Periodic and Chaotic Dynamic Responses of Face Gear Transmission System

2013 ◽  
Vol 834-836 ◽  
pp. 1273-1280
Author(s):  
Ze Hua Hu ◽  
Jin Yuan Tang ◽  
Si Yu Chen
Keyword(s):  
Periodic Motion ◽  
Chaotic Dynamic ◽  
Rotational Frequency ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System

The periodic and chaotic dynamic responses of face gear transmission system considering time-varying mesh stiffness and backlash nonlinearity are studied. Firstly, a nonlinear time-varying dynamic model of face gear pair is developed and the motion equations are presented, the real accurate mesh stiffness is obtained by applying Finite element approach. Then, the dynamic equations are solved using Runge-Kutta numerical integral method and bifurcation diagrams are presented and analyzed. The stability properties of steady state responses are illustrated with Floquet multipliers and Lyapunov exponents. The results show that a process of periodic-chaotic-periodic motion exists with the dimensionless pinion rotational frequency as control parameters. The analysis can be a reference to avoid the chaotic motion and unstable periodic motion through choosing suitable rotational frequency.

Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Zehua Hu ◽  
Jinyuan Tang ◽  
Siyu Chen ◽  
Duncai Lei
Keyword(s):  
Dynamic Response ◽  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Gear Transmission System ◽  
The Face ◽  
Time Invariant ◽  
Backlash Nonlinearity

The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

scholarly journals Study on Dynamics of a Two-Stage Gear Transmission System with and without Tooth Breakage

Processes ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 2141
Author(s):  
Deyi Fu ◽  
Shiqiao Gao ◽  
Haipeng Liu
Keyword(s):  
Numerical Simulation ◽  
Periodic Motion ◽  
Domain Analysis ◽  
Transmission System ◽  
Gear Transmission ◽  
Time Varying ◽  
Two Stage ◽  
Meshing Stiffness ◽  
Vibration Condition ◽  
Gear Transmission System

This paper studies the dynamics of a two-stage gear transmission system in both the normal state and the fault state with tooth breakage. The torsional vibration model of the two-stage parallel shaft gear was developed by using the lumped parameter method. The time-varying meshing stiffness of the gear transmission system is described by Fourier series which is determined by the periodical meshing characteristics of the gears with both the single-tooth and the double-tooth contacts. By introducing the pulse into the regular time-varying meshing stiffness, the tooth breakage existing in the gear transmission system is mimicked. Based on the numerical simulation of the developed dynamic model, both the time domain analysis and the frequency domain analysis of the gear transmission system under both the normal condition and the tooth breakage are compared accordingly. The influence of the tooth breakage on the dynamic characteristics of the gear transmission system is analyzed comprehensively. Furthermore, based on the developed test bench of a two-stage gear transmission system, the experimental research was carried out, and the experimental results show great agreements with the results of numerical simulation, and thus the validity of the developed mathematical model is demonstrated. By comparing the periodic motion with the chaotic motion, the fault identification for the gear transmission system is verified to be tightly related to its vibration condition, and the control of the vibration condition of the gear transmission system as periodic motion is of great significance to the fault diagnosis.

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.

Analysis of tooth stiffness of nutation face gear

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Guangxin Wang ◽  
Lili Zhu ◽  
Peng Wang
Keyword(s):  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Face Gear ◽  
Content Type ◽  
Gear Teeth ◽  
Meshing Stiffness ◽  
Single Tooth ◽  
Tooth Stiffness ◽  
External Face

Purpose The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission. Design/methodology/approach From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear. Findings The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained. Originality/value Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

Dynamical Analysis of Planetary Gear Transmission System Under Support Stiffness Effects

2020 ◽  
Vol 30 (06) ◽  
pp. 2050080
Author(s):  
Ling Xiang ◽  
Zeqi Deng ◽  
Aijun Hu
Keyword(s):  
Excitation Frequency ◽  
Global Bifurcation ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Dynamical Analysis ◽  
Largest Lyapunov Exponent ◽  
Meshing Stiffness ◽  
Gear Transmission System

