Study on the form shaping theory for machine tools and its applications

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In this co-operative work, the form shaping theory for machine tools was systematized for comprehensive applications to machine tool design, error analysis as well as compensation, and programing for multi-axis machine tools. The main results obtained in this study are summarized as follows :(1)By applying the homogeneous coordinate transfer matrix, a comprehensive form shaping theory for machine tools was established. This mathematical model of machine tools enables us to simulate the generating motion of machine tools in the computer. Errors in the machine tools such as positioning error, straightness error, and alignment errors, can be taken into account in the simulation.(2)The influences of those errors on the machining accuracy were investigated quantitatively for turning machines and milling machines. Such evaluations were performed for some variations of turning and milling machines which were derived by changing the order of the form shaping code.(3)The algorithm based on the form shaping theory makes it possible to select the possible to select the possible configurations which have 5 degrees of freedom. An algorithm was also proposed to evaluate the machine tool configuration from the view point of floor space.(4)The method for identifying the error sources in a machine tool through the measurement of machined workpiece accuracy was proposed.The availability of the method was confirmed by computer simulations.(5)The general post-processor which converts collision-free CL data for 5-axis control NC machine tools consisting of three translational axs and two rotational ones were established. To improve the machining accuracy and efficiency, the study was extended to make use of the most of side cutting edge of tapered boll endmill as well as top cutting one. The use of side cutting edge was experimentally found to be valid.