形位误差计算机评定系统的研究

【作者】 郑鹏；

【导师】 侯伯杰；

【作者基本信息】 郑州大学 ， 机械电子工程， 2003， 硕士

【摘要】 零件的形位误差对机械产品的质量有很大的影响，因此准确测得和评定零件的形位误差一直是国内外普遍关注的问题。 自从形状和位置公差的国家标准GB1958-80颁布以来，有关形位误差的评定理论、评定方法等受到了广泛的关注。与长度测量、角度测量及其误差评定相比，形位误差测量和评定有较高的难度，我国开始着手研究的时间较短，但它已经对我国的工业生产和科学技术进步起到了很大的促进作用，关于形位误差评定的理论方法、数学模型及解算方法的研究，已达到了国际先进水平。但从整体上看，理论研究还不够系统和完善，距实际生产应用还有一定的差距。又因为对于它的研究要涉及到较多的近代数学知识，因而成为工程科学和基础科学共同关心的课题。 本文探讨了应用线性规划研究形位误差评定的理论和方法，将各种形位误差的包容评定统一于一个线性规划模型之中，据此既可进行问题的理论研究，又便于程序运算，确保了结果精确、解算快速。 为了开发形位误差评定系统，在形位误差评定理论及方法进行了研究和探讨，围绕该课题本文主要进行了以下几个方面的研究工作： 1．本文首先讨论了数学规划与线性规划的一般原理，阐明了线性规划的分类、数学表述、几何解释、解的性质，提出了求解线性规划的单纯形解法，并为该算法编制了相应的计算机程序。 2．形位误差的几何模型建立。在回转运动群及微分几何学的基础上，探讨了曲线、曲面的微分形式及标架运算。从而结合各类形位误差的特征，建立了形位误差评定的几何模型。对于非线性模型，基于“小偏差假设”和“小误差假设”将其转化为线性模型。 3．形位误差的规划模型建立。根据线性规划的特点，分析了形位误差包容评定的特征，系统地研究了目标函数及约束条件，对样点数据进行了坐标变换的处理，建立了评定形位误差的线性数学规划模型，具体包括单包容评定和双包容评定。并对规划模型的可靠性进行了分析，给出线性模型的误差估计。 4．以最小条件作为评定的基本原则，应用极差极小化理论探讨了形位误差评定的判别准则，并对最小条件的充分性进行了论述。利用多维画法几何图解法对判别准则进行了几何图示，使判别具有更强的直观性。 5．编制形位误差评定软件，运用VC++6.0语言编程，通过系统的分类，找出各摘要种评定问题的共性。大量实算验证所编评定软件，考察了目标函数和约束条件的正确性、程序的可行性。通过用本方法得到的数据处理结果，与现有的几种求解形位误差的评定方法进行对比，以求对形状误差的评定能够在精度与速度上有所突破。 利用形位误差评定软件，并采用数控技术和光电技术可以开发与其配合的硬件系统，改造现有的误差测量仪，实现微机控制下的形位误差数据采集和智能评定。更多还原

【Abstract】 The geometric error of workpiece makes great effect to mechanical product, therefore, that measuring accurately and evaluating the geometric error of workpiece are the question that always be paid attention to in the world.The theory and method of the geometric error evaluation get extensive attention when GB19 58-80 was enacted. Comparing with the measure of length and angle, the measure and evaluation of the geometric error are very difficult. Our country begin to research on it not long ago, but it is already important to the developing our industry and technology. The theory, the mathematical model and arithmetic of the geometric error evaluation are studied have caught up with international level. But the study of theory is not systematism or perfect. There is some distance to the practical production. Because it relates to the morden mathematical knowledge, it is concerned by the engineering science and foundation science.In this paper, the theory and methods of the geometric error evaluation by linear programming are discussed, and a universal model of the geometric error evaluation is established. So it is be used to study not only on the theory but also on programing, and it makes sure that can be accurate and rapid calculation.Centered around the subject, this paper mainly studies the theory and method of the geometric error evaluation, and the main work is as follows:1. In the first part of paper the mathematical programming and linear programming basic theory are discussed. The classification, mathematical expression, geometric explanation, character of the solution are explicated .and the simplex method for linear programming is put forward to solve the models, and the computer program for the solution is worked out.2. The geometric model of the geometric error evaluation is established. On the basis of the rotation groups and the theory of differential geometry, the paper studies the curves and surface fundamental differential form and the method of moving frames. According the character of the geometric error, the model of evaluation is established, nonlinear mathematical model can be linearized on the basis of the theory of "the littlewarp" and "the little error".3. The programming theory of the geometric error evaluation is established. In terms of the characteristics of linear programming, the features of the geometric error enclosure evaluation are analysed. The objective functions and restrictive conditions are systematically researched, and the coordinate transformation to sampled data is made. The linear programming models are established to evaluate the geometric error, which include the single enclosure evaluation and double enclosure evaluation. The reliability of models are checked and the errors of the linear programming models are presented.4. On the basis of the analysis of the minimum condition, the judgement principle of the geometric error evaluation is given according to the theory on minimizing the extremal difference function, and also the sufficiency of minimum condition is discussed. The geometric criteria is presented by using graphic solution in polydimensional descriptive geometry, which makes more clearly for the evaluation.5. The programs of the geometric error evaluation can be obtained using VC++6.0 language, and systematic classification is made which shows the common characteristics of the problems .By running the program with some practical examples, the coorectness of the objective functions and restriction and the feasibility of the program are checked. By way of large amount of comparison among the method put forward in the paper and some existing methods for geometric error evaluation, it is indicated that the mathematical models and arithmetic established in the paper are more accurate and efficient in calculation.By using the software, the technology of NC and the technology of optics, we can impolder the hardware system, develop the measure instrument. The system of data acquisiton and intelligentize更多还原