Abstract

Computer numerical control (CNC) worktable is the most important part of CNC machines. The CNC worktable exhibits complex nonlinear dynamic behaviors in the milling process. The physical model and mathematical model of CNC worktable are presented, where the nonlinear factors such as clearance and friction are considered. The primary resonance of computer numerical control worktable with clearance and friction under harmonic excitation is investigated. The approximate analytical solution of primary resonance is obtained by using the averaging method. The stability condition of the steady-state solution is also exhibited. It is found that the clearance affects the dynamic characteristics of the system in the form of equivalent nonlinear stiffness, and the friction coefficient acts in the form of equivalent nonlinear damping. The correctness of the approximate analytical solutions is verified by comparing the numerical results with the approximate analytical solutions. The approximate analytical solution is in good agreement with its corresponding numerical solution. The effects of clearance and friction on the dynamic characteristics of the system are analyzed in detail. The stick-slip vibration induced by friction is also analyzed by phase portrait at low feed velocity of machine tool. The results can provide a reference for the dynamic analysis of CNC worktable.

References

References
1.
Muvengei
,
O.
,
Kihiu
,
J.
, and
Ikua
,
B.
,
2012
, “
Dynamic Analysis of Planar Multi-Body Systems With LuGre Friction at Differently Located Revolute Clearance Joints
,”
Multibody Syst. Dyn.
,
28
(
4
), pp.
369
393
.10.1007/s11044-012-9309-8
2.
Xiang
,
L.
,
Zhang
,
Y.
,
Gao
,
N.
,
Hu
,
A.
, and
Xing
,
J.
,
2018
, “
Nonlinear Dynamics of a Multistage Gear Transmission System With Multi-Clearance
,”
Int. J. Bifurcation Chaos
,
28
(
03
), pp.
1850034
1850595
.10.1142/S0218127418500347
3.
Zheng
,
E.
,
Zhu
,
R.
,
Zhu
,
S.
, and
Lu
,
X.
,
2016
, “
A Study on Dynamics of flexible Multi-Link Mechanism Including Joints With Clearance and Lubrication for Ultra-Precision Presses
,”
Nonlinear Dyn.
,
83
(
1–2
), pp.
137
159
.10.1007/s11071-015-2315-7
4.
Duan
,
L.
,
An
,
Z.
,
Yang
,
R.
, and
Fu
,
Z.
,
2016
, “
Mechanical Model of Coupling Rolling and Sliding Friction in Real-Time Non-Clearance Precision Ball Transmission
,”
Tribol. Int.
,
103
, pp.
218
227
.10.1016/j.triboint.2016.06.032
5.
Zhang
,
Y.
,
Chen
,
D. W.
, and
Yu
,
H. W.
,
2018
, “
Nonlinear Bifurcation Analysis of Landing Gear Shimmy Considering Freeplay
,”
Aeronaut. Comput. Tech.
,
48
(
1
), pp.
53
57
.10.3969/j.issn.1671-654X.2018.01.014
6.
Zhao
,
Y.
, and
Bai
,
Z. F.
,
2011
, “
Dynamics Analysis of Space Robot Manipulator With Joint Clearance
,”
Acta Astronaut.
,
68
(
7–8
), pp.
1147
1155
.10.1016/j.actaastro.2010.10.004
7.
Hu
,
H. Y.
,
1994
, “
Numerical Analysis to Periodic Response Nonsmooth Dynamic Systems of High-Dimension
,”
J. Solid Mech.
,
15
(
2
), pp.
135
143
.10.19636/j.cnki.cjsm42-1250/o3.1994.02.006
8.
Ding
,
W. C.
,
Zhang
,
Y. Q.
, and
Xie
,
J. H.
,
2008
, “
Analysis of Nonlinear Dynamics of Dry Friction Oscillators With Symmetric Clearance
,”
Tribology
,
28
(
2
), pp.
155
160
.10.16078/j.tribology.2008.02.014
9.
Luo
,
A. C. J.
, and
Zwiegart
,
P.
,
2008
, “
Existence and Analytical Predictions of Periodic Motions in a Periodically Forced, Nonlinear Friction Oscillator
,”
J. Sound Vib.
,
309
(
1–2
), pp.
129
149
.10.1016/j.jsv.2007.06.067
10.
Ji
,
J. C.
, and
Hansen
,
C. H.
,
2005
, “
On the Approximate Solution of a Piecewise Nonlinear Oscillator Under Super-Harmonic Resonance
,”
J. Sound Vib.
,
283
(
1–2
), pp.
467
474
.10.1016/j.jsv.2004.05.033
11.
Feng
,
R. C.
,
Rui
,
Z. Y.
,
Wu
,
Q.
, and
Li
,
H. Y.
,
2012
, “
Nonlinear Vibration Characteristics Analysis of CNC Machine Tool Feed System
,”
Adv. Mater. Res.
,
472–475
, pp.
626
631
.10.4028/www.scientific.net/AMR.472-475.626
12.
Zhao
,
F.
,
Chen
,
J.
, and
Zhang
,
C.
