行星齿轮装置动态载荷的齿廓磨损外文文献翻译、中英文翻译

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英文：

Dynamic tooth loads of planetary gear sets having tooth

profile wear

C. Yuksel a, A. Kahraman b,*

a The University of Toledo, Toledo, OH 43606, USA

b Department of Mechanical Engineering, The Ohio State University, Room 255, 650

Ackerman

Road,

Columbus, OH 43202, USA

Received 25 June 2003; received in revised form 12 January 2004; accepted 10 February

2004

Abstract

A computational model of a planetary gear set is employed to study the influence of

surface wear on thedynamic behavior of a typical planetary gear set. The overall

computational scheme combines a wear modelthat defines geometric description of contacting

gear tooth surfaces having wear and a deformable-bodydynamic model of a planetary gear set.

The wear model employ s a quasi-static gear contact model tocompute contact pressures and

Archa rd’s wear model to determine the wear depth distributions. The wornsurfaces are input

into the dynamic model to quantify the impact of wear on gear tooth and mesh dynamicforces.

The results on a planetary gear set having a fixed planet carrier indicates that the dynamic

behavioris nonlinear due to tooth separations in its resonance regions. The results for worn

gear surfaces indicatethat surface wear has a signi cant in uence in off-resonance speed 

ranges while its influence diminishes nearresonance peaks primarily due to tooth

Keywords: Planetary gear sets; Gear dynamics; Gear wear

1. Introduction

Planetary gear sets, also known as Epicyclic gear drives, are commonly used in a large

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number ofautomotive, aerospace and industrial applications. They posses numerous

advantages over parallel-axis gear trains including compactness of design, availability of

multiple speed reduction ratios, and less demanding bearing requirements. Most common

examples of planetary gear sets can be foundin automatic transmissions, gas turbines, jet

engines, and helicopter drive trains. A typical simple planetary gear set consists of a sun gear,

a ring gear and a number of identical planet gears meshing both with the sun and ring gears.

A common carrier holds the planets in place.Dynamic analysis of planetary gears is essential

for eliminating noise and vibration problems of the products they are used in. The dynamic

forces at the sun-planet and ring-planet meshes are the main sources of such problems.

Although planetary gear sets have generally more favorable noise and vibration characteristics

compared to parallel-axis gear systems, planetary gear set noise still remains to be a major

problem. The dynamic gear mesh loads that are much larger than the static loads are

transmitted to the supporting structures, in most cases, increasing gear noise. Larger dynamic

loads also shorten the fatigue life of the components of the planetary gear set including gears

and bearings.

Surface wear is considered one of the major failure modes in gear systems. In case of

planetary gear sets, experimental data has shown that especially the sun gear meshes might

experience significant surface wear when run under typical operating conditions. While wear

is a function of a large number of parameters, sliding distance and contact pressure were

shown to be most significant parameters influencing gear wear. Wear of tooth profiles results

in a unique surface geometry that alters the gear mesh excitations in the form of kinematic

motion errors, enhancing the dynamic effects.

Modeling of planetary gear set dynamics received significant attention for the last 30 years.

A number of studies proposed lumped-parameter models to predict free and forced vibration

characteristics of planetary gear sets. These models assumed rigid gear wheels, connected to

each other by springs representing the flexibility of the meshing teeth. In these studies,

nonlinear effects due to gear backlash and time-varying parameters due to gear mesh stiffness

fluctuations were neglected. The corresponding Eigen value solution of the linear equations of

motion resulted in natural modes. Modal summation technique was typically used to find the

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forced response due to external gear mesh displacement excitations defined to represent

motion transmission errors. These lumped-parameter models vary in degrees of freedom

included, from purely torsional models to two or three-dimensional transverse-torsional

models. While these models served well in describing the dynamic behavior of planetary gear

sets qualitatively, they lacked certain critical features. First, the gear mesh models were quite

simplistic with a critical assumption that complex gear mesh contact interaction can be

represented by a simple model formed by a linear spring and a damper. These models demand

that the values of the gear mesh stiffness and damping, as well as the kinematic motion

transmission error excitation, mustbe known in advance. It is also assumed that these

parameter values determined quasi-statically remain unchanged under dynamic conditions. In

addition, gear rim deflections and Hertzian contact deformations are also neglected. Another

group of recent models used more sophisticated finite element-based gear contact mechanics

models. These computational models address all of the shortcomings of the lumped-parameter

models since the gear mesh conditions are modeled as individual nonlinear contact problems.

The need for externally defined gear mesh parameters is eliminated with these models. In

addition, rim deflection and spline support conditionsare modeled accurately . These models

are also capable of including the influence of the tooth profile variations in the form of

intentional profile modifications, manufacturing errors or wear on the dynamic behavior of

the system.

The study of wear of gear contact is becoming one of the emerging areas in gear technology.

A number of recent gear wear modeling effortsform a solid foundation for more accurate,

larger system analyses. All of these models use Archard’s wear model in conjunction with a

gear contact model and relative sliding calculations. These studies focused on prediction of

wear of either spur or helical gear pairs in aparallel-axis configuration. The tooth contact

pressures were computed in these models using either simplified Hertzian contact or boundary

element formulations under quasi-static conditions. Sliding distance calculations were carried

out kinematically by using the involute geometry and Archard’s wear model was used with an

empirical wear coefficient to compute the surface wear depth distribution. A number of

studies investigated the influence of wear on gear dynamics response . Among them, Kuang

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第1页共18页英文：DynamictoothloadsofplanetarygearsetshavingtoothprofilewearC.Yuksela,A.Kahramanb,*aTheUniversityofToledo,Toledo,OH43606,USAbDepartmentofMechanicalEngineering,TheOhioStateUniversity,Room255,650AckermanRoad,Columbus,OH43202,USAReceived25June2003;receivedinrevisedform12January2004;accepted10Fe...

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