渐开线圆柱齿轮各偏差项计算及精度等级评定

发布时间：2018-01-07 05:19

本文关键词：渐开线圆柱齿轮各偏差项计算及精度等级评定　出处：《苏州大学》2012年硕士论文　论文类型：学位论文

【摘要】：齿轮是重要的传动零件，其制造精度对机械的传动效率、传动质量及使用寿命影响很大。为保证齿轮的传动品质，必须对工件齿轮进行测量，，以确定其制造精度是否满足工艺要求。渐开线齿轮的质量指标众多，以前各项指标通常采用不同的仪器测量，这些仪器大多结构精密、价格昂贵、操作与维护要求很高。随着三坐标测量仪的发展与普及，齿轮的三坐标仪测量的探索与实践已成为近年来的研究热点，其主要关注点是齿轮齿廓点的测量及其根据齿廓点的测量值确定齿轮各偏差项数值的计算方法。本文以渐开线圆柱齿轮为对象，研究各偏差项的计算途径和方法，主要内容如下：介绍了常用的齿轮测量方法，确定了利用三坐标测量仪测量齿轮齿廓坐标值和利用公法线千分尺测量齿轮公法线长度的实验方案，并介绍了处理原始测量数据的拉依达法则。介绍了计算齿廓偏差的渐开线法向法和渐开线拟合法，分析了两种方法的局限性与不足之处。在此基础上，提出了新的齿廓偏差计算方法——渐开线起点法，该方法首先确定通过齿廓测量点的理论渐开线的起始点，再通过起始点的坐标值确定轮齿的齿廓偏差。根据公法线长度原理，导出了适用于直/斜齿标准/变位齿轮公法线长度和跨测齿数的通用公式，提出了利用最值法确定跨测齿数的方法，并建立了公法线长度偏差数学模型。介绍了最小二乘法、分段三次Hermite插值法和三次样条插值法等常用的曲线拟合方法，分析了三种拟合方法的优缺点。在此基础上，确定采用最小二乘法拟合渐开线齿轮齿廓，并导出了齿廓偏差的计算公式。借助于MATLAB-GUI可视化设计软件，根据处理好的数据和建立的数学模型，开发了计算渐开线圆柱齿轮各偏差项的GUI软件。以某渐开线圆柱齿轮为例，利用开发的计算软件，计算了齿轮各偏差项，并依据计算结果对齿轮精度等级进行评定。
[Abstract]:Gear is an important transmission part, its manufacturing accuracy has great influence on the transmission efficiency, transmission quality and service life of machinery. To ensure the transmission quality of gear, we must measure the workpiece gear to determine whether the manufacturing accuracy meets the process requirements.
The quality index of involute gear is numerous, the previous indicators commonly used instruments to measure different, these instruments are expensive, precise structure, operation and maintenance requirements are very high. With the development and popularization of the three coordinate measuring instrument, the exploration and practice of three coordinate measuring instrument of gear has become a hot research topic in recent years, its main concern is the measurement of gear tooth profile and tooth profile points according to the measurement point to determine the value of the deviation of gear numerical calculation method. In this paper, the involute cylindrical gear as the object of study, ways and methods of the deviation calculation, the main contents are as follows:
The gear measurement method commonly used, was determined using three coordinate measuring instrument for measuring gear tooth profile coordinates experimental scheme of micrometer gear common normal line length and the normal line, and introduces the original measurement data the Pauta rule.
Introduces the method for calculating the involute profile deviation to involute method and fitting method, analyzes the limitations and shortcomings of the two methods. On this basis, put forward the new tooth profile deviation calculation method of involute method firstly to determine the starting point, the starting point of the tooth profile measuring point theory of involute, then to determine the tooth profile deviation by the coordinate value of the starting point.
According to the principle of common normal length, a general formula for common normal line length and span measuring tooth number of straight / helical teeth standard / modified gears is derived. The method of determining the number of cross measuring teeth by the maximum value method is put forward, and the mathematical model of the length deviation of common normal line is established.
This paper introduces the least square method, piecewise curve fitting method commonly used three Hermite interpolation and three spline interpolation method, analyzes the advantages and disadvantages of the three fitting methods. On this basis, determined by the least squares fitting of involute gear, and deduces the calculation formula of profile deviation.
With the help of MATLAB-GUI software visualization, according to the processed data and establish the mathematical model developed for calculation of involute cylindrical gear of the deviation of the GUI software. Using an involute cylindrical gear as an example, using the software, the gear deviation is calculated according to the calculation results to evaluate the gear precision.

【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH132.41

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