Abstract

Highly dynamic machining forces can cause excessive and unstable vibrations when industrial robots are used to perform high-force operations such as milling and drilling. Implementing appropriate optimization and control strategies to suppress vibrations during robotic machining requires accurate models of the robot’s vibration response to the machining forces generated at its tool center point (TCP). The existing models of machining vibrations assume the linearity of the structural dynamics of the robotic arm. This assumption, considering the inherent nonlinearities in the robot’s revolute joints, may cause considerable inaccuracies in predicting the extent and stability of vibrations during the process. In this article, a single degree-of-freedom (SDOF) system with the nonlinear restoring force is used to model the vibration response of a KUKA machining robot at its TCP (i.e., machining tool-tip). The experimental identification of the restoring force shows that its damping and stiffness components can be approximated using cubic models. Subsequently, the higher-order frequency response functions (HFRFs) of the SDOF system are estimated experimentally, and the parameters of the SDOF system are identified by curve fitting the resulting HFRFs. The accuracy of the presented SDOF modeling approach in capturing the nonlinearity of the TCP vibration response is verified experimentally. It is shown that the identified models accurately predict the variation of the receptance of the nonlinear system in the vicinity of well-separated peaks, but nonlinear coupling around closely spaced peaks may cause inaccuracies in the prediction of system dynamics.

