A Study on Mathematical Model of NC Machining and Cutting Tools Using Differential Geometry
| Autor: | Chang-Tzuoh Wu, 吳昌祚 |
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| Rok vydání: | 2000 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 88 Complex surface machining, including manufacture of cutting tool, is a highly theoretical task. Specific mathematical theories and methods, such as differential geometry, engagement relationship, numerical method, coordinate transformation and optimum method is frequently utilized in solving this problem. On the other hand, it is also a practical task in engineering. Therefore, establishing mathematical model, integrated theoretical and practical methods, can provide effective way in solving specific manufacturing problem for advanced study. The purpose of this study is to illustrate the application of differential geometry and solving methods for inverse envelope problem in complex surface machining. The development of the mathematical model and machining methods for complex surface machining, including NC machining approaches and manufacturing model of special cutters are discussed and summarized as following: 1.For the establishment of manufacturing model, the key points are developing the solution methods for solving envelope and inverse problems. In this paper, two kind of inverse problem are concluded and six methods for approaching the solution are also presented. 2.The complex surfaces are divided into three kinds of region by utilizing the principles of differential geometry. Under the consideration of different contact-order, the correlative mathematical model for defining the cutter parameters, such as path-intervals, radius of cutter, titling angle and directional vector of tool axis in NC machining of the surfaces are described based on the feature of regions. 3.Based on the engagement relationship between groove surface and grinding wheel surface, general mathematical approaches, including analytical and numerical resolutions for the relative direct and inverse problems, have been developed by utilizing the principles of differential geometry. A systematic approach that integrates design, manufacture, simulation and remedy is developed for revolving cutter in this paper. 4.A new method for producing accurate helical pinion cutters for Sykes-9C machine based on the analysis of the tool and the grinding geometry is presented. By employing the plane envelope theory, the reference contour of grinding wheel is determined and then modified by using the theory of mid-point and mid-line. Based on above cases, the problems of machining complex surface are discussed broadly. Such systematic procedures can provide a valuable reference for other cutters. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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