scholarly journals Influence of the Eccentric Error of Star Gear on the Bifurcation Properties of Herringbone Star Gear Transmission with Floating Sun Gear

2018 ◽  
Vol 2018 ◽  
pp. 1-32
Author(s):  
Fang Guo ◽  
Zongde Fang ◽  
Xijin Zhang ◽  
Yanmei Cui
Keyword(s):  
Load Balancing ◽  
Numerical Method ◽  
Dynamic Model ◽  
Phase Plane ◽  
Natural Frequencies ◽  
Rotation Frequency ◽  
Gear Transmission ◽  
Time Varying ◽  
Bifurcation Diagrams ◽  
Mesh Stiffness

Taking a herringbone star gear transmission (HSGT) with floating sun gear as an example, the system bifurcation characteristics with the changing of the eccentric error of star gear and the working frequencies are analyzed. For this analysis, a generalized dynamic model of HSGT considering the manufacturing eccentric errors, time-varying mesh stiffness, and load balancing mechanism is established and solved by numerical method. The floating process of sun gear is explained. In this paper, there are seven cases about the eccentric errors of star gears which are calculated, respectively. To study the effect of the working frequencies (including meshing frequency and rotation frequency), the calculation is done at three kinds of input speed in which the working frequencies are close to the system natural frequencies. The results are demonstrated in detail by the bifurcation diagrams, phase plane plots, and Poincare maps. The system bifurcation characteristics are particularly analyzed and compared in every case. This work provides important guidance to the engineering of HSGT.

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

Survey of nonlinear vibration of gear transmission systems

2003 ◽  
Vol 56 (3) ◽  
pp. 309-329 ◽  
Author(s):  
Jianjun Wang ◽  
Runfang Li and ◽  
Xianghe Peng
Keyword(s):  
Nonlinear Vibration ◽  
Review Article ◽  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Transmission Systems ◽  
Driven Systems ◽  
The Past ◽  
Critical Issues ◽  
Basic Concepts

In this paper, the progress in nonlinear dynamics of gear driven systems in the past twenty years is reviewed, especially the gear dynamic behavior, by considering the backlash and time-varying mesh stiffness of teeth. The basic concepts, the mathematical models and the solving methods for the non-linear dynamics of geared systems are then reviewed. The critical issues for further research on the nonlinear vibration in gear transmission systems are also discussed. There are 204 references cited in this review article.

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.

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.

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.

scholarly journals Dynamic Analysis of Planetary Gear with Root Crack in Sun Gear Based on Improved Time-Varying Mesh Stiffness

2020 ◽  
Vol 10 (23) ◽  
pp. 8379
Author(s):  
Jian Shen ◽  
Niaoqing Hu ◽  
Lun Zhang ◽  
Peng Luo
Keyword(s):  
Fault Diagnosis ◽  
Dynamic Model ◽  
Theoretical Basis ◽  
Planetary Gear ◽  
Vibration Response ◽  
Gear System ◽  
Transition Curve ◽  
Parameter Method ◽  
Time Varying ◽  
Mesh Stiffness

The time-varying mesh stiffness (TVMS) is the crucial parameter of the dynamic model of the gear system. Accurate calculation of TVMS is essential for effective fault diagnosis of the gear system. A mesh stiffness improved method considering both the gear tooth transition curve and deformation of the gear body is presented in this paper, and the stiffness calculation expressions under healthy and crack states are given, respectively. Based on the lumped parameter method, the dynamic model of planetary gear with crack in sun gear is constructed, and the vibration response is solved. The simulation results show when the tooth root cracks appear, the vibration response of the tooth has obvious shock response characteristics. The characteristic frequency and frequency multiplication of sun gear fault can be found obviously by envelope analysis. The simulation signal and the test signal obtained by the drivetrain dynamics simulator gearbox test rig are compared and verified. The comparison and verification results show that the proposed TVMS calculation method and the dynamic model are accurate, which can provide a certain theoretical basis for the fault diagnosis of planetary gear with crack fault. The test results are consistent with the numerical analysis results, which provides a theoretical basis for the fault diagnosis of tooth crack.

Research on Dynamics of Double-Mesh Helical Gear Set

2012 ◽  
Vol 215-216 ◽  
pp. 1021-1025 ◽  
Author(s):  
Fu Chun Yang ◽  
Qi Lin Huang ◽  
Yong Wang ◽  
Jun Gang Wang
Keyword(s):  
Natural Frequencies ◽  
Vibration Mode ◽  
Helical Gear ◽  
Dynamic Responses ◽  
Time Varying ◽  
Sensitive Area ◽  
Axial Vibration ◽  
Mesh Stiffness ◽  
Natural Modes ◽  
Rotational Vibration

A dynamic model of double-mesh helical gear set was established including the torsional vibration, axial vibration and time varying mesh stiffness. The natural modes were systematically analyzed and classified into three types: rotational vibration mode, axial vibration mode and overall vibration mode. The influence of time varying mesh stiffness and the dynamic responses of the gear set were also investigated. The results showed that several natural frequencies are excited in the dynamic response and there is a frequency sensitive area which may cause large dynamic load.

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.

Influence of Sliding Friction on the Dynamic Characteristics of a Planetary Gear Set With the Improved Time-Varying Mesh Stiffness

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Wei Luo ◽  
Baijie Qiao ◽  
Zhixian Shen ◽  
Zhibo Yang ◽  
Hongrui Cao ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Friction Forces ◽  
Basic Model ◽  
Internal Excitation ◽  
Improved Model

Abstract Acting as an important internal excitation, sliding friction can cause the vibration and noise of the planetary gear set. In this paper, a dynamic model is developed to study the influence of sliding friction on the dynamic characteristics of the planetary gear set by including the time-varying mesh stiffness (TVMS), sliding friction forces and torques. An improved analytical model is proposed to calculate the TVMS with sliding friction. The explicit analytical expressions of the sliding friction forces and torques are also derived. Three kinds of different models are applied to investigate the influence of sliding friction: (1) the basic model: sliding friction is neglected in the dynamic model; (2) the improved model I: only the sliding friction forces and torques are considered in the dynamic model; and (3) the improved model II: both the influence of sliding friction on the TVMS and the sliding friction forces and torques are introduced into the dynamic model. The planetary gear set with three equally spaced planet gears is applied to analyze the dynamic characteristics under sliding friction. The simulation results show that the dynamic characteristics can be enhanced or disturbed by sliding friction. In the end, the dynamic model is validated by the experiments. Therefore, the influence of sliding friction is non-negligible when investigating the dynamic characteristics of the planetary gear set. The developed dynamic model provides a feasible dynamic research scheme for the planetary gear set with sliding friction.

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