References

References
1.
Chen
,
Y.
, and
Dong
,
F.
,
2013
, “
Robot Machining: Recent Development and Future Research Issues
,”
Int. J. Adv. Manuf. Technol.
,
66
(
9–12
), pp.
1489
1497
. 10.1007/s00170-012-4433-4
2.
Verl
,
A.
,
Valente
,
A.
,
Melkote
,
S.
,
Brecher
,
C.
,
Ozturk
,
E.
, and
Tunc
,
L. T.
,
2019
, “
Robots in Machining
,”
CIRP. Ann.
,
68
(
2
), pp.
799
822
. 10.1016/j.cirp.2019.05.009
3.
Altintas
,
Y.
, and
Weck
,
M.
,
2004
, “
Chatter Stability of Metal Cutting and Grinding
,”
CIRP. Ann.
,
53
(
2
), pp.
619
642
. 10.1016/S0007-8506(07)60032-8
4.
Quintana
,
G.
, and
Ciurana
,
J.
,
2011
, “
Chatter in Machining Processes: A Review
,”
Int. J. Mach. Tools. Manuf.
,
51
(
5
), pp.
363
376
. 10.1016/j.ijmachtools.2011.01.001
5.
Munoa
,
J.
,
Beudaert
,
X.
,
Dombovari
,
Z.
,
Altintas
,
Y.
,
Budak
,
E.
,
Brecher
,
C.
, and
Stepan
,
G.
,
2016
, “
Chatter Suppression Techniques in Metal Cutting
,”
CIRP Ann.
,
65
(
2
), pp.
785
808
. 10.1016/j.cirp.2016.06.004
6.
Li
,
J.
,
Li
,
B.
,
Shen
,
N.
,
Qian
,
H.
, and
Guo
,
Z.
,
2017
, “
Effect of the Cutter Path and the Workpiece Clamping Position on the Stability of the Robotic Milling System
,”
Int. J. Adv. Manuf. Technol.
,
89
(
9–12
), pp.
2919
2933
. 10.1007/s00170-016-9759-x
7.
Altintaş
,
Y.
, and
Budak
,
E.
,
1995
, “
Analytical Prediction of Stability Lobes in Milling
,”
CIRP. Ann.
,
44
(
1
), pp.
357
362
. 10.1016/S0007-8506(07)62342-7
8.
Eksioglu
,
C.
,
Kilic
,
Z.
, and
Altintas
,
Y.
,
2012
, “
Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems
,”
ASME J. Manuf. Sci. Eng.
,
134
(
6
), p.
061006
. 10.1115/1.4007622
9.
Yang
,
Y.
,
Zhang
,
W.-H.
,
Ma
,
Y.-C.
, and
Wan
,
M.
,
2016
, “
Chatter Prediction for the Peripheral Milling of Thin-Walled Workpieces With Curved Surfaces
,”
Int. J. Mach. Tools. Manuf.
,
109
(
1
), pp.
36
48
. 10.1016/j.ijmachtools.2016.07.002
10.
Cordes
,
M.
,
Hintze
,
W.
, and
Altintas
,
Y.
,
2019
, “
Chatter Stability in Robotic Milling
,”
Rob. Comput. Int. Manuf.
,
55
(
1
), pp.
11
18
. 10.1016/j.rcim.2018.07.004
11.
Insperger
,
T.
,
Mann
,
B. P.
,
Stépán
,
G.
, and
Bayly
,
P. V.
,
2003
, “
Stability of Up-Milling and Down-Milling, Part 1: Alternative Analytical Methods
,”
Int. J. Mach. Tools. Manuf.
,
43
(
1
), pp.
25
34
. 10.1016/S0890-6955(02)00159-1
12.
Mejri
,
S.
,
Gagnol
,
V.
,
Le
,
T.-P.
,
Sabourin
,
L.
,
Ray
,
P.
, and
Paultre
,
P.
,
2016
, “
Dynamic Characterization of Machining Robot and Stability Analysis
,”
Int. J. Adv. Manuf. Technol.
,
82
(
1–4
), pp.
351
359
. 10.1007/s00170-015-7336-3
13.
Tunc
,
L. T.
, and
Shaw
,
J.
,
2016
, “
Experimental Study on Investigation of Dynamics of Hexapod Robot for Mobile Machining
,”
Int. J. Adv. Manuf. Technol.
,
84
(
5–8
), pp.
817
830
.
14.
Mousavi
,
S.
,
Gagnol
,
V.
,
Bouzgarrou
,
B. C.
, and
Ray
,
P.
,
2017
, “
Dynamic Modeling and Stability Prediction in Robotic Machining
,”
Int. J. Adv. Manuf. Technol.
,
88
(
9–12
), pp.
3053
3065
. 10.1007/s00170-016-8938-0
15.
Mousavi
,
S.
,
Gagnol
,
V.
,
Bouzgarrou
,
B. C.
, and
Ray
,
P.
,
2018
, “
Stability Optimization in Robotic Milling Through the Control of Functional Redundancies
,”
Rob. Comput. Int. Manuf.
,
50
(
1
), pp.
181
192
. 10.1016/j.rcim.2017.09.004
16.
Huynh
,
H. N.
,
Assadi
,
H.
,
Rivière-Lorphèvre
,
E.
,
Verlinden
,
O.
, and
Ahmadi
,
K.
,
2020
, “
Modelling the Dynamics of Industrial Robots for Milling Operations
,”
Rob. Comput. Int. Manuf.
,
61
(
1
), p.
101852
. 10.1016/j.rcim.2019.101852
17.
Ruderman
,
M.
,
Hoffmann
,
F.
, and
Bertram
,
T.
,
2009
, “
Modeling and Identification of Elastic Robot Joints With Hysteresis and Backlash
,”
IEEE Trans. Ind. Electron.
,
56
(
10
), pp.
3840
3847
. 10.1109/TIE.2009.2015752
18.
Trendafilova
,
I.
, and
Van Brussel
,
H.
,
2001
, “
Non-Linear Dynamics Tools for the Motion Analysis and Condition Monitoring of Robot Joints
,”
Mech. Syst. Signal Proces.
,
15
(
6
), pp.
1141
1164
. 10.1006/mssp.2000.1394
19.
Cordes
,
M.
, and
Hintze
,
W.
,
2017
, “
Offline Simulation of Path Deviation Due to Joint Compliance and Hysteresis for Robot Machining
,”
Int. J. Adv. Manuf. Technol.
,
90
(
1–4
), pp.
1075
1083
. 10.1007/s00170-016-9461-z
20.
Kircanski
,
N. M.
, and
Goldenberg
,
A. A.
,
1997
, “
An Experimental Study of Nonlinear Stiffness, Hysteresis, and Friction Effects in Robot Joints With Harmonic Drives and Torque Sensors
,”
Int. J. Rob. Res.
,
16
(
2
), pp.
214
239
.
21.
Elosegui
,
P.
,
1994
, “
Measurement of the Dynamic Model of a Puma 560 Robot Using Experimental Modal Analysis
,”
ASME J. Mech. Des.
,
116
(
1
), pp.
75
79
.
22.
Mohammadi
,
Y.
, and
Ahmadi
,
K.
,
2020
, “
Structural Nonlinearity of Robotic Machining Systems
,”
ASME 15th International Manufacturing Science and Engineering Conference (MSEC)
,
Virtual, Online Proceedings
,
Sept. 3
.
23.
Worden
,
K.
, and
Tomlinson
,
G. R.
,
2001
,
Nonlinearity in Structural Dynamics: Detection, Identification and Modelling
,
IOP Publishing
,
Bristol, Philadelphia
.
24.
Ewins
,
D. J.
,
1984
,
Modal Testing: Theory and Practice
,
Research Studies Press
,
Letchworth
.
25.
Mohammadi
,
Y.
, and
Ahmadi
,
K.
,
2019
, “
Effect of Axial Vibrations on Regenerative Chatter in Robotic Milling
,”
Procedia CIRP.
,
82
(
1
), pp.
503
508
.
26.
Lee
,
G.-M.
,
1997
, “
Estimation of Non-Linear System Parameters Using Higher-Order Frequency Response Functions
,”
Mech. Syst. Signal Proc.
,
11
(
2
), pp.
219
228
.
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