This paper studies the stiffness characteristics of preloaded duplex angular contact ball bearings. First, a five degrees-of-freedom (5DOF) quasi-static model of the preloaded duplex angular contact ball bearing is established based on the Jones bearing model. Three bearing configurations (face-to-face, back-to-back, and tandem arrangements) and two preload mechanisms (constant pressure preload and fixed position preload) are included in the proposed model. Subsequently, the five-dimensional stiffness matrix of the preloaded duplex angular contact ball bearing is derived analytically. Then, an experimental setup is developed to measure the radial stiffness and the angular stiffness of duplex angular contact ball bearings. The simulated results match well with those from experiments, which prove the validity of the proposed model. Finally, the effects of bearing configuration, preload mechanism, and unloaded contact angle on the angular stiffness and the cross-coupling are studied systematically.

References

References
1.
Gunduz
,
A.
, and
Singh
,
R.
,
2013
, “
Stiffness Matrix Formulation for Double Row Angular Contact Ball Bearings: Analytical Development and Validation
,”
J. Sound Vib.
,
332
(
22
), pp.
5898
5916
.
2.
Bercea
,
I.
,
Nelias
,
D.
, and
Cavallaro
,
G.
,
2003
, “
A Unified and Simplified Treatment of the Nonlinear Equilibrium Problem of Double-Row Bearings—Part I: Rolling Bearing Model
,”
Proc. Inst. Mech. Eng., Part J
,
217
(
3
), pp.
205
212
.
3.
Abele
,
E.
,
Altintas
,
Y.
, and
Brecher
,
C.
,
2010
, “
Machine Tool Spindle Units
,”
CIRP Ann.-Manuf. Technol.
,
59
(
2
), pp.
781
802
.
4.
Yang
,
Z.
,
Chen
,
H.
, and
Yu
,
T.
,
2017
, “
Effects of Rolling Bearing Configuration on Stiffness of Machine Tool Spindle
,”
Proc. Inst. Mech. Eng., Part C
,
232
(
5
), pp. 775–785.
5.
Li
,
H.
, and
Shin
,
Y. C.
,
2004
, “
Analysis of Bearing Configuration Effects on High Speed Spindles Using an Integrated Dynamic Thermos-Mechanical Spindle Model
,”
Int. J. Mach. Tools Manuf.
,
44
(
4
), pp.
347
364
.
6.
Hwang
,
Y. K.
, and
Lee
,
C. M.
,
2010
, “
A Review on the Preload Technology of the Rolling Bearing for the Spindle of Machine Tools
,”
Int. J. Precis. Eng. Manuf.
,
11
(
3
), pp.
491
498
.
7.
Cao
,
H.
,
Holkup
,
T.
, and
Altintas
,
Y.
,
2011
, “
A Comparative Study on the Dynamics of High Speed Spindles With Respect to Different Preload Mechanisms
,”
Int. J. Adv. Manuf. Technol.
,
57
(
9–12
), pp.
871
883
.
8.
Zhang
,
J.
,
Fang
,
B.
,
Zhu
,
Y.
, and
Hong
,
H.
,
2017
, “
A Comparative Study and Stiffness Analysis of Angular Contact Ball Bearings Under Different Preload Mechanisms
,”
Mech. Mach. Theory
,
115
, pp.
1
17
.
9.
Gunduz
,
A.
,
Dreyer
,
J. T.
, and
Singh
,
R.
,
2012
, “
Effect of Bearing Preloads on the Modal Characteristics of a Shaft-Bearing Assembly: Experiments on Double Row Angular Contact Ball Bearings
,”
Mech. Syst. Signal Process.
,
31
(
6
), pp.
176
195
.
10.
Hong
,
S. W.
, and
Tong
,
V. C.
,
2016
, “
Rolling-Element Bearing Modeling: A Review
,”
Int. J. Precis. Eng. Manuf.
,
17
(
12
), pp.
1729
1749
.
11.
Lin
,
C. W.
,
Lin
,
Y. K.
, and
Chu
,
C. H.
,
2013
, “
Dynamic Models and Design of Spindle-Bearing Systems of Machine Tools: A Review
,”
Int. J. Precis. Eng. Manuf.
,
14
(
3
), pp.
513
521
.
12.
Zhang
,
X.
,
Han
,
Q.
,
Peng
,
Z.
, and
Chu
,
F.
,
2013
, “
Stability Analysis of a Rotor-Bearing System With Time-Varying Bearing Stiffness Due to Finite Number of Balls and Unbalanced Force
,”
J. Sound Vib.
,
332
(
25
), pp.
6768
6784
.
13.
Lim
,
T. C.
, and
Singh
,
R.
,
1990
, “
Vibration Transmission Through Rolling Element Bearings—Part 1: Bearing Stiffness Formulation
,”
J. Sound Vib.
,
139
(
2
), pp.
179
199
.
14.
Houpert
,
L.
,
1997
, “
A Uniform Analytical Approach for Ball and Roller Bearings Calculations
,”
ASME J. Tribol.
,
119
(
4
), pp.
851
858
.
15.
Hernot
,
X.
,
Sartor
,
M.
, and
Guillot
,
J.
