project report on simulink analysis of tool chtter vibration on lathe
TRANSCRIPT
Investigation of tool chatter in turning operation on lathe
Submitted by:Aakash Gautam (111601)
Abhay Rai (111603)Aditya Kumar (111610)
Devanshu Yadav (111628)Vijay Pratap (111689)
Under the guidance: Dr. Bhagat Singh Assistant Professor(SG)
Submitted to: Dr. Arun Kumar PandeyAssistant Professor(SG)
• Objectives
• Introduction
• Review of literature
• Theoretical analysis
• Simulink Model
• Fourier Frequency Spectrum
• Conclusion
OVERVIEW
OBJECTIVES
• Study of various parameters resulting in tool chatter during
orthogonal turning operation.
• Theoretical Analysis using Spring-Mass model.
• Simulation of vibration signal of tool chatter in turning operation
using MATLAB Simulink.
• Effect of various parameters on Tool Chatter.
INTRODUCTION
• What is tool chatter?
Tool chatter is defined as the relative movement between the work
piece and the cutting tool.
It results from vibration
Tool bounces in and out of the work piece
The vibrations result in waves on the machined surface
This affects typical machining processes, such as turning,
milling and drilling etc. It results in chatter marks
Chatter marks are irregular surface flaws developed on
the work piece during turning operation on a lathe, due to
machining vibrations
Results in a poor surface finish, high-pitch noise and
accelerated tool wear
This in turn reduces machine tool life, reliability and
safety of the machining operation
LITERATURE SURVEY
(1) Chatter was first identified as a limitation of machining productivity by Taylor [1], who
carried out extensive studies on metal- cutting processes as early as in the1800s.
(2) Arnold [2] examined numerous influences to which a tool is subjected during cutting
analytically as well as experimentally for lathes and other machines.
(3) Chatter is caused by instability in the cutting processes, which was first understood by
Tobias and Fishwick [3].
(4) Tlusty and Polacek [4] presented a stability condition in which stability limits can be
calculated based upon the system dynamics for orthogonal cutting.
(5) Knight [5] presented experimental stability charts for turning with a simplified
machine–tool structure model for various cutting conditions.
(6) Shanker [6] proposed a general method for the analytical evaluation of the stability
limit in oblique turning of a slender workpiece, held between the centers.
(7) Nurulamin [7] studied the mechanism of instability of chip formation on micro section
metallographic specimens of chip roots, received by instantly stopping the cutting process at
different phases of the full cycle of instability as well as on micro-section metallographic
specimens of the chip.
(8) Rahman and Ito [8] presented a method to determine the onset of chatter by online
measurement of the horizontal deflection of the workpiece using eddy current type
displacement pick- ups.
(9) Lee et al. [9] showed that the ploughing force acts like an additional damper in the
system after applying the ploughing force model in numerical simulations.
(10) Chiou et al. [10] approximated this chatter model with a linear model with first order
Fourier transform.
(11) Dimla and Lister [11] have used tool-post dynamometer as a force sensor to measure all
three cutting force components to find the static and dynamic components of the cutting
force.
(12) Chiou et al. [12] used an AE sensor to detect chatter in the presence of tool wear.
(13) Clancy and Shin [13] presented a three-dimensional frequency domain chatter
stability prediction model for face turning by including tool wear in the model. The results
showed that the flank wear and the stability limit were directly proportional to each other.
(14) Mahdavinejad [14] predicted the stability of a turning operation by finite element
analysis using ANSYS software. The flexibility of the machine’s structure, workpiece and
tool has been considered in this FEA model.
(15) Budak and Ozlu [15] compared a SDoF and multi-dimensional stability models by
several simulations and chatter experiments.
(16) Altintas et al. [16] presented a linear model to predict chatter stability.
(17) Suzuki et al. [17] presented an SDoF and a 2DoF analytical model by defining
equivalent transfer function to understand the effects of the cross transfer function and the
cutting force ratio on chatter stability.
(18) Urbikain et al. [18] presented an algorithm to predict stability in straight turning of a
flexible workpiece by Chebyshev collocation method.
A mathematical model considering a Single Degree of Freedom (SDoF)
orthogonal turning process with a flexible tool and relatively rigid work piece is
considered as shown in Fig. 2. The model incorporates various forces acting on
the physical system like the inertia force, damping force, spring force and the
cutting force.
