摘 要

变速器是汽车的重要部件，而处于常啮合状态的变速器主减速齿轮对，作为变速器的重要零件，它承受着汽车传动的全部扭矩。同时因为汽车频繁的换档和车速变化，造成变速器主减速齿轮对的寿命缩短。主减速齿轮价格昂贵，不可随意调换，制造精度比较高。而齿轮的承载能力主要受接触强度和弯曲强度的限制，因此，对主减速齿轮副的弯曲应力和接触应力进行科学的分析，就显得十分必要。

本文对变速器在发动机最大输出扭矩（变速器最大输入扭矩）时，齿轮副的受载和约束情况进行了分析，重点介绍了渐开线斜齿轮啮合最恶加载线的定义，并根据此定义对变速器主减速齿轮副的最恶加载线进行了计算，利用最恶加载线对齿轮施加载荷。求解计算后，分别对主动和从动齿轮的弯曲应力分布状况进行了研究，得出齿轮中较危险弯曲应力的位置，在实际的齿轮设计中可以作为理论参考，同时在齿轮制造和热处理过程中可以对弯曲应力最大的地方考虑特殊处理，以增加齿轮的寿命和可靠性。

本文为使齿轮副非线性接触分析的计算速度加快，结果更精确，对齿轮副啮合模型做简化，取大齿轮的四个齿和小齿轮的三个齿进行接触有限元分析。建立接触对（指定接触面和目标面、创建目标面和接触面单元、调整接触初始条件），计算在载荷和约束作用下的力值，得出直观的齿轮副接触面上接触应力变化云图。从图分析知等效接触应力最大值为 929.6 MPa，齿面接触应力成线形分布，即沿接触线分布，分布不均，两端靠近中间的位置接触应力相对较大，中间位置相对较小，最大的接触应力出现在节线附近靠近齿根处。分析得出的齿轮中较危险接触应力位置，在实际的齿轮设计中可以作为理论参考，同时在齿轮制造和热处理过程中可以对接触应力最大的地方考虑特殊处理，以增加齿轮的寿命和可靠性。与弯曲应力计算结果比较分析相似，计算公式得到的接触应力值偏小些，说明工程中，按有限元法进行设计和校核，是偏安全的。对接触强度进行了校核。

关键词：主减速齿轮；有限元法；接触应力；弯曲应力

The Gear Transmission Analysis Research

Based on ANSYS

ABSTRACT

Transmission is an important part of vehicle and main reduction gears which are often in the meshing state, as one of the important transmission parts, will be beared all the torque from the vehicle. At the same time, lift of the main reduction gears will be shorten because of the vehicle frequent shift and unstaic speed. Because of main reduction gear is expensive, cannot exchange optional, manufacturing precision is very high, and the bearing capacity of the gear is mainly restricted by the contaction strength and bending strength. Therefore, it is necessary to do scientific analyze to main reduction gears’ contaction strength and bending strength.

This paper analyze the gear pair’s load and constraint conditions when engine output maximum torque (transmission maximum input torque). And emphatically introduce the definition of helical gear meshing most evil loading line, and according to the definition of it, the main reduction gear’s most evil loading line are calculated, and load the loading to the gears base on the most evil load line. After solving, the activing and driven gears’ bending stress distribution are studied respectively, obtain the most dangerous position for gear bending stress. This can as a reference to actual gear design, and can as a reference to do the special process at the position of the biggest bending stress by the manufacture and heat treatment process for increase life and reliability of gear. Using finite element analysis results to check bending strength, the maximum allowable stress is less than material elastic stress, it is concluded that gear bending strength is enough. This is consistent to the fact that main reduction gear seldom occur bending broken.

In order to up the speed for the nonlinear contact analysis of the gear meshing modeling and up the accuracy of the result, this paper simplify the gear meshing modeling, and take four big gear tooth and three of the small gear tooth to do the finite element analysis. Establish contact pairs (design contact and target face, create target face and contact elements, adjust contact initial conditions), calculation the stress with influence behind load and constraint, obtain the contact stress change map. Analyze the map, we can know that the max contact stress is 929.6 MPa, The contact stress of gear tooth surface become linear distribution, the biggest contact stress appear in the gear root. Obtain the most dangerous position of gear contact stress, it can as a reference to actual gear design, and can as a reference to do the special process at the position of the biggest bending stress by the manufacture and heat treatment process for increase the life and reliability of gear. Similar with bending analyze, compare with traditional calculation and finite element method, the result obtain by the calculation formula will be less than finite element method, and it prove that the design and check by finite element method is safe in the real work. Use the finite element method to check the contact strength.

Keyword：Main reduction gears; Finite element method; Contact stress; Bending stress

目 录

1 绪论 1

1.1课题研究的意义 1

1.2国内外研究发展概况 1

1.3课题的来源 2

1.4课题的主要研究目的 3

1.5课题主要研究内容 3

1.5.1有限元模型的建立 3

1.5.2 齿轮对弯曲应力分析 3

1.5.3 齿轮对接触分析 3

1．6 本章小节 4

2 有限元分析法 5

2．1 有限元分析法介绍 5

2.1.1 有限元法求解的步骤 5

2．2 有限元静态分析法 6

2．3 接触问题的有限元分析 7

2.3.1 接触有限元法的基本思想 8

2.3.2 弹性接触问题 10

2．4 有限元 ANSYS 软件及现状 11

2.4.1 ANSYS 简介 11

2.4.2 ANSYS 的接触分析 12

2.4.3 ANSYS 接触算法分析 13