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.

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.

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.

scholarly journals Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

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.

Dynamic Analysis of Hybrid Gear Trains With Flexible Ring Gear Rim

2017 ◽  
Author(s):  
Xiangyang Xu ◽  
Junbin Lai ◽  
Yanfang Liu
Keyword(s):  
Dynamic Behavior ◽  
Planetary Gear ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Train ◽  
Gear Pair ◽  
Ring Gear ◽  
Gear Trains ◽  
Helical Gear Pair ◽  
Flexible Ring

In this paper, the dynamic behavior of a hybrid gear train (HGT), consists of a single-stage helical planetary gear set and a helical gear pair, is analyzed. A ring gear rim is connected with an internal gear in a helical planetary gear set and an external gear in a helical gear pair. Power flows from the helical gear pair to the helical planetary gear set. Therefore, loads in the external gear would cause additional axial force and radial force, which would lead to unexpected moment and force. As a result, deflections of ring gear rim must be taken into consideration. Under this condition, a three-dimensional dynamic model of a HGT with flexible ring gear rim is developed, in which six degrees of freedom including three translational motions and three rotational motions are employed. Coupling effects of the bearing support stiffness, gear mesh stiffness and time-varying transmission error are taken into consideration. The model also takes flexible supporting shafts and planet carrier into consideration by using finite element method. Then, the equations of motion in matrix form are established and solved to predict the forced vibration response due to the transmission error excitations. Subsequently, effects of positions of the helical gear pair relative to the planetary gear set and the thickness of ring gear rim on dynamic behavior of the HGT are discussed. The results show that the proposed model is potential and can be used to guide the design of hybrid gear trains.

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.

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.

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.

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.

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