,
2014
, “
Vibration Analysis of High-Speed Ball-Screw Drive in Machine Tool Feed System
,” 13th International Conference on Control Automation Robotics & Vision (
ICARCV
), Singapore, Dec. 10–12, pp.
1604
1608
. 10.1109/ICARCV.2014.7064555
13.
Wang
,
B. S.
,
Zuo
,
J. M.
, and
Wang
,
M. L.
,
2011
, “
Analysis and Compensation of Stiffness in CNC Machine Tool Feed System
,”
J. Adv. Manuf. Syst.
,
10
(
01
), pp.
77
84
.10.1142/S0219686711002004
14.
Behzad
,
M.
, and
Bastami
,
A. R.
,
2004
, “
Effect of Centrifugal Force on Natural Frequency of Lateral Vibration of Rotating Shafts
,”
J. Sound Vib.
,
274
(
3–5
), pp.
985
995
.10.1016/S0022-460X(03)00659-X
15.
Verl
,
A.
, and
Frey
,
S.
,
2012
, “
Improvement of Feed Drive Dynamics by Means of Semi-Active Damping
,”
CIRP Ann.-Manuf. Technol.
,
61
(
1
), pp.
351
354
.10.1016/j.cirp.2012.03.135
16.
Zhao
,
P. B.
,
Huang
,
J.
, and
Shi
,
Y. Y.
,
2017
, “
Nonlinear Dynamics of the Milling Head Drive Mechanism in Five-Axis CNC Machine Tools
,”
Int. J. Adv. Manuf. Technol.
,
91
(
9–12
), pp.
3195
3210
.10.1007/s00170-017-9989-6
17.
Wu
,
Q.
,
Rui
,
Z. Y.
, and
Yang
,
J. J.
,
2014
, “
Parametric Analysis of Influencing Vibration Characteristics of Workbench of CNC Machines
,”
China Mech. Eng.
,
25
(
19
), pp.
2588
2591
. http://www.cmemo.org.cn/CN/Y2014/V25/I19/2588
18.
Wu
,
Q.
, and
Yang
,
J. J.
,
2013
, “
The Vibration Characteristic Analysis of Feed System of CNC Machine Tool
,”
Appl. Mech. Mater.
,
482
, pp.
169
173
.10.4028/www.scientific.net/AMM.482.169
19.
Zhang
,
H. D.
,
Tan
,
Q. C.
, and
Pei
,
Y. C.
,
2008
, “
The Dynamic Analysis of the Worktable of Machines
,”
Mach. Tool Hydraulic Pressure
,
36
(
9
), pp.
68
71
.10.3969/j.issn.1001-3881.2008.09.022
20.
Choi
,
Y. H.
,
Cha
,
S. M.
,
Hong
,
J. H.
, and
Choi
,
J. H.
,
2004
, “
A Study on the Vibration Analysis of a Ball Screw Feed Drive System
,”
Mater. Sci. Forum
,
471–472
, pp.
149
154
.10.4028/www.scientific.net/MSF.471-472.149
21.
Wang
,
L.
,
Wu
,
B.
,
Du
,
R.
, and
Yang
,
S.
,
2008
, “
Dynamic Characteristics of NC Table With SVD
,”
Front. Mech. Eng. China
,
3
(
4
), pp.
385
391
.10.1007/s11465-008-0052-z
22.
Wang
,
L.
,
Wu
,
B.
,
Du
,
R.
, and
Yang
,
S.
,
2009
, “
Dynamic Characteristics of an NC Table With Phase Space Reconstruction
,”
Front. Mech. Eng. China
,
4
(
2
), pp.
179
183
.10.1007/s11465-009-0018-9
23.
Liu
,
L.
, and
Wu
,
Z.
,
2015
, “
Comprehensive Parameter Identification of Feed Servo Systems With Friction Based on Responses of the Worktable
,”
Mech. Syst. Signal Process.
,
64–65
, pp.
257
265
.10.1016/j.ymssp.2015.04.012
24.
Yeh
,
S. S.
, and
Su
,
H. C.
,
2011
, “
Development of Friction Identification Methods for Feed Drives of CNC Machine Tools
,”
Int. J. Adv. Manuf. Technol.
,
52
(
1–4
), pp.
263
278
.10.1007/s00170-010-2720-5
25.
Wu
,
N. X.
,
Sun
,
Q. H.
, and
Feng
,
J. H.
,
2004
, “
Study of Influence on Machine-Tool Dynamic Characteristics of Nonlinear Friction and Its Compensation
,”
J. Southeast Univ. (Nat. Sci. Ed.)
,
34
(
6
), pp.
771
774
.10.3969/j.issn.1001-0505.2004.06.012
26.
Yang
,
J. J.
,
Wu
,
Q.
,
Rui
,
Z. Y.
, and
Lei
,
C. L.
,
2013
, “
Research on Dynamical Characteristics for the Feed System Considering Nonlinear Friction Force
,”
Appl. Mech. Mater.
,
365–366
, pp.
299
303
.10.4028/www.scientific.net/AMM.365-366.299
27.
Dong
,
Y. H.
, and
Tian
,
S. L.
,
2013
, “
Simulation Analysis of Friction Nonlinear for NC Servo System
,”
Appl. Mech. Mater.
