Machining processes are usually multi-station processes involving a large number of operations and several locating datum changes. Machining errors are thus introduced, transformed and accumulated as the workpiece is being machined. This paper introduces procedures for expressing the influence of errors in fixtures, locating datum features and measurement datum features on dimensional errors in machining. These procedures are essential in the derivation of the Stream of Variation model of dimensional machining errors using the CAD/CAPP parameters of the machining process. The linear state space form of the Stream of Variation model allows for advanced control theory achievements to be employed in formal solutions to problems in multi-station machining. Modeling procedures presented in this paper were experimentally verified in machining of an automotive cylinder head.

1.
Hu
,
S.
, and
Wu
,
S. M.
,
1992
, “
Identifying Root Causes of Variation in Auto-Body Assembly Using Principal Component Analysis
,”
Transactions of NAMRI
,
20
, pp.
311
316
.
2.
Roan
,
C. M.
, and
Hu
,
S. J.
,
1995
, “
Monitoring and Classification of Dimensional Faults in Automotive Body Assembly
,”
International Journal of Flexible Manufacturing Systems
,
7
(
2
), pp.
103
125
.
3.
Ceglarek
,
D.
, and
Shi
,
J.
,
1995
, “
Dimensional Variation Reduction for Automotive Body Assembly
,”
Manufacturing Review
,
8
, pp.
139
154
.
4.
Ceglarek
,
D.
, and
Shi
,
J.
,
1996
, “
Fixture Failure Diagnosis for the Autobody Assembly Using Pattern Recognition
,”
ASME J. Ind. Eng.
,
118
(
1
), pp.
55
66
.
5.
Yang
,
K.
,
1996
, “
Improving Automotive Dimensional Quality by Using Principal Component Analysis
,”
International Journal of Quality and Reliability
,
12
(
6
), pp.
401
409
.
6.
Hu
,
S. J.
,
1997
, “
Stream of Variation Theory for Automotive-Body Assembly
,”
CIRP Ann.
,
46
(
1
), pp.
1
6
.
7.
Jin
,
J.
, and
Shi
,
J.
,
1999
, “
State Space Modeling of Sheet Metal Assembly for Dimensional Control
,”
ASME J. Manuf. Sci. Eng.
,
121
(
4
), pp.
756
762
.
8.
Ding, Y., Ceglarek, D., and Shi, J., 2000, “Modeling and Diagnosis of Multistage Manufacturing Processes, Part I—State Space Model,” Japan-USA Symposium, Ann Arbor, Michigan.
9.
Ding, Y., Ceglarek, D., and Shi, J., 2000, “Modeling and Diagnosis of Multistage Manufacturing Processes, Part II—Fault Diagnosis,” Japan-USA Symposium, Ann Arbor, Michigan.
10.
Appley
,
D.
, and
Shi
,
J.
,
1998
, “
Diagnosis of Multiple Fixture Faults in Panel Assembly
,”
ASME J. Manuf. Sci. Eng.
,
120
, pp.
793
801
.
11.
Ceglarek
,
D.
,
Shi
,
J.
, and
Wu
,
S. M.
,
1994
, “
A Knowledge-Based Diagnostic Approach for the Launch of the Auto-Body Assembly Processes
,”
ASME J. Eng. Ind.
,
116
, pp.
491
499
.
12.
Ding
,
Y.
,
Ceglarek
,
D.
, and
Shi
,
J.
,
2002
, “
Fault Diagnosis of Multi-Stage Manufacturing Processes by Using State Space Approach
,”
ASME J. Manuf. Sci. Eng.
,
124
, pp.
313
322
.
13.
Zhou, S., Ding, Y., Chen, Y., and Shi, J., 2003, “
Variance Components Analysis Methods for Diagnosability of Multi-Stage Manufacturing Systems,” Technometrics, November.
14.
Ding
,
Y.
,
Shi
,
J.
, and
Ceglarek
,
D.
,
2002
, “
Diagnosability Analysis of Multi-Station Manufacturing Processes
,”
ASME J. Dyn. Syst., Meas., Control
,
124
, pp.
1
13
.
15.
Khan
,
A.
,
Ceglarek
,
D.
, and
Ni
,
J.
,
1998
, “
Sensor Location Optimization for Fault Diagnosis in Multi-Fixture Assembly Systems
,”
ASME J. Manuf. Sci. Eng.
,
120
, pp.
781
792
.
16.
Mantripragada
,
R.
, and
Whitney
,
D. E.
,
1999
, “
Modeling and Controlling Variation Propagation in Mechanical Assemblies Using State Transition Models
,”
IEEE Trans. Rob. Autom.
,
15
(
1
), pp.
124
140
.
17.
Huang, Q., Zhou, N., and Shi, J., 2000, “Stream of Variation Modeling and Diagnosis of Multi-Station Machining Processes,” Proc. of IMECE 2001, Orlando, FL.
18.
Djurdjanovic
,
D.
, and
Ni
,
J.
,
2001
, “
Linear State Space Modeling of Dimensional Machining Errors
,”
Trans. of NAMRI/SME
,
29
, pp.
541
548
.
19.
Zhou
,
S.
,
Huang
,
Q.
, and
Shi
,
J.
,
2003
, “
State Space Modeling of Multi-Stage Machining Systems by Using Differential Motion Vector
,”
IEEE Trans. Rob. Autom.
,
19
(
2
), pp.
296
309
.
20.
Djurdjanovic, D., 2002, “Stream of Variation Modeling of Machining Errors and Its Applications,” Doctoral Dissertation, University of Michigan.
21.
Djurdjanovic, D., and Ni, J., 2001, “Stream of Variation Based Analysis and Synthesis of Measurement Schemes in Multi-Station Machining Systems,” Proc. of the ASME IMECE 2001.
22.
Whitney
,
D. E.
,
Gilbert
,
O. L.
, and
Jastrzebski
,
M.
,
1994
, “
Representation of Geometric Variations Using Matrix Transforms for Statistical Tolerance Analysis in Assemblies
,”
Res. Eng. Des.
,
6
, pp.
191
210
.
23.
Cai
,
W.
,
Hu
,
S. J.
, and
Yuan
,
J. X.
,
1997
, “
A Variational Method of Robust Fixture Design for 3-D Worpieces
,”
ASME J. Manuf. Sci. Eng.
,
119
, pp.
593
602
.
24.
Asada
,
H.
, and
By
,
A. B.
,
1985
, “
Kinematic Analysis of Workpart Fixturing for Flexible Assembly With Automatically Reconfigurable Fixtures
,”
IEEE J. Rob. Autom.
,
RA-1
, pp.
86
94
.
25.
Slocum, A. H., 1992, Precision Machine Design, Prentice Hall, pp. 58–114.
26.
Rong, Y., and Bai, Y., 1995, “Locating Error Analysis for Computer-Aided Fixture Design and Verification,” Proc. of the ASME Computers in Engineering Database Symposium, pp. 825–831.
27.
Rugh, W. J., 1996, Linear System Theory, Prentice Hall, pp. 462–476.
28.
VSA, 1998, “VSA-3D Release 12.5, User Manual,” Variation System Analysis, Inc., 300 Maple Park Blvd., St. Clair Shores, MI 48081.
29.
Frey, D. D., 2000, http://design.mit.edu/ddfrey/MVAA_i intro.htm
30.
Frey, D. D., Otto, K. N., and Pflager, W., 1997, “Swept Envelopes of Cutting Tools in Integrated Machine and Workpiece Error Budgeting,” Annals of the CIRP, 46(1), pp. 475–480.
You do not currently have access to this content.