When a spiral groove is formed using superplastic molding, precision casting, additive manufacturing, or other non?mechanical processing technology, it is diffcult to meet the molding precision required for direct use...When a spiral groove is formed using superplastic molding, precision casting, additive manufacturing, or other non?mechanical processing technology, it is diffcult to meet the molding precision required for direct use, and the surface quality and accuracy of the shape need to be improved through a finishing process. In view of the poor reachability of the current tool?based polishing process, a tool?less polishing method using free?abrasive grains for complex spiral grooves is proposed. With this method, by controlling the movement of the workpiece, the design basis and relative motion of the abrasive particles along a helical path remain consistent, resulting in a better polishing profile. A spiral groove of a revolving body is taken as the research object; the influence of the installation method and the position of the parts, as well as the effect of the rotational speed of the abrasive ball on its relative motion along a helical trajectory, are studied, and the polishing cutting process of an abrasive ball is reasonably simplified. A consistent math?ematical model of the trajectory of an abrasive ball relative to the design helix is constructed. The grooved drum parts are verified through a polishing experiment. The spiral groove of the revolving body is modified and polished. Experiments show that the process not only corrects the shape a spiral groove error, but also reduces the surface roughness of a spiral groove. This study provides a theoretical basis for achieving free?abrasive, tool?free polishing.展开更多
In this paper,we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body.The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation,which tends...In this paper,we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body.The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation,which tends to a given radially symmetric subsonic spiral flow at far field.The optimal decay rate at far field is also derived by Kelvin ’s transformation and some elliptic estimates.By extracting spiral subsonic solutions as the approximate sequences,we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness.The main ingredients of our analysis are methods of calculus of variations,the theory of second-order quasilinear equations and the compensated compactness framework.展开更多
基金Supported by Key Scientific&Technological Research Project of Henan Province,China(Grant No.102102210497)
文摘When a spiral groove is formed using superplastic molding, precision casting, additive manufacturing, or other non?mechanical processing technology, it is diffcult to meet the molding precision required for direct use, and the surface quality and accuracy of the shape need to be improved through a finishing process. In view of the poor reachability of the current tool?based polishing process, a tool?less polishing method using free?abrasive grains for complex spiral grooves is proposed. With this method, by controlling the movement of the workpiece, the design basis and relative motion of the abrasive particles along a helical path remain consistent, resulting in a better polishing profile. A spiral groove of a revolving body is taken as the research object; the influence of the installation method and the position of the parts, as well as the effect of the rotational speed of the abrasive ball on its relative motion along a helical trajectory, are studied, and the polishing cutting process of an abrasive ball is reasonably simplified. A consistent math?ematical model of the trajectory of an abrasive ball relative to the design helix is constructed. The grooved drum parts are verified through a polishing experiment. The spiral groove of the revolving body is modified and polished. Experiments show that the process not only corrects the shape a spiral groove error, but also reduces the surface roughness of a spiral groove. This study provides a theoretical basis for achieving free?abrasive, tool?free polishing.
基金partially supported by National Natural Science Foundation of China(11701431,11971307,12071359)。
文摘In this paper,we investigate two dimensional subsonic and subsonic-sonic spiral flows outside a porous body.The existence and uniqueness of the subsonic spiral flow are obtained via variational formulation,which tends to a given radially symmetric subsonic spiral flow at far field.The optimal decay rate at far field is also derived by Kelvin ’s transformation and some elliptic estimates.By extracting spiral subsonic solutions as the approximate sequences,we obtain the spiral subsonic-sonic limit solution by utilizing the compensated compactness.The main ingredients of our analysis are methods of calculus of variations,the theory of second-order quasilinear equations and the compensated compactness framework.
