Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

A Study on Planetary Gear Dynamics With Tooth Profile Modification

2011 ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Transmission Error ◽  
Tooth Profile ◽  
Peak Amplitude ◽  
Profile Modification ◽  
Tooth Profile Modification ◽  
Static Transmission Error ◽  
The Impact

This study investigates the impact of tooth profile modification on planetary gear dynamic response. Micro-scale geometric deviations from an involute gear tooth profile add an additional excitation source, potentially reducing gear vibration. In order to take account of the excitation, tooth profile modification is included in an analytical planetary gear model. Nonlinearity due to tooth contact loss is considered. Time-varying mesh stiffness and both rotational and translational gear motions are modeled. The accuracy of the proposed model for dynamic analysis is correlated against a benchmark finite element analysis. Perturbation analysis is employed to obtain a closed-form approximation of planetary gear dynamic response with tooth profile modification. Mathematical expressions from the perturbation solution allow one to easily estimate the peak amplitude of resonant response using known parameters. Variation of the peak amplitude with the amount and the length of profile modification illustrates the effect of tooth profile modification on planetary gear dynamic response. For a given external load, the tooth profile modification parameters for minimal response are readily obtained. Static transmission error and dynamic response are minimized at different amounts of profile modification, which contradicts common practical thinking regarding strong correlation between static transmission error and dynamic response. Contrary to the expectation of further reduced vibration, the combination of the optimum sun-planet and ring-planet mesh tooth profile modifications that minimizes response when applied individually increases dynamic response.

Perturbation Analysis and Parametric Study of Planetary Gear Vibration

2012 ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Dynamic Response ◽  
Perturbation Analysis ◽  
Parametric Instability ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Contact Ratio ◽  
System Parameters ◽  
Analysis System ◽  
The Impact ◽  
Perturbation Solutions

This study analytically investigates the impact of system parameters on planetary gear vibration by using perturbation solutions. Closed-form expressions, which explicitly includes the system parameters such as contact ratio, mesh stiffness, damping, and number of planets, of the peak resonant response amplitude and parametric instability width of subharmonic resonance are obtained from perturbation analysis. System parameters related with sun-planet and ring-planet meshes show different influence on dynamic response. The effects of the system parameters are found to be sensitive to vibration modes. With use of the well-defined planetary gear modal properties, mathematical expressions of the weighting factors are derived to quantify the different sensitivity of dynamic response to the sun-planet and ring-planet meshes and to the vibration modes. The perturbation solutions are effective to examine the dependence of dynamic response on the system parameters and help one seek optimal parameters to reduce planetary gear vibration.

scholarly journals Analysis of transmission error and load distribution of a hoist two-stage planetary gear system

2018 ◽  
Vol 233 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Xi Zhang ◽  
Xiaolin Tang ◽  
Wei Yang
Keyword(s):  
Dynamic Model ◽  
Planetary Gear ◽  
Transmission Error ◽  
Transmission System ◽  
Gear Transmission ◽  
Two Stage ◽  
Profile Modification ◽  
Load Distributions ◽  
Multi Stage ◽  
Planetary Gear System

The research described in this study is aimed at exploring the transmission characteristics of a two-stage planetary-gear transmission system. Firstly, a novel rigid-flexible coupled dynamic model was established with the consideration of gear clearance, time-varying meshing stiffness, and the deformation of the bearing and shaft. Secondly, based on the novel dynamic model, different profile modification parameters are carried out to optimize the transmission error, load distributions, and harmonic quantity of the transmission system. The analysis results show that dynamic characteristics can be improved by optimizing the multi-stage planetary gear profile. The study provides a valuable reference for the design of multi-stage planetary-gear transmission systems of hoist industry.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

Dynamics of the Gear Train Set in Wind Turbine

2011 ◽  
Vol 697-698 ◽  
pp. 701-705
Author(s):  
D.D. Ji ◽  
Y.M. Song ◽  
J. Zhang
Keyword(s):  
Wind Turbine ◽  
Dynamic Model ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Gear Train ◽  
Dynamic Responses ◽  
Multi Stage ◽  
Lumped Parameter ◽  
Cartesian Coordinate ◽  
The Impact

A lumped-parameter dynamic model for gear train set in wind turbine is proposed to investigate the dynamics of the speed-increasing gear box. The proposed model is developed in a universal Cartesian coordinate, which includes transversal and torsional deflections of each component, time-varying mesh stiffness, gear profile errors and external excitations. By solving the dynamic model, a modal analysis is performed. The results indicate that the modal properties of the multi-stage gear train in wind turbine are similar to those of a single-stage planetary gear set. A harmonic balance method (HBM) is used to obtain the dynamic responses of the gearing system. The responses give insight into the impact of excitations on the vibrations.