Fig. 2. SDoF orthogonal turning model
Spring-Mass Model
When this SDoF flexible tool is cutting a rigid work piece, the equation of
motion of the dynamic system can be modeled in the radial (feed) direction as:
fmx t cx t kx t F t
f fF t K b x t T x t
is the cutting coefficient in feed direction,
b is the chip width (width of cut),
T is the time delay between current time and previous time,
[x(t-T)-x(t)] is the dynamic chip thickness due to tool vibration.
fK
(1)
(2)
The tool parameters m, k and c are the mass, stiffness and damping co-efficient,
respectively,
Substituting Eq.(2) in Eq.(1) and dividing by m gives:
fK bc k kx t x t x t x t T x tm m k m
(3)
Applying Laplace transform and using relations,
2n
km
2 ncm
fK bk
and assuming,
2 2 22 1sTn n ns s e (4)
From Eq. (4), the transfer function of the system with a sharp tool can be
obtained by direct derivation from differential equation as:
2 21
2 n ns
s s
(5)
Substituting into Eq.(5),where is the chatter vibration frequency,
the real and imaginary parts of the transfer function are found as:
s j
2 2nGR
2 nHR
(Real part)
(Imaginary part)
2 22 2 22n nR where
FACTORS INFLUENCING TOOL CHATTER
Speed
Feed
Depth of cut
Cutting parameters
The cutting parameters affecting tool chatter are shown in Figure
below in turning are:
Speed
Feed
Depth of cut (DOC)
Speed: At slow speed (relative to the vibration frequency),
as speed increases, chatter gets more significant.
Feed: Does not greatly influence stability, but control
amplitude of vibration.
DOC: The primary cause and control of chatter.
SIMULINK Used to model, analyze and simulate dynamic systems using
block diagrams.
Fully integrated with MATLAB , easy and fast to learn and
flexible.
It has comprehensive block library which can be used to
simulate linear, non–linear or discrete systems – excellent
research tools.
C codes can be generated from Simulink models for
embedded applications and rapid prototyping of control
systems.
SIMULINK MODEL
Aforesaid simulink model is used to generate time domain
signal at different cutting parameters.
Some of the signal in time domain are presented.
Further Fast Fourier Transformation (FFT) is done on these
signal in order to extract the frequency features of the
respective signals:
2.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-10
-5
0
5
10
15A
mpl
itude
( m
)
-10
-5
0
5
10
15
Fig 3. Simulated vibration signal.(a) Case1: depth of cut: 1mm.
Fig. 4. Simulated vibration signal.(a) Case2: depth of cut: 2mm.
0.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-30
-20
-10
0
10
20
30
Am
plitu
de (
m)
-30
-20
-10
0
10
20
30
1.xls
c:\documents and settings\b.singh\desktop\tc4\amplitude\1.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-30
-20
-10
0
10
20
30
40
Am
plitu
de (
m)
-30
-20
-10
0
10
20
30
40
Fig. Simulated vibration signal.(a) Case3: depth of cut: 3mm
5.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-1
-0.5
0
0.5
1
1.5
Am
plitu
de (
m)
-1
-0.5
0
0.5
1
1.5
Fig. Simulated vibration signal.(a) Case 4: feed: 0.6mm/rev
3.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-3
-2
-1
0
1
2
3
4
Am
plitu
de (
m)
-3
-2
-1
0
1
2
3
4
Fig. Simulated vibration signal.(a) Case 5: feed: 0.8mm/rev
2.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-10
-5
0
5
10
15
Am
plitu
de (
m)
-10
-5
0
5
10
15
Fig. Simulated vibration signal.(a) Case 6: feed: 1.0 mm/rev
9.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-0.1
-0.05
0
0.05
0.1
0.15
Am
plitu
de (
m)
-0.1
-0.05
0
0.05
0.1
0.15
Fig. Simulated vibration signal.(a) Case 7: speed 1200 rpm
11.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Am
plitu
de (
m)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Fig. Simulated vibration signal.(a) Case 8: speed 1600 rpm
8.xls
0 0.2 0.4 0.6 0.8 1Time (s)
-0.75
-0.5
-0.25
0
0.25
0.5
0.75A
mpl
itude
( m
)
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
Fig. Simulated vibration signal.(a) Case 9: speed 2000 rpm
From these time domain spectrum it is quite evident that the depth of cut is the
most influential parameter. With the increase in depth of cut chatter increases.
Feed is the second important parameter governing chatter. With the increase in
feed chatter increases.
Speed is the third important parameter controlling chatter. With the increase in
feed chatter increases.
