Dynamic Analysis of a Planetary Gear System

1992 ◽  
Author(s):  
Mark G. Donley ◽  
Glen C. Steyer
Keyword(s):  
Dynamic Response ◽  
System Dynamics ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Transmission Errors ◽  
Planetary Gear Sets ◽  
Planetary Gear System ◽  
Critical Components ◽  
Gear Meshes

Abstract Noise reduction in geared systems is usually achieved by minimizing transmission error or by changing the gear train’s dynamic response. While considerable research has been directed in the past to understanding and controlling the transmission error, the same can not be said of the system dynamic response. Recent efforts at modifying the dynamic response to reduce the sensitivity to transmission error have proven to be very rewarding for parallel shaft gearing applications. In this paper, these efforts are extended to planetary gear set applications. A major difference between planetary gear sets and parallel shaft gears is that in planetary gear sets many gear meshes carry load instead of just one. This feature poses a modeling problem as to how to combine responses due to transmission errors at each loaded mesh to determine the total response. A method is proposed in this paper in which transmission errors at different gear meshes are combined into net vertical, net lateral and net tangential transmission errors. A methodology for computing dynamic mesh force response due to these net transmission errors and for identifying critical components that control the gear train system dynamics is presented. These techniques are useful in understanding the effects of system dynamics on gear noise and in developing quiet gear design. To demonstrate the salient features of the proposed method, an example analysis of a transmission with a planetary gear set is presented.

Dynamic meshing incentive analysis for wind turbine planetary gear system

2017 ◽  
Vol 69 (2) ◽  
pp. 306-311 ◽  
Author(s):  
Yuxiang Chen ◽  
Mutellip Ahmat ◽  
Zhong-tang Huo
Keyword(s):  
Wind Turbine ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear System ◽  
The Sun ◽  
Content Type ◽  
Impact Stress ◽  
Planetary Gear System ◽  
The Impact ◽  
Gear Meshes

Purpose Irregular windy loads are loaded for a wind turbine. This paper aims to determine the form of gear failure and the working life of the gear system by assessing the dynamic strength of gears and dynamic stress distribution. Design/methodology/approach The helical planetary gear system of the wind turbine growth rate gearbox was investigated, and while a variety of clearance and friction gear meshing processes were considered in the planetary gear system, a finite element model was built based on the contact–impact dynamics theory, solved using the explicit algorithm. The impact stress of the sun gear of the planetary gear system was calculated under different loads. An integrated planetary gear meshing stiffness, and the error of system dynamic transmission error were investigated when the planetary gear meshes with the sun or ring gears. Findings The load has little effect on the sun gear of the impact stress which was known. The varying stiffness is different while the planetary gear meshes with the sun and ring gears. There were differences between the planetary gear system and the planetary gear, and with load, the planetary gear transmission error decreases. Originality/value This study will provide basis knowledge for the planetary gear system.

Study on Dynamic Load Sharing Behavior of Two-Stage Planetary Gear Train Based on a Nonlinear Vibration Model

2011 ◽  
Vol 86 ◽  
pp. 611-614 ◽  
Author(s):  
Tong Jie Li ◽  
Ru Peng Zhu ◽  
He Yun Bao
Keyword(s):  
Planetary Gear ◽  
Load Sharing ◽  
Gear Train ◽  
Two Stage ◽  
Transmission Errors ◽  
Meshing Stiffness ◽  
Vibration Model ◽  
Planetary Gear System ◽  
Dynamic Load Sharing ◽  
Sharing Behavior

The nonlinear torsional vibration model of a two-stage planetary gear system is established taking errors of transmission, time varying meshing stiffness and multiple gear backlashes into account. The solution of the equations is determined by using ODE45. The influences of transmission errors on the load sharing behavior are assessed and some useful theoretical guidelines for the design of planetary gear systems are provided at last.

Dynamic Model and Vibration Characteristics of Planetary Gear Train Based on Transmission Errors

2014 ◽  
Vol 668-669 ◽  
pp. 160-163 ◽  
Author(s):  
Kai Xu ◽  
Ping Jia ◽  
Ming Qiu ◽  
Jian Jun Yang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Experimental Investigations ◽  
Tooth Contact Analysis ◽  
Gear Noise ◽  
Transmission Errors ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
Noise Vibration

The paper defines the transmission errors of planetary gear trains, derives from kinetic tooth contact analysis. The method to calculate transmission errors of planetary gear trains is put forward. An integrated platform was constructed for measuring gear noise, vibration and transmission error to verify the effectiveness and feasibility of the analytical. Finally, experimental investigations of the gear noise and vibration spectrum in time domain are introduced, which was solved and simulated in Matlab software.

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.

An Analytical and Numerical Investigation of Modulation Sidebands of a Planetary Gear Under Fluctuated External Torque

2018 ◽  
Author(s):  
Yunbo Yuan ◽  
Wei Liu ◽  
Yahui Chen ◽  
Donghua Wang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Operating Conditions ◽  
Radial Acceleration ◽  
External Torque ◽  
Gear Mesh ◽  
Planetary Gear Sets ◽  
Static Transmission Error ◽  
Frequency Modulations ◽  
Mesh Phasing

Certain operating conditions such as fluctuation of the external torque to planetary gear sets can cause additional sidebands. In this paper, a mathematical model is proposed to investigate the modulation mechanisms due to a fluctuated external torque (FET), and the combined influence of such an external torque and manufacturing errors (ME) on modulation sidebands. Gear mesh interface excitations, namely gear static transmission error excitations and time-varying gear mesh stiffness, are defined in Fourier series forms. Amplitude and frequency modulations are demonstrated separately. The predicted dynamic gear mesh force spectra and radial acceleration spectra at a fixed position on ring gear are both shown to exhibit well-defined modulation sidebands. Comparing with sidebands caused by ME, more complex sidebands appear when taking both FET and ME into account. An obvious intermodulation is found around the fundamental gear mesh frequency between the FET and ME in the form of frequency modulations, however, no intermodulation in the form of amplitude modulations. Additionally, the results indicate that some of the sidebands are cancelled out in radial acceleration spectra mainly due to the effect of planet mesh phasing, especially when only amplitude modulations are present.

