Shaft Instabilities in Two-Stage Gear Systems

2013 ◽  
Vol 275-277 ◽  
pp. 930-935
Author(s):  
Zhe Rao ◽  
Chun Yan Zhou
Keyword(s):  
Multiple Scale ◽  
Gear System ◽  
Dynamic Equations ◽  
Time Varying ◽  
Kutta Method ◽  
Two Stage ◽  
Scale Method ◽  
System A ◽  
Runge Kutta Method ◽  
Intermediate Shaft

The present paper is focused on the torsional instabilities of the intermediate shaft in a two stage gear system. A theoretical model is established taking account in the torsional flexibility of the intermediate shaft and the meshing time-varying stiffness of the gears. Multiple scale method is applied to analysis the instability areas of the gear system for which the generalized modal coordinate is adopted. The result is certificated by numerical integrals of the dynamic equations by Runge-Kutta Method.

The Effects of Bearing Stiffness on Nonlinear Dynamic Behaviors of Multi-Mesh Gear Train

2012 ◽  
Author(s):  
T. N. Shiau ◽  
T. H. Young ◽  
J. R. Chang ◽  
K. H. Huang ◽  
C. R. Wang
Keyword(s):  
Chaotic Motion ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
Gear Train ◽  
Time Varying ◽  
Kutta Method ◽  
Dynamic Behaviors ◽  
Runge Kutta Method ◽  
Bearing Stiffness

In this study, the nonlinear dynamic analysis of the multi-mesh gear train with elastic bearing effect is investigated. The gear system includes the three rigid shafts, two gear pairs and elastic bearings. The stiffness and damper coefficient of elastic bearing are considered. The equations of motion of nonlinear time-varying system are derived using Lagrangian approach. The Runge-Kutta Method is employed to determine the system dynamic behaviors including the bifurcation and chaotic motion. The results show that the periodic motion, quasi-periodical motion and chaos can be excited with the elastic bearing effect. Especially, the results also indicate the dynamic response will go from periodic to quasi-periodical before the chaotic motion when the bearing stiffness is increased.

Nonlinear Dynamics Analysis of Gear System Considering Unbalance and Loosening Faults

2014 ◽  
Vol 875-877 ◽  
pp. 1976-1981 ◽  
Author(s):  
Li Cui ◽  
Da Fang Shi ◽  
Jian Rong Zheng ◽  
Xiao Guang Song
Keyword(s):  
Nonlinear Dynamic ◽  
Gear System ◽  
Dynamic Equations ◽  
Radial Clearance ◽  
Nonlinear Dynamic Model ◽  
Mesh Stiffness ◽  
Diverse Range ◽  
Runge Kutta Method ◽  
Nonlinear Dynamic Equations ◽  
Chaos Motion

Considering backlash, radial clearance of bearing and time-varying mesh stiffness, nonlinear dynamic model of gear bearing rotor system is established considering unbalance and loosening fault. Nonlinear dynamic equations are solved using Runge-Kutta method and Newton-Raphson method. Numerical simulations of the dynamic equations and the affection of the depth of crack and length of wear to the nonlinear dynamic behavior are studied. The results shows that tooth off, bilateral impact phenomenon are occurred, with increasing gear failure when unbalance occurs, and the gear system exhibits a diverse range of periodic, quasi-periodic and chaotic motion. When loosening fault occurs, the range of chaos motion is increased, and gear burnishing is also intensified.

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.

Effects of gear eccentricity on time-varying mesh stiffness and dynamic behavior of a two-stage gear system

2019 ◽  
Vol 33 (3) ◽  
pp. 1019-1032 ◽  
Author(s):  
Xiuzhi He ◽  
Xiaoqin Zhou ◽  
Zhen Xue ◽  
Yixuan Hou ◽  
Qiang Liu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Gear System ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Two Stage

Dynamic Characteristics and Load Coefficient Analysis of Involute Spline Couplings

2014 ◽  
Vol 889-890 ◽  
pp. 450-454
Author(s):  
Xiang Zhen Xue ◽  
San Min Wang
Keyword(s):  
Dynamic Model ◽  
Fourth Order ◽  
Dynamic Characteristics ◽  
Dynamic Load ◽  
Dynamic Equations ◽  
Kutta Method ◽  
Meshing Stiffness ◽  
Runge Kutta Method ◽  
Spline Coupling ◽  
Involute Spline

As one of the important components of aviation and space transmission systems, dynamic characteristics of involute spline couplings influence its lifetime and reliability seriously. Here, taking the backlash of spline joint into account, considering the meshing stiffness varying with the teeth engaged, established the dynamic model with varying stiffness and dynamic equations, and calculated the number of actual meshing teeth and comprehensive meshing stiffness while bearing the varying torque, then, solved dynamic equations using the fourth order Runge - Kutta method, finally, get the teeth meshing number is 23,and the maximum dynamic load coefficient gets smaller from 1.19 to1.15 with the decrease of . This provides a numerical basis for wear`s studying and lifetime`s forecasting of involute spline coupling.

Nonlinear Forced Oscillations and Stability Analysis of the Automotive Gearbox System

2010 ◽  
Author(s):  
Hamed Moradi ◽  
Hasan Salarieh
Keyword(s):  
Mathematical Modeling ◽  
Stability Analysis ◽  
Multiple Scale ◽  
Dynamic Parameter ◽  
Gear System ◽  
Forced Oscillations ◽  
Jump Phenomenon ◽  
Scale Method ◽  
Vibration Responses ◽  
Manufacturing Parameters

In this paper, nonlinear oscillation of the automobile gear system is studied. The backlash dynamic parameter is included in the nonlinear mathematical modeling of the problem. Using multiple scale method, forced vibration responses of the gear system including Primary, Sub-harmonic and Super-harmonic resonances are investigated. In each case, the jump phenomenon and stability analysis are studied. In addition, the effect of dynamic and manufacturing parameters of the gear system on the time responses are analyzed. Simulation and nonlinear analysis of the problem are developed in MAPLE and MATLAB environments.

scholarly journals Bifurcation Analysis of Gear Pair with Continuous and Intermittent Mesh Stiffness Using Enhanced Compliance Method

2020 ◽  
Vol 30 (10) ◽  
pp. 2050156
Author(s):  
De-Shin Liu ◽  
Chuen-Ren Wang ◽  
Ting-Nung Shiau ◽  
Kuo-Hsuan Huang ◽  
Wei-Chun Hsu
Keyword(s):  
Equation Of Motion ◽  
Time Varying ◽  
Sine Function ◽  
Kutta Method ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Gear Mesh Stiffness ◽  
Impact Motion

The nonlinear dynamics of a multigear pair with the time-varying gear mesh stiffness are investigated using an enhanced compliance-based methodology. In the proposed approach, Lagrangian theory and Runge–Kutta method are used to derive the equation of motion of the multigear pair and solve its dynamic response for various values of the gear mesh frequency, respectively. The simulation results obtained for the dynamic behavior of the multigear pair are compared with those obtained by using continuous (cosine, sine and offset sine function) and intermittent representations of the time-varying gear mesh stiffness. It is shown that periodic, quasi-periodic, aperiodic and chaos motions are induced at different values of the gear mesh frequency. In addition, the bifurcation diagram reveals the occurrence of both nonimpact motion and single-sided impact motion, and Lyapunov exponent can easily diagnose the chaos phenomenon of system.

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