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.

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 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

scholarly journals Research on Meshing Stiffness and Vibration Response of Pitting Fault Gears with Different Degrees

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jie Liu ◽  
Chengye Wang ◽  
Wenchao Wu
Keyword(s):  
Potential Energy ◽  
Energy Method ◽  
Time History ◽  
Vibration Response ◽  
Gear System ◽  
Normal Distribution Function ◽  
Meshing Stiffness ◽  
Calculation Results ◽  
Driving Wheel ◽  
Potential Energy Method

In order to study the influence of pitting on meshing stiffness, the normal distribution function is used to simulate the pitting location of pitting gear, and the potential energy method is used to analyze the influence of pitting on meshing stiffness. At the same time, the meshing stiffness of pitting gears with different degrees is analyzed by finite element method, and the validity of the calculation results with potential energy method is verified. On the basis of meshing stiffness, the dynamic model of gear system is established, and the vibration response of pitting gear system with different degrees is analyzed. The results show that with the increase of pitting area, the meshing stiffness decreases; the closer the meshing area of the driving wheel is to the pitting line, the more the meshing stiffness decreases, resulting in the intensification of vibration response and periodic impact; and in the time history diagram, there is a small spurious frequencies near the meshing frequency; in the phase diagrams and the Poincare diagram, trajectory and discrete point aggregation area is gradually increased.

scholarly journals Research on the Influence of Backlash on Mesh Stiffness and the Nonlinear Dynamics of Spur Gears

2019 ◽  
Vol 9 (5) ◽  
pp. 1029 ◽  
Author(s):  
Yangshou Xiong ◽  
Kang Huang ◽  
Fengwei Xu ◽  
Yong Yi ◽  
Meng Sang ◽  
...  
Keyword(s):  
Low Frequency ◽  
Time History ◽  
Fourier Series Expansion ◽  
Fast Fourier Transformation ◽  
Time Varying ◽  
Stiffness Coefficient ◽  
Mesh Stiffness ◽  
Rate Of Decline ◽  
Low Frequency Motion ◽  
Potential Energy Method

In light of ignoring the effect of backlash on mesh stiffness in existing gear dynamic theory, a precise profile equation was established based on the generating processing principle. An improved potential energy method was proposed to calculate the mesh stiffness. The calculation result showed that when compared with the case of ignoring backlash, the mesh stiffness with backlash had an obvious decrease in a mesh cycle and the rate of decline had a trend of decreasing first and then increasing, so a stiffness coefficient was introduced to observe the effect of backlash. The Fourier series expansion was employed to fit the mesh stiffness rather than time-varying mesh stiffness, and the stiffness coefficient was fitted with the same method. The time-varying mesh stiffness was presented in terms of the piecewise function. The single degree of freedom model was employed, and the fourth order Runge–Kutta method was utilized to investigate the effect of backlash on the nonlinear dynamic characteristics with reference to the time history chart, phase diagram, Poincare map, and Fast Fourier Transformation (FFT) spectrogram. The numerical results revealed that the gear system primarily performs a non-harmonic-single-periodic motion. The partially enlarged views indicate that the system also exhibits small-amplitude and low-frequency motion. For different cases of backlash, the low-frequency motion sometimes shows excellent periodicity and stability and sometimes shows chaos. It is of practical guiding significance to know the mechanisms of some unusual noises as well as the design and manufacture of gear backlash.

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