The Homotopy Analysis for the Nonlinear Dynamics of Planetary Gear Trains

2018 ◽  
Author(s):  
Chao Xun ◽  
Sujuan Jiao ◽  
Yong Chen ◽  
Xinhua Long
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Nonlinear Problems ◽  
Planetary Gear ◽  
Displacement Function ◽  
Strongly Nonlinear ◽  
Planetary Gear Trains ◽  
Homotopy Analysis ◽  
Gear Trains ◽  
The Impact

In this paper, the homotopy analysis method (HAM) is proposed to study the nonlinear oscillators of planetary gear trains, in which the periodically time-varying mesh stiffness and gear backlash are included through a nonlinear displacement function. In contrast to the traditional perturbation methods, the HAM does not require a small parameter in the equation under study, and then can be applied to both of the weakly and strongly nonlinear problems. In this article, firstly the closed-form approximations for the dynamic response of planetary gear trains are obtained by HAM. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. The accuracy of HAM solutions is evaluated by numerical integration simulations. Results indicate that with large tooth separation times, the amplitude-frequency curves obtained by HAM agree better with the results obtained by NI than those obtained by the MMS.

The homotopy analysis for the nonlinear dynamics of planetary gear trains

2020 ◽  
Vol 234 (16) ◽  
pp. 3154-3165
Author(s):  
Chao Xun ◽  
Sujuan Jiao ◽  
He Dai ◽  
Xinhua Long
Keyword(s):  
Numerical Integration ◽  
Homotopy Analysis Method ◽  
Nonlinear Dynamic Analysis ◽  
Primary Resonance ◽  
Planetary Gear ◽  
Analysis Method ◽  
Planetary Gear Trains ◽  
Homotopy Analysis ◽  
Gear Trains ◽  
Harmonic Resonance

In this paper, the nonlinear oscillation of planetary gear trains is investigated by the homotopy analysis method. The nonlinearity of planetary gear trains due to the periodically time-varying mesh stiffness and contact loss are included. In contrast to the perturbation analysis, the homotopy analysis method is independent of the contact loss ratio, and then can be applied to both small and large contact loss ratios. In this article, firstly the closed-form approximations for the primary resonance, sub-harmonic resonance, and super-harmonic resonance are obtained by homotopy analysis method. The accuracy of homotopy analysis method solutions is evaluated by numerical integration simulations. Results indicate that with relatively large contact loss ratios, the amplitude–frequency curves obtained by homotopy analysis method agree better with the results obtained by numerical integration than those obtained by the method of multiple scales. This study lays a higher accurate foundation for more complex nonlinear dynamic analysis of planetary gear trains.

Nonlinear Dynamics of Planetary Gears With Equal Planet Spacing

2007 ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Harmonic Balance ◽  
Gear Tooth ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Nonlinear Effects ◽  
Planetary Gears ◽  
Parallel Finite Element ◽  
The Impact

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. The resulting vibration causes tooth separation leading to nonlinear effects such as classical jump phenomena and sub- and superharmonic resonance. The nonlinear dynamics of the planetary gear is examined by both numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is validated by parallel finite element and numerical integration simulations.

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.

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.

A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains

2002 ◽  
Vol 124 (4) ◽  
pp. 662-675 ◽  
Author(s):  
V. V. N. R. Prasad Raju Pathapati ◽  
A. C. Rao
Keyword(s):  
Graph Isomorphism ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Graph Representations ◽  
Planetary Gear Trains ◽  
Gear Trains ◽  
A New Technique

The most important step in the structural synthesis of planetary gear trains (PGTs) requires the identification of isomorphism (rotational as well as displacement) between the graphs which represent the kinematic structure of planetary gear train. Previously used methods for identifying graph isomorphism yielded incorrect results. Literature review in this area shows there is inconsistency in results from six link, one degree-of-freedom onwards. The purpose of this paper is to present an efficient methodology through the use of Loop concept and Hamming number concept to detect displacement and rotational isomorphism in PGTs in an unambiguous way. New invariants for rotational graphs and displacement graphs called geared chain hamming strings and geared chain loop hamming strings are developed respectively to identify rotational and displacement isomorphism. This paper also presents a procedure to redraw conventional graph representation that not only clarifies the kinematic structure of a PGT but also averts the problem of pseudo isomorphism. Finally a thorough analysis of existing methods is carried out using the proposed technique and the results in the category of six links one degree-of-freedom are established and an Atlas comprises of graph representations in conventional form as well as in new form is presented.

Dynamic Modeling of the Torsional Vibration of the Slewing Mechanism of a Hydraulic Excavator

2012 ◽  
Vol 253-255 ◽  
pp. 2102-2106 ◽  
Author(s):  
Xu Juan Yang ◽  
Zong Hua Wu ◽  
Zhao Jun Li ◽  
Gan Wei Cai
Keyword(s):  
Torsional Vibration ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Moment Of Inertia ◽  
Hydraulic Excavator ◽  
Planetary Gear Trains ◽  
Vibration Model ◽  
Gear Trains ◽  
The Moment ◽  
Relationship Of

A torsional vibration model of the slewing mechanism of a hydraulic excavator is developed to predict its free vibration characteristics with consideration of many fundamental factors, such as the mesh stiffness of gear pairs, the coupling relationship of a two stage planetary gear trains and the variety of moment of inertia of the input end caused by the motion of work equipment. The natural frequencies are solved using the corresponding eigenvalue problem. Taking the moment of inertia of the input end for example to illustrate the relationship between the natural frequencies of the slewing mechanism and its parameters, based on the simulation results, just the first order frequency varies significantly with the moment of inertia of the input end of the slewing mechanism.

scholarly journals The multi-attribute topological graph method and its application on power flow analysis in closed planetary gear trains

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879410 ◽  
Author(s):  
Yahui Cui ◽  
Jing Gao ◽  
Xiaomin Ji ◽  
Xintao Zhou ◽  
Haitao Yan
Keyword(s):  
Power Flow ◽  
Flow Analysis ◽  
Planetary Gear ◽  
Topological Graph ◽  
Template Model ◽  
Power Flow Analysis ◽  
Analysis Process ◽  
Planetary Gear Trains ◽  
Graphical View ◽  
Gear Trains

The concept of multi-attribute topological graph is proposed in this article to represent the characteristics of both structure and state for typical one-degree-of-freedom planar spur closed planetary gear trains. This method is well applied in power flow analysis and provides a graphical view for the types, values, directions, and transmission relationship of power flow, especially for the recirculation power representation. Furthermore, a template model of multi-attribute topological graph for closed planetary gear trains is also presented, which would be helpful to the multi-attribute topological graph generation for some certain types of closed planetary gear trains just by changing symbols in the template model. A corresponding software is also developed to make the analysis process more convenient. By inputting different parameters, the different visual results can be obtained automatically, thus benefiting engineers in conceptual design.

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