5.xls
Fourier Frequency Spectrum
30.202
31.772
46.346
51.292
0 100 200 300 400 500Frequency (Hz)
0
0.4
0.8
1.2
1.6
2
Am
plitu
de (
m)
0
0.4
0.8
1.2
1.6
2
2.xls
Fourier Frequency Spectrum
36.995
0 100 200 300 400 500Frequency (Hz)
0
0.5
1
1.5
2
2.5A
mpl
itude
( m
)
0
0.5
1
1.5
2
2.5
1.xls
Fourier Frequency Spectrum
251.91
0 100 200 300 400 500Frequency (Hz)
0
0.6
1.2
1.8
2.4
3A
mpl
itude
( m
)
0
0.6
1.2
1.8
2.4
3
From these frequency spectrum it is quite evident that the instantaneous
frequency is spread throughout.
Moreover, in these spectrum we are not able to interpret the time information
i.e. at which corresponding time the frequency peaks are not desirable.
So, it is imperative that in order to have better understanding and analysis of
the chatter in turning we must go for other alternative approach.
Conclusions
• In this study, a chatter identification method for turning process was
presented.
• Simulink model was developed to simulate tool chatter in noisy
environment.
• It was observed , depth of cut, feed and speed governs the phenomenon
of tool chatter.
• Depth of cut is the predominant governing factor.
References
[1] F. Taylor, On the art of cutting metals, Transactions of ASME 28 (1907).
[2] R.N. Arnold, The mechanism of tool vibration in the cutting of steel, Proceedings of the Institution
of Mechanical Engineers 154 (1946) 261–284.
[3] S.A. Tobias, W. Fishwick, The chatter of lathe tools under orthogonal cutting conditions,
Transactions of ASME 80 (1958) 1079–1088.
[4] J. Tlusty, M. Polacek, The stability of machine tools against self excited vibrations in machining,
in: Proceedings of the International Research in Production Engineering Conference, Pittsburgh, PA,
ASME, New York, 1963, pp. 465–474.
[5] W.A. Knight, Chatter in turning: some effects of tool geometry and cutting conditions, International
Journal of Machine Tool Design and Research 12 (1972) 201–220.
[6] A. Shanker, An analysis of chatter vibration while turning slender work- pieces between centres,
Annals of CIRP 25 (1976) 273–276.
[7] A.K.M. Nurulamin, Investigation of the mechanism of chatter formation during metal cutting
process, Mechanical Engineering Res Bulleting 6 (1983) 11–18.
[8] M. Rahman, Y. Ito, Stability analysis of chatter vibration in turning processes, Journal of Sound and
Vibration 102 (1985) 515–525.
[9] B. Lee, Y. Tarng, S. Ma, Modeling of the force in chatter vibration, International Journal of Machine
Tools and Manufacture 35 (1995) 951–962.
[10] Y.S. Chiou, E.S. Chung, S.Y. Liang, Analysis of tool wear effect on chatter stability in turning,
International Journal of Mechanical Sciences 37 (1995) 391–404.
[11] D.E. Dimla, P.M. Lister, On-line metal cutting tool condition monitoring: I: Force and vibration
analyses, International Journal of Machine Tools and Manufacture 40 (2000) 739–768.
[12] R.Y. Chiou, S.Y. Liang, Analysis of acoustic emission in chatter vibration with tool wear effect in
turning, International Journal of Machine Tools and Manufacture 40 (2000) 927–941.
[13] B.E. Clancy, Y.C. Shin, A comprehensive chatter prediction model for face turning operation
including tool wear effect, International Journal of Machine Tools and Manufacture 42 (2002) 1035–
1044.
[14] R. Mahdavinejad, Finite element analysis of machine and workpiece instability in turning,
International Journal of Machine Tools and Manufacture 45 (2005) 753–760.
[15] E. Budak, E. Ozlu, Analytical modeling of chatter stability in turning and boring operations: a
multidimensional approach, CIRP Annals—Manufacturing Technology 56 (2007) 401–404.
[16] Y. Altintas, M. Eynian, H. Onozuka, Identification of dynamic cutting force coefficients and
chatter stability, CIRP Annals—Manufacturing Technology 57 (2008) 371–374.
[17] N. Suzuki, K.N.E. Shamoto, K. Yoshino, Effect of cross transfer function on chatter stability in
plunge cutting, Journal of Advanced Mechanical Design, Systems, and Manufacturing 4 (2010) 883–
891.
[18] G. Urbikain, L. N. Lopez de Lacalle, F. J. Campa, A. Fernandez, A. Elias, Stability prediction in
straight turning of a flexible workpiece by collocation method, International Journal of Machine Tools
and Manufacture 54–55 (2012) 73–81.