工件自由度判断的几何定理及应用

发布时间：2018-08-25 12:46

【摘要】：机床夹具是零件加工中重要的工艺装备,其设计质量直接影响到零件的加工质量和效率,而工件自由度的正确判断是夹具设计最基本的内容,传统判断工件自由度的方法是六点定位原则,它只能够感性地判断工件在夹具中的自由度,难以解决一些疑难定位问题,例如对于复杂曲面定位、异面组合定位的工件,用传统的方法判断其自由度往往会因为缺少具体的规则而导致错判而使夹具设计失败。我们认为传统方法有两个问题没有得到很好的解决,其一,对工件自由度的分析与判断未能够抽象成数学法则,不便于计算机辅助夹具设计对工件自由度的判断;其二,在工程实践中经常会遇到各种不规则工件定位,往往夹具限制工件某方向的自由度并不是坐标轴方向,而是空间其它任意方向,传统方法难以适应。经过研究发现工件在夹具中的自由度完全取决于工件定位法线的数量及其几何关系,为此本文提出定位法线与定位法面概念,由定位法线的数量及其几何关系推导出一组判断工件自由度的几何定理,从而实现了对工件自由度的理性判断,为生产实际、教学、计算机辅助夹具设计提供一种具体、简单易行的方法。本文的主要研究内容如下:(1)探讨了工件在定位元件中自由度被限制的根本原因,从力学的角度出发,建立了工件定位的力学模型;同时,从运动学的角度也建立相应的运动学模型。(2)将实际生产中工件在夹具中的定位转移至工件定位的力学模型和运动学模型中,研究分析工件的自由度限制情况。(3)提出定位法线、定位法面和转动定位法面的基本概念,进而总结出判断工件自由度的几何定理,并给出相应的理论证明;结合几何定理,总结出判断工件过定位的具体方法,大大提高判断工件定位状态的效率。(4)利用几何定理给出常用定位元件对工件自由度的限制个数;给出工件定位具体实例,结合几何定理判断工件自由度限制情况,对不合理的定位给出相应改进方案。(5)结合矩阵和函数的知识实现判断工件自由度的程序化,为计算机辅助夹具设计中判断工件定位状态提供了相应的基础理论依据;举出工件定位实例,对提出理论的正确性进行验证。本文的主要研究结论如下:(1)工件在夹具中的自由度完全取决于工件在夹具中定位法线的数量及其几何关系。(2)用几何定理容易处理各种疑难自由度分析,可有效避免欠定位与过定位,为改进不合理的定位方案提供重要理论依据。(3)利用定位法线的等效,可将法线复杂的空间关系简化,从而便于使用几何定理判断工件的自由度限制情况。(4)用几何定理分析判断工件自由度更具理性且简单直观,适合计算机辅助判断工件的自由度。
[Abstract]:Jig is an important process equipment in the machining of parts, and its design quality directly affects the machining quality and efficiency of the parts, and the correct judgment of the degree of freedom of the workpiece is the most basic content of the fixture design. The traditional method of judging the degree of freedom of a workpiece is the six-point positioning principle. It can only judge the degree of freedom of the workpiece in the fixture sensitively. It is difficult to solve some difficult localization problems, for example, for the workpiece with complex surface localization and cross-plane combination localization. The traditional method of judging the degree of freedom often leads to the failure of fixture design due to the lack of specific rules. We think that two problems have not been solved well in the traditional method. One is that the analysis and judgment of the degree of freedom of the workpiece can not be abstracted into the mathematical rule, which is not convenient for the computer aided fixture design to judge the degree of freedom of the workpiece. In engineering practice, various kinds of irregular workpiece positioning are often encountered. It is often difficult to adapt the traditional methods to restrict the degree of freedom of the workpiece in one direction, not in the axis direction, but in any other direction of the space. It is found that the degree of freedom of the workpiece in the fixture depends entirely on the number of the normal alignment of the workpiece and its geometric relationship. In this paper, the concepts of the normal alignment and the normal plane are proposed in this paper. A set of geometric theorems for judging the degree of freedom of workpiece are deduced from the quantity of orientation normal and its geometric relationship, and the rational judgment of degree of freedom of workpiece is realized, which provides a concrete method for production practice, teaching and computer aided fixture design. A simple and easy method. The main contents of this paper are as follows: (1) the fundamental reason of the degree of freedom of the workpiece in the positioning element is discussed, and the mechanical model of the workpiece positioning is established from the point of view of mechanics, at the same time, The kinematics model is also established from the point of view of kinematics. (2) the positioning of the workpiece in the fixture is transferred to the mechanical model and the kinematics model of the workpiece positioning, and the degree of freedom limitation of the workpiece is studied and analyzed. (3) the localization normals are proposed. The basic concepts of locating normal plane and rotating positioning normal surface are summarized, then the geometric theorem of judging the degree of freedom of workpiece is summarized, and the corresponding theoretical proof is given, and the concrete method of judging the overpositioning of workpiece is summarized according to the geometric theorem. It greatly improves the efficiency of judging the position state of workpiece. (4) the limited number of degrees of freedom of workpiece is given by using geometric theorem, the concrete example of workpiece location is given, and the limit of degree of freedom of workpiece is judged according to geometric theorem. The corresponding improvement scheme for the unreasonable positioning is given. (5) programming the degree of freedom of the workpiece is realized by combining the knowledge of matrix and function, which provides the corresponding basic theoretical basis for judging the position state of the workpiece in the computer-aided fixture design; An example of workpiece location is given to verify the correctness of the proposed theory. The main conclusions of this paper are as follows: (1) the degree of freedom of the workpiece in the fixture depends entirely on the number of normal lines located in the fixture and its geometric relationship. (2) it is easy to deal with the analysis of various difficult degrees of freedom by using geometric theorems. It can effectively avoid underpositioning and over-positioning, and provide an important theoretical basis for improving unreasonable positioning schemes. (3) by using the equivalence of normal alignment, the complex spatial relationship of normal lines can be simplified. It is convenient to use geometric theorem to judge the degree of freedom of workpiece. (4) it is more rational and simple to judge the degree of freedom of workpiece by using geometric theorem, which is suitable for computer aided judgment of degree of freedom of workpiece.
【学位授予单位】：太原科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TG75

【参考文献】