In this paper we present the second generation receptance coupling substructure analysis (RCSA) method, which is used to predict the tool point response for high-speed machining applications. This method divides the spindle-holder-tool assembly into three substructures: the spindle-holder base; the extended holder; and the tool. The tool and extended holder receptances are modeled, while the spindle-holder base subassembly receptances are measured using a “standard” test holder and finite difference calculations. To predict the tool point dynamics, RCSA is used to couple the three substructures. Experimental validation is provided.

1.
Halley
,
J.
,
Helvey
,
A.
,
Smith
,
K. S.
, and
Winfough
,
W. R.
, 1999, “
The Impact of High-Speed Machining on the Design and Fabrication of Aircraft Components
,”
Proc. of the 17th Biennial Conference on Mechanical Vibration and Noise, ASME Design and Technical Conferences
, Las Vegas, NV, September 12–16.
2.
Arnold
,
R. N.
, 1946, “
The Mechanism of Tool Vibration in the Cutting of Steel
,”
Proc. Inst. Mech. Eng.
0020-3483,
154
, pp.
261
284
.
3.
Tobias
,
S. A.
, and
Fishwick
,
W.
, 1958, “
The Chatter of Lathe Tools under Orthogonal Cutting Conditions
,”
Trans. ASME
0097-6822,
80
, p.
1079
.
4.
Tlusty
,
J.
, and
Polocek
,
M.
, 1963, “
The Stability of the Machine-Tool Against Self-Excited Vibration in Machining
,”
Proc. of the International Research in Production Engineering Conference
, Pittsburgh, PA,
ASME
, NY, p.
465
.
5.
Tobias
,
S. A.
, 1965,
Machine-Tool Vibration
,
Blackie and Sons Ltd.
, Glasgow, Scotland.
6.
Koenisberger
,
F.
, and
Tlusty
,
J.
, 1967,
Machine Tool Structures—Vol. I: Stability Against Chatter
,
Pergamon
, NY
7.
Merrit
,
H.
, 1965, “
Theory of Self-Excited Machine Tool Chatter
,”
J. Eng. Ind.
0022-0817,
87
, pp.
447
454
.
8.
Kegg
,
R. L.
, 1965, “
Cutting Dynamics in Machine Tool Chatter
,”
J. Eng. Ind.
0022-0817,
87
, pp.
464
470
.
9.
Shridar
,
R.
,
Hohn
,
R. E.
, and
Long
,
G. W.
, 1968, “
A General Formulation of the Milling Process Equation
,”
J. Eng. Ind.
0022-0817,
90
, p.
317
.
10.
Shridar
,
R.
,
Hohn
,
R. E.
, and
Long
,
G. W.
, 1968, “
A Stability Algorithm for the General Milling Process
,”
J. Eng. Ind.
0022-0817,
90
, p.
330
.
11.
Hanna
,
N. H.
, and
Tobias
,
S. A.
, 1974, “
A Theory of Nonlinear Regenerative Chatter
,”
J. Eng. Ind.
0022-0817,
96
, pp.
247
255
.
12.
Schmitz
,
T.
, and
Donaldson
,
R.
2000, “
Predicting High-Speed Machining Dynamics by Substructure Analysis
,”
CIRP Ann.
0007-8506,
49
, pp.
303
308
.
13.
Schmitz
,
T.
,
Davies
,
M.
, and
Kennedy
,
M.
, 2001, “
Tool Point Frequency Response Prediction for High-Speed Machining by RCSA
,”
J. Manuf. Sci. Eng.
1087-1357,
123
, pp.
700
707
.
14.
Schmitz
,
T.
,
Davies
,
M.
,
Medicus
,
K.
, and
Snyder
,
J.
, 2001, “
Improving High-Speed Machining Material Removal Rates by Rapid Dynamic Analysis
,”
CIRP Ann.
0007-8506,
50
, pp.
263
268
.
15.
Schmitz
,
T.
, and
Burns
,
T.
, 2003, “
Receptance Coupling for High-Speed Machining Dynamics Prediction
,”
Proc. of the 21st International Modal Analysis Conference
, February 3–6, Kissimmee, FL (on CD).
16.
Bishop
,
R. E. D.
, and
Johnson
,
D. C.
, 1960,
The Mechanics of Vibration
,
Cambridge University Press
, Cambridge, UK.
17.
Hurty
,
W. C.
, 1965, “
Dynamic Analysis of Structural Systems Using Component Modes
,”
AIAA J.
0001-1452,
3
, pp.
678
685
.
18.
Klosterman
,
A. L.
, and
Lemon
,
J. R.
, 1969, “
Building Block Approach to Structural Dynamics
,”
American Society of Mechanical Engineering Annual Vibration Conference
, publication VIBR-30.
19.
Klosterman
,
A. L.
,
McClelland
, and
Sherlock
,
W. I.
, 1977, “
Dynamic Simulation of Complex Systems Utilizing Experimental and Analytical Techniques
,” ASME Publication 75-WA/Aero-9.
20.
