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

Double involute gear is a new type of gear,which is put forward on the basis of summarizing the research results of involute gear and double arc gear,etc.Its gear profile is composed of two-phase staggered involute and one phase connected transition curve.At present,the contact stress and contact stiffness of double-involute gears are all calculated based on the traditional Hertz contact model.This model ignores the influence of micro-characteristics such as roughness on the contact characteristics of gears,which will have a great impact on the strength calculation of gears and the selection of related parameters.Due to the influence of roughness,the mechanical contact surface is regarded as multiple micro-convex bodies contacting at the same time in actual contact.Based on the fractal theory,this paper studies the contact characteristics of double involute gear.The main research contents and innovations are as follows:(1)A fractal contact model of double involute gears is proposed,which based on the fractal theory and the classical Hertz contact theory.On the basis of the M-B fractal contact model established by Majumdar and Bhushan,the contact surface correction coefficient is introduced to obtain the contact area distribution function of gear,and the contact stress fractal model of double involute gear is established.Based on MATLAB programming,the impacts of fractal dimension,roughness amplitude and material characteristic parameters on the model are analyzed,and the validity of the model is verified.(2)A fractal model of contact stiffness of double involute gears is established.Using the contact mechanics model of micro-convex body,the static contact stiffness is studied from single micro-convex body to multi-micro-convex body,and the impact of combined axial load on the real contact area of gear tooth surface is studied.The normal contact stiffness fractal model and tangential contact stiffness fractal model of double involute gear are established.The influence law of each parameter on the model is analyzed and the theoretical basis is laid for the optimization of the tooth profile parameters of double involute gear.(3)A comparative analysis of the fractal model and the finite element model simulation of the contact characteristics of double involute gears is carried out.Based on the three dimensional parametric modeling technology,the double involute gear is modeled and assembled,which provided the basis for the finite element analysis.The finite element analysis of the contact stress,normal contact stiffness and tangential contact stiffness of the double involute gear was carried out through a practical case,and the comparison with the numerical calculation results of the fractal model in this paper verified the rationality and advance of the study on the contact characteristics of the double involute gear based on the fractal theory.