Digital Modeling Of Planar Enveloping Worm Based On Homogeneous Transformation Matrix

As the planar enveloping toroidal worm has a series of advantages,such as multi-tooth meshing,instantaneous two-wire contact,carrying capacity,high transmission efficiency,easy to automatically lubricate,long life and so on,which is widely used in the reduction device,mining machinery,rolling mill of the pressure device.At present,there are still many problems in computer modeling and NC machining of planar enveloping worm,which affect the promotion and use of the toroidal worm.Therefore,it is of great practical significance to carry out computer solid modeling and numerical control machining and manufacturing of toroidal worm.The paper first discusses the development of toroidal worm,the characteristics of toroidal worm,and the research results at home and abroad,then the existence of the problem is analyzed and explored simply.According to homogeneous transformation matrix and spatial meshing theory,the meshing equation and the tooth surface equation of the planar enveloping worm gear are deduced,the theoretical mathematical model of the worm is obtained,the foundation is laid for the later digital modeling.Based on the theoretical tooth equation,rely on Matlabnumerical calculation capabilities and programming capabilities,the tooth surface equation is programmed,and tooth surface equation is simulated by Matlab,simulation graphics of toroidal worm is got.And then use VB for secondary development of Solidworks,make the tooth face point into Solidworks,the API function is used to generate the entity after processing the tooth face point,and finally the solid model of toroidal worm is got.The numerical control machining theory and the CNC lathe with X,Z and C are briefly described.And then use the spatial transformation matrix to convert the helix equation into a fixed coordinate system,convert the data into knife data,and the principle of NC machining of toroidal worm is Elaborated.Finally,use Vericut to build virtual turning tools and lathes,choose to use the CNC system,import the NC program into VERICUT for simulation turning,thus verifying the rationality of the processing principle.Finally,the error of processing principles is analyzed,CNC lathes are used as roughing or semi-finishing of toroidal worms,Which provides a basis for the finishing of the worm.