scholarly journals Dynamic Analysis of Flexible Rotor Based on Transfer Symplectic Matrix

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Hao Deng ◽  
Xi Fang ◽  
Huachun Wu ◽  
Yiming Ding ◽  
Jinghu Yu ◽  
...  
Keyword(s):  
Transfer Matrix ◽  
Matrix Method ◽  
Critical Speed ◽  
Reference Method ◽  
Rotor System ◽  
High Order ◽  
Symplectic Matrix ◽  
Hamilton System ◽  
System A ◽  
Relative Errors

In view of the numerical instability and low accuracy of the traditional transfer matrix method in solving the high-order critical speed of the rotor system, a new idea of incorporating the finite element method into the transfer matrix is proposed. Based on the variational principle, the transfer symplectic matrix of gyro rotors suitable for all kinds of boundary conditions and supporting conditions under the Hamilton system is derived by introducing dual variables. To verify the proposed method in rotor critical speed, a numerical analysis is adopted. The simulation experiment results show that, in the calculation of high-order critical speed, especially when exceeding the sixth critical speed, the numerical accuracy of the transfer symplectic matrix method is obviously better than that of the reference method. The relative errors between the numerical solution and the exact solution are 0.0347% and 0.2228%, respectively, at the sixth critical speed. The numerical example indicates the feasibility and superiority of the method, which provides the basis for the optimal design of the rotor system.

Extension of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions

1980 ◽  
Vol 102 (1) ◽  
pp. 122-129 ◽  
Author(s):  
M. S. Darlow ◽  
B. T. Murphy ◽  
J. A. Elder ◽  
G. N. Sandor
Keyword(s):  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Critical Speed ◽  
Axial Direction ◽  
Matrix Analysis ◽  
Beam Elements ◽  
Conical Section ◽  
Rotor Model

The transfer matrix method for rotordynamic analysis (alternately known as the HMP or LMP method) has enjoyed wide popularity due to its flexibility and ease of application. A number of computer programs are generally available which use this method in various forms to perform undamped critical speed, unbalance response, damped critical speed and stability analyses. For all of these analyses, the assembly of the transfer matrices from the rotor model is essentially the same. In all cases, the rotor model must be composed entirely of cylindrical beam elements. There are two situations when this limitation is not desirable. The first situation is when the rotor being modelled has one or more sections whose cross sections vary continually in the axial direction. The most common of these sections is the conical section. Presently, a conical section must be modelled as a series of “steps” of cylindrical sections. This adversely affects both the simplicity and accuracy of the rotor model. The second situation when current transfer matrix techniques are not accurate is when the rotor being modelled has one or more sections that do not behave as beam elements. The most common example is a trunnion which behaves as a plate. This paper describes the analytical basis and the method of application for direct representation of conical sections and trunnions for a transfer matrix analysis. Analytical results are currently being generated to demonstrate the need for and advantages of these modelling procedures.

VIBRATIONS OF A ROTOR SYSTEM WITH MULTIPLE COUPLER OFFSETS

2011 ◽  
Vol 35 (1) ◽  
pp. 81-100
Author(s):  
Chao-Yang Tsai ◽  
Shyh-Chin Huang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Rotational Speed ◽  
Matrix Method ◽  
Rotor System ◽  
Response Amplitude ◽  
External Excitation ◽  
Phase Offset ◽  
Major Response ◽  
Before And After

In this paper, a transfer matrix method (TMM) for rotors with multiple coupler offsets was derived. The studies showed the coupler’s stiffness altered the rotor’s critical speeds but offset caused additional external excitation. The cases of two offsets in- and anti-phase in a typical rotor were given as examples. In the in-phase case, significantly increased response amplitude occurred at lower rotational speed and the increase was linearly proportional to the offset value. As to the anti-phase case, the increased response was insignificant, implying an opposite offset would cancel out a major response of the previous offset. The whirling orbits before and after the offset couplers were also illustrated. The results, as expected, showed the in-phase offset displayed much larger radii than the anti-phase’s. The rotor’s orbits changed the whirling direction once the rotation fell within a certain range and this feature seemed to be unaffected by coupler offsets.

