Abstract

This study investigated the stiffness characteristics of crossed-roller bearings (XRBs) subjected to various loading and boundary conditions. A five-degrees-of-freedom XRB model was adopted that considers the effect of roller roundness deformation, which was developed by the authors in a prior study. The analytical formulation for a fully occupied (5 × 5) stiffness matrix of XRB was obtained. Extended simulations were performed to determine the XRB stiffness and internal load distribution considering the effects of the external loads, axial preloads, axial clearance, and angular misalignment. The numerical results confirmed that the bearing stiffness possessed significant nonlinearity with respect to the external loads. Increasing the axial clearance reduced the stiffness of the bearing under radial and moment loading, but it did not affect the stiffness of the pure axially loaded bearing. The stiffness of the bearing with axial clearance increased consistently with the misalignment angle. The stiffness behavior of the preloaded bearing depended on the misalignment angle.

References

1.
Cao
,
Y.
, and
Altintas
,
Y.
,
2007
, “
Modeling of Spindle-Bearing and Machine Tool Systems for Virtual Simulation of Milling Operations
,”
Int. J. Mach. Tools Manuf.
,
47
(
9
), pp.
1342
1350
.
2.
Gargiulo
,
E. P.
,
1980
, “
A Simple Way to Estimate Bearing Stiffness
,”
Mach. Des.
,
52
(
17
), pp.
107
110
.
3.
Wardle
,
F. P.
,
Lacey
,
S. J.
, and
Poon
,
S. Y.
,
1983
, “
Dynamic and Static Characteristics of a Wide Speed Range Machine Tool Spindle
,”
Precis. Eng.
,
5
(
4
), pp.
175
183
.
4.
Harris
,
T. A.
,
2001
,
Rolling Bearing Analysis
, 4th ed.,
John Wiley & Sons
,
New York
.
5.
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
.
6.
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
.
7.
Tong
,
V. C.
, and
Hong
,
S. W.
,
2017
, “
Modeling and Analysis of Double-Row Cylindrical Roller Bearings
,”
J. Mech. Sci. Technol.
,
31
(
7
), pp.
3379
3388
.
8.
Tong
,
V. C.
, and
Hong
,
S. W.
,
2017
, “
Analysis of the Stiffness and Fatigue Life of Double-Row Angular Contact Ball Bearings
,”
J. Korean Soc. Precis. Eng.
,
34
(
11
), pp.
813
821
.
9.
Zheng
,
J.
,
Ji
,
J.
,
Yin
,
S.
, and
Tong
,
V. C.
,
2020
, “
Internal Loads and Contact Pressure Distributions on the Main Shaft Bearing in a Modern Gearless Wind Turbine
,”
Tribol. Int.
,
141
, p.
105960
.
10.
Than
,
V. T.
, and
Huang
,
J. H.
,
2016
, “
Nonlinear Thermal Effects on High-Speed Spindle Bearings Subjected to Preload
,”
Tribol. Int.
,
96
, pp.
361
372
.
11.
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
.
12.
Sjovall
,
H.
,
1933
, “
The Load Distribution Within Ball and Roller Bearings Under Given External Radial and Axial Load
,”
Tekniks Tidskrift Mek.
h.9.
13.
Noel
,
D.
,
Ritou
,
M.
,
Furet
,
B.
, and
Le Loch
,
S.
,
2013
, “
Complete Analytical Expression of the Stiffness Matrix of Angular Contact Ball Bearings
,”
ASME J. Tribol.
,
135
(
4
), p.
041101
.
14.
Lim
,
T. C.
, and
Singh
,
R.
,
1990
, “
Vibration Transmission Through Rolling Element Bearings, Part I: Bearing Stiffness Formulation
,”
J. Sound Vib.
,
139
(
2
), pp.
179
199
.
15.
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
.
16.
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
, pp.
176
195
.
17.
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. Sig. Process.
,
50–51
, pp.
139
160
.
18.
Zhuo
,
Y.
,
Zhou
,
X.
, and
Yang
,
C.
,
2014
, “
Dynamic Analysis of Double row Self-Aligning Ball Bearings due to Applied Loads, Internal Clearance, Surface Waviness and Number of Balls
,”
J. Sound Vib.
,
333
(
23
), pp.
6170
6189
.
19.
Geng
,
K.
, and
Lin
,
S.
,
2020
, “
Effect of Angular Misalignment on the Stiffness of the Double-row Self-Aligning Ball Bearing
,”
Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
234
(
4
), pp.
946
962
.
20.
Lin
,
S.
, and
Jiang
,
S.
,
2019
, “
Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings
,”
ASME J. Tribol.
,
141
(
3
), p.
032204
.
21.
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
, pp.
32
45
.
22.
Tong
,
V. C.
,
Jeong
,
E. W.
, and
Hong
,
S. W.
,
2020
, “
Modeling of Crossed Roller Bearings Considering Roller Roundness Deformation
,”
ASME J. Tribol.
,
142
(
12
), p.
121201
.
23.
Harris
,
T. A.
, and
Kotzalas
,
M. N.
,
2006
,
Advanced Concepts of Bearing Technology: Rolling Bearing Analysis
,
CRC Press
,
Boca Raton, FL
.
24.
ISO/TS 16281
,
2008
, “
Rolling Bearings—Methods for Calculating the Modified Reference Rating Life for Universally Loaded Bearings
,” ISO/TS 16281.
25.
Tong
,
V. C.
, and
Hong
,
S. W.
,
2016
, “
Fatigue Life of Tapered Roller Bearing Subject to Angular Misalignment
,”
Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
,
230
(
2
), pp.
147
158
.
26.
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 II: Application to Roller Bearings and Experimental Verification
,”
ASME J. Tribol.
,
111
(
1
), pp.
149
155
.
You do not currently have access to this content.