Increased use of high speed machining creates the need to predict spindle-bearing performance at high speeds. Previous spindle-bearing models simplify either spindle or bearing dynamics to the extent of prohibiting a detailed analysis of a spindle with high speed motion. At high speeds, centrifugal loading in the bearing causes stiffness softening, creating a change in natural frequency. Therefore, spindle modeling requires a comprehensive representation of the dynamics of shafts with complex geometry rotating at high speeds and supported by non-linear bearings. This paper presents a coupled system of spindle and bearing dynamic models with numerical solution. Spindle dynamics are modeled using the influence coefficient method of discrete lumped masses, based on Timoshenko beam theory. Both linear and rotational bearing stiffness are included in the spindle model through solution of the angular-contact bearing model. The parameters of cutting loads, tool mass, and rotational speed are analyzed, and all are shown to affect the natural frequency. The computer model is both rapid and robust, and shows excellent agreement with experimental analysis.

Issue Section:
Research Papers
Topics:
Bearings, Cutting, Dynamics (Mechanics), Stress, Stiffness, Computers, Dynamic models, Experimental analysis, Geometry, High speed machining, Modeling, Timoshenko beam theory
1.
Al-Shareef
K. J. H.
, and
Brandon
J. A.
, “
On the Effects of Variations in the Design Parameters on the Dynamic Performance of Machine Tool Spindle-Bearing Systems
,”
Int. J. of Machine Tools and Manufac.
, Vol.
30
, pp.
431
–
445
,
1990
.
2.
Brandon
J. A.
, and
Al-Shareef
K. J. H.
, “
On the Validity of Several Common Assumptions in the Design of Machine Tool Spindle-Bearing Systems
,”
Int. J. of Machine Tools and Manufac.
, Vol.
31
, pp.
235
–
248
,
1991
.
3.
Brandon
J. A.
, and
Al-Shareef
K. J. H.
, “
Optimization Strategies for Machine Tool Spindle-Bearing Systems: A Critical Review
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
114
, pp.
244
–
253
,
1992
.
4.
Chen
C. H.
,
Wang
K. W.
, and
Shin
Y. C.
, “
An Integrated Approach Toward the Modeling and Dynamic Analysis of High-Speed Spindles
,”
ASME Journal of Vibration and Acoustics
, Vol.
116
, pp.
506
–
513
,
1994
.
5.
De Mul
J. M.
,
Vree
J. M.
, and
Maas
D. A.
, “
Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction
,”
ASME Journal of Tribology
, Vol.
111
, pp.
149
–
155
,
1989
.
6.
Griffel, W., “New Equations Simplify Analysis of Beams and Stepped Shafts,” Product Engr., pp. 82–86, 1965.
7.
Harris, T. A., Rolling Bearing Analysis, 3rd ed., John Wiley, New York, 1990.
8.
Jones, A. B., “A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions,” ASME Journal of Basic Engineering, pp. 309–320, 1960.
9.
Kawamura
H.
, and
Touma
K.
, “
Motion of Unbalanced Balls in High-Speed Angular Contact Ball Bearings
,”
ASME Journal of Tribology
, Vol.
112
, pp.
105
–
110
,
1989
.
10.
Matsubara
M.
,
Rahnejat
H.
, and
Gohar
R.
, “
Computational Modeling of Precision Spindles Supported by Ball Bearings
,”
Int. J. of Machine Tools and Manufac.
, Vol.
28
, pp.
429
–
442
,
1988
.
11.
Reddy
V. R.
, and
Sharan
A. M.
, “
The Static and Dynamic Analysis of Machine Tools Using Dynamic Matrix Reduction Technique
,”
Int. J. of Machine Tools and Manufac.
, Vol.
27
, pp.
105
–
112
,
1987
.
12.
Shin, Y. C., “Bearing Nonlinearity and Stability Analysis in High Speed Machining,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY, pp. 23–30, 1992.
13.
Wang
W. R.
, and
Chang
C. N.
, “
Dynamic Analysis and Design of a Machine Tool Spindle-Bearing System
,”
ASME Journal of Vibration and Acoustics
, Vol.
116
, pp.
280
–
285
,
1994
.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.