scholarly journals Nonlinear Dynamics of a Power-Split Transmission Unit with a Planetary Gear Train and Selectable One-Way Clutches

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Zhizhou Jia ◽  
Pingkang Li
Keyword(s):  
Comprehensive Evaluation ◽  
Damping Ratio ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Mesh Stiffness ◽  
Parallel Transmission ◽  
Planetary Gear Train ◽  
Power Split ◽  
In Series

A Planetary Gear Train (PGT) can be used in series-parallel transmission to redistribute powers. Selectable one-way clutches (SOWCs), compared with traditional friction clutches, can simplify controls and diversify patterns especially for hybrid transmissions. In this paper, a nonlinear torsional model of a power-split PGT coupled with three SOWCs is proposed. Piecewise nonlinearities of SOWCs as well as clearance, time-varying mesh stiffness, and synthetic transmission error of the PGT are considered. With a specified group of comprehensive evaluation indices, influences of piecewise nonlinearities of SOWCs are explored. Simulation results show that the piecewise nonlinearities of SOWCs can diminish collision range and reduce resonances of the PGT. Further research studies on parameter configurations of each SOWC reveal that of the three SOWCs, stiffness and radius of the SOWC connected to the sun gear of the PGT are dominant factors. Large stiffness and effective radius of the SOWC render the PGT fall into chaos on lower meshing frequencies; however, enormous impact vibrations occur to the SOWC if it gets too soft. Additionally, the increase of the damping ratio of the SOWC connected to sun gear can distinctly reduce the vibration and maximum dynamic load of the system on the entire working range.

Dynamic features of planetary gear train with tooth errors

2014 ◽  
Vol 229 (10) ◽  
pp. 1769-1781 ◽  
Author(s):  
Zaigang Chen ◽  
Yimin Shao
Keyword(s):  
Gear Tooth ◽  
Planetary Gear ◽  
Transmission Error ◽  
Geometric Error ◽  
Gear Train ◽  
Dynamic Features ◽  
Mesh Stiffness ◽  
Planetary Gear Train ◽  
Proposed Model ◽  
Dynamic Excitations

As one of the inherited displacement excitation sources which are related to the gear vibration and noise problems, gear transmission error always consists of two parts: gear tooth geometric error and tooth elastic deformation under transmitted load. The gear tooth geometric errors were directly employed as the displacement excitations in previous papers, which are not accurate. In this paper, a new method is developed to transform the gear tooth errors (TEs) to be the appropriate dynamic excitations through the mesh stiffness and the unloaded static transmission error (USTE), where the obtained displacement excitation curves, namely the USTE curves, are very different from the TE curves. Incorporation of the proposed model into the dynamic model of a planetary gear train enables the investigation of the TE effect on the dynamic excitations and vibrations. Two groups of TEs with different amplitudes are employed in the case studies. The results verify that the micro-scale TEs influence not only the dynamic displacement excitation, but also the total mesh stiffness and the planetary gear vibrations greatly.

Study on Characteristics of Metal V-Belt Infinitely Variable Power-Split Transmission

2011 ◽  
Vol 383-390 ◽  
pp. 785-789 ◽  
Author(s):  
Hui Pan ◽  
Xing Cai
Keyword(s):  
Planetary Gear ◽  
Gear Ratio ◽  
Gear Transmission ◽  
Gear Train ◽  
Speed Ratio ◽  
Planetary Gear Train ◽  
Power Split ◽  
In Series ◽  
Variable Power ◽  
Changing Rate

Six kinds of torque-splitting and speed-converging metal V-belt IVPST were raised; their global speed ratio and torque ratio of metal V-belt CVT output to metal V-belt IVPST output were derived. Two different torque-splitting and speed-converging metal V-belt IVPSTs were sum up: series and parallel metal V-belt IVPSTs. In series metal V-belt IVPST, speed ratio changing rate and torque ratio were related to gear ratio of planetary gear train and fixed gear transmission, but in parallel metal V-belt IVPST, that were only related to gear ratio of planetary gear train.

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.