The transverse-torsional nonlinear model of multistage gear transmission system which is comprised of a planetary gear set and two parallel gear stages is proposed with time-varying meshing stiffness, comprehensive gear errors and gear backlash. The nonlinear dynamic responses are analyzed by applying excitation frequency and support stiffness as the bifurcation parameters. The motions of the system are identified through global bifurcation diagram, largest Lyapunov exponent (LLE) and Poincaré map. The numerical results demonstrate that the support stiffness affects the system, especially on planetary gear set. The motions of the system with the changes of the support stiffness are diverse including some different multiperiodic motions. Also, the state of the system undergoes 2T-periodic motion, chaos, quasi-periodic behavior and multiperiodic motion. For the support stiffness or other nonlinear factors of the gear system, the suitable range of working frequencies could make the system stable. Correspondingly, parameters of the system should be designed properly and controlled for the better operation and enhancing the life of the system.

Effects of gearbox housing flexibility on dynamic characteristics of gear transmission system

2020 ◽  
pp. 107754632095373
Author(s):  
Xiannian Kong ◽  
Jinyuan Tang ◽  
Chen Siyu ◽  
Zehua Hu
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Lightweight Design ◽  
Transmission System ◽  
Structure Design ◽  
Gear Transmission ◽  
Dynamic Responses ◽  
Dynamic Behaviors ◽  
Gear Transmission System ◽  
Rotor Bearing

The lightweight design of the gear system is the current tendency. The gearbox housing is modeled as a rigid body and is neglected in the gear dynamic analysis. It is of great significance to introduce the gearbox housing flexibility into the dynamic analysis and analyze the influence of the gearbox housing flexibility on the dynamic behaviors of the gear transmission system, as this can provide important instructions for the lightweight structure design of the housing. The gear–rotor–bearing model and the gear–rotor–bearing–housing model are established by the finite element node method. A Timoshenko beam element is used to represent the shafts. To illustrate the housing effect, two kinds of housing model are established: one tends to be rigid and the other to be flexible and lighter. The housings are simplified as a super element obtained by the dynamic substructure method. Natural frequencies and dynamic responses are illustrated to indicate the effects of housing flexibility. Comparisons of numerical results show that the rigid housing can be neglected for its little effect on the dynamic analysis. The flexibility of the housing slightly reduces the natural frequencies of the gear transmission system, and the maximum reduction is 6.05%. Meanwhile, the amplitudes of the first two resonance peaks of the dynamic transmission error decrease by 9.5% and 5.05%. Besides, more response peaks emerge at higher speeds when the flexibility of housing increases. The complete phenomena of dynamic behaviors of the gear transmission system can be obtained by considering the housing flexibility.

scholarly journals Influence of Asymmetric Mesh Stiffness on Dynamics of Spiral Bevel Gear Transmission System

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Li Yinong ◽  
Li Guiyan ◽  
Zheng Ling
Keyword(s):  
Dynamic Response ◽  
Transmission System ◽  
Bevel Gear ◽  
Gear Transmission ◽  
Spiral Bevel Gear ◽  
Mesh Stiffness ◽  
Light Load ◽  
Gear Transmission System ◽  
Spiral Bevel ◽  
Asymmetric Mesh

An 8-DOF (degrees-of-freedom) nonlinear dynamic model of a spiral bevel gear pair which involves time-varying mesh stiffness, transmission error, backlash, and asymmetric mesh stiffness is established. The effect of the asymmetric mesh stiffness on vibration of spiral bevel gear transmission system is studied deliberately with numerical method. The results show that the mesh stiffness of drive side has more effect on dynamic response than those of the coast side. Only double-sided impact region is affected considerably by mesh stiffness of coast side while single-sided impact and no-impact regions are unchanged. In addition, the increase in the mesh stiffness of drive side tends to worsen the dynamic response of the transmission system especially for light-load case.

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