The Impact of Iron Core Model on Dynamic Behavior of Three-Phase Power Transformer Dynamic Model

2015 ◽  
Vol 51 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Klemen Dezelak ◽  
Martin Petrun ◽  
Miran Roser ◽  
Drago Dolinar ◽  
Gorazd Stumberger
Keyword(s):  
Dynamic Model ◽  
Dynamic Behavior ◽  
Power Transformer ◽  
Core Model ◽  
Iron Core ◽  
Three Phase ◽  
The Impact

Dynamic Analysis of Helical Planetary Gear Train

2013 ◽  
Vol 404 ◽  
pp. 312-317 ◽  
Author(s):  
Xian Zeng Liu ◽  
Jun Zhang
Keyword(s):  
Steady State ◽  
Free Vibration ◽  
Dynamic Model ◽  
Planetary Gear ◽  
Gear Train ◽  
Dynamic Responses ◽  
Design Parameters ◽  
Planetary Gear Train ◽  
State Dynamic ◽  
The Impact

A dynamic model for helical planetary gear train (HPGT) is proposed. Based on the model, the free vibration characteristics, steady-state dynamic responses and effects of design parameters on system dynamics are investigated through numerical simulations. The free vibration of the HGPT is classified into 3 categories. The classified vibration modes are demonstrated as axial translational and torsional mode (AT mode), radial translational and rotational mode (RR mode) and planet mode (P mode) followed by the characteristics of each category. The simulation results agree well with those of previous discrete model when neglecting the component flexibilities, which validates the correctness of the present dynamic model. The steady-state dynamic responses indicate that the dynamic meshing forces fluctuate about the average static values and the time-varying meshing stiffness is one of the major excitations of the system. The parametric sensitivity analysis shows that the impact of the central component bearing stiffness on the dynamic characteristic of the HPGT system is significant.

Study on Helical Tooth Profile Modification of Planetary Gear Transmission on the Basis of Gear Transmission Error

2011 ◽  
Vol 86 ◽  
pp. 47-50
Author(s):  
Yu Tang ◽  
Shan Chang ◽  
Zhi Qiang Wang ◽  
Kun Zhang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Tooth Profile ◽  
Gear Transmission ◽  
Mesh Stiffness ◽  
Profile Modification ◽  
Gear Mesh ◽  
Tooth Profile Modification ◽  
Planetary Transmission ◽  
Gear Mesh Stiffness

In order to minimize the fluctuation of gear transmission error (GTE) about the planetary gear transmission. A method was developed to deciding tooth profile modification curves of planetary transmission. According to the condition of the invariable design load, computing the dynamic characteristics of the planetary transmission system under modified and un-modified gear. At the same time, the compare is carried through of the dynamic characteristics for modified and un-modified gear. The results of the dynamic calculation indicate that the profile modification method can make the amplitudes of gear mesh stiffness change calmness and reduce the amplitudes of gear mesh stiffness by this method in paper. At last, the conclusion can be obtained that the tooth profile modification can reduce the vibration and noise of the planetary transmission system.

scholarly journals Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Qilin Huang ◽  
Yong Wang ◽  
Zhipu Huo ◽  
Yudong Xie
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Dynamic Model ◽  
Total Mass ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Gear Transmission System

A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM). Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

scholarly journals Dynamic Response Analysis of Spur Gear System with Backlash

2021 ◽  
Vol 276 ◽  
pp. 01012
Author(s):  
Chao Li ◽  
Jigang Wang
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear System ◽  
Response Analysis ◽  
Response Curves ◽  
Nonlinear Dynamic Response ◽  
Dynamic Response Analysis ◽  
Return Difference

There are few studies on space-driven gear systems in the existing literature. In this paper, a spacedriven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. A nonlinear dynamic response analysis was performed. The backlash was introduced into the dynamic model, and the time-varying stiffness was corrected to make the theoretical model closer to reality. By comparing two kinds of dynamic response curves with and without return difference, it was illustrated that the influence of return difference on dynamic transmission error in a gear system. The results obtained in this paper provide a reference and basis for subsequent research.

Sign in / Sign up

Export Citation Format

Share Document