scholarly journals Generation Mechanism and Evolution of Five-state Meshing Behavior of a Spur Gear System Considering Gear-tooth Time-varying Contact Characteristics

2021 ◽  
Author(s):  
Shi Jian-Fei ◽  
Xiang-feng Gou ◽  
Ling-yun Zhu
Keyword(s):  
Chaotic Behavior ◽  
Gear Tooth ◽  
Time History ◽  
Spur Gear ◽  
Gear System ◽  
Generation Mechanism ◽  
Load Factor ◽  
Back Side ◽  
Time Varying ◽  
Dynamic Meshing

Abstract Teeth disengaging or back-side teeth meshing induced by backlash reduces the transmission quality and dynamic performance of gear systems, and accurate interpretation of multi-state meshing behavior can provide guidance for structural optimization and performance evaluation. Therefore, the multi-state meshing behavior of the gear system is elaborated. A new nonlinear dynamic model of a spur gear system with five-state meshing behavior is proposed based on time-varying backlash and contact ratio. The time-varying meshing stiffness and time-varying backlash considering the elastic contact of gear teeth, gear temperature rise and lubrication are included in the model. The five-state meshing behavior is clearly characterized by constructing five Poincaré maps, and its generation mechanism is studied using dynamic meshing force time history, teeth relative displacement time history and phase portrait. The bifurcation and evolution of five-state meshing behavior are analyzed under the effects of load factor, meshing frequency and error coefficient. The results show that the mutation in the direction of dynamic meshing force leads to teeth disengaging and back-side single or double teeth contact, forming multi-state meshing behavior. Bifurcation caused by parameter changes greatly affects the evolution of five-state meshing behavior, particularly grazing bifurcation can decrease the number of teeth disengagement. Chaotic behavior or trajectory expansion inspires multi-state meshing vibration of the system. Previous gear system models could not reveal these phenomena due to ignoring the multi-state meshing behavior.

Dynamic analysis of nonlinear time-varying spur gear system subjected to multi-frequency excitation

2018 ◽  
Vol 25 (6) ◽  
pp. 1210-1226 ◽  
Author(s):  
Yi Yang ◽  
Mengjuan Xu ◽  
Yang Du ◽  
Pan Zhao ◽  
Yiping Dai
Keyword(s):  
Spur Gear ◽  
Numerical Results ◽  
Gear System ◽  
Working Environment ◽  
Single Frequency ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Varying ◽  
Harmonic Excitations ◽  
Frequency Excitation

Due to the complex working environment, gear systems always suffer from multiple excitations in actual engineering. This paper concerns the frequency response characteristics of a nonlinear time-varying spur gear system subjected to multi-frequency excitation. Firstly, a single degree-of-freedom gear pair model is established with consideration of the gear backlash, time-varying mesh stiffness and multiple harmonic excitations. Then, using the multiple time scales method, a comprehensive theoretical study is conducted to analyze various resonant cases including primary, parametric and combination resonances. Besides, parametric studies are accomplished to reveal the effects of the multi-frequency excitation on gear dynamics and to provide some useful references for reducing the vibration level. With the help of the fifth-order Runge–Kutta method, the numerical results are obtained to verify the validity of the analytical solutions and to emphasize the significances of the multi-frequency excitation. In addition, a comparison is performed between the numerical results and the published experimental results to validate the proposed gear model. Results show that the presence of the multi-frequency excitation will introduce the interaction between different harmonic excitations, which significantly affects the nonlinear vibration characteristics of a spur gear system. The proposed gear model with multi-frequency excitation could be more reliable and universal than that with single-frequency excitation. In addition, the results of parametric study could provide some suggestions to designers and researchers attempting to obtain desirable dynamic behaviors of a gear system subjected to multi-frequency excitation.

Torsional Vibration of a Spur Gear System With Time-Varying and Square Nonlinearities

2013 ◽  
Author(s):  
Qian Ding ◽  
Wei Zhang
Keyword(s):  
Torsional Vibration ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Spur Gear ◽  
Gear System ◽  
Phase Portraits ◽  
Resonant Peak ◽  
Time Varying ◽  
Frequency Spectra ◽  
Input Torque

This paper investigates the torsional vibration of a spur gear system with time-varying and square nonlinearities, by both the analytical method and numerical simulation. First, the equations of motion of a rotating spur gear system are established. Then a single-dof equivalent system is induced to describe the relative motion or torsional vibration of the gears. The harmonic balance method is used to obtain the steady-state response. Influence of the input torque on the response is discussed and a phenomenon, one resonant peak split up into two peaks when the input torque is high enough is revealed. Last, numerical simulations are carried out and bifurcation diagrams and amplitude-frequency curve is given by taking the excitation frequency as control parameter. Selected typical motions are also presented in detail by time-histories, phase portraits, Poincaré map and frequency spectra.