Research on Calculation of Unloaded Transmission Error of Planetary Gear Train Caused by Eccentricity

2017 ◽  
Author(s):  
Shuaidong Zou ◽  
Guangjian Wang ◽  
Li Yu
Keyword(s):  
Curve Fitting ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Computational Formula ◽  
Planetary Gear Train ◽  
Ratio Error ◽  
Load Transmission ◽  
Planet Gear ◽  
Load Conditions

In this paper, calculation of no-load transmission error (TE) of planetary gear train is studied. The theory computational model of the eccentric planetary gear train with single planet gear (SPG) under no-load conditions is constructed initially for acquiring the formulas of no-load transmission ratio error and unloaded transmission error (UTE) of internal and external gear pairs. Then computational formula of the UTE of planetary gear train with SPG caused by eccentricity is presented. Through simulation TE and the developed formula of UTE, the eccentricities and initial phasing are uncoupled by curve fitting. Simultaneously, formula of UTE of planet gear train with SPG is validated. At the same time, different groups of initial phasing are analyzed to acquire the relatively good initial phasing group. In addition, the UTE of planetary gear train with multiple planet gears (MPG) caused by eccentricity is developed.

Modeling and Bifurcation Characteristics of Double Stage Planetary Gear Train With Multiple Clearances

2015 ◽  
Author(s):  
Rupeng Zhu ◽  
Dongping Sheng ◽  
Fengxia Lu ◽  
Miaomiao Li ◽  
Heyun Bao
Keyword(s):  
Strong Coupling ◽  
Chaotic Motion ◽  
Damping Ratio ◽  
Period Doubling ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Bifurcation Parameter ◽  
Planetary Gear Train ◽  
Motion State

This paper proposes a new non-linear transverse-torsional coupled model for double stage planetary gear train, and gear’s geometric eccentricity error, synthetical transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair’s backlashes and sun gear’s bearing clearance are taken into account. The differential governing equations of motion are derived and solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state is investigated systematically and qualitatively, and exhibits diverse bifurcation and chaos characteristics under different bifurcation parameters including meshing frequency, sun-planet backlash and planet-ring backlash. Analysis results showed that the increasing damping could suppress the region of chaotic motion and improve the system’s stability significantly; the route of period-doubling to chaotic motion was observed for both first and second stage’s motion state under the bifurcation parameter of meshing frequency; The routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; Besides, the increasing damping ratio could split the bifurcation diagram window into different sections and strong coupling effects are generated to second stage’s motion. Several different types of routes to chaos were observed under the bifurcation parameter of planet-ring backlash including period doubling and 3T-periodic channel; Besides, it concluded that planet-ring backlash could generate a strong coupling effect to both stage’s nonlinear behavior.

Reliability sensitivity analysis of tooth modification on dynamic transmission error of helical planetary gears

2020 ◽  
Vol 234 (19) ◽  
pp. 3903-3918
Author(s):  
Zhang Jun ◽  
Tang Wei-min ◽  
Chen Qin ◽  
Chen Tao
Keyword(s):  
Quantitative Relationship ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
Planetary Gear Train ◽  
Dynamic Transmission Error ◽  
Tooth Modification ◽  
Meshing Characteristics

As one of the most influential factors leading to gear vibrations, transmission errors of the engaging gears must be controlled to achieve a desirable dynamic performance for a power transmission system. It is well known that tooth modification is an effective way to reduce the fluctuations of the transmission error of a gear pair. The challenge is determining how to establish a quantitative relationship between the tooth modification parameters and the transmission error fluctuations of a gear pair. The present study aims to reveal the sensitivity of the tooth modification parameters on the transmission error fluctuations of a helical planetary gear train in a wind turbine gearbox. For this purpose, a sophisticated parametric three-dimensional contact model that included the micro-geometries of the tooth modification is developed in the ROMAX® environment. Based on this model, a loaded tooth contact analysis is carried out to compute the meshing characteristics, such as the contact pressure and transmission error of each gear pair in the planetary gear train. With the obtained meshing characteristics, the tooth modification amounts of the engaging gears were determined using empirical formulas. These modification amounts are designated as the mean values of the samples generated by the central composite method. After repeating the loaded tooth contact analysis process for each generated sample, a quadratic polynomial function is derived using the response surface method to describe the quantitative relationship between the tooth modification parameters and the dynamic transmission error fluctuations. A large number of random samples are generated using a Monte Carlo method, and the corresponding dynamic transmission error fluctuations are determined with the aforementioned quadratic polynomial function. Based on these samples, a reliability sensitivity analysis is carried out to demonstrate the effects of the tooth modification parameters on the dynamic transmission error fluctuations of the helical planetary gear train.