Ewins
,
D. J.
, 1986, “
Analysis of Modified or Coupled Structures Using FRF Properties
,” Internal Report 86002,
Dynamics Section, Department of Mechanical Engineering, Imperial College
, London, UK.
21.
Craig
, Jr.,
R. R.
, 1987, “
A Review of Time-Domain and Frequency Domain Component-Mode Synthesis Methods
,”
Int. J. Anal. Exp. Modal Anal.
0886-9367,
2
pp.
59
72
.
22.
Jetmundsen
,
B.
,
Bielawa
,
R. L.
, and
Flannelly
,
W. G.
, 1988, “
Generalized Frequency Domain Substructure Synthesis
,”
J. Am. Helicopter Soc.
0002-8711,
33
, pp.
55
64
.
23.
Otte
,
D.
,
Leuridan
,
J.
,
Grangier
,
H.
, and
Aquilina
,
R.
, 1991, “
Prediction of the Dynamics of Structural Assemblies Using Measured FRF Data: Some Improved Data Enhancement Techniques
,”
Proc. of the 9th International Modal Analysis Conference (IMAC-1991)
, Florence, Italy, pp.
909
918
.
24.
Farhat
,
C.
, and
Geradin
,
M.
, 1992, “
A Hybrid Formulation of a Component Mode Synthesis Method
,”
33rd Structural Dynamics and Materials Conference
, AIAA paper 92-2383-CP, Dallas, TX, pp.
1783
1796
.
25.
Ren
,
Y.
, and
Beards
,
C. F.
, 1993, “
A Generalized Receptance Coupling Technique
,”
Proc. of the 11th International Modal Analysis Conference (IMAC-1993)
, Kissimmee, FL, pp.
868
871
.
26.
Ren
,
Y.
, and
Beards
,
C. F.
, 1995, “
On Substructure Synthesis with FRF Data
,”
J. Sound Vib.
0022-460X,
185
, pp.
845
866
.
27.
Ewins
,
D. J.
, 2000,
Modal Testing: Theory, Practice and Application
, 2nd ed.,
Research Studies Press
, Philadelphia, PA.
28.
Lui
,
W.
, and
Ewins
,
D. J.
, 2002, “
Substructure Synthesis Via Elastic Media
,”
J. Sound Vib.
0022-460X,
257
, pp.
361
379
.
29.
Ferreira
,
J. V.
, and
Ewins
,
D. J.
, 1996, “
Nonlinear Receptance Coupling Approach Based on Describing Functions
,”
Proc. of the 14th International Modal Analysis Conference (IMAC-1996)
, Dearborn, MI, pp.
1034
1040
.
30.
Yigit
,
A. S.
, and
Ulsoy
,
A. G.
, 2002, “
Dynamic Stiffness Evaluation for Reconfigurable Machine Tools Including Weakly Non-Linear Joint Characteristics
,”
Proceedings of the I MECH E Part B Journal of Engineering Manufacture
,
216
, pp.
87
101
.
31.
Park
,
S.
,
Altintas
,
Y.
, and
Movahhedy
,
M.
, 2003, “
Receptance Coupling for End Mills
,”
Int. J. Mach. Tools Manuf.
0890-6955,
43
, pp.
889
896
.
32.
Ferreira
,
J.
, and
Ewins
,
D.
, 1995, “
Nonlinear Receptance Coupling Approach Based on Describing Functions
,”
Proc. of the 14th International Modal Analysis Conference
, Dearborn, MI, pp.
1034
1040
.
33.
Bishop
,
R.
, 1955, “
The Analysis of Vibrating Systems which Embody Beams in Flexure
,”
Proc. Inst. Mech. Eng.
0020-3483,
169
, pp.
1031
1050
.
34.
Weaver
, Jr.,
W.
,
Timoshenko
,
P.
, and
Young
,
D.
, 1990,
Vibration Problems in Engineering
, 5th Ed.,
John Wiley and Sons
, New York.
35.
Sattinger
,
S.
, 1980, “
A Method for Experimentally Determining Rotational Mobilities of Structures
,”
Shock Vibr. Bull.
,
50
, pp.
17
27
.
36.
Mathworks
, 2002,
Matlab 6.5.0 Release 13: High-Performance Numeric Computation and Visualization Software
, Natick, MA.
37.
Schmitz
,
T.
,
Ziegert
,
J.
,
Burns
,
T.
,
Dutterer
,
B.
, and
Winfough
,
W.
, 2004, “
Tool-Length Dependent Stability Surfaces
,”
Mach. Sci. Technol.
1091-0344,
8
(
3
), pp.
1
21
.
38.
Altintas
,
Y.
and
Budak
,
E.
, 1995, “
Analytical Prediction of Stability Lobes in Milling
,”
CIRP Ann.
0007-8506,
44
, pp.
357
362
.
39.
Yokoyama
,
T.
, 1990, “
Vibrations of a Hanging Timoshenko Beam Under Gravity
,”
J. Sound Vib.
0022-460X,
141
, pp.
245
258
.
40.
Hutchinson
,
J.
, 2001, “
Shear Coefficients for Timoshenko Beam Theory
,”
J. Appl. Mech.
0021-8936,
68
, pp.
87
92
.
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