Research On Duplex Helical Machining Technology Of Spiral Bevel Gear

Spiral bevel gear is a critical component in the field of modern mechanical transmission.It has the characteristics of low noise,smooth transmission,strong bearing capacity and high reliability.The processing of spiral bevel gear is more complex,the domestic common use is "five-cut process method" and the completing method,the "five-cut process method" is slowly fading out in the field of spiral bevel gear processing,replaced by the completing method.The duplex helical method of the completing method is bound to become the mainstream method in bevel gear machining with its many advantages such as high machining efficiency and low production cost.At present,the mainstream CNC spiral bevel gear machining machine generally has the function of high-order motion correction,including roll ratio correction,helical motion correction,vertical motion correction and so on.However,the machine tool settings and the first-order helical motion coefficient were calculated in the actual cutting calculation,and other high-order motion coefficients are not used,which failed to play the universal motion characteristics of CNC machine tools.And in the actual processing of bevel gears,the operator is not aware of the influences of the higher-order motion coefficient in the machine tool settings on the tooth surface topology when adjusting the contact area of the gear pair,so the adjustment of the tooth surface shape and contact area cannot be fully realized.In addition,when the duplex helical method is used,the concave and convex surfaces of the gear pair are processed by the same the machine tool settings,so that the contact characteristics of their surfaces are related to each other.Therefore,there are still difficulties in the calculation principle of cutting,contact area adjustment and tooth profile error correction,and it is difficult to obtain the ideal machine tool settings.Solving these difficulties is the key to the theory and technology of spiral bevel gear machining.In order to realize the digital and intelligent manufacturing of spiral bevel gear,the key technology of the duplex helical method machining of spiral bevel gear is studied in this paper.The main research content of this paper is as follows:(1)Based on the duplex helical machining principle and gear meshing principle of the tooth surface,considering high-order motion coefficient is established by using vector arithmetic method according to the relative position and relative motion relationship between cutting tool and workpiece in machining.The tooth surface of spiral bevel gear is meshed based on tooth surface meshing standard.According to the mathematical model of the tooth surface,the spatial coordinates and unit normal vector of each discrete point on the tooth surface are calculated by using the binary iterative algorithm.(2)Based on the tooth surface mathematical model,the tooth shape error analysis model was established,and the tooth shape error analysis software was prepared using VB.The influence of various high-order motion coefficients(including high-order helical motion,high-order vertical motion,high-order roll ratio correction,up to the sixth-order)on tooth surface shape is analyzed by arithmetic examples.Based on the mathematical model of tooth surface and the principle of tooth surface contact analysis,the software of tooth surface contact analysis is compiled by VB.The influence of the change of motion coefficient on the meshing contact area,transmission error and transmission error curve of gear pair tooth surface is analyzed by arithmetic examples.It provides a theoretical reference for the adjustment of gear sub-mesh contact area in actual machining.(3)Based on the tooth surface mathematical model,the tooth shape error correction model is established by considering the basic adjustment parameters,tool parameters and higher order motion coefficients,and the LevenbergMarquardt algorithm is applied to solve the overdetermined system of equations,which can obtain the change of machine adjustment parameters to correct the tooth shape error.The software of tooth profile error correction is compiled by VB,which lays a foundation for digital closed-loop manufacturing of spiral bevel gear.(4)Based on the above research results,the experiments of tooth grinding and tooth profile error detection were carried out by using domestic H350GH NC spiral bevel gear grinding machine and L65G gear measuring center.The accuracy of the mathematical model of the tooth surface and the analysis method of the tooth profile error is verified by changing the high-order motion coefficient of the workpiece.By measuring the tooth profile error of the actual workpiece and correcting the tooth profile error,the correctness of the tooth profile error correction algorithm established in this paper is verified.