The Analysis of Linear Rotor-Bearing Systems: A General Transfer Matrix Method

1993 ◽  
Vol 115 (4) ◽  
pp. 490-497 ◽  
Author(s):  
An-Chen Lee ◽  
Yuan-Pin Shih ◽  
Yuan Kang
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Three Dimensional ◽  
Continuous System ◽  
State Variables ◽  
Rotor Bearing ◽  
Steady State Responses ◽  
State Responses

A general transfer matrix method (GTMM) is developed in the present work for analyzing the steady-state responses of rotor-bearing systems with an unbalancing shaft. Specifically, we derived the transfer matrix of shaft segments by considering the state variables of shaft in a continuous system sense to give the most general formulation. The shaft unbalance, axial force, and axial torque are all taken into consideration so that the completeness of transfer matrix method for steady-state analysis of linear rotor-bearing systems is reached. To demonstrate the effectiveness of this approach, a numerical example is presented to estimate the effect of three-dimensional distribution of shaft unbalance on the steady-state responses by GTMM and finite element method (FEM).

A Modified Transfer Matrix Method for Asymmetric Rotor-Bearing Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 309-317 ◽  
Author(s):  
Yuan Kang ◽  
An-Chen Lee ◽  
Yuan-Pin Shih
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Harmonic Balance Method ◽  
Continuous System ◽  
Euler Beam ◽  
Rotating Shaft ◽  
Rotor Bearing ◽  
Asymmetric Rotor ◽  
Steady State Responses

A modified transfer matrix method (MTMM) is developed to analyze rotor-bearing systems with an asymmetric shaft and asymmetric disks. The rotating shaft is modeled by a Rayleigh-Euler beam considering the effects of the rotary inertia and gyroscopic moments. Specifically, a transfer matrix of the asymmetric shaft segments is derived in a continuous-system sense to give accurate solutions. The harmonic balance method is incorporated in the transfer matrix equations, so that steady-state responses of synchronous and superharmonic whirls can be determined. A numerical example is presented to demonstrate the effectiveness of this approach.

A Modified Transfer Matrix Method for Linear Rotor-Bearing Systems

1991 ◽  
Vol 58 (3) ◽  
pp. 776-783 ◽  
Author(s):  
An-Chen Lee ◽  
Yuan Kang ◽  
Shin-Li Liu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Continuous System ◽  
Large Degree ◽  
System Concept ◽  
Rotor Bearing ◽  
Steady State Responses ◽  
Time Marching ◽  
Fixed Matrix

The steady-state responses of linear flexible rotor-bearing systems are analyzed by the modified transfer matrix method. The transfer matrix has the advantage of solving the problems in frequency domain with fixed matrix size. This makes the method more economical in analyzing a large degree-of-freedom rotor system than many time-marching integrating methods. In this paper, the modifications of transfer matrix method include that the transfer matrix of shaft is derived from the “continuous system” concept instead of conventional “lumped system” concept, and the paper tries to extend the transfer matrix method to fit synchronous elliptical orbit and nonsynchronous multi-lobed whirling orbit. To demonstrate the applications of the method, three examples are presented; two synchronous and one nonsynchronous.

Nonlinear Steady-State Rotordynamic Analysis Using Transfer Coefficient Method

1991 ◽  
Author(s):  
M. Kobayashi ◽  
S. Saito ◽  
S. Yamauchi
Keyword(s):  
Steady State ◽  
Transfer Coefficient ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Degrees Of Freedom ◽  
Computation Time ◽  
Squeeze Film ◽  
State Variables ◽  
Coefficient Method

Abstract This paper proposes a new method for steady-state, large-order nonlinear rotordynamic calculations: it uses a method called the transfer coefficient method (TCM), which is more convenient than the transfer matrix method. Since TCM calls for only the displacement as the independent variable, whereas both the displacement and the force are needed as the state variables in the conventional transfer matrix method, TCM promises a substantial saving of computation time without incurring loss in the accuracy of calculation. First, the outline of TCM is explained, then the nonlinear calculations for a rotor of many degrees of freedom are presented. This steady-state nonlinear calculation method is based on the discreet Fourier transform (DPT, FFT) and substructure synthesis. As an example, the nonlinear response due to unbalance mass is calculated and discussed in the case of the rotor which is supported by three bearings with two nonlinear squeeze film dampers.

