Study On Modeling And Contact Analysis Of Spiral Bevel Gear Based On Machine Parameter

Spiral bevel gears can change the transmission direction,compared with spur bevel gears,spiral bevel gears have the advantages of strong bearing capacity,stable transmission and low noise,thus they are widely used in engineering machinery and other fields.Because the traditional design method of spiral bevel gear is the local conjugate,it needs to modify the tooth surface and make the gear tolerate more mounting errors,so the adjustment parameters of the machine tool play a decisive role on the tooth surface shape of helical bevel gears.In the process of traditional spiral bevel gear machining,the calculating of machine tool parameters only focusses on the reference of flank,it will cause different kind of contact fault,for example,top or root contact,diagonal contact.The workers need to check the gear pair and adjust the parameters repeatedly.For this reason,the research on machine tool parameters based on contact analysis is significance.The model of machine tool and the gear cutter model are established,based on the structure of the actual spiral bevel gear machine.According to the motion relationship between the parts of the machine tool and the meshing principle of gears,the relationship between different parameters of machine tool is analyzed and the equation of tooth surface of spiral bevel gear is established.The tooth surface is discretized by the method of meshing mesh.According to the tooth surface equation,the method of calculating the tooth depth and tool phase angle initial value is studied,and the surface equation is analyzed and solved.Based on the tooth surface equation and gear assembly model,this paper studies the relative relationship of vector between spiral bevel gears,establishes the contact equation,and studies the solution of the contact equation with the midpoint of the tooth surface as the initial contact point.Based on the principle of differential geometry and the result of contact equation,the contact trajectory and transmission error curve of spiral bevel gears are calculated,and the contact ellipse is computed by using parameters such as the torsion and curvature of the tooth surface.Numerical methods are used to quantify the contact quality of gear tooth surface.The definition of the normal deformation of spiral bevel gear tooth surface is studied,and the comprehensive influence of the adjustment parameters of the machine tool on the tooth surface is analyzed.Based on the variation of each discrete point,the influence of the adjustment parameters of the machine tool on the tooth surface deformation is studied.The fitting method of the difference surface and the geometrical meaning of each coefficient are studied,and the influence of the adjustment parameters of the spiral bevel gears on the coefficients of the difference surfaces is studied.Based on contact analysis,the influence of different adjustment parameters on contact quality is further studied,and the contact quality is quantitatively analyzed.Based on the study of the adjustment parameters and contact analysis of the machine tool,the adjustment and optimization method of spiral bevel gears are studied.Based on the method of the adjustment of the gear contact,the adjustment parameters of the target tooth surface are studied,and the adjustment parameters of the machine tool are modified to improve the contact defects of the gears,so as to avoid the top or root contact,heel or toe contact.The transmission error curve of spiral bevel gear is optimized based on genetic algorithm,which takes the parameter of machine tool as optimization variable and the symmetry of transmission error curve as the optimization target.