Finite Element Analysis Of Meshing Characteristic And Ease-off Topology Modification Design For Skew Bevel Gears

Compared with straight bevel gears,skew bevel gears have characteristics of high contact ratio,high bearing capacity,and steady transmission,which is important components in high speed and heavy load transmission systems.Due to the uniqueness and complexity of skew bevel gears tooth flank,in order to ensure the reliability,strength and accuracy requirements of skew bevel gears transmission,it is necessary to conduct in-depth research on its meshing characteristics in practical engineering.Based on the analysis of meshing characteristics,in order to pre-control the meshing performance of skew bevel gear and improve the edge contact,this paper proposes an Ease-off topology modification method for skew bevel gears based on the conjugate meshing principle and the tooth flank mathematical model of the producing gear.The main research contents are as follows:(1)Based on the generating machining principle and the space geometric kinematics theory,the meshing coordinate system of skew bevel gears is established,and combined with tooth profile of the left-handed and right-handed producing gear,the mathematical models of the tooth flank for skew bevel gears is established.The tooth flank contact simulation of skew bevel gear pairs is carried out in MATLAB,the contact point of a certain meshing position is obtained by solving the meshing equation,and use the least squares method to linearly fit the contact points.(2)The tooth flank mathematical models of skew bevel gears with equivocal modification is established,the tooth flank area in the rotating shaft section is divided into several grids,and the coordinates of each grid point are calculated.According to the rotation mapping relationship between the mesh point of the gear shaft section and the tooth flank point,the coordinates of tooth flank point are calculated by numerical algorithm,and an accurate 3D geometric model of skew bevel gear pair is established in UG software.(3)Based on the Hertzian contact theory,the mesh density of finite element model was determined,and the finite element mesh model of seven gear pairs for skew bevel gear is established in Hyper Mesh.The load contact analysis of skew bevel gear pair was carried out by using software ABAQUS,and the position of edge contact in a meshing period,as well as the variation curves of contact stress and bending stress under different loads are obtained,the meshing performance parameters of skew bevel gears under different load conditions is accurately calculated,such as rotating angle,load transmission error,contact force,contact ratio,load distribution coefficient,etc,and the influence of load on meshing performance parameters is analyzed.The results show that skew bevel gear has high transmission precision and contact ratio,and the edge contact occurs at the whole tooth top and tooth root when entering and exiting the meshing,the load distribution coefficient of skew bevel gear decreases with the increase of the load.(4)According to the reference flank surface of pinion,by predesigning the Symmetrical parabolic transmission error and the contact ellipse,a bidirectional modification of the pinion tooth flank is conducted along the contact path and the contact line,the Ease-off topology of modification tooth flank was constructed by calculating the deviations between the pinion modification tooth flank and base tooth flank,the meshing line and the distribution of the loading contact area of the tooth flank before and after modification were compared and analyzed by using contact analysis method and loading contact analysis method,and the influence of the load on the loading contact area of the modified tooth flank was analyzed.The result shows that the contact area of the tooth surface with modification is located in the center of the tooth surface,the edge contact area is greatly reduced,and the contact stress distribution of the tooth flank is improved.