Study On Contact Characteristics Of Planar Sinusoidal Steel Ball Transmission Mechanism Based On Fractal Theory

Planar sinusoidal steel ball transmission mechanism is a new movable tooth transmission mechanism with strong bearing capacity,compact structure and large transmission ratio,which has been widely used in precision transmission field.When the transmission mechanism is working under high load,the contact surface between the steel ball and the track is easy to produce irreversible plastic deformation and contact fatigue damage,because the research on the contact characteristics of the movable tooth contact surface is particularly important.At present,the research on the contact characteristics of movable gear transmission mechanism almost relies on the traditional Hertz contact theory.However,the parameters related to the microstructure and material properties of contact surface are not paid attention to,which leads to the lack of accuracy in the calculation of contact characteristics model and the error in the numerical analysis results of contact characteristics.This article applies fractal theory to the sinusoidal drive mechanism of steel ball contact characteristics in study,the establishment of a mechanism of steel ball and transmission element equivalent contact model,the transformation of "smooth" semicircle rail contact surface rough surface of innumerable micro convex body,considered the micro convex body geometry shape and material properties such as the influence of related parameters on the contact surface contact characteristics.The contact model based on fractal theory is more reliable and accurate.The main research contents are as follows:(1)The correction coefficient λ of the area function of the microconvex body on the ball-semicircle track contact surface is constructed.In this mechanism,the active disk-ball contact,the driven disk-ball contact and the retainer-ball contact are all curved surfaces,while the fractal model is only applicable to the plane contact.In order to apply the fractal model reasonably to this mechanism,the correction coefficient of the microconvex body area function suitable for the active disk-ball contact surface is constructed.(2)Establish the contact stress fractal model of the active disk-steel ball.According to the correction coefficient of the area distribution function of microconvex body on the contact surface,the elasto-plastic deformation model of single microconvex body and the area distribution function of microconvex body on the contact surface were deduced.Then,the contact stress fractal model was established by combining the mechanical model of movable tooth steel ball with the calculation formula of the contact area of active disk-steel ball.(3)The fractal model of contact stiffness between active disk-steel ball was established.By combining the contact mechanical model of single microconvexity with the modified area distribution function of microconvexity,the contact stiffness function from single microconvexity to multiple microconvexity was derived,and the fractal model of contact stiffness of active disk-steel ball was established.(4)The contact characteristics of the active disk-steel ball fractal model are verified.The contact stress,normal contact stiffness and tangential contact stiffness of the fractal model and Hertz contact model were numerically calculated respectively to verify the rationality of the application of fractal theory in the contact characteristics of transmission mechanism.