The off-axis parabolic mirror plays more and more important role in high-tech areas since the advantages of reducing space and improving the quality of imaging. Two ultra-precision manufacturing methods are often applied to machining the off-axis ellipsoidal mirror, which one is revolving the cylindrical blank around the axis of ellipsoidal surface and another one is revolving around the axis of cylindrical surface. But which machining method can produce a better result has no rounded comparisons and analysis according to previous research. In this paper, the tool path generation method is presented and the corresponding tool paths of each manufacturing method for the off-axis ellipsoidal mirror are calculated respectively. The motion characteristics are also analyzed and compared correspondingly. Finally, the effects of diamond tool parameters are further analyzed in theory to avoid the tool interference. The studies processed in this paper provide a theoretical basis of choosing the ultra-precision manufacturing method for the off-axis ellipsoidal mirror and can improve the efficiency and precision of processing.
Tool path generation is an important part of ultra-precision manufacturing, and spiral tool path is one typical driving path. For single point diamond turning (SPDT), two methods are commonly used to generate the driving points on the spiral tool path, which are equally spaced angles and equally spaced arcs for two adjacent cutting points. But these two methods both have the defects for machining radial sinusoidal surface with SPDT. In this paper, the theoretical analyses of the two different methods are conducted and compared respectively. Then, an optimal method of generating the spiral cutting tool path is proposed on the base of theoretical analyses, which can avoid disadvantages of two original methods. The proposed method can enhance the machining accuracy and fabricating efficiency for ultra-precision machining of the radial sinusoidal surface with SPDT.
With the development of CAD/CAM, reverse engineering, geometric modeling, animation and computer graphics. In the past fifty years, many kinds of spline curve fitting methods have been produced. But, to authors knowledge, quality evaluation criterion about different spline curves are still not established and there is a lack of a comparing standard for analyzing different spline curves. Two spline curve fitting method comparing theorem is given and several various spline curves affecting factors are analyzed in this paper. Some comparable results are obtained by using the proposed quality evaluating theorem to different spline curves.
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