The Static And Dynamic Characteristics Of Single-action Membrane Restrictor And Hydrostatic Lead Screw

In industrial applications,the straight feed motion of NC machine tools is achieved in three ways:linear motor system,ball screw with servo motor,and hydrostatic lead screw(including hydrostatic lead screw and aerostatic lead screw).This study focuses on the hydrostatic lead screw.Compared to ball screw,hydrostatic lead screw has many advantages such as low vibration,low noise,no wear,and high accuracy;compared to linear motors,hydrostatic screws have a higher load capacity,better adaptability to processing situations,better positional stability,and greater vibration resistance,which is particularly advantageous in situations requiring higher feed thrust and frequent vibration loads.Because of these advantages,researchers have paid more and more attention to hydrostatic screws in recent years.The hydrostatic screw compensated with constant pressure pump must use a restrictor,The restrictor can be divided into two types:fixed restrictor(such as capillary,orifice)and variable restrictor(membrane restrictor,spool-type restrictor,etc.).With proper design,the static stiffness of equipment compensated with membrane restrictor can be independent of external load,this characteristic could improve the processing accuracy of the equipment.The variable restrictor also causes the system instability.The The study of hydrostatic screw compensated with single-action membrane restrictor is presented as follows:1.The adjustable pre-pressure single-action membrane restrictor and hydrostatic lead screw are designed,The method to build an accurate model for the performance calculation of hydrostatic screw subsets by creating a three-dimensional structural mesh is investigated.A program for efficient automatic generation of hexahedral structural meshes of hydrostatic screw is built using MATLAB.After giving the block information,the program uses the mapping and sweeping methods to generate each block mesh,and then merges the block meshes,defines the boundary conditions,and finally outputs the mesh in cfx5 format.This program generates a series of 3D meshes of the hydrostatic screw with different pitch errors and oil film thicknesses.The mesh generation time is greatly reduced compared to that of commercial software,and the theoretical errors caused by the conversion of the non-expandable spiral surface into a 2D sectoral plane in the traditional modeling method are overcome.The static characteristics of the hydrostatic screw were then calculated with the help of FLUENT and the results of the models containing different pitch errors were compared to determine the effect of pitch errors on the load carrying capacity,temperature and cavitation of the system.2.The performance calculation modeling method of single-action membrane restrictor was studied,and the performance of single-action flat membrane restrictor(SFMR)and single-action island type membrane restrictor(SITMR),was compared.Firstly,the mathematical models of fluid pressure within the restricted region of SFMR and SITMR are established,and the analytical solution of fluid pressure within the restricted region of SITMR and the numerical solution of fluid pressure within the restricted region of SFMR are given;then,the lumped mass model for calculating the membrane deformation of SITMR and the finite element method for calculating the membrane deformation of SFMR are established respectively;the Euler method is used to ensure the fluid-structure interaction boundary conditions.Finally,a comparative study of the performance of the two throttles is carried out.It is found that the use of the flat gap assumption to calculate the static flow rate of single-action flat membrane restrictor causes huge errors due to the fact that this method overestimates the stiffness of membrane.It was clarified that when the difference between supply pressure and restrictor outlet pressure is low,SFMR and SITMR can have the same static flow rate,but the SITMR brings better dynamic performance to the system.When the difference between supply pressure and restrictor outlet pressure is high,the SFMR can reduce static flow rate and thus reduce system power.3.An arbitrary boundary method is proposed to solve the problem of large difference between theoretically calculated and experimental static flow rates.The source of the discrepancy is that the membrane boundary is neither the fixed boundary nor the simply-supported boundary,but a boundary in between.In order to integrate the computational model with the actual working conditions,an arbitrary boundary method based(on the Mindlin plate finite element model and the Kirchhoff plate finite element model is proposed in this study.The arbitrary boundary method adds a set of displacement springs and torsion springs to the boundary nodes of the finite element