Research On Pitch Error Mechanism And Motion Characteristics Of Hydrostatic Lead Screws

The development of CNC machines towards the direction of high speed,heavy load,and high accuracy brings new opportunities for the application of hydrostatic lead screws.However,design and research materials are clearly insufficient.Pitch errors significantly influence static and dynamic characteristics,transmission accuracy and motion characteristics,and bring many unavoidable problems for the design and application of hydrostatic lead screws.How to give full play to the superior characteristics of hydrostatic lead screws?There is an urgent need for a more perfect theoretical research fully considering actual working conditions as a guide.This paper makes up the lack of design and research materials,and researches the performance of hydrostatic lead screws considering the influence of the pitch errors.Firstly,the mathematical model of oil film characteristics in hydrostatic lead screws is established.The generalized Reynolds equation for the spiral type of oil film is deduced,by means of the equivalent sectorial plane of the flank surface of threads,and based on simplified Navier-Stokes equations,mass conservation principle and no slip boundary condition.The model of oil film clearance including pitch errors of the nut is established,which combines with the velocity boundary of oil film to deduce the specific form of the Reynolds equation in hydrostatic lead screws.The perturbed form of the Reynolds equation and flow continuity equation are deduced by using the small perturbation theory.The formulas are given for calculating the axial load capacity,axial stiffness coefficient and axial damping coefficient of hydrostatic lead screws.Secondly,the pressure distribution and perturbed pressure distribution of capillary and double-action membrane compensated hydrostatic lead screws with discontinuous helical recesses are numerical solved using the finite difference method,considering the periodic pitch errors with period of 2? and cumulative pitch errors in the nut.Then the axial static and dynamic characteristics are obtained.The change laws of the static and dynamic characteristics with the fluctuation displacement of the nut are comparatively studied under various cases.In order to reveal the mechanism of the pitch error,the change laws are emphatically analyzed and explained.From the perspective of being favorable to generating hydrodynamic effect,a new method of utilizing the rational allocation of hydrostatic recesses and periodic pitch errors of the nut is proposed for improving the static and dynamic characteristics,i.e.the inter-recess lands are put on the trough of oil film clearance,so that after flowing out of the recesses,the lubricant flows into the convergent wedge as a "climbing" form along the helical direction,which greatly enhances the hydrodynamic effect on the land.Under this layout,the change laws of the axial load capacity,axial dynamic stiffness and axial damping of hydrostatic lead screws are calculated and analyzed.The results indicate that the new method significantly improves the static and dynamic characteristics.Thirdly,the transmission accuracy of the hydrostatic nut and the averaging effect of oil film on pitch errors are analyzed.Considering the pitch errors of both the lead screw and the nut,the governing equations of oil film characteristics are given.Based on the quasi-static equilibrium of the hydrostatic nut,the motion errors of the hydrostatic nut are calculated under low speed and constant external load.The influences of the different components of pitch errors on motion accuracy are studied.The results indicate that when the lead screw only has cumulative pitch errors,the motion errors of the hydrostatic nut are equal to the average value of the cumulative pitch errors located on the two flank surfaces of the lead screw.The averaging coefficient quantitatively measures the averaging effect on periodic pitch errors of the lead screw.The results indicate that the number of nut threads with helical recesses and the period of the pitch errors of the lead screw are the main factors affecting on the averaging coefficient.Furthermore,the influences of the helical recess layout and the radial displacement and tilt of the nut on the averaging coefficient are analyzed.The results indicate that the averaging coefficient presents bulges at specific spatial frequencies for the hydrostatic nut with discontinuous helical recesses,and the radial displacement and tilt of the nut have little influence on the averaging coefficient.Finally,the high-speed motion characteristics of the hydrostatic nut are analyzed.The motion nonlinear model of hydrostatic nut suitable for high speeds is established,based on the motion equation of the hydrostatic nut,and introducing the Euler equation as a bridge between the motion equation and the governing equations of oil film characteristics.The motion characteristics of the hydrostatic nut are analyzed under high speeds and variable external loads,including lower static loads,higher static loads,step loads,and sinusoidal loads.The results indicate that the fluctuations of the fluctuation displacement curves of the hydrostatic nut have little change under high speeds and lower static loads.The conclusions about the averaging effect on pitch errors in hydrostatic lead screws under low speeds can be extended to the conditions of high speeds and lower static loads.Under step loads,the hydrostatic nut has a smooth and non-overshoot transient process,showing good smoothness of motion.Under sinusoidal loads,the amplitude of response fluctuation displacement decreases with an increase in the frequency of the sinusoidal load.