回转精度测评的运动几何学原理与不变量方法  

Kinematic Geometry Principles and Invariants Method for Rotational Accuracy Measurements and Evaluations

作　　者：王智[1] 董惠敏[1] 王德伦[1] WANG Zhi;DONG Huimin;WANG Delun(School of Mechanical Engineering,Dalian University of Technology,Dalian 116024)

机构地区：[1]大连理工大学机械工程学院,大连116024

出　　处：《机械工程学报》2020年第4期11-24,共14页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(51775079)。

摘　　要：提出轴系回转精度测评的误差运动几何学原理,由转子误差运动、被测几何要素、传感器测试参数等三要素构造轴系回转精度测量的运动几何学模型,建立测量闭环矢量基本方程;推导出轴系误差运动参数测量的完备性条件,讨论回转误差运动参数测量的完备性及其演变形式,阐明各类回转精度测量数据与评价指标的运动几何学内涵。给出轴系回转误差运动的不变量定理,得到轴系回转误差运动的最小球面像曲线与最小准线,从而将轴系回转误差运动分解为角摆误差运动与平移误差运动,建立角摆误差运动不变量、平移误差运动不变量与各类回转精度指标之间的关系,形成轴系回转精度评价的不变量方法,有效地避免被测几何要素不同对测评结果的影响,为轴系回转精度的测量与评价提供理论依据。The error-included kinematic geometry principles for rotational accuracy measurements and evaluations of revolute pairs are presented for the first time,which are represented by the kinematic geometry models and the basic closed-loop vector equations formed by three basic elements,including the error motion of the rotor,the geometric elements tested and the measuring parameters of the sensors.The completeness conditions for measuring rotational accuracy are derived according to the error-included kinematic geometry principles.The integrality of the measured kinematic parameters of the rotational error motion is discussed based on the existence of solutions of the basic equations,whose evolution forms are tied to the measuring methods and used to clarify the kinematic and geometric meanings of the measured data and their accuracy indexes.The invariants theorem of rotational error motion are given by considering the kinematic geometry properties of the error motion;the minimal spherical image curve and the minimal striction curve of the rotational error motion are obtained,which separates the rotational error motion of the rotor into angular error motion and translational error motion.The relationships between the current accuracy indexes and the invariants,such as the angular error and the translational error,are set up;these help to develop a new invariants method for rotational accuracy evaluation,which can avoid the influences of different geometric elements tested.It provides a theoretical basis for measuring and evaluating rotational accuracy of revolute pairs.

关 键 词：运动几何学 轴系 回转精度 误差运动 不变量 

分 类 号：TG156[金属学及工艺—热处理]