| Heavy duty gear mainly refers to the gear of mining,mining vehicles,rail transit,wind power,aerospace,military equipment and other host supporting gear and gear in the general reducer,which has the characteristics of large transmission power,large bearing capacity,low speed and large impact load.These characteristics also make the heavy duty spiral bevel gear pair prone to edge contact and contact stress concentration during operation,thereby reducing the service life of the spiral bevel gear pair.The duplex helical method has the advantages of high machining efficiency and high-speed dry cutting,and is gradually replacing the traditional machining method “five–cut method” of spiral bevel gears.Therefore,this dissertation takes the spiral bevel gears machined by duplex helical method as the research object.Aiming at the problems of edge contact and stress concentration of heavy duty spiral bevel gear pair,the mathematical modeling,tooth surface error correction and tooth surface modification methods of spiral bevel gear pair machined by duplex helical method are studied.The main research contents and achievements of this dissertation are as follows:(1)Mathematical modeling and meshing performance analysis of heavy duty spiral bevel gear machined by the duplex helical method.In view of the problems of ignoring the root fillet resulted in incomplete tooth flank and the root bending stress could not be analyzed when the tooth surface cutting model was established,and the difficulty of dividing the mesh of the tooth surface mesh when loading tooth surface contact analysis,based on the theory of meshing principle and differential geometry,the spiral bevel gear pair with the gear machined by the forming method and the pinion machined by duplex helical method is the research object.Considering the root fillet of the tooth surface,a mathematical model of simultaneous cutting of concave and convex tooth surfaces based on the relative movement of the cutting tool,the machine tool and the machined gear was established.On this basis,an precise finite element loading tooth surface contact analysis model for gear pair was established,and the meshing performance of the spiral bevel gear pair under heavy load was analyzed to provide a theoretical basis for the subsequent tooth surface error correction and tooth surface modification.(2)Research on the error correction method of concave and convex double tooth surface based on duplex helical method.Aiming at the difficulty in correcting errors in the simultaneous machining of concave and convex sides of spiral bevel gears by the duplex helical method,the mathematical model of the tooth surface machined by the duplex helical method was used to analyze the influence of the machining parameters on the tooth surface error,and the tooth surface error correction model was established.The Levenberg–Marquard algorithm with trust region strategy was used to synchronously correct the errors of the concave and convex tooth surfaces.After the correction,the theoretical maximum absolute error of tooth surface and the sum of square error of concave and convex double tooth surface are reduced by 83.8% and 98.4%respectively.At the same time,the tooth surface error correction method also provides a numerical solution method for the reverse calculation of the machining parameters of the subsequent tooth surface modification.(3)Research on the tool profile modification method with edge contact of heavy duty bevel gears machined by duplex helical method.Aiming at the problems of edge contact and contact stress concentration on the tooth surface of the spiral bevel gear pair under heavy load,the mathematical model of four-segment line cutter profile modification corresponding to tooth tip,middle contact region,tooth root and arc transition region of tooth root was established.The concave and convex tooth surfaces of the pinion were synchronously modified by four-segment line cutter profile.The results show that the gear pair modified with four-segment line profile avoids the problem of stress concentration of tooth tip edge contact and tooth surface contact,and improves the distribution of tooth surface contact stress.(4)Research on the whole tooth surface section modification method with low sensitivity to installation error of heavy duty bevel gears machined by duplex helical method.In order to reduce the sensitivity of heavy bevel gear pair to installation error,the pinion tooth surface was divided into five regions,namely,tooth tip,tooth root,toe,heel and middle contact area,and the different regions of the tooth surface were modified.First,along the long axis of the contact ellipse,three sections of cosine curve were designed for the first modification of the toe and heel of the tooth surface,and the machining parameters satisfying the modification were inversely calculated.Then,a four-section line profile was designed to modify the tooth top and tooth root of the concave and convex surfaces for the second time,so as to achieve the full tooth surface sectional modification.The results show that the whole tooth surface section modification avoids the serious edge contact problem on the tooth surface of the gear under the installation error,and the stress concentration and contact stress at the entry point of the convex surface of the gear,convex and concave surfaces of the pinion were reduced greatly.Thus,the sensitivity of the gear pair to installation errors was reduced.(5)Research on the diagonal modification method with high coincidence degree of heavy duty bevel gears machined by duplex helical method.In order to reduce the adverse effect of tooth surface modification on transmission error fluctuation and gear pair overlap degree,a diagonal modification method was proposed.Firstly,the initial gear was used as the machine tools to generate the reference tooth surface of the pinion which was completely conjugated with the initial gear;Then the transmission error curve,contact path direction and three cosine curves along the long axis of the contact ellipse were designed to modify the reference tooth surface of the pinion,and the reverse solution of the machining parameters satisfying the modification tooth surface was carried out.Finally,a four-segment line profile was designed to synchronously modify the tooth tip and tooth root of the concave and convex tooth surfaces,so as to realize the diagonal modification of the tooth surface.The results show that the proposed diagonal modification reduces the fluctuation of transmission error and increases the coincidence degree of the gear pair while eliminating the tooth surface edge contact and stress concentration.(6)Experimental test of correction tooth surface and modified tooth surfaces and their meshing properties machining by duplex helical method.The tooth cutting experiments were carried out on the error surface by using the error correction parameters,and use the machining parameters and modification parameters to carry out the tooth cutting experiment for the gear pair before and after modification,and the tooth surface error,contact marks and transmission errors of the gear pairs before and after the modification were tested and analyzed.The results show that: Using the synchronous correction method for the concave and convex double tooth surface error proposed in this dissertation,the actual maximum absolute value error of the tooth surface was reduced by 78%and controlled within the range of 7 μm,which verified the effectiveness and accuracy of tooth surface error correction method.The contact imprints and their variation laws of the tooth surface before and after the modification obtained by the experimental test were basically consistent with the simulation results,which verifies the accuracy of the tooth surface modification method.107 figures,27 tables,and 176 references... |