Matrix-Based Operation Method for Detecting Structural Isomorphism of Planetary Gear Train Structures

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Xiangyang Xu ◽  
Hanqiao Sun ◽  
Yanfang Liu ◽  
Peng Dong
Keyword(s):  
Planetary Gear ◽  
Gear Train ◽  
Synthesis Algorithm ◽  
Automatic Transmissions ◽  
Detection Approach ◽  
Planetary Gear Sets ◽  
Transmission Structure ◽  
Structural Isomorphism ◽  
Hybrid Configuration ◽  
Isomorphic Structure

Abstract Planetary gear sets (PGSs) have been widely used in automatic transmissions (AT) and dedicated hybrid transmissions (DHTs). In this paper, a novel isomorphic detection method for planetary gear transmission structure is proposed based on matrix operation. The isomorphic detection process includes two main parts. In the first part, various components of the transmission structure are classified. In the second part, isomorphic structures of the numerous structures are detected. Through the application of the proposed detection approach, the structures obtained by different synthesis algorithms can be greatly reduced. Furthermore, by the analysis and transformation of the hybrid configuration to conventional transmission configuration, the scope of use of the algorithm can be expanded through the method. The proposed detection approach is capable of automatically detecting the isomorphic structure of the potential structures obtained by synthesis algorithm.

Harmonic Balance Method for Nonlinear Vibration of Compound Planetary Gear Sets

2015 ◽  
Author(s):  
Weilin Zhu ◽  
Shijing Wu ◽  
Xiaosun Wang
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Response Characteristic ◽  
Transmission Error ◽  
Balance Method ◽  
Time Varying ◽  
Algebraic Equations ◽  
Gear Backlash ◽  
Planetary Gear Sets

In this paper, a new nonlinear time-varying dynamic model for compound planetary gear sets, which incorporates the time-varying meshing stiffness, transmission errors and gear backlash, has been presented. The harmonic balance method (HBM), which is an analytical approach widely used for nonlinear oscillators, is employed to investigate the dynamic characteristics of the gear sets. The matrix form iteration algebraic equations has been established and solved by HBM and single rank inverse Broyden method to reveal the effect of transmission error and gear backlash on the frequency response characteristic of the system. Sub-harmonic resonant, super-harmonic resonant and jump phenomenon have been illustrated by several examples.

Tooth Contact Analysis of Planetary Gear Trains with Equally Spaced Planets

2010 ◽  
Vol 43 ◽  
pp. 279-282
Author(s):  
Kai Xu ◽  
Xiao Zhong Deng ◽  
Jian Jun Yang ◽  
Guan Qiang Dong
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Spur Gear ◽  
Contact Analysis ◽  
Gear Train ◽  
Tooth Contact Analysis ◽  
Planetary Gear Train ◽  
Tooth Contact ◽  
Gear Trains ◽  
Equal Space

Based on Tooth Contact Analysis (TCA), a feasible approach for Transmission Error (TE) of planetary gear train is proposed in this paper. With a view to getting the total TE curve of the planetary gear train, a specific analysis of the TE from the planetary gear train with only one planet should be proceed firstly, the second step is to calculate each phase difference of planets in the gear train. The applicable conditions for the simplified calculation are spur gear or involute gear pairs in the gear train. Due to equal space between them, planets have the same phase angle.

Dynamic Response Analysis of Wind Turbine Planetary Gear System With Interval Stiffness Parameters

2014 ◽  
Author(s):  
Sha Wei ◽  
Qinkai Han ◽  
Zhipeng Feng ◽  
Yanhua Shen ◽  
Fulei Chu
Keyword(s):  
Wind Turbine ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear System ◽  
Dynamic Responses ◽  
Lumped Parameter Model ◽  
Response Analysis ◽  
Mesh Stiffness ◽  
Gear Trains ◽  
Planetary Gear System

Planetary gear transmission system is one of the primary parts of the wind turbine drive train. Due to the assembly state, lubrication conditions and wear, the mesh stiffness of the planetary gear system is an uncertain parameter. In this paper, taking the uncertainty of mesh stiffness into account, the dynamic responses of a wind turbine gear system subjected to wind loads and transmission error excitations are studied. Firstly, a lumped-parameter model is extended to include both the planetary and parallel gears. Then the fluctuation ranges of dynamic mesh forces are predicted quantitatively and intuitively based on the combined Chebyshev interval inclusion function and numerical integration method. Finally, examples of gear trains with different interval mesh stiffnesses are simulated and the results show that tooth separations are becoming more obvious at the resonant speed by considering the fluctuating mesh stiffness of the second parallel gear stage. The nonlinear tooth separations are degenerated obviously as the fluctuation error of the mesh stiffness of the second parallel gear set is increased.

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