similar results to the original case
18, but 18A’s oscillation frequency was much higher. 18C as with all of the C cases had
an increase in X direction oscillations. On the other hand the Y direction oscillations
decreased greatly. This was due to the tool dampening and stiffness that was present in
all of the C cases. Case 23 had the highest overall forces, but the oscillations were the
smallest of all of the high force/vibration oscillation cases. It makes sense that case 23
had the highest forces and low oscillations because it had a feed rate of 1mm twice that of
case 18 and more than six times that of cases 2 and 8. The increase in the feed rate
caused the waviness of the surface to be a much smaller factor than if the tool was closer
to the surface. Case 23C followed the previous trend having a much rougher surface cut
than 23, 23A, or 23B. Again this was expected due to the stiffness and dampening
coefficients added to case 23C. Similarities noticed with all of the high force/vibration
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oscillation cases were that they all had low cutting speeds. These cutting speeds were
less than 200 m/min. The high force/vibrations cases also showed that feed rate was a
factor in producing force/vibration oscillations but it was not as substantial as the cutting
speed. It was also seen that the depth of cut was a factor, but again it was not as
substantial as the cutting speed.
4.2 Medium Force/Vibration Oscillations
There were very few cases that I classified the original runs as medium force/vibration
cases. The only distinguishing factor that was noted with the medium force/vibration
cases was that they had speeds in-between the high and low force/vibration cases.
Medium force vibration cases are much less likely to cause chatter therefore a limited
amount of time will be spent discussing these results. The original case 5 had
force/vibration oscillation in the X direction from approximately 180N + 40N and force
in the Y direction was approximately 100N + 60N. Large force/vibration difference were
noticed when the surface was changed from the original flat case (5) to the irregular (5A),
and wavy surfaces (5B, 5C). See figure 4.3 for these noted differences. Case 11 runs had
very similar results to case 5 and will not be discussed further. The similarities noticed
with all of medium force/vibration oscillation cases was that they had medium cutting
speeds that ranged from approximately 400 m/min to approximately 2000 m/min.
Figure 4.3 Cases 5, 5A, 5B and 5C (from left to right top to bottom)
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
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4.2 Low Force/Vibration Oscillations
The low force/vibration cases include cases 1, 14, 15, 22 and 30. The low force vibration
cases like the medium cases are much less likely to cause vibrations and chatter therefore
a limited amount of time will be spent discussing the low force vibration results. The
original cases had force/vibration oscillation from the mean axis in the X direction from
approximately + 30N and in the Y direction of approximately + 40N. A large difference
was noticed as the surface was changed from the original flat (1,14,15, 22, 30) to the
irregular (1A, 14A, 15A, 22A, 30A), and wavy surfaces ((1B-C, 14B-C, 15B-C, 22B-C,
30B-C). The distinguishing factor with all of the low force/vibration oscillation cases
was that they had higher cutting speeds from 4000 m/min to approximately 16,000
m/min. Even though the depth of cut and feed rate had an impact on the overall
force/vibrations seen it again was not the most influential factor. Figure 4.4 shows an
example of the low force/vibration cases.
Figure 4.4 Original, A, B and C (from left to right top to bottom)
Conclusion:
It is evident that Third wave Systems AdvantEdge software is a robust means of
numerically solving for turning force/vibration oscillation problems. The observations
made in this paper can apply to many vibrations and chatter avoidance situations. The
finite element analysis software used produces results that are consistent with historical
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
21
data in the field of vibration and chatter analysis. It was also noted that the most
important factor in controlling force/vibration oscillations was to maximize the cutting
speed while minimizing the feed rate and depth of cut. This was beneficial because at
higher turning speeds it is more likely to be under the stability lobes and therefore in a
stable region without the presence of chatter. Even though the feed rate and depth of cut
were contributing factors to reducing the force/vibration oscillations, they were not as a
substantial factor as the cutting speed. Furthermore, the work piece surface, as expected,
had an impact on the amount of force/vibration oscillations seen during the turning
process. The original standard flat work piece surface saw fewer oscillations than the
irregular and the wavy surfaces. It was also noted that even though the forces in the Y
direction were less for the cases with added tool stiffness and dampening, the post cut
surfaces saw an increase in the amount of waviness, which is a less desired surface for
the avoidance of force/vibration oscillations and chatter. The increase in surface
waviness would lead to an increased likely hood of seeing greater forces/vibration
oscillations and therefore chatter with each future pass.