An Improved Transfer Matrix Method for Steady-State Analysis of Nonlinear Rotor-Bearing Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 303-310 ◽  
Author(s):  
J. W. Zu ◽  
Z. Ji
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Roller Bearing ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Rotating Shaft ◽  
Damping Characteristics ◽  
Rotor Bearing

An improved transfer matrix method is developed to analyze nonlinear rotor-bearing systems. The rotating shaft is described by the Timoshenko beam theory which considers the effect of the rotary inertia and shear deformation. A typical roller bearing model is assumed which has cubic nonlinear spring and linear damping characteristics. Transfer matrices for the Timoshenko shaft element, disk element, and nonlinear bearing element are derived and the global transfer matrix is formed. The steady-state response of synchronous, subharmonic, and superharmonic whirls is determined using the harmonic balance method. Two numerical examples are presented to demonstrate the effectiveness of this approach.

Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method

1995 ◽  
Author(s):  
Siu-Tong Choi ◽  
Sheng-Yang Mau
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Analysis ◽  
Transmission Error ◽  
Mode Shapes ◽  
Rotor Systems ◽  
Gear Mesh ◽  
Mass Unbalance ◽  
Rotor Bearing

Abstract In this paper, an analytical study of the dynamic characteristics of geared rotor-bearing systems by the transfer matrix method is presented. Rotating shafts are modeled as Timoshenko beam with shear deformation and gyroscopic effects taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set and a transmission-error exciter. The transfer matrix of a gear mesh is developed. The coupling motions of the lateral and torsional vibration are studied. In free vibration analysis of geared rotor systems, natural frequencies and corresponding mode shapes, and the whirl frequencies under different spin speeds are determined. Effects of bearing stiffness, isotropic and orthotropic bearings, pressure angle of the gear mesh are studied. In steady-state vibration analysis, responses due to the excitation of mass unbalance and the transmission error are studied. Parametric characteristics of geared rotor systems are discussed.

Riccati Transfer Equations for Linear Multibody Systems with Indeterminate In-Span Conditions

2019 ◽  
Vol 86 (6) ◽  
Author(s):  
Jianshu Zhang ◽  
Xiaoting Rui ◽  
Junjie Gu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Multibody Systems ◽  
Internal Force ◽  
State Variables ◽  
Transfer Matrices ◽  
Transfer Equations ◽  
Mechanical Elements

The transfer matrix method for linear multibody systems is capable of providing precise solutions for the dynamics of various mechanical systems, but it may also suffer from numerical instability in some cases, where serial chains with a large number of mechanical elements are involved or high-frequency harmonic responses are computed. Combining such a transfer strategy with the Riccati transformation yields the Riccati transfer matrix method (RTMM), which can help improve the numerical stability. According to the existing method, the conventional transfer matrices of all the mechanical elements should be obtained first; in other words, the existence of conventional transfer matrices is a prerequisite for the application of the RTMM. Thus, it seems that the RTMM is incapable of performing the dynamics analysis of linear multibody systems with indeterminate in-span conditions due to the nonexistence of the corresponding conventional transfer matrices. Observe that, for any state variables with indeterminate input–output relationships, the complementary state variables (the complementary state variable of a displacement is the corresponding internal force and vice versa) are identically equal to zero, and that the dimension of the Riccati transfer equation is only half of that of the conventional transfer equation. It reveals that the Riccati transfer equations for the connection points associated with indeterminate in-span conditions can be formulated directly, and that there is no need to rely on the conventional transfer equation. Two numerical examples are simulated and the computational results are compared with those obtained by the finite element method, which verifies the proposed method.

Study of Transfer Matrix of Rolling Bearing Including Squeeze Film Damper

2012 ◽  
Vol 490-495 ◽  
pp. 618-622
Author(s):  
Hua Tao Tang ◽  
Xin Yue Wu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Rolling Bearing ◽  
Squeeze Film ◽  
Body System ◽  
Squeeze Film Damper ◽  
Rotor Bearing ◽  
Multi Body ◽  
Bearing System

The transfer matrix of rolling bearing including squeeze film damper (SFD) is studied, and the rotor – bearing system is modeled by transfer matrix method of multi-body system. It is proved by an example that the method, which provides a new idea to solve the problem of complex rotor – bearing system, is feasible and effective.

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