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.

Delay-Bond Graph Models for Geared Torsional Systems

1974 ◽  
Vol 41 (2) ◽  
pp. 366-370 ◽  
Author(s):  
N. T. Tsai ◽  
S. M. Wang
Keyword(s):  
Transmission Line ◽  
Gear Tooth ◽  
Nonlinear Damping ◽  
Bond Graph ◽  
Dynamic Responses ◽  
State Variables ◽  
Graph Models ◽  
Wave Variables ◽  
Tooth Stiffness ◽  
Line Elements

The dynamic responses of geared torsional systems are analyzed with the delay-bond graph technique. By transforming the power variables into torsional wave variables, the torsional elements are modeled as transmission line elements. The nonlinear elements, e.g., varying tooth stiffness, gear-tooth backlash, and nonlinear damping, are incorporated into the ideal transmission line element. A computational algorithm is established where the state variables of the system are expressed in terms of wave scattering variables and the dynamic responses are then obtained in both time and space domains. The simulation results of several simple examples of linear and nonlinear geared torsional systems are presented to demonstrate the feasibility of this algorithm.

Dynamic analysis of a 2-lobe geometrically imperfect journal bearing system

2016 ◽  
Vol 231 (7) ◽  
pp. 934-950 ◽  
Author(s):  
Dharmendra Jain ◽  
Satish C Sharma
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Constant Flow ◽  
Kutta Method ◽  
Transient Motion ◽  
Nonlinear Transient ◽  
Linear And Nonlinear ◽  
Nonlinear Equations Of Motion ◽  
Bearing System ◽  
Flow Valve

The present study is concerned with the linear and nonlinear transient motion analysis of a 2-lobe geometrically imperfect hybrid journal bearing system compensated with constant flow valve restrictor. The trajectories of journal center motion for a geometrically imperfect rotating journal (barrel, bellmouth and undulation type journal) have been numerically simulated by solving the linear and nonlinear equations of motion of journal center using a fourth order Runga–Kutta method. The numerically computed results for the journal center trajectories indicate that the 2-lobe bearing [Formula: see text] is more stable with geometrically imperfect journal as compared to the circular bearing with imperfect journal.

Multibody Dynamics Model for Predicting the Vibration Response and Transient Tooth Loads for Planetary Gear Systems

2011 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Michael Lee Stark
Keyword(s):  
Multibody Dynamics ◽  
Contact Surface ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Gear Train ◽  
Dynamics Model ◽  
Normal Contact ◽  
Tooth Stiffness ◽  
Stiffness And Damping ◽  
Multibody Dynamics Model

A high-fidelity multibody dynamics model for predicting the transient response of planetary gear trains is presented. The model supports an arbitrary number of gears, stages and arms. The model accurately accounts for the effects of gear tooth stiffness/damping/friction and tooth backlash. The multibody system representing the system is modeled using rigid bodies, revolute joints and rotational actuators. A penalty model is used to impose the joint and normal contact constraints. The normal contact penalty stiffness and damping are used to model the tooth stiffness and damping. The contact model detects contact between discrete points on the surface of a gear tooth (master contact surface) and a polygonal surface representation of the mating gear tooth (slave contact surface). A recursive bounding box/bounding sphere contact search algorithm is used to allow fast contact detection. An asperity friction model or an elasto-hydrodynamic lubrication model can be used for the contact friction forces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model is partially validated by comparing its predictions of the resonant frequencies of a planetary gear train to those of a previously published steady-state dynamic model. The model can help improve the design of planetary gear boxes including increasing the range of operating speeds, torque capacity and durability.

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.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

Comparison of Linear and Nonlinear Damping Effects on a Ring Vibration Isolator

2020 ◽  
pp. 13-22
Author(s):  
Ze-Qi Lu ◽  
Dong-Hao Gu ◽  
Ye-Wei Zhang ◽  
Hu Ding ◽  
Walter Lacarbonara ◽  
...  
Keyword(s):  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Linear And Nonlinear ◽  
Damping Effects

Nonlinear Transient Response and its Sensitivity Using Finite Elements in Time

1995 ◽  
Author(s):  
Rakesh K. Kapania ◽  
Sungho Park
Keyword(s):  
Finite Elements ◽  
Transient Response ◽  
Legendre Polynomials ◽  
Design Parameters ◽  
Algebraic Equations ◽  
System Parameters ◽  
Nonlinear Transient ◽  
Linear And Nonlinear ◽  
Bilinear Formulation ◽  
The One

Abstract The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the sensitivity of the transient response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, the Hermite, the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various system parameters can be obtained.

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.

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