Five-axis computer numerical control (CNC) machining is characterized with a multitude of errors. Among them an important component comes from the computer-aided manufacturing software known as the geometry-based errors. A new and accurate method to determine these errors is presented in this paper as opposed to the conventional chordal deviation method. The present method allows establishing the exact linearly interpolated tool positions between two cutter contact points on a given tool path, based on the inverse kinematics analysis of the machine tool. A generic procedure has been developed to ensure wide applicability of the proposed method. Analytical derivation of the geometry-based errors provides insights regarding the origin of these errors and their affecting parameters. Due to the highly non-linear characteristics of the problem, analytical solutions can only be obtained for simple surface geometry. Numerical computation is able to determine the errors for general surface shapes but it would be difficult to uncover further insightful information from the calculated error values. Besides the local surface geometry, the configuration of the kinematic chain of the CNC machine has been found to be the primary factor controlling the resulting value and type of the geometry-based errors. Implementations with a typical complex free-form surface demonstrated that the conventional chordal deviation method was not reliable and could significantly underestimate the geometry-based errors.

Issue Section:
Technical Papers
Keywords:
machine tools, computerised numerical control, path planning, error analysis, machining, surface treatment, cutting tools, interpolation, position control, kinematics, mechanical engineering computing, inverse problems, computer aided manufacturing
Topics:
Errors, Geometry, Machinery, Machining, Kinematics
1.
Lo
,
C. C.
,
1999
, “
Real-Time Generation and Control of Cutter Path for 5-Axis CNC Machining
,”
Int. J. Mach. Tools Manuf.
,
39
, pp.
471
–
488
.
2.
Vickers
,
G. W.
, and
Quan
,
K. W.
,
1989
, “
Ball-Mills Versus End-Mills for Curved Surface Machining
,”
ASME J. Eng. Ind.
,
111
, pp.
22
–
26
.
3.
Choi
,
B. K.
,
Park
,
J. W.
, and
Jun
,
C. S.
,
1993
, “
Cutter-Location Data Optimization in 5-Axis Surface Machining
,”
Comput.-Aided Des.
,
25
, pp.
377
–
386
.
4.
Cho
,
H. D.
,
Jun
,
Y. T.
, and
Yang
,
M. Y.
,
1993
, “
Five-Axis CNC Milling for Effective Machining of Sculptured Surfaces
,”
Int. J. Prod. Res.
,
31
, pp.
2559
–
2573
.
5.
Li
,
S. X.
, and
Jerard
,
R. B.
,
1994
, “
5-Axis Machining of Sculptured Surfaces with a Flat-End Cutter
,”
Comput.-Aided Des.
,
26
, pp.
165
–
178
.
6.
Rao
,
N.
,
Bedi
,
S.
, and
Buchal
,
R.
,
1996
, “
Implementation of the Principal-Axis Method for Machining of Complex Surfaces
,”
Int. J. of Advan. Manuf. Tech.
,
11
, pp.
249
–
257
.
7.
Bedi
,
S.
,
Gravelle
,
S.
, and
Chen
,
Y. H.
,
1997
, “
Principal Curvature Alignment Technique for Machining Complex Surfaces
,”
ASME J. Manuf. Sci. Eng.
,
119
, pp.
756
–
765
.
8.
Wang
,
Y.
, and
Tang
,
X.
,
1999
, “
Five-Axis NC Machining of Sculptured Surfaces
,”
Int. J. of Advan. Manuf. Tech.
,
15
, pp.
7
–
14
.
9.
Bohez
,
E.
,
Makhanov
,
S. S.
, and
Sonthipermpoon
,
K.
,
2000
, “
Adaptive Nonlinear Tool Path Optimization for Five-Axis Machining
,”
Int. J. Prod. Res.
,
38
, pp.
4329
–
4343
.
10.
Lee
,
Y. S.
,
1998
, “
Non-Isoparametric Tool Path Planning by Machining Strip Evaluation for 5-Axis Sculptured Surface Machining
,”
Comput.-Aided Des.
,
30
, pp.
559
–
570
.
11.
Lo
,
C. C.
,
1999
, “
Efficient Cutter-Path Planning for Five-Axis Surface Machining with a Flat-End Cutter
,”
Comput.-Aided Des.
,
31
,
557
–
566
.
12.
Rao
,
N.
,
Ismail
,
F.
, and
Bedi
,
S.
,
2000
, “
Integrated Tool Positioning and Tool Path Planning for Five-Axis Machining of Sculptured Surfaces
,”
Int. J. Prod. Res.
,
38
, pp.
2709
–
2724
.
13.
Chiou
,
C. J.
, and
Lee
,
Y. S.
,
2002
, “
A Machining Potential Field Approach to Tool Path Generation for Multi-Axis Sculptured Surface Machining
,”
Comput.-Aided Des.
,
34
, pp.