On Dynamic Tooth Load and Stability of a Spur-Gear System Using the State-Space Approach

1985 ◽  
Vol 107 (1) ◽  
pp. 54-60 ◽  
Author(s):  
A. S. Kumar ◽  
T. S. Sankar ◽  
M. O. M. Osman
Keyword(s):  
State Space ◽  
Dynamic Load ◽  
Initial Conditions ◽  
Gear Tooth ◽  
Spur Gear ◽  
The State ◽  
Gear System ◽  
Computational Time ◽  
Steady State Condition ◽  
The Stability

In this study, a new approach using the state-space method is presented for the dynamic load analysis of spur gear systems. This approach gives the dynamic load on gear tooth in mesh as well as information on the stability of the gear system. Also a procedure is given for the selection of proper initial conditions that enable the steady-state condition to be reached faster, conditions that result in considerable savings in computational time. The variations in the dynamic load with respect to changes in contact position, operating speed, backlash, damping, and stiffness are also investigated. In addition, the stability of the gear system is studied, using the Floquet theory and the well-known stability conditions of difference systems.

scholarly journals Time-varying Response Analysis of Spur Gear System

2021 ◽  
Vol 276 ◽  
pp. 01007
Author(s):  
Chao Li ◽  
Hongwei Liu
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
High Load ◽  
Gear System ◽  
Theoretical Formula ◽  
Response Analysis ◽  
Time Varying ◽  
System A ◽  
Drive Systems ◽  
Return Difference

In this paper, a space-driven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. Considering the high load characteristics of the space drive system and the time-varying stiffness and tooth clearance of the gear system, a nonlinear dynamic response analysis was performed. The characteristics of the vibration acceleration, shock and transmission error of the gear system are studied in this paper. This paper analyzes the relationship between backlash and return difference, and derives the theoretical formula between the two. The time-varying stiffness was corrected to make the theoretical model closer to reality. The research in this paper enriches the study on space drive systems and high load gear systems.

Back-Side Contact Gear Mesh Stiffness

2011 ◽  
Author(s):  
Yichao Guo ◽  
Robert G. Parker
Keyword(s):  
Gear Tooth ◽  
Back Side ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Tooth Contact ◽  
Gear Mesh ◽  
Variation Function ◽  
Analytical Formulae ◽  
Gear Mesh Stiffness ◽  
The Relationship

Back-side gear tooth contact happens when the anti-backlash (or scissor) gears are applied or tooth wedging occurs. An accurate description of the back-side gear tooth mesh stiffness is important to any study on gear dynamics that involves tooth wedging or anti-backlash mechanism. This work studies the time-varying back-side mesh stiffness and its correlation with backlash by analyzing the relationship between the drive-side and back-side mesh stiffnesses. Results of this work yield the general form of the back-side mesh stiffness or gear tooth variation function for an arbitrary gear pair. The resultant analytical formulae are confirmed by the simulation results from Calyx that precisely tracks gear tooth contact without any predefined relations.

A Numerical FEM Solution of Gear Root Stress in Offset Axial Mesh Misalignment

2013 ◽  
Vol 393 ◽  
pp. 375-380 ◽  
Author(s):  
Mohd Rizal Lias ◽  
Mokhtar Awang ◽  
T.V.V.L.N. Rao
Keyword(s):  
Stress Distribution ◽  
Critical Path ◽  
Gear Tooth ◽  
Contact Region ◽  
Moving Load ◽  
Spur Gear ◽  
Load Factor ◽  
Tooth Root ◽  
Load Model ◽  
The Impact

Gear offsets mesh in axial misalignment always leads to unevenness of load transferred contributing the impact of stress value and distribution along important critical path of the tooth root. Its happening due to overpress fitting when the gear is mounted onto the shaft as an interference hub fit. Current design methodology based on empirical model provide solution by approximation load factor fail to attributes in detailed regarding this phenomenon This paper determined to focus on this phenomenon in term of methodology to the stress distribution at the critical contact region of the tooth root of the gears. Pair of spur gear with real geometrical construction and condition was constructed with offset parameter. A moving load quasi-static model with a numerical FEM solution using ANSYS is presented with modification in loading variation. For verification, the stress value at the critical path of the tooth root is compared between standard high point single tooth contacts (HPSTC) loading to moving load model. As the result, a numerical FEM methodology to calculate the stress distribution of the gear tooth root in offset axial misalignment with moving load model approach is determined. The proposed method is also found reliable as an alternative solution to define an accurate load factor calculation compared to the approximation provided by the standard empirical procedure.

Study of Transient Elastohydrodynamic Lubrication of Spur Gears under Impact Load

2011 ◽  
Vol 121-126 ◽  
pp. 3506-3509
Author(s):  
You Qiang Wang ◽  
Zhi Cheng He ◽  
Wei Su
Keyword(s):  
Film Thickness ◽  
Impact Load ◽  
Gear Tooth ◽  
Elastohydrodynamic Lubrication ◽  
Spur Gear ◽  
Time Varying ◽  
Spur Gears ◽  
Lubrication Film ◽  
The Impact ◽  
Contact Parameters

Spur gear contacts experience a number of time-varying contact parameters including the load, surface velocities, radii of curvature, and slide-to-roll ratio. It is very hard to obtain transient elastohydrodynamic lubrication (EHL) solution of spur gears. In this study, a transient EHL model of involute spur gear tooth contacts is proposed. A full transient EHL solution of involute spur gear under impact load is obtained by utilizing the multigrid technique. The influences of impact load on the EHL of spur gear are analyzed in the paper. The numerical results show that the approach impact load has strong transient influence on the oil film thickness and pressure distribution between contact zones. The impact load may lead to instantaneous lubrication film deterioration between contact teeth of involute spur gears.

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