Nonlinear dynamics of hypoid gear with coupled dynamic mesh stiffness

2022 ◽  
Vol 168 ◽  
pp. 104589
Author(s):  
Zhenghong Shi ◽  
Sheng Li
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Mesh ◽  
Hypoid Gear ◽  
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.

scholarly journals Investigation of the effect of the angle between drive shafts on vibration responses of main reducer

2018 ◽  
Vol 189 ◽  
pp. 06009 ◽  
Author(s):  
Xiaogang Liu ◽  
Zhaoyu Wu ◽  
Weiguang Shu ◽  
Jie Lu
Keyword(s):  
Hypoid Gear ◽  
Force Analysis ◽  
Lumped Mass ◽  
Mesh Stiffness ◽  
Gear Backlash ◽  
Lumped Mass Method ◽  
Vibration Model ◽  
Vibration Responses ◽  
Transfer Error ◽  
Final Drive

The drive shaft arrangement has a considerable influence on the vibration responses of the shaft-final drive system. In this research, a coupled vibration model is developed based on force analysis of hypoid gear and lumped mass method. The effect of time-varying mesh stiffness, gear backlash and transfer error are included to investigate the effect of the angle between drive shafts on vibration responses of main reducer. The vibration responses of main reducer are acquired using this model. The results show that the vibration amplitude of the gears of main reducer increase with the angle between drive shafts. This paper presents an analytical method to determine the value of the angle between drive shafts, so as to control the vibration of main reducer.

Analytical Solution for the Nonlinear Dynamics of Planetary Gears

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Harmonic Balance ◽  
Gear Tooth ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Mesh Stiffness ◽  
Planetary Gears ◽  
Parallel Finite Element ◽  
The Impact

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. At resonance, the resulting vibration causes tooth separation leading to nonlinear effects such as jump phenomena and subharmonic resonance. This work examines the nonlinear dynamics of planetary gears by numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. Correlation between the amplitude of response and external torque demonstrates that tooth separation occurs even under large torque. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is evaluated by parallel finite element and numerical integration simulations.

scholarly journals On Dynamic Mesh Force Evaluation of Spiral Bevel Gears

2019 ◽  
Vol 2019 ◽  
pp. 1-26 ◽  
Author(s):  
Xiaoyu Sun ◽  
Yongqiang Zhao ◽  
Ming Liu ◽  
Yanping Liu
Keyword(s):  
Single Point ◽  
Transmission Error ◽  
Dynamic Mesh ◽  
Mesh Stiffness ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Mesh Model ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Tooth Pair

The mesh model and mesh stiffness representation are the two main factors affecting the calculation method and the results of the dynamic mesh force. Comparative studies considering the two factors are performed to explore appropriate approaches to estimate the dynamic meshing load on each contacting tooth flank of spiral bevel gears. First, a tooth pair mesh model is proposed to better describe the mesh characteristics of individual tooth pairs in contact. The mesh parameters including the mesh vector, transmission error, and mesh stiffness are compared with those of the extensively applied single-point mesh model of a gear pair. Dynamic results from the proposed model indicate that it can reveal a more realistic and pronounced dynamic behavior of each engaged tooth pair. Second, dynamic mesh force calculations from three different approaches are compared to further investigate the effect of mesh stiffness representations. One method uses the mesh stiffness estimated by the commonly used average slope approach, the second method applies the mesh stiffness evaluated by the local slope approach, and the third approach utilizes a quasistatically defined interpolation function indexed by mesh deflection and mesh position.

scholarly journals On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Jun Wang ◽  
Teik C. Lim
Keyword(s):  
Linear Response ◽  
High Speed ◽  
Mean Value ◽  
Dynamic Mesh ◽  
Jump Discontinuity ◽  
Hypoid Gear ◽  
Jump Phenomenon ◽  
The Mean ◽  
Primary Focus ◽  
Point Line

A nonlinear time-varying (NLTV) dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

Torque Load Effects on Mesh and Dynamic Characteristics of Hypoid Geared System

2013 ◽  
Author(s):  
Yawen Wang ◽  
Teik C. Lim ◽  
Junyi Yang
Keyword(s):  
Dynamic Characteristics ◽  
Gear Tooth ◽  
Great Influence ◽  
Transmission Error ◽  
Hypoid Gear ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Tooth Contact Analysis ◽  
Torque Load ◽  
Loaded Tooth Contact Analysis

From the existing experimental results and previous studies, the torque load has great influence on the mesh and dynamic characteristics of hypoid gear drive. To have more insights on the load dependent mesh parameters and dynamic response of hypoid and spiral bevel gear, a load dependent mesh model is developed by using 3-dimensional loaded tooth contact analysis (LTCA). The contact ratio and time-varying mesh parameters including the mesh stiffness, transmission error, mesh point and line-of-action of the mesh force are examined within a wide torque range. Then a nonlinear multi-body dynamic analysis is performed considering the effect of backlash nonlinearity. Simulation results show that the contact ratio and mesh stiffness generally increases as the toque load increases. The effect of torque load on dynamic mesh force is found to be frequency dependent due to the resonance frequency shifts and peak magnitude changes. This study provides an in-depth understanding of hypoid gear tooth load sharing and dynamic behaviors in terms of change in operating load. Therefore, the proposed model can be employed to assist in gear design optimization.

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