Analysis of Meshing Stiffness of Variable Hyperbolic Arc Gear based on Finite Element Method

In order to study the meshing stiffness of variable hyperbolic arc gear， the tooth surface equation of variable hyperbolic arc gear is obtained according to the forming principle， and its accurate three-dimensional model is established. Based on the theory of contact finite element analysis， the calculation method of meshing stiffness is studied. Using the finite element software， a pair of gear finite element model is constructed. The comprehensive elastic deformation of the tooth surface is extracted， and the normal contact force of the tooth surface is calculated by the torque formula. The single tooth mesh stiffness and the double tooth comprehensive mesh stiffness are calculated， which the results show that the stiffness curve of single tooth mesh increases first and then decreases with the increase of driving wheel angle. Then， the influence of different loads on the meshing stiffness curve is analyzed. The results show that the peak value of the stiffness curve increases with the increase of the load， and the load has more obvious influence on the peak value of the comprehensive meshing stiffness curve of the double teeth. At last， the influence of different tooth radius on the meshing stiffness curve is analyzed. The results reveal that the peak stiffness curve decreases with the increase of tooth radius， and the stiffness difference between the meshing area of single and double teeth decreases.