Planetary Gear Train Used in Wind Driver Generator Based on TCA

2014 ◽  
Vol 672-674 ◽  
pp. 251-254
Author(s):  
Kai Xu ◽  
Ping Jia ◽  
Ming Qiu ◽  
Jian Jun Yang
Keyword(s):  
Time Domain ◽  
Planetary Gear ◽  
Transmission Error ◽  
Measurement Model ◽  
Gear Train ◽  
Periodic Signal ◽  
Mesh Stiffness ◽  
Gear Noise ◽  
Noise Vibration ◽  
Speed Fluctuations

By the disadvantage of the speed fluctuations to the gear noise and vibration spectrum in time domain, a new method to measuring the periodic signal was put forward in pulse time domain. The multi-channel simultaneous measurement model were brought out, aimed at analyzing the gear meshing state and its frequency characteristics. Then, the 14 DOF nonlinear vibration equations was derived from kinetic analysis on the planetary gear pair meshing model, which was solved and simulated in Matlab software, containing with transmission error, time-varying mesh stiffness, clearance and other factors. Finally, an integrated platform was constructed for measuring gear noise, vibration and transmission error to verify the effectiveness and feasibility of the analytical.

Research on Tooth Profile Modification of the Herringbone Planetary Gear Train

2015 ◽  
Author(s):  
Heyun Bao ◽  
Huan Liu ◽  
Rupeng Zhu ◽  
Fengxia Lu ◽  
Miaomiao Li
Keyword(s):  
Rotational Speed ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Maximum Magnitude ◽  
Nonlinear Dynamic Model ◽  
Planetary Gear Train ◽  
Straight Line ◽  
The Impact ◽  
Herringbone Planetary Gear Train

A bending-torsional coupled nonlinear dynamic model which contains the modification parameters of herringbone planetary gear train is presented. A formula of modification incentive is analyzed and deduced. The impact of the straight line and parabolic modification parameters on the amplitude of system transmission error is researched. The optimum modification parameters are acquired according to the minimum amplitude of system transmission error. Different amplitudes of the system transmission error, before and after modification, are compared at different rotational speed. The results indicate that the straight line modification parameters on the amplitude of system transmission error are more sensitive. Modification parameters on the amplitude of system transmission error are researched. When the length of the modification is specified, the amplitude of system transmission error is reduced sharply at first, then increased rapidly with the maximum magnitude of the modification increasing; When the maximum magnitude of the modification is specified, the amplitude of system transmission error is increased weakly at first, then decreased sharply, and increased rapidly in the end, with the length of the modification increasing. The modification parameters could form a crescent-shaped zone which can reduce the system transmission error amplitude significantly. The amplitudes of the system transmission error with modification are all reduced at different rotational speed, especially when there is a sympathetic vibration.

Tooth Contact Analysis of Planetary Gear Trains and its Transmission Error Experiments and Frequency Spectrum Analysis

2014 ◽  
Author(s):  
Kai Xu ◽  
Aijun Xu ◽  
Jianjun Yang ◽  
Ming Qiu ◽  
Jianxin Su
Keyword(s):  
Spectrum Analysis ◽  
Planetary Gear ◽  
Transmission Error ◽  
Contact Analysis ◽  
Gear Train ◽  
Tooth Contact Analysis ◽  
Planetary Gear Train ◽  
Tooth Contact ◽  
Planetary Gear Trains ◽  
Gear Trains

Based on Tooth Contact Analysis (TCA), a feasible approach for Transmission Error (TE) of planetary gear train is proposed in this paper as follows: the first step is to proceed a specific analysis of the TE from the planetary gear train with only one planet, the second step is to calculate each phase difference of planets in the gear train. Then the total TE of a planetary gear train can be calculated simply by the two steps. The paper points out 3 kinds of positional difference of planets: coincidence, equalization, imparity and their respective effect on the total TE of the gear train, then draws a conclusion that the equalization is the optimized one among the above three. Eventually, the TE experiment of the planetary gear train is performed, and spectrum analysis is adopted in the paper.

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