基于集合概念的虚公差理论与应用

doi:10.3901/JME.2019.07.172

机械工程学报 ›› 2019, Vol. 55 ›› Issue (7): 172-177.doi: 10.3901/JME.2019.07.172

基于集合概念的虚公差理论与应用

王晓慧^1,2, 郭士意^1,2, 车冬冬^1,2, 兰国生²

1. 太原重型机械装备协同创新中心太原 030024;
2. 太原科技大学机械工程学院太原 030024

收稿日期:2018-04-11 修回日期:2018-09-29 出版日期:2019-04-05 发布日期:2019-04-05
通讯作者: 王晓慧(通信作者),男,1959年出生,教授。主要研究方向为尺寸工程,机械精度设计理论及应用,计算机辅助夹具设计。E-mail:houmawxh@sina.com
作者简介:郭士意,男,1993年出生,硕士研究生。主要研究方向为现代制造技术。
基金资助:
国家自然科学基金（51575373，51175360）和山西省“1331工程”重点学科建设计划资助项目。

Theory and Application of Virtual Tolerance Based on Set Concept

WANG Xiaohui^1,2, GUO Shiyi^1,2, CHE Dongdong^1,2, LAN Guosheng²

1. The Coordinative Innovation Center of Taiyuan Heavy Machinery Equipment, Taiyuan 030024;
2. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024

Received:2018-04-11 Revised:2018-09-29 Online:2019-04-05 Published:2019-04-05

摘要/Abstract

摘要： 将上偏差小于下偏差的公差定义为虚公差，把具有公差（包括虚公差）要求的两个极限值之间的尺寸用一个集合表达，探究公差值由正数连续变小成为负数时产生质变的过程，抽象出虚公差的物理意义：虚公差的绝对值为误差补偿量，两极限值之间的尺寸为误差补偿范围。从量纲和谐原理、尺寸链通用公式存在的条件、公差计算结果的准确性等方面阐述提出虚公差概念的必要性及其与公差的对立统一关系。通过实例验证，在虚公差物理意义明确后，可大大简化带补偿件的装配尺寸链分析计算过程，使之计算更加灵活方便，并可实现误差与误差补偿量的并行分析计算，使公差分配更加经济合理；推导出机械加工过程中假废品尺寸区间的通用计算公式，提出了概率法确定假废品尺寸区间的方法，有效地提高了假废品判断的效率。

关键词: 概率法, 公差质变过程, 集合表达, 误差补偿

Abstract: Virtual tolerance is defined as the tolerance that its upper deviation is smaller than lower deviation. In order to abstract the physical meaning of virtual tolerance, the absolute value of the virtual tolerance is the error compensation and the dimensions between the two extreme values is the error compensation range, utilizing a set to elaborate the dimensions with tolerance requirements (virtual tolerance included) between two extreme values and explore the process from quantitative changes to qualitative changes when the virtual tolerance decreases from a positive number to a negative number. The principles of dimensional homogeneity, the existence condition of general formula of dimension chain and the accuracy of tolerance's calculation are introduced to illustrate the necessity of raising the concept of virtual tolerance and the opposition and unification relations between tolerance and virtual tolerance. It has been experimental verified that the definition of virtual tolerance's physical meaning can significantly simplify the analysis and calculation process of assembly dimension chain, which result in a convenient and flexible computation and fulfill parallel analysis between calculation of error and error compensation, which result in a reasonable tolerance distribution. And by getting the general calculation formula of the fake rejects' dimensional interval during mechanical processing, a way to determine fake rejects' dimensional interval-Probability method is conducted, which greatly improved the efficiency when determining fake rejects.

Key words: error compensation, probability method, set expression, tolerance of qualitative change

中图分类号:

TG801

王晓慧, 郭士意, 车冬冬, 兰国生. 基于集合概念的虚公差理论与应用[J]. 机械工程学报, 2019, 55(7): 172-177.

WANG Xiaohui, GUO Shiyi, CHE Dongdong, LAN Guosheng. Theory and Application of Virtual Tolerance Based on Set Concept[J]. Journal of Mechanical Engineering, 2019, 55(7): 172-177.

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基于集合概念的虚公差理论与应用

Theory and Application of Virtual Tolerance Based on Set Concept

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