Study the Effects From Gear Rim Thickness on the Gear Pair Time-Varying Mesh Stiffness and Dynamic Behaviors

2017 ◽  
Author(s):  
Zi Wang ◽  
Caichao Zhu ◽  
Chaosheng Song
Keyword(s):  
Potential Energy ◽  
Elastic Deformation ◽  
Energy Method ◽  
The Body ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Dynamic Behaviors ◽  
Gear Mesh ◽  
Potential Energy Method

This work will introduce two methods for calculating the gear mesh stiffness which includes the potential energy method and Finite Element/ Contact Mechanics method. The elastic theory of Muskhelishvili will be used to calculate the elastic deformation from the gear body during one mesh cycle for the gear pair in the potential energy method. Also the involute curve, the geometric and kinematics properties of the gear mesh pair will be taken into account of these two methods. The quasi-static time-varying mesh stiffness considering the deflection of gear rim body is learned in detail. Results from both two methods will show the importance of gear rim body elasticity on the gear pair mesh stiffness and the comparison of the results will reveal the validity and efficiency of the methods. Then lumped-parameter model is presented for studying the whole system dynamic behaviors. The effect from the body elastic deformation from component itself on the macro rigid body motion of the system is investigated. The conclusion from the results shows that the elasticity from gear rim body will take prominent effects on the gear pair dynamic behaviors, which should be regarded as an important factor during the design process.

scholarly journals Study of the Influences of Transient Crack Propagation in a Pinion on Time-Varying Mesh Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Youmin Hu ◽  
Jikai Fan ◽  
Jin Yu
Keyword(s):  
Potential Energy ◽  
Energy Method ◽  
Propagation Model ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Propagation Models ◽  
Material Fatigue ◽  
Stiffness Variation ◽  
Short Time ◽  
Potential Energy Method

Cracks in a cracked gear may further propagate by a tiny length in a very short time for several reasons, such as material fatigue and load fluctuations. In this paper, this dynamic process is defined as transient propagation of cracks. This research aims to calculate the time-varying mesh stiffness of gears when transient propagation of cracks arises, which has not been extensively studied in existing literatures. The transient propagation of cracks is modelled. An improved potential energy method is proposed by incorporating the propagation model into the potential energy method. The improved method can also be utilised to calculate the mesh stiffness of gears when transient propagation of cracks arises. Different transient propagation models are considered to simulate the propagation of cracks in a short amount of time. Different deterioration levels of cracks before transient propagation and different lengths and models of transient propagation are also examined. The variation rules of mesh stiffness caused by the transient propagation of cracks are summarised. The influence of the deterioration level of cracks on mesh stiffness variation when transient propagation arises is obtained. Simulation results show that the proposed method accurately calculates time-varying mesh stiffness when transient propagation of cracks arises. Furthermore, the method improves the monitoring of further propagation of cracks in gears from the perspective of time-varying mesh stiffness.

Evaluating the time-varying mesh stiffness of a planetary gear set using the potential energy method

2013 ◽  
Vol 228 (3) ◽  
pp. 535-547 ◽  
Author(s):  
Xihui Liang ◽  
Ming J Zuo ◽  
Tejas H Patel
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Potential Energy ◽  
Energy Method ◽  
Analytical Method ◽  
Planetary Gear ◽  
Time Varying ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Potential Energy Method

Time-varying mesh stiffness is a periodic function caused by the change in the number of contact tooth pairs and the contact positions of the gear teeth. It is one of the main sources of vibration of a gear transmission system. An efficient and effective way to evaluate the time-varying mesh stiffness is essential to comprehensively understand the dynamic properties of a planetary gear set. According to the literature, there are two ways to evaluate the gear mesh stiffness, the finite element method and the analytical method. The finite element method is time-consuming because one needs to model every meshing gear pair in order to know the mesh stiffness of a range of gear pairs. On the other hand, analytical method can offer a general approach to evaluate the mesh stiffness. In this study, the potential energy method is applied to evaluate the time-varying mesh stiffness of a planetary gear set. Analytical equations are derived without any modification of the gear tooth involute curve. The developed equations are applicable to any transmission structure of a planetary gear set. Detailed discussions are given to three commonly used transmission structures: fixed carrier, fixed ring gear and fixed sun gear.

scholarly journals Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Wang ◽  
Lei Zhang ◽  
Yuan-Qing Luo ◽  
Chang-Zheng Chen
Keyword(s):  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Experimental Result ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Internal Excitation ◽  
Modulation Sideband

In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.

scholarly journals Modeling and analysis of mesh stiffness for straight beveloid gear with parallel axes based on potential energy method

2018 ◽  
Vol 12 (7) ◽  
pp. JAMDSM0122-JAMDSM0122 ◽  
Author(s):  
Chaosheng SONG ◽  
Siwei ZHOU ◽  
Caichao ZHU ◽  
Xingyu YANG ◽  
Zufeng LI ◽  
...  
Keyword(s):  
Potential Energy ◽  
Energy Method ◽  
Mesh Stiffness ◽  
Modeling And Analysis ◽  
Potential Energy Method

A hybrid analytical-numerical method based on Isogeometric Analysis for determination of time varying gear mesh stiffness

2021 ◽  
Vol 160 ◽  
pp. 104291
Author(s):  
Andreas Beinstingel ◽  
Michael Keller ◽  
Michael Heider ◽  
Burkhard Pinnekamp ◽  
Steffen Marburg
Keyword(s):  
Numerical Method ◽  
Isogeometric Analysis ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

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
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