Study On The Rolling-sliding Coupling Mechanics Model And Friction Heat Of Precision Steel Ball Transmission

Precision steel ball transmission offers numerous advantages such as zero backlash,compact structure,high precision,low noise,low reduction ratio,high efficiency et al and is applied widely in robot arm drive,precision rotary parts and semiconductor wafer equipment position location.The elastic element in the precision steel ball transmission can adjust the clearance between the ball and the cycloid slot in real time to improve the transmission precision.The transmission system has multi body space meshing engagement pair,and the movement of steel balls in the cycloid groove space is complex.Most of the studies focus on the plane motion,the ball in the cycloid groove is considereed in the state of pure rolling and sliding friction is neglected in the modeling process.Therefore,it is important to establish model of the space relative velocity vector and the mechanic model of the rolling and sliding coupling to improve the transmission precision.According to the geometric model and transmission principle of precision steel ball transmission,the spatial coordinate system of each component is established.Based on the relative kinematic relationship of the transmission mechanism,the D-H coordinate transformation matrix is derived.The variation rule of the principal curvature radius curve is discussed,and the location of the occurrence angle of the singular point is obtained.The changing rule of the occurrence angle with the groove angle,the number of teeth and the cycloid short amplitude coefficient is analyzed.Using the internal and external meshing formation method of inner and outer cycloid,the movement between the center plate and the combined cycloid plate and the steel ball is analyzed.In view of conversion method and geometric modeling,space relative velocity vector model between the ball and the center plate is established.The change rule of the velocity curve of the steel ball relative to the cycloid groove in three directions is discussed.The rule of the velocity of the steel ball relative to the center plate and the combined planetary plate with the groove angle,the number of steel balls and the short amplitude coefficient is analyzed.The non Hertz contact between steel balls and cycloidal grooves in transmission mechanism is discussed.Based on the balance equation of force and moment,the pure slip and the pure rolling four point contact mechanics model are established.The normal force of meshing pair of pure sliding contact mechanics model which has four points is compared with the two point contact mechanical model.The change law of meshing force with groove angle,sliding friction coefficient,steel ball number and short amplitude coefficient is discussed.Based on the rolling-sliding contact theory,the contact elliptical area and the area of the adhesive zone are calculated.The definition of the coupling coefficient of rolling and sliding is also given.The iterative solution of the coupling coefficient of rolling and sliding is solved by the fixed point iteration method.The influence of the groove angle,the sliding friction coefficient,the number of steel ball and the short amplitude coefficient on the coupling coefficient of rolling and sliding is analyzed.Considering the existence of rolling and sliding,a mechanical model of rolling and sliding coupling is established and the change law of meshing force is analyzed.The change rules of normal force of meshing pair with the parameters such as the groove angle,the sliding friction coefficient,the number of steel ball and the short amplitude coefficient are discussed.The area of the ellipse in the meshing pair is calculated and the change law of length and short axis the ellipse is discussed.In view of the model of relative velocity of vector between steel ball and the cycloid groove and the mechanical model of rolling-sliding coupling,a friction heat generation model based on the theory of vector calculus is established.The components of frictional heat generated in rolling and sliding model in three directions are analyzed.Finite element models of rolling sliding coupling mechanics and friction heat are established respectively,simulation results and calculation results have good consistency;an experimental scheme for measuring the temperature rise between the steel ball and the cycloidal groove is designed,and the temperature rise measurement experiment is carried out.The experimental datas are compared with the calculation results of the model,and two agreement with each other.The comparison results verify the reliability of the rolling-sliding coupling model,and provide a theoretical basis for improving the transmission precision.