,
2000
, “
Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach
,”
ASME J. Mech. Des.
,
122
(
1
), pp.
83
90
.
16.
Guo
,
Y.
, and
Parker
,
R. G.
,
2012
, “
Stiffness Matrix Calculation of Rolling Element Bearings Using a Finite Element/Contact Mechanics Model
,”
Mech. Mach. Theory
,
51
(
5
), pp.
32
45
.
17.
Walters
,
C. T.
,
1971
, “
The Dynamics of Ball Bearings
,”
ASME J. Lubr. Technol.
,
93
(
1
), pp.
1
10
.
18.
Gupta
,
P. K.
,
1979
, “
Dynamics of Rolling-Element Bearings—Part III: Ball Bearing Analysis
,”
ASME J. Lubr. Technol.
,
101
(
3
), pp.
312
318
.
19.
Nakhaeinejad
,
M.
, and
Bryant
,
M. D.
,
2011
, “
Dynamic Modeling of Rolling Element Bearings With Surface Contact Defects Using Bond Graphs
,”
ASME J. Tribol.
,
133
(
1
), p.
011102
.
20.
Jones
,
A. B.
,
1960
, “
A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions
,”
ASME J. Basic Eng.
,
82
(
2
), pp.
309
320
.
21.
de Mul
,
J. M.
,
Vree
,
J. M.
, and
Maas
,
D. A.
,
1989
, “
Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part I: General Theory and Application to Ball Bearings
,”
ASME J. Tribol.
,
111
(
1
), pp.
142
148
.
22.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
,
2006
,
Advanced Concepts of Bearing Technology: Rolling Bearing Analysis
,
5th ed.
, Taylor & Francis, New York.
23.
Jedrzejewski
,
J.
, and
Kwasny
,
W.
,
2010
, “
Modelling of Angular Contact Ball Bearings and Axial Displacements for High-Speed Spindles
,”
CIRP Ann.-Manuf. Technol.
,
59
(
1
), pp.
377
382
.
24.
Cao
,
Y.
, and
Altintas
,
Y.
,
2004
, “
A General Method for the Modeling of Spindle-Bearing Systems
,”
ASME J. Mech. Des.
,
126
(
6
), pp.
1089
1104
.
25.
Wang
,
W.
,
Hu
,
L.
,
Zhang
,
S.
,
Zhao
,
Z.
, and
Ai
,
S.
,
2014
, “
Modeling Angular Contact Ball Bearing Without Raceway Control Hypothesis
,”
Mech. Mach. Theory
,
82
(
24
), pp.
154
172
.
26.
Zhao
,
C.
,
Yu
,
X.
,
Huang
,
Q.
,
Ge
,
S.
, and
Gao
,
X.
,
2015
, “
Analysis on the Load Characteristics and Coefficient of Friction of Angular Contact Ball Bearing at High Speed
,”
Tribol. Int.
,
87
, pp.
50
56
.
27.
Sheng
,
X.
,
Li
,
B.
,
Wu
,
Z.
, and
Li
,
H.
,
2014
, “
Calculation of Ball Bearing Speed-Varying Stiffness
,”
Mech. Mach. Theory
,
81
(
11
), pp.
166
180
.
28.
Noel
,
D.
,
Ritou
,
M.
,
Furet
,
B.
, and
Loch
,
S. L.
,
2013
, “
Complete Analytical Expression of the Stiffness Matrix of Angular Contact Ball Bearings
,”
ASME J. Tribol.
,
135
(
4
), p.
041101
.
29.
Royston
,
T. J.
, and
Basdogan
,
I.
,
1998
, “
Vibration Transmission Through Self-Aligning (Spherical) Rolling Element Bearings: Theory and Experiment
,”
J. Sound Vib.
,
215
(
5
), pp.
997
1014
.
30.
Kogan
,
G.
,
Klein
,
R.
,
Kushnirsky
,
A.
, and
Bortman
,
J.
,
2013
, “
Toward a 3D Dynamic Model of a Faulty Duplex Ball Bearing
,”
Mech. Syst. Signal Process.
,
54–55
, pp.
243
258
.
31.
Petersen
,
D.
,
Howard
,
C.
,
Sawalhi
,
N.
,
Ahmadi
,
A. M.
, and
Singh
,
S.
,
2015
, “
Analysis of Bearing Stiffness Variations, Contact Forces and Vibrations in Radially Loaded Double Row Rolling Element Bearings With Raceway Defects
,”
Mech. Syst. Signal Process.
,
50–51
, pp.
139
160
.
32.
Zhang
,
J.
,
Fang
,
B.
,
Hong
,
J.
,
Wan
,
S.
, and
Zhu
,
Y.
,
2017
, “
A General Model for Preload Calculation and Stiffness Analysis for Combined Angular Contact Ball Bearings
,”
J. Sound Vib.
,
411
, pp.
435
449
.
33.
Alfares
,
M. A.
, and
Elsharkawy
,
A. A.
,
2003
, “
Effects of Axial Preloading of Angular Contact Ball Bearings on the Dynamics of a Grinding Machine Spindle System
,”
J. Mater. Process. Technol.
,
136
(
1–3
), pp.
48
59
.
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