变截面涡旋盘的阿基米德螺线拟合方法  

The Method of Curve Fitting of Archimedes Spiral for Variable Cross-Section Scroll Plate

作　　者：刘涛[1] 张春林 LIU Tao;ZHANG Chun-lin(School of Mechanical and Electrical Engineeringe,Lanzhou University of Technology,Gansu Lanzhou730050,China)

机构地区：[1]兰州理工大学机电工程学院,甘肃兰州730050

出　　处：《机械设计与制造》2020年第4期28-31,共4页Machinery Design & Manufacture

基　　金：国家自然科学基金资助项目(51265027、51665035)。

摘　　要：建立了圆渐开线—高次曲线—圆渐开线组合型线的变截面涡旋盘数学模型,利用阿基米德螺线拟合方法对组合型线进行逼近,介绍此方法的基本原理和详细的推导过程,并使用MATLAB软件计算该方法产生的理论拟合误差,提出了步长的取值流程。将提出的阿基米德螺线拟合和直线拟合、圆弧拟合进行对比,结果表明阿基米德螺线拟合方法在拟合误差小于0.001mm条件下,拟合节点数比直线拟合方法少90%,比圆弧拟合方法少70%,该方法对非圆弧类型线的加工有一定的实用价值。In this paper,a mathematical model of a variable cross-section scroll composed by circular involute-high order curve-circle involute combination line is established.It adopts method of Archimedes spiral fitting to approximate and fit the combined scroll.The basic principle and the detailed derivation process of this method will be introduced,and use MATLAB to calculate the theoretical fitting error produced by this method,The step-length value process is proposed.The method of Archimedes spiral fittingcompared with linear fitting and single arc fitting,The results show that the Archimedes spiral fitting method is 90%less than the line fitting and 70%less than the arc fitting in fitting note under the condition that the fitting error is less than 0.001mm.This method has certain practical value for the machining of non-arc type thread.

关 键 词：组合型线 拟合 阿基米德螺线 

分 类 号：TH16[机械工程—机械制造及自动化]