Torsional Response of a Gear Train System

1972 ◽  
Vol 94 (2) ◽  
pp. 583-592 ◽  
Author(s):  
S. M. Wang ◽  
I. E. Morse
Keyword(s):  
Numerical Solutions ◽  
Coupling Effect ◽  
Gear Tooth ◽  
Gear Train ◽  
Mode Shapes ◽  
Mass System ◽  
Low Frequencies ◽  
Torsional Response ◽  
Applied Forces ◽  
Train System

A gear train system can be represented by a spring-mass system having many degrees of freedom. The transfer matrix technique [1, 2] has been applied to give the static and dynamic torsional response of a general gear train system. The method develops, directly from drawings, all equations necessary for the solution of the problem. Effects that can be included in the formulation are the gear tooth stiffnesses, gear web stiffness, nonuniform cross section of shafts, external torques, special types of joints, general boundary conditions, and multi-geared branched systems. A general computer program has been written to obtain numerical solutions. The experimental evaluation of a gear train system has been conducted using an electrohydraulic exciter and an Automatic Mechanical Impedance Transfer Function Analyzer System (TFA). The spindle shaft of a non-rotating, preloaded gear train system is excited by applied forces in the bending and torsional directions. The computed torsional natural frequencies and mode shapes correlate at low frequencies. At higher frequencies, there is a coupling effect between the motion in torsion and transverse motions. The presented analytical and experimental technique may be a practical method to evaluate the torsional response of a gear train system.

Time Varying Meshing Stiffness of Cracked Sun and Ring Gears of Planetary Gear Train

2015 ◽  
Vol 772 ◽  
pp. 164-168
Author(s):  
Arif Abdullah Muhammad ◽  
Guang Lei Liu
Keyword(s):  
Gear Tooth ◽  
Planetary Gear ◽  
Mesh Point ◽  
Gear Train ◽  
Time Varying ◽  
Planetary Gear Train ◽  
Meshing Stiffness ◽  
Face Width ◽  
The Face ◽  
Applied Forces

The time varying meshing stiffness of normal and cracked spur gears of planetary gear train is studied by applying the unit normal forces at mesh point on the face width along the line of action of the single gear tooth in FE based software Ansys Workbench 14.5. The tooth deflections due to the applied forces at one mesh point are noted and a deflection matrix is established which is solved using Matlab to get net deflection and finally the meshing stiffness of gear tooth at particular mesh point. The process is repeated for other mesh points of gear tooth by rotating it to get meshing stiffness for whole gear tooth.

Analysis of Nonlinear Transient Motion of a Geared Torsional

1974 ◽  
Vol 96 (1) ◽  
pp. 51-59 ◽  
Author(s):  
S. M. Wang
Keyword(s):  
Gear Tooth ◽  
Nonlinear Damping ◽  
Gear Train ◽  
Transient Motion ◽  
Closed Form Solutions ◽  
Torsional Response ◽  
Tooth Stiffness ◽  
Nonlinear Transient ◽  
Linear And Nonlinear ◽  
Torsional Analysis

The dynamic torsional analysis of gear train systems has implemented many practical system designs. A computer analysis to predict the steady-state torsional response of a gear train system is presented in reference [1]. The current paper extends this work to the linear and nonlinear transient analysis of complex torsional gear train systems. Factors considered in the formulation are time-varying gear tooth stiffness, gear web rigidity, gear tooth backlash, shafts of nonuniform cross section, linear and nonlinear damping elements, multishock loadings, and complex-geared branched systems. For linear systems, the equations of transient motion are derived and closed-form solutions can be obtained by the state transition method [2]. For nonlinear systems, numerical methods are also presented. The method may be used as a means to analyze gear train start/stop operational problems, as well as constant speed response subject to internal and external disturbances.

Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

2015 ◽  
Vol 15 (02) ◽  
pp. 1450040 ◽  
Author(s):  
Seyed Mojtaba Hozhabrossadati ◽  
Ahmad Aftabi Sani ◽  
Masood Mofid
Keyword(s):  
Technical Note ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Mass System ◽  
Rotational Spring ◽  
Beam System ◽  
Sample Frequency ◽  
Elastically Restrained ◽  
Euler Bernoulli Beam

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses.

scholarly journals Mesh Phase Analysis of Encased Differential Gear Train for Coaxial Twin-Rotor Helicopter

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Donglin Zhang ◽  
Rupeng Zhu ◽  
Bibo Fu ◽  
Wuzhong Tan
Keyword(s):  
Phase Difference ◽  
Gear Tooth ◽  
Phase Relations ◽  
Gear Train ◽  
Time Varying ◽  
Gear Pair ◽  
Meshing Stiffness ◽  
Differential Gear ◽  
Starting Point ◽  
Twin Rotor

Dynamic excitation caused by time-varying meshing stiffness is one of the most important excitation forms in gear meshing process. The mesh phase relations between each gear pair are an important factor affecting the meshing stiffness. In this paper, the mesh phase relations between gear pairs in an encased differential gear train widely used in coaxial twin-rotor helicopters are discussed. Taking the meshing starting point where the gear tooth enters contact as the reference point, the mesh phase difference between adjacent gear pairs is analyzed and calculated, the system reference gear pair is selected, and the mesh phase difference of each gear pair relative to the system reference gear pair is obtained. The derivation process takes into account the modification of the teeth, the processing, and assembly of the duplicate gears, which makes the calculation method and conclusion more versatile. This work lays a foundation for considering the time-varying meshing stiffness in the study of system dynamics, load distribution, and fault diagnosis of compound planetary gears.

In-Plane Vibration Analysis of Rotating Tapered Timoshenko Beams

2016 ◽  
Vol 08 (05) ◽  
pp. 1650064 ◽  
Author(s):  
Jianshi Fang ◽  
Ding Zhou
Keyword(s):  
Chebyshev Polynomials ◽  
Coupling Effect ◽  
Mode Shapes ◽  
Transverse Motion ◽  
Timoshenko Beams ◽  
Rotational Angle ◽  
Plane Vibration ◽  
Present Solution ◽  
Boundary Functions ◽  
Geometric Boundary

Modal analysis of rotating tapered cantilevered Timoshenko beams undergoing in-plane vibration is investigated. The coupling effect of axial motion and transverse motion is considered. The Kane dynamic method is applied to deriving the governing eigenvalue equations. The displacement and rotational angle components are approximately described by the products of Chebyshev polynomials and corresponding boundary functions. Chebyshev polynomials guarantee the numerical robustness while the boundary functions guarantee the satisfaction of the geometric boundary conditions. The excellent convergence of the present solution is exhibited. The results are compared with those available in literature, good agreement is observed. The parametric studies on modal characteristics are presented in detail. The tuned rotational speed is examined and the eigenvalue loci veering phenomenon along with the corresponding mode shapes is investigated.

scholarly journals Numerical and Experimental Investigations of Coupling Effects in Anisotropic Elastic Rotors

1999 ◽  
Vol 5 (4) ◽  
pp. 263-271 ◽  
Author(s):  
Horst Irretier ◽  
Georges Jacquet-Richardet ◽  
Frank Reuter
Keyword(s):  
Coupling Effect ◽  
Experimental Results ◽  
Mode Shapes ◽  
Experimental Investigations ◽  
Coupling Effects ◽  
Symmetry Approach ◽  
Anisotropic Elastic ◽  
Elastic Modes ◽  
Bending Modes ◽  
The One

It is known that in elastic disc-shaft systems in particular, the one-nodal-diameter mode of the discs can be highly coupled with the bending modes of the shaft. Consequently, when the system rotates, the elastic modes of the flexible discs are coupled with the gyroscopic modes of the flexible shaft equipped with rigid discs. In the paper this coupling effect is investigated numerically and experimentally.A numerical model, based on a finite element cyclic symmetry approach, is presented. This model has been developed for studying the wheel-shaft coupling effects on the global behavior of turbomachinery rotors. In order to better illustrate the phenomenon involved and to validate the model, the method is applied here to a thin tuned and detuned circular disc mounted on an elastic shaft. Related frequency and mode shapes of the rotating assembly are discussed. Additional experimental results, based on an experimental modal analysis technique for rotating structures, are presented. Both numerical and experimental results are compared.

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