Considering the great impacts of the application sequence of multiclamps on the workpiece machining accuracy, this paper analyzes and optimizes clamping sequence. A new methodology that takes into account the varying contact forces and friction force during clamping is presented for the first time. A new analysis model is established to capture the effect of clamping sequence on contact force distributions and workpiece machining accuracy. It reveals that the historical accumulation of clamping steps influences heavily the final distribution of contact forces in the workpiece-fixture system. Therefore, the present contact forces in each clamping step are solved incrementally in terms of contact forces of the precedent step by means of the principle of the total complementary energy. Furthermore, based on the fact that the variation of contact forces from one step to another results in different workpiece deformations and position, a novel design model is formulated to select optimally the clamping sequence in order to minimize the workpiece deformation and position errors. Workpieces of low stiffness and high stiffness are investigated separately in order to simplify the modeling of clamping sequence optimization. Some numerical tests are finally demonstrated to validate the proposed model and method. Computational results are discussed and compared with experimental results available in the reference.

1.
Asada
,
H.
, and
By
,
A. B.
, 1985, “
Kinematic Analysis of Workpiece Fixturing for Flexible Assembly With Automatically Reconfigurable Fixtures
,”
IEEE J. Rob. Autom.
0882-4967,
RA-1
(
2
), pp.
86
94
.
2.
Asada
,
H.
, and
Kitagawa
,
M.
, 1989, “
Kinematic Analysis and Planning for Form Closure Grasps by Robotic Hands
,”
Rob. Comput.-Integr. Manufact.
0736-5845,
5
(
4
), pp.
293
225
.
3.
Cai
,
W.
,
Hu
,
S. J.
, and
Yuan
,
J. X.
, 1997, “
A Variational Method of Robust Fixture Configuration Design for 3-D Workpieces
,”
J. Manuf. Sci. Eng.
1087-1357,
119
(
11
), pp.
593
602
.
4.
Yoshikawa
,
T.
, 1999, “
Passive and Active Closures by Constraining Mechanisms
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
121
, pp.
418
424
.
5.
Shapiro
,
A.
,
Rimon
,
E.
, and
Burdick
,
J. W.
, 2001, “
Passive Force Closure and its Computation in Compliant-Rigid Grasp
,”
Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems
, Maui, HI, October 29–November 3,
2
, pp.
1769
1775
.
6.
Qin
,
G. H.
,
Zhang
,
W. H.
, and
Wan
,
M.
, “
A Mathematical Approach to Analysis and Optimal Design of Fixture Locating Scheme
,”
Int. J. Adv. Manuf. Technol.
(in press).
7.
Qin
,
G. H.
,
Zhang
,
W. H.
, and
Wan
,
M.
, 2005, “
Modeling and Application of Workpiece Stability Based on the Linear Programming Technique
,”
Chin. J. Mech. Eng.
0577-6686,
41
(
9
), pp.
33
37
.
8.
Chou
,
Y. C.
,
Chandru
,
V.
, and
Barash
,
M. M.
, 1989, “
A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis
,”
ASME J. Eng. Ind.
0022-0817,
111
(
11
), pp.
299
306
.
9.
Trappey
,
A. J. C.
, and
Liu
,
C. R.
, 1992, “
An Automatic Workholding Verification System
,”
Rob. Comput.-Integr. Manufact.
0736-5845,
9
, pp.
321
326
.
10.
Fuh
,
J. Y. H.
,
Chang
,
C. H.
, and
Melkanoff
,
M. A.
, 1993, “
An Integrated Fixturing and Analysis System for Machining Processes
,”
Rob. Comput.-Integr. Manufact.
0736-5845,
10
(
5
), pp.
339
353
.
11.
Gui
,
X. W.
,
Fuh
,
J. Y. H.
, and
Nee
,
A. Y. C.
, 1996, “
Modeling of Frictional Elastic Fixture-Workpiece System for Improving Location Accuracy
,”
IIE Trans.
0740-817X,
28
, pp.
821
827
.
12.
Li
,
B.
, and
Melkote
,
S. N.
, 2001, “
Fixture Clamping Force Optimization and its Impact on Workpiece Location Accuracy
,”
Int. J. Adv. Manuf. Technol.
0268-3768,
17
, pp.
104
113
.
13.
Li
,
B.