357
–
371
.
14.
Balasubramaniam
,
M.
,
Ho
,
S.
,
Sarma
,
S.
, and
Adachi
,
Y.
,
2002
, “
Generation of Collision-Free 5-Axis Tool Paths Using a Haptic Surface
,”
Comput.-Aided Des.
,
34
, pp.
267
–
279
.
15.
Balasubramaniam
,
M.
,
Sarma
,
S. E.
, and
Marciniak
,
K.
,
2003
, “
Collision-Free Finishing Toolpaths from Visibility Data
,”
Comput.-Aided Des.
,
35
, pp.
359
–
374
.
16.
Sarma
,
R.
, and
Rao
,
A.
,
2000
, “
Discretizors and Interpolators for Five-Axis CNC Machines
,”
ASME J. Manuf. Sci. Eng.
,
122
, pp.
191
–
197
.
17.
Sakamoto
,
S.
, and
Inasaki
,
I.
,
1993
, “
Analysis of Generating Motion for Five-Axis Machining Centers
,”
Trans. of N. American Manuf. Research Instit. of SME Publisher Soc. of Manuf. Eng.
XXI
, pp.
287
–
293
.
18.
Bohez
,
E. L. J.
,
2002
, “
Five-Axis Milling Machine Tool Kinematic Chain Design and Analysis
,”
Int. J. Mach. Tools Manuf.
,
42
, pp.
505
–
520
.
19.
Srivastava
,
A. K.
,
Veldhuis
,
S. C.
, and
Elbestawi
,
M. A.
,
1995
, “
Modelling Geometric and Thermal Errors in a Five-Axis CNC Machine Tool
,”
Int. J. Mach. Tools Manuf.
,
35
, pp.
1321
–
1337
.
20.
Rao
,
A.
, and
Sarma
,
R.
,
2000
, “
On Local Gouging in Five-Axis Sculptured Surface Machining Using Flat-End Tools
,”
Comput.-Aided Des.
,
32
, pp.
409
–
420
.
21.
Hwang
,
Y. R.
, and
Ho
,
M. T.
,
2000
, “
Estimation of Maximum Allowable Step Length for Five-Axis Cylindrical Machining
,”
Journal of Manufacturing Processes
,
2
, pp.
15
–
24
.
22.
Bohez
,
E. L. J.
,
2002
, “
Compensating for Systematic Errors in 5-Axis NC Machining
,”
Comput.-Aided Des.
,
34
, pp.
391
–
403
.
23.
Huang
,
Y.
, and
Oliver
,
J. H.
,
1994
, “
Non-Constant Parameter NC Tool Path Generation on Sculptured Surfaces
,”
Int. J. of Adv. Manuf. Tech.
,
9
, pp.
281
–
290
.
24.
Reshetov, D. N., and Portman, V. T., 1988, Accuracy of Machine Tools, ASME Press, New York.
25.
Chen
,
F. C.
,
2001
, “
On the Structural Configuration Synthesis and Geometry of Machining Centres
,”
J. Mech. Eng. Sci.
,
215
, pp.
641
–
652
.
26.
Lee
,
R. S.
, and
She
,
C. H.
,
1997
, “
Developing a Postprocessor for Three Types of Five-Axis Machine Tools
,”
Int. J. of Adv. Manuf. Tech.
,
13
, pp.
658
–
665
.
27.
Cheng
,
H. Y.
, and
She
,
C. H.
,
2002
, “
Studies on the Combination of the Forward and Reverse Postprocessor for Multiaxis Machine Tools
,”
Journal of Engineering Manufacture
,
216
, pp.
77
–
86
. Proceedings of the Institute of Mechanical Engineers. J. of Engineering Manufacture - Part B.
28.
Warkentin, A., Hoskins, P., Ismail, F., and Bedi, S., 2001, “Computer Aided 5-Axis Machining,” Systems Techniques and Computational Methods, C. T. Leondes, ed., CRC Press, Boca Raton, Florida.
29.
Feng
,
H. Y.
, and
Li
,
H.
,
2002
, “
Constant Scallop-Height Tool Path Generation for Three-Axis Sculptured Surface Machining
,”
Comput.-Aided Des.
,
34
, pp.
647
–
654
.
30.
Tutunea-Fatan
,
O. R.
, and
Feng
,
H. Y.
, “
Configuration Analysis of Five-Axis Machine Tools Using a Generic Kinematic Model
,”
Int. J. Mach. Tools Manuf.
,
44
, pp.
1235
–
1243
.
31.
Kim
,
T.
, and
Sarma
,
S. E.
,
2002
, “
Toolpath Generation along Directions of Maximum Kinematic Performance; A First Cut at Machine-Optimal Paths
,”
Comput.-Aided Des.
,
34
, pp.
453
–
468
.
Copyright © 2005
 by ASME
You do not currently have access to this content.