Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machining of a ball-end cutter.A measure is then defined to quantify the effects of cutter orientation variation.According to ...Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machining of a ball-end cutter.A measure is then defined to quantify the effects of cutter orientation variation.According to the measure,a novel model and algorithm are proposed to wholly optimize cutter orientations based on a cutter contact(CC) point mesh.The method has two advantages.One is that the cutter orientation smoothnesses along the feed direction and pick-feed direction are both wholly optimized.The other is that only the accessibility cones of mesh points are required to compute and the computation efficiency is improved.These advantages are shown by simulating the machining efficiency,the stability of feed velocities and the smoothness of cutting force.A computational example and a cutting experiment are finally given to illustrate the validity of the proposed method.展开更多
We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic ...We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.展开更多
基金supported by the National Basic Research Program of China ("973" Program)(Grant No.2005CB724103)the National Natural Science Foundation of China (Grant No.50805093) the Science & Technology Commission of Shanghai Municipality (Grant No.07JC14028)
文摘Cutting forces with respect to different cutter orientations are analyzed for five-axis NC machining of a ball-end cutter.A measure is then defined to quantify the effects of cutter orientation variation.According to the measure,a novel model and algorithm are proposed to wholly optimize cutter orientations based on a cutter contact(CC) point mesh.The method has two advantages.One is that the cutter orientation smoothnesses along the feed direction and pick-feed direction are both wholly optimized.The other is that only the accessibility cones of mesh points are required to compute and the computation efficiency is improved.These advantages are shown by simulating the machining efficiency,the stability of feed velocities and the smoothness of cutting force.A computational example and a cutting experiment are finally given to illustrate the validity of the proposed method.
文摘We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.
