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.

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.

A PLANETARY GEAR TRAIN WITH RING-INVOLUTE TOOTH

2008 ◽  
Vol 32 (2) ◽  
pp. 251-266
Author(s):  
Shyue-Cheng Yang ◽  
Tsang-Lang Liang
Keyword(s):  
Planetary Gear ◽  
Conjugate Problem ◽  
Gear Ratio ◽  
Gear Train ◽  
Tooth Surface ◽  
The Sun ◽  
Ring Gear ◽  
Planetary Gear Train ◽  
Envelope Method ◽  
Planet Gear

This paper proposes a planetary gear train with ring-involute tooth profile. Inherent in a planetary gear train is the conjugate problem among the sun, the planet gears and the ring gear. The sun gear and the planet gear can be obtained by applying the envelope method to a one-parameter family of a conical tooth surface. The conical tooth rack cutter was presented in a previous paper [5]. The obtained planet gear then becomes the generating surface. The double envelope method can be used to obtain the envelope to the family of generating surfaces. Subsequently the profile of a ring gear of the planetary gear trains can be easily obtained, and using the generated planet gear and applying the gear theory, the ring gear is generated. To illustrate, the planetary gear train with a gear ratio of 24:10:7 is presented. Using rapid prototyping and manufacturing technology, a sun gear, four planet gears, and a ring gear are designed. The RP primitives provide an actual full-size physical model that can be analyzed and used for further development. Results from these mathematical models are applicable to the design of a planetary gear train.

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.

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.

A Novel Algorithm for Enumeration of the Planetary Gear Train Based on Graph Theory

2011 ◽  
Vol 199-200 ◽  
pp. 392-399 ◽  
Author(s):  
Ming Yue Ma ◽  
Xiang Yang Xu
Keyword(s):  
Graph Theory ◽  
Mechanism Design ◽  
Planetary Gear ◽  
Gear Train ◽  
Enumeration Algorithm ◽  
Planetary Gear Train ◽  
The Core ◽  
Planet Gear ◽  
Gear Trains ◽  
Novel Algorithm

As well known, graph theory is a powerful tool for mechanism design. The enumeration of planet gear trains can be converted the synthesis of graphs while a planetary gear train is converted to a graph. During the enumeration of graphs, the problem of isomorphism should be solved. This paper proposes a novel algorithm used to generate non-isomorphism graphs and thereby omits the part of isomorphism detection. The vertex characteristic is firstly defined in this paper that is the core of the enumeration algorithm. This paper also gives an example of the application for the algorithm.

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.

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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