, and
Melkote
,
S. N.
, 1999, “
An Elastic Contact Model for the Prediction of Workpiece-Fixture Contact Forces in Clamping
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
121
, pp.
485
493
.
14.
Xiong
,
C. H.
,
Xiong
,
Y. L.
, and
Wang
,
M. Y.
, 2003, “
On Prediction of Passive Contact Forces of Workpiece-Fixture Systems
,”
Proceedings of ASME 8th Design for Manufacturing Conference
, Chicago, IL, September 2–6, ASME, New York, pp.
1
10
.
15.
Wang
,
M. Y.
, and
Pelinescu
,
D. M.
, 2003, “
Contact Force Prediction and Force Closure Analysis of a Fixtured Rigid Workpiece With Friction
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
125
, pp.
325
332
.
16.
Wang
,
M. Y.
, and
Liu
,
Y. H.
, 2003, “
Force Passivity in Fixturing and Grasping
,”
Proceedings of IEEE International Conference on Robotics and Automation
, Taipei, Taiwan, September 14–19, pp.
2236
2241
.
17.
Raghu
,
A.
, and
Melkote
,
S. N.
, 2003, “
Analysis of the Effects of Fixture Clamping Sequence on Part Location Errors
,”
Int. J. Mach. Tools Manuf.
0890-6955,
44
, pp.
373
382
.
18.
Kang
,
Y. Z.
, 2001, “
Computer Aided Fixture Design Verification
,” Ph.D. thesis, Worcester Polytechnic Institute, MA.
19.
Cogun
,
C.
, 1992, “
The Importance of the Application Sequence of Clamping Forces on Workpiece Accuracy
,”
ASME J. Eng. Ind.
0022-0817,
114
, pp.
539
543
.
20.
Lee
,
J. D.
, and
Haynes
,
L. S.
, 1987, “
Finite-Element Analysis of Flexible Fixturing System
,”
ASME J. Eng. Ind.
0022-0817,
109
, pp.
134
139
.
21.
Cai
,
W.
,
Hu
,
S. J.
, and
Yuan
,
J. X.
, 1996, “
Deformable Sheet Metal Fixturing: Principles, Algorithms, and Simulations
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
118
, pp.
318
324
.
22.
Menassa
,
R. J.
, and
DeVries
,
W. R.
, 1991, “
Optimization Methods Applied to Selecting Support Positions in Fixture Design
,”
ASME J. Eng. Ind.
0022-0817,
113
, pp.
412
418
.
23.
Kashyap
,
S.
, and
DeVries
,
W. R.
, 1999, “
Finite Element Analysis and Optimization in Fixture Design
,”
Struct. Optim.
0934-4373,
18
, pp.
193
201
.
24.
Kulankara
,
K.
,
Satyanarayana
,
S.
, and
Melkote
,
S. N.
, 2002, “
Iterative Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
124
, pp.
119
125
.
25.
Liao
,
Y. J. G.
, and
Hu
,
S. J.
, 2000, “
Flexible Multibody Dynamics Based Fixture-Workpiece Analysis Model for Fixturing Stability
,”
Int. J. Mach. Tools Manuf.
0890-6955,
40
, pp.
343
362
.
26.
DeMeter
,
E. C.
,
Xie
,
W.
,
Choudhuri
,
S.
,
Vallapuzha
,
S.
, and
Trethewey
,
M. W.
, 2001, “
A Model to Predict Minimum Required Clamp Pre-loads in Light of Fixture-Workpiece Compliance
,”
Int. J. Mach. Tools Manuf.
0890-6955,
41
, pp.
1031
1054
.
27.
Hurtado
,
J. F.
, and
Melkote
,
S. N.
, 2002, “
Modeling and Analysis of the Effect of Fixture-Workpiece Conformability on Static Stability
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
17
, pp.
104
113
.
28.
Pilkey
,
W. D.
, and
Wunderlich
,
W.
, 1994,
Mechanics of Structures: Variational and Computational Methods
,
CRC
,
Boca Raton, FL
.
29.
DeMeter
,
E. C.
, 1994, “
Restraint Analysis of Fixtures Which Rely on Surface Contact
,”
ASME J. Eng. Ind.
0022-0817,
116
, pp.
207
214
.
30.
Johnson
,
K. J.
, 1985,
Contact Mechanics
,
Cambridge University Press
, Cambridge.
This content is only available via PDF.
You do not currently have access to this content.