,
274
, pp.
642
645
.10.4028/www.scientific.net/AMM.274.642
28.
Yao
,
L.
,
Jiang
,
M.
, and
Huang
,
B. D.
,
2007
, “
The Modeling and Simulation of the NC Lathe Feed Drive System
,”
J. Southwest Univ. Sci. Technol.
,
22
(
1
), pp.
56
61
. 10.3969/j.issn.1671-8755.2007.01.013
29.
Luo
,
L.
,
Zhang
,
W. M.
,
Zhou
,
M. J.
, and Fleischer, J.,
2015
, “
Dynamic Characteristics Modeling and Simulation of Ball Screw Feed Drive System Based on Lumped Mass Model
,”
J. Agric. Mach.
,
46
(
12
), pp.
370
377
.10.6041/j.issn.1000-1298.2015.12.050
30.
Zhu
,
X. D.
,
2010
,
Research on Positioning Precision Control of Servo–Actuated Feeding System of High Speed Machine Tools
,
Harbin Engineering University
, Harbin, China.
31.
Liu
,
L. L.
,
Liu
,
H. Z.
,
Wu
,
Z. Y.
, and Zhang, M. H.,
2010
, “
Modeling and Analysis of Machine Tool Feed Servo Systems With Friction and Backlash
,”
J. Agric. Mach.
,
41
(
11
), pp.
212
218
.http://www.j-csam.org/jcsam/ch/reader/view_abstract.aspx?file_no=20101142&flag=1
32.
Vicente
,
D. A.
,
Hecker
,
R. L.
,
Villegas
,
F. J.
, and
Flores
,
G. M.
,
2012
, “
Modeling and Vibration Mode Analysis of a Ball Screw Drive
,”
Int. J. Adv. Manuf. Technol.
,
58
(
1–4
), pp.
257
265
.10.1007/s00170-011-3375-6
33.
Frey
,
S.
,
Dadalau
,
A.
, and
Verl
,
A.
,
2012
, “
Expedient Modeling of Ball Screw Feed Drives
,”
Prod. Eng. Res. Develop.
,
6
(
2
), pp.
205
211
.10.1007/s11740-012-0371-0
34.
Rebelein
,
C.
,
Vlacil
,
J.
, and
Zaeh
,
M. F.
,
2017
, “
Modeling of the Dynamic Behavior of Machine Tools: Influences of Damping, Friction, Control and Motion
,”
Prod. Eng. Res. Develop.
,
11
(
1
), pp.
61
74
.10.1007/s11740-016-0704-5
35.
Constantin
,
G.
,
2018
,
Dynamic Definition of Machine Tool Feed Drive Models in Advanced Machine Tools
. In Proceedings of Third International Conference on the Industry 4.0 Model for Advanced Manufacturing (Lecture Notes in Mechanical Engineering),
J.
Ni
,
V.
Majstorovic
,
D.
Djurdjanovic
, eds.,
AMP Springer
,
Cham, Switzerland
.
36.
Pislaru
,
C.
,
Ford
,
D.
, and
Holroyd
,
G.
,
2004
, “
Hybrid Modelling and Simulation of a Computer Numerical Control Machine Tool Feed Drive
,”
Proc. Inst. Mech. Eng., Part I
,
218
(
2
), pp.
111
120
.10.1177/095965180421800205
37.
Zinjade
,
P. B.
, and
Mallik
,
A. K.
,
2007
, “
Impact Damper for Controlling Friction-Driven Oscillations
,”
J. Sound Vib.
,
306
(
1–2
), pp.
238
251
.10.1016/j.jsv.2007.05.017
38.
Argatov
,
I.
, and
Butcher
,
E. A.
,
2011
, “
On the Separation of Internal and Boundary Damage in Slender Bars Using Longitudinal Vibration Frequencies and Equivalent Linearization of Damaged Bolted Joint Response
,”
J. Sound Vib.
,
330
(
13
), pp.
3245
3256
.10.1016/j.jsv.2011.01.023
39.
Sanders
,
J. A.
,
Verhulst
,
F.
, and
Murdock
,
J.
,
2007
,
Averaging Methods in Nonlinear Dynamical Systems
,
Springer
,
New York
.
40.
Thomsen
,
J. J.
, and
Fidlin
,
A.
,
2003
, “
Analytical Approximations for Stick-Slip Vibration Amplitudes
,”
Int. J. Non-Linear Mech.
,
38
(
3
), pp.
389
403
.10.1016/S0020-7462(01)00073-7
41.
Liu
,
Z. J.
,
2012
,
Science Computing Books of MATLAB
,
Publishing House of Electronics Industry
,
Beijing
.
42.
Yang
,
X.
,
Liu
,
H.
,
Lu
,
D.
, and
Zhao
,
W.
,
2018
, “
Investigation of the Dynamic Electromechanical Coupling Due to the Thrust Harmonics in the Linear Motor Feed System
,”
Mech. Systems Signal Process.
,
111
, pp.
492
508
.10.1016/j.ymssp.2018.03.062
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