Aiming at the issue of the grinding integrity of face-gear with worm wheel, the envelope mathematical model of shaper, worm wheel and face-gear is established based on theories of differential geometry and gear mesh. ...Aiming at the issue of the grinding integrity of face-gear with worm wheel, the envelope mathematical model of shaper, worm wheel and face-gear is established based on theories of differential geometry and gear mesh. The judgment of completely grinding the face-gear with the avoidance of singularities is established, and the mathematical expression to show the reason why singularities appear is derived, through the research on the surface contact area and singularity rules of the worm thread surface. The disadvantage of current face-gear grinding method that only part of the working surface of the face-gear can be covered is analyzed and the influence of coefficient of judgment is studied through changing the design parameters.展开更多
Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivati...Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.展开更多
We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of...We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.展开更多
基金Projects(51275530,51535012) supported by the National Natural Science Foundation of ChinaProject(2011CB706800) supported by the National Basic Research Program of China
文摘Aiming at the issue of the grinding integrity of face-gear with worm wheel, the envelope mathematical model of shaper, worm wheel and face-gear is established based on theories of differential geometry and gear mesh. The judgment of completely grinding the face-gear with the avoidance of singularities is established, and the mathematical expression to show the reason why singularities appear is derived, through the research on the surface contact area and singularity rules of the worm thread surface. The disadvantage of current face-gear grinding method that only part of the working surface of the face-gear can be covered is analyzed and the influence of coefficient of judgment is studied through changing the design parameters.
基金Project supported by the National Natrual Science Foundation of China (No.10271106) the Natrual Science Foundation of Zhejiang Province, China (No.102033).
文摘Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11101072 and 11271063)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.