The Dynamics Modeling and Simulation of Spindle System of Ultra-High Speed Grinding Machine Tool

2011 ◽  
Vol 175 ◽  
pp. 206-210 ◽  
Author(s):  
Ya Li Hou ◽  
Chang He Li
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Performance Optimization ◽  
Matrix Method ◽  
High Speed ◽  
Critical Speed ◽  
Dynamics Modeling ◽  
Spindle System ◽  
Ultra High Speed ◽  
Grinding Machine

This study was focused on the theoretical modeling and numerical simulation about the dynamic characteristics of spindle system of ultra-high speed grinder. Based on the rotor dynamics and structural system dynamics, a dynamic model was established using the transfer matrix method and the overall transfer matrix method. The critical speeds of first three orders, the modes of variation and other dynamic characteristic parameters of the spindle system were analyzed and calculated. The results showed that the working speed of the spindle system is much lower than the primary critical speed and can therefore stay away the resonance range effectively. Furthermore, the span of the fulcrum bearing and the overhang had significant influences on the critical speed within a certain range, and the study provided the basis and guidance for the structural design and performance optimization of the spindle system.

Dynamic Analysis of Complex Composite Rotor Systems With Substructure Transfer Matrix Method

1985 ◽  
Author(s):  
Yan Litang
Keyword(s):  
Dynamic Analysis ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Synthesis Method ◽  
Frequency Equation ◽  
Rotor System ◽  
Combination Method ◽  
Rotor Systems ◽  
Modal Synthesis

A substructure transfer matrix method for the dynamic analysis of multi-Rotor systems and complex composite systems is presented. When calculating, the rotor system should be decomposed into several single rotor shafts (substructures). Corresponding unknown external loads and deflections are applied to the separated surfaces, rigid support sections and ball joint sections respectively to replace the original connections. According to the connective and boundary conditions of the whole rotor system, a system of equations is established, from which the frequency equation results. The calculating formulas of vibration modes and of unbalanced response will be easily formed by linear combination method. All computations are performed with the transfer matrix method. This method is intelligible, readily programmed and much simpler than the current transfer matrix method and modal synthesis method.

scholarly journals Investigation of the Steady-State Response of a Dual-Rotor System With Inter-Shaft Squeeze Film Damper

1985 ◽  
Author(s):  
Qihan Li ◽  
Litang Yan ◽  
James F. Hamilton
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Rotor System ◽  
Squeeze Film ◽  
Turbine Engine ◽  
Squeeze Film Damper ◽  
State Response ◽  
Unbalance Response

This paper presents an analysis of the steady-state unbalance response of a dual-rotor gas turbine engine with a flexible intershaft squeeze film damper using a simplified transfer matrix method. The simplified transfer matrix method is convenient for the evaluation of the critical speed and response of the rotor system with various supports, shaft coupling, intershaft bearing, etc. The steady-state unbalance response of the rotor system is calculated for different shaft rotation speeds. The damping effects of an intershaft squeeze film damper with different radial clearances under various levels of rotor unbalance are investigated.

Study on the Coupled Bending and Torsional Vibrations of Turbo-Generator Unit with Rub-Impact

2012 ◽  
Vol 246-247 ◽  
pp. 1273-1277
Author(s):  
Cheng Bing He ◽  
Shi Chao Wang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Vibration Amplitude ◽  
Critical Speed ◽  
Torsional Vibrations ◽  
Mass Model ◽  
Mass Unbalance ◽  
Turbo Generator ◽  
Generator Unit

An increment transfer matrix equations based on step-by-step integration method and traditional transfer matrix method are deduced Combined with multi-mass model and Riccati method, the increment transfer matrix method is put forward, that can be directly used to analyze the dynamic response of the coupled bending and torsional vibrations of turbo-generator shafts with rub-impact. Taking a turbo-generator unit as example, the vibration character of rub-impact fault is analyzed when unit starts up. The research results show that rubbing will make vibration amplitude increase when the rotational speed is lower than the first critical speed; however, when the speed is higher than the first critical speed, rubbing will make the rotor mass unbalance reduce, thereby vibration amplitude will reduce slightly.

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