| 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... |
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