非圆齿轮数控滚切加工误差分析研究
发布时间：2018-08-17 08:42
【摘要】：非圆齿轮既有凸轮的优点又有圆柱齿轮的优点,广泛地应用在各种场合。常见的非圆齿轮有椭圆齿轮、Pascal(巴斯噶)蜗线齿轮等,其精密加工一直是研究的热点。滚齿是一种最为常见的非圆齿轮加工方式,随着对非圆齿轮精度要求的日益提高,非圆齿轮滚切加工误差分析显得尤为重要。对此,论文首先推导非圆齿轮滚切加工运动模型,获得机床运动轴与误差源的关系。在此基础上,分析工艺误差对非圆齿轮部分精度指标(节曲线、齿距和根切)的影响,研究插补算法对非圆齿轮滚切加工的影响。根据数控伺服进给系统模型,以椭圆齿轮节曲线为例,研究非圆齿轮节曲线轮廓误差形成机理。本文的主要研究工作和获得的结论如下： (1)根据推导出的非圆齿轮滚切加工运动模型,获得运动轴与误差源的关系。 (2)根据非圆齿轮滚切加工运动模型,分别推导工作台转角误差和中心距误差作用下非圆齿轮节曲线误差矢量表达式,以及工作台转角误差和齿条水平移动量误差作用下非圆齿轮齿距误差的表达式,并进行实例计算。 根据齿条与工件间的相对速度和啮合方程,提出并建立非圆齿轮根切界限函数。以椭圆齿轮为例,分析非圆齿轮发生根切的极角位置和工艺误差、设计参数对椭圆齿轮根切的影响。 (3)根据推导的非圆齿轮滚切加工运动模型,获得非圆齿轮滚切插补算法,从程序段弧长和机床运动轴两方面研究不同插补算法对非圆齿轮滚切加工的加工精度和控制难易程度的影响。为对比程序段弧长的均匀性,提出程序段弧长均匀度的概念。 (4)根据数控伺服进给系统模型,以椭圆齿轮节曲线为例,分析一阶、二阶、高阶伺服进给系统动态特性对非圆齿轮节曲线轮廓误差的影响规律。借助数学推导获得非圆齿轮节曲线轮廓误差的形成机理。为减小轮廓误差,提出PID交叉耦合控制方法(cross-coupled control,简称CCC方法)。仿真结果表明交叉耦合控制能改善非圆齿轮节曲线的轮廓精度。
[Abstract]:Non-circular gears have the advantages of both cam and cylindrical gears, so they are widely used in various situations. The common non-circular gears include elliptical gears Pascal (Basga) cochlear line gears and so on. Hobbing is one of the most common machining methods for non-circular gears. With the increasing demand for the accuracy of non-circular gears, it is particularly important to analyze the machining error of non-circular gears. In order to solve this problem, the paper first deduces the motion model of non-circular gear hobbing, and obtains the relationship between machine tool motion shaft and error source. On this basis, the influence of process error on the accuracy index (pitch curve, pitch and root cut) of non-circular gear is analyzed, and the influence of interpolation algorithm on the machining of non-circular gear is studied. According to the numerical control servo feed system model, taking elliptical gear pitch curve as an example, the forming mechanism of contour error of non-circular gear pitch curve is studied. The main research work and conclusions obtained in this paper are as follows: (1) according to the motion model of non-circular gear rolling machining, the relationship between motion shaft and error source is obtained. (2) according to the motion model of non-circular gear rolling machining, The vector expression of non-circular gear pitch curve error under the action of table angle error and center distance error, and the expression of non-circular gear pitch error under the action of table rotation angle error and rack horizontal movement error are derived respectively. An example is calculated. According to the relative velocity and meshing equation between rack and workpiece, the root tangent limit function of non-circular gear is proposed and established. Taking elliptical gear as an example, this paper analyzes the pole position and technological error of root tangent of non-circular gear, and the influence of design parameters on root cutting of elliptical gear. (3) according to the model of rolling machining of non-circular gear, The non-circular gear cutting interpolation algorithm is obtained. The influence of different interpolation algorithms on the machining accuracy and control difficulty of non-circular gear rolling machining is studied from two aspects: program segment arc length and machine tool motion axis. In order to compare the uniformity of program segment arc length, the concept of program segment arc length uniformity is proposed. (4) according to the numerical control servo feed system model, the elliptical gear pitch curve is taken as an example to analyze the first and second order. The influence of dynamic characteristics of high order servo feed system on the profile error of non-circular gear pitch curve. The forming mechanism of contour error of non-circular gear pitch curve is obtained by mathematical derivation. In order to reduce the contour error, cross-coupled control (CCC method) is proposed for PID cross coupling control. The simulation results show that the cross coupling control can improve the contour accuracy of the non-circular gear pitch curve.
【学位授予单位】：兰州理工大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH132.424;TG612
，
本文编号：2187078
[Abstract]:Non-circular gears have the advantages of both cam and cylindrical gears, so they are widely used in various situations. The common non-circular gears include elliptical gears Pascal (Basga) cochlear line gears and so on. Hobbing is one of the most common machining methods for non-circular gears. With the increasing demand for the accuracy of non-circular gears, it is particularly important to analyze the machining error of non-circular gears. In order to solve this problem, the paper first deduces the motion model of non-circular gear hobbing, and obtains the relationship between machine tool motion shaft and error source. On this basis, the influence of process error on the accuracy index (pitch curve, pitch and root cut) of non-circular gear is analyzed, and the influence of interpolation algorithm on the machining of non-circular gear is studied. According to the numerical control servo feed system model, taking elliptical gear pitch curve as an example, the forming mechanism of contour error of non-circular gear pitch curve is studied. The main research work and conclusions obtained in this paper are as follows: (1) according to the motion model of non-circular gear rolling machining, the relationship between motion shaft and error source is obtained. (2) according to the motion model of non-circular gear rolling machining, The vector expression of non-circular gear pitch curve error under the action of table angle error and center distance error, and the expression of non-circular gear pitch error under the action of table rotation angle error and rack horizontal movement error are derived respectively. An example is calculated. According to the relative velocity and meshing equation between rack and workpiece, the root tangent limit function of non-circular gear is proposed and established. Taking elliptical gear as an example, this paper analyzes the pole position and technological error of root tangent of non-circular gear, and the influence of design parameters on root cutting of elliptical gear. (3) according to the model of rolling machining of non-circular gear, The non-circular gear cutting interpolation algorithm is obtained. The influence of different interpolation algorithms on the machining accuracy and control difficulty of non-circular gear rolling machining is studied from two aspects: program segment arc length and machine tool motion axis. In order to compare the uniformity of program segment arc length, the concept of program segment arc length uniformity is proposed. (4) according to the numerical control servo feed system model, the elliptical gear pitch curve is taken as an example to analyze the first and second order. The influence of dynamic characteristics of high order servo feed system on the profile error of non-circular gear pitch curve. The forming mechanism of contour error of non-circular gear pitch curve is obtained by mathematical derivation. In order to reduce the contour error, cross-coupled control (CCC method) is proposed for PID cross coupling control. The simulation results show that the cross coupling control can improve the contour accuracy of the non-circular gear pitch curve.
【学位授予单位】：兰州理工大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TH132.424;TG612
，
本文编号：2187078
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