Research On Dynamic Characteristics Of Double Involute Gear Based On Fractal Theory

With the economic and social development towards high quality,gears as industrial core components are developing towards high speed and precision.Due to the machining characteristics of gears,the microscopic morphology of tooth surfaces shows irregular distribution of micro-convex bodies,which affects the dynamic performance of gear systems.The double involute gear is a new type of gear that combines the advantages of a stepped double arc gear and an involute gear,with a single side profile consisting of two stepped involutes and a transition curve.The dynamics of double involute gears are increasingly well researched,but there is less research on the dynamics of double involute gears from a microscopic point of view,taking into account tooth surface morphology.This paper is based on fractal theory and Hertzian contact theory,and considers tooth surface morphology and friction to carry out research on the timevarying meshing stiffness and non-linear dynamic characteristics of double involute gears.The main research elements are as follows.（1）The contact line of a double involute gear is "segmented" at each moment of meshing by considering the tooth surface microform and friction,and the contact line length and radius of curvature are calculated for the double involute gear.The contact on each segment is equated to a pair of cylindrical contacts,and a fractal model of the time-varying mesh stiffness of double involute gears is developed based on M-B fractal theory and Hertzian contact theory,taking into account tooth surface morphology and friction,and compared with the results of ISO 6336-1:2006（E）to verify the rationality of the proposed fractal model.（2）A three-dimensional model of a double involute gear pair is established based on the tooth profile equations of the end face of the double involute gear.A finite element model of the double involute time-varying meshing stiffness is established by the relationship between the torsional meshing stiffness of the gear and the meshing stiffness,and the difference in single tooth meshing stiffness between the double involute gear and the normal involute helical gear is compared.The results of the fractal model,the finite element model and the ISO 6336-1:2006（E）method are compared and analysed.（3）The dynamic characteristics of a double involute gear system are investigated by combining a fractal model of the time-varying meshing stiffness of a double involute gear with a non-linear model that takes into account the effects of tooth surface topography parameters,friction factors and contact damping and other non-linear factors.A comparison is made between the dynamic characteristics of double involute gears and those of ordinary involute helical gears.The effects of tooth profile parameters,friction factors and operating conditions on the dynamic characteristics of double involute gears are investigated.（4）Set up a gear train test bench.Dynamic performance tests are carried out on double involute gears and common involute helical gears under the same parameters and operating conditions.By means of the control variable method,the vibration and acceleration fluctuations,oil temperature changes and transmission efficiency changes in the circumferential,radial and axial directions of the double involute gears and the common involute helical gears are compared and analysed.The vibration acceleration fluctuations of the double involute gears are investigated under different operating conditions.The experimental results will be compared with the theoretical research results to verify the correctness of the theoretical research.