Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model, as well as mathematical method, which contains $2n+2 degrees$ of freedom, is presented for calculating the dynamical characteristics of tilting-pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement, and the generalized force vector are chosen. The concise transformation of generalized displacement, generalized force, and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using the Newton–Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration. Numerical results show that the reduced damping coefficients and the threshold speed can be effectively enhanced by giving suitable pad pivot stiffness and damping simultaneously, and this analytical method can be applied to analyze dynamical behavior of the tilting-pad journal bearing rotor system.

1.
Lund
,
J. W.
, 1964, “
Spring and Damping Coefficients for the Tilting-Pad Journal Bearing
,”
ASLE Trans.
0569-8197,
7
, pp.
342
352
.
2.
Hashimoto
,
H.
,
,
S.
, and
Marukawa
,
T.
, 1985, “
Performance and Characteristics of Large Scale Tilting-Pad Journal Bearing
,”
Bull. JSME
0021-3764,
242
(
28
), pp.
1761
1765
.
3.
Lund
,
J. W.
, 1987, “
The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing
,”
ASME J. Tribol.
0742-4787,
109
, pp.
65
70
.
4.
Kirk
,
R. G.
, 1988, “
Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
0739-3717,
110
, pp.
165
171
.
5.
Rouch
,
K. E.
, 1982, “
,”
ASLE Trans.
0569-8197,
26
(
1
), pp.
102
109
.
6.
Dmochowski
,
W.
, 2007, “
Dynamic Properties of Tilting-Pad Journal Bearings: Experimental and Theoretical Investigation of Frequency Effects Due to Pivot Flexibility
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
129
, pp.
865
869
.
7.
Gardner
,
W. W.
, 1998, “
Journal Bearing Having Vibration Damping Elements
,” U.S. Patent No. 5738445.
8.
Deckler
,
D. C.
, and
Veiliette
,
R. J.
, 2004, “
Simulation and Control of an Active Tilting-Pad Journal Bearing
,”
Tribol. Trans.
1040-2004,
47
, pp.
440
458
.
9.
Qiao
,
G.
,
Wang
,
L. P.
, and
Zheng
,
T. S.
, 2007, “
Linear Stability Analysis of a Tilting-Pad Journal Bearing System
,”
ASME J. Tribol.
0742-4787,
129
, pp.
348
353
.
10.
Yan
,
Z.
,
Wang
,
L.
,
Qiao
,
G.
, and
Zheng
,
T.
, 2010, “
An Analytical Model for Complete Dynamical Coefficients of Tilting Pad Journal Bearing
,”
Tribol. Int.
0301-679X,
43
(
1–2
), pp.
7
15
.
11.
Zheng
,
T. S.
, and
Hasebe
,
N.
, 2000, “
Calculation of Equilibrium Position and Dynamic Coefficients of a Journal Bearing Using Free Boundary Theory
,”
Trans. ASME, J. Tribol.
0742-4787,
122
, pp.
616
21
.