Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack

2016 ◽  
Vol 66 ◽  
pp. 502-514 ◽  
Author(s):  
Zaigang Chen ◽  
Wanming Zhai ◽  
Yimin Shao ◽  
Kaiyun Wang ◽  
Guohua Sun
Keyword(s):  
Analytical Model ◽  
Spur Gear ◽  
Gear Pair ◽  
Tooth Root ◽  
Mesh Stiffness ◽  
Root Crack

An Analytical Model for Spur Gear Dynamics

1997 ◽  
Author(s):  
Jao-Hwa Kuang ◽  
Ah-Der Lin
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
Analytical Solutions ◽  
Dynamic Contact ◽  
Spur Gear ◽  
Dynamic Loads ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Detailed Model ◽  
Gear Dynamics

Abstract A mathematical model for a spur gear pair with two-step mesh stiffness is proposed. Two constant values of mesh stiffness are used to approximate the complicated compliance alternation of contact tooth pairs between one and two during meshing. Analytical solutions of the dynamic loads are derived. The method has been employed to calculate the dynamic contact load, transmitted torque and the bearing forces. The results compared favorably with a more detailed model found in the literature.

Influence of simultaneous time-varying bearing and tooth mesh stiffness fluctuations on spur gear pair vibration

2019 ◽  
Vol 97 (2) ◽  
pp. 1403-1424 ◽  
Author(s):  
Guanghui Liu ◽  
Jun Hong ◽  
Robert G. Parker
Keyword(s):  
Spur Gear ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness

Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nan Gao ◽  
Shiyu Wang ◽  
Muhammad Asad Ur Rehman Bajwa
Keyword(s):  
Nonlinear Dynamics ◽  
Amplitude Modulation ◽  
Spur Gear ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Chaotic Motions ◽  
Content Type ◽  
Modulation Function ◽  
Nonlinear Behaviors

PurposeGear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.Design/methodology/approachAn approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.FindingsThe comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.Originality/valueThe research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair

2001 ◽  
Vol 123 (3) ◽  
pp. 311-317 ◽  
Author(s):  
J. H. Kuang ◽  
A. D. Lin
Keyword(s):  
Dynamic Load ◽  
Sliding Wear ◽  
Vibration Spectrum ◽  
Tooth Wear ◽  
Spur Gear ◽  
Damping Factor ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Wear Process ◽  
The Mathematical Model

In this paper, the effect of tooth wear on the vibration spectrum variation of a rotating spur gear pair is studied. In order to approximate the dynamic characteristics of an engaging spur gear pair, the load sharing alternation, position dependent mesh stiffness, damping factor and friction coefficient are considered in the mathematical model. The wear prediction model proposed by Flodin et al. is used to simulate the tooth profile wear process. The variation of the vibration spectra introduced from the interaction between the sliding wear and the dynamic load is simulated and analyzed. Numerical results indicate that the dynamic load histogram of an engaging spur gear pair may change greatly with the tooth wear. This finding implies that the variation of the gear vibration spectrum might be used to monitor the tooth wear of an engaging spur gear pair.

Dynamic Analysis of Sliding Friction in a Gear Pair

2003 ◽  
Author(s):  
Rajendra Gunda ◽  
Rajendra Singh
Keyword(s):  
Load Distribution ◽  
Sliding Friction ◽  
Spur Gear ◽  
Time Instant ◽  
Friction Torque ◽  
Speed Ratio ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Static Mode

Chief objective of this article is to evaluate the role of sliding friction in gear dynamics, and more specifically the effect of the periodic variations in mesh stiffness, load distribution and friction torque during a mesh cycle. A non-unity speed ratio spur gear is considered. Only the torsional degree of freedom of the gear pair, with ideal Coulomb friction law, is analyzed. Previous studies by Vaishya and Singh [1–3] make idealized assumptions about temporal (or spatial) variation of mesh stiffness and load sharing in order to obtain more tractable analytical solutions. In our formulation, an accurate Finite Element/Contact Mechanics analysis code [4] is run in the static mode to compute the mesh stiffness and load distribution at every time instant of the mesh. The computed parametric variation of stiffness is then incorporated into our dynamic formulation that includes frictional torques. Next, we use appropriate numerical techniques to solve for the dynamic response in time domain. This study, though preliminary in nature, examines the effects of pinion speed, coefficient of friction and mean input torque. This, along with work in progress, should yield further insights into the role of friction sources in gear vibro-acoustics.

scholarly journals Nonlinear Dynamic Characteristic Analysis of a Coated Gear Transmission System

Coatings ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 39
Author(s):  
Yangyi Xiao ◽  
Liyang Fu ◽  
Jing Luo ◽  
Wankai Shi ◽  
Minglin Kang
Keyword(s):  
Dynamic Characteristic ◽  
Time History ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Phase Curve ◽  
Gear Pair ◽  
Characteristic Analysis ◽  
Mesh Stiffness ◽  
Gear Transmission System

Coatings can significantly improve the load-carrying performance of a gear surface, but how they affect the vibration characteristic of the system is an urgent issue to be solved. Taking into account the nonlinear factors like the variable mesh stiffness, friction, backlash, and transmission error, a six-degree-of-freedom spur gear transmission system with coatings is presented. Meanwhile, the finite element method is applied to acquire the time-varying mesh stiffness of the coated gear pair in the engagement process. With the support of the time-history curve, phase curve, Poincare map, and fast Fourier transform spectrum, the dynamic characteristics and the effects of the coating elastic modulus on vibration behaviors of a gear transmission system are minutely dissected by using a numerical integration approach. Numerical cases illustrate that the dynamic characteristic of a gear transmission system tends toward a one-period state under the given operating condition. They also indicate that, compared with softer coatings, stiffer ones can properly enhance the transmission performance of the coated gear pair. Numerical results are also compared with previous studies, and can establish a theoretical basis for dynamic design and vibration control of the coated gear transmission system.

Numerical and experimental investigation of a spur gear pair with unloaded static transmission error

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Duncai Lei ◽  
Xiannian Kong ◽  
Siyu Chen ◽  
Jinyuan Tang ◽  
Zehua Hu
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Content Type ◽  
High Order Harmonic ◽  
Static Transmission Error ◽  
Harmonic Components

Purpose The purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and experimentally and the influences of the system factors including mesh stiffness, error excitation and torque on the dynamic transmission error (DTE). Design/methodology/approach A simple lumped parameters dynamic model of a gear pair considering time-varying mesh stiffness, backlash and unloaded STE excitation is developed. The STE is calculated from the measured tooth profile deviation under the unloaded condition. A four-square gear test rig is designed to measure and analyze the DTE and vibration responses of the gear pair. The dynamic responses of the gear transmission are studied numerically and experimentally. Findings The predicted numerical DTE matches well with the experimental results. When the real unloaded STE excitation without any approximation is used, the dynamic response is dominated by the mesh frequency and its high order harmonic components, which may not be result caused by the assembling error. The sub-harmonic and super-harmonic resonant behaviors are excited because of the high order harmonic components of STE. It will not certainly prevent the separations of mesh teeth when the gear pair is under the condition of high speed and heavy load. Originality/value This study helps to improve the modeling method of the dynamic analysis of spur gear transmission and provide some reference for the understanding of the influence of mesh stiffness, STE excitation and system torque on the vibration behaviors.

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