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
List of symbols:
m is the mass of the system (kg)
y(t) current displacement of the tool (m)
y(t-T) previous displacement during the previous pass (m)
a is the cutting depth
ho is the feed of the tool (m)
T is the time delay (T=60/spindle speed in rpm)
kf is the work piece material cutting stiffness, cutting constant (N/m2)
k is the stiffness of the system (N/m)
h(t) is the total uncut chip thickness (m)
Fc is the cutting force (N)
c damping coefficient (Ns/m)
Kcut cutting stiffness (N/m)
N spindle speed (RPM)
22
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
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References:
[1] Thomas Childs, Katsuhiro Maekawa, Toshiyuki Obikawa, Yasuo Yamane. Metal
Machining, Theory and Applications. John Wiley & Sons. New York, 2000.
[2] Model for simulation of chatter in turning. REF: Tlusy, G. Manufacturing Processes
and Equipment Prentice-Hall, NJ, 2000, pp. 570-575. 3. A. Ganguli, A. Deraemaekar,
M. Horodinca, A. Preumont. Active damping of chatter in machine tools –
demonstration with a “hardware in the loop” simulator, Accepted, Journal of Systems
and Control Engineering, Proceedings of the Institution of Mechanical Engineers, vol
219, N°15, p. 359-369, 2005
[3] Investigations of Process Damping Forces in Metal Cutting, Running title: Process
Damping Forces in Metal Cutting, Emily Stone & Suhail Ahmed Department of
Mathematics and Statistics Utah State University and Abe Askari & Hong Tat
Mathematics and Computing Technology The Boeing Company, August 23, 2005
[4] Sources of nonlinearities, chatter generation and suppression in metal cutting, Marian
Weircigroch and Erhan Budak, University of Aderdeen UK, Sabanci University,
Istanbul, Turkey., The Royal Society, Phil. Trans. R. Soc. Lond. A, 359 pp 663-693,
2001
[5] Active damping of chatter in machine tools – Demonstration with a "Hardware in the
Loop" simulator, A. Ganguli1¤, A. Deraemaeker1, M. Horodinca2, A. Preumont
Active Structures Lab, Universite Libre de Bruxelles, Brussels, Belgium.
Universitatea Technica "Gh.Asachi", Iasi, Romania.
[6] MMS online. Rapid Traverse Technology and Trends Spotted By The Editors of
Modern Machine Shop. Find The Right Speed For Chatter-Free Milling
http://www.mmsonline.com/articles/0300rt2.html
[7] Harper, Randy, Mold MakingTechnology, Chatter Myths: Pieces of the Puzzle in
Maximized Machining In today's avoid, Gardner Publications, Inc, copyright 2005
[8] Schrnitz, Tony; University of Florida, Davies, Matthew; University of NC, The
Dynamics of High Speed Machining, ASPE Tutorial, October 2003
[9] Wiercigroch, Marian and Krivtxov Anton, Frictional chatter in orthogonal metal
cutting, The Royal Society, Phil. Trans. R. Soc. Lond. A, 359 pp 713-738, 2001
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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[10] Sims, Neil D., The Self-Excitation Damping Ratio: A Chatter Criterion for TimeDomain Milling Simulations, Journal of Manufacturing Science and Engineering,
ASME, Vol 127, pp 433-445, AUGUST 2005
[11] E. Buckwar, R. Kuske B. L'Esperance, T. Soo, Noise-sensitivity in machine tool
vibrations, Institut f•ur Mathematik Humboldt-University at Berlin, DE, Department
of Mathematics, University of British Columbia, Vancouver, BC Canada, University
of Montreal, Quebec, Canada, Department of Mathematics, University of British
Columbia, Vancouver, BC Canada
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
Appendix A - Third wave Systems AdvantEdge Runs
1
1A
2C
1B
1
C
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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2A
2B
2C2C
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5
5A
5B
5
C
Engineering Seminar MANE6900HEG, Rensselaer Hartford, Spring 2006
Vibration and Chatter analysis using Third Wave System’s AdvantEdge - David Singletary
4-20-2006
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8B
28
8A
8
C
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11
11
A
11B
11
C
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14
$4
4
14A
14B
14C
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15
15A
15B
15C
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18B
32
18A
18C
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22
22A
22B
22C
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23B
34
23A
23C
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30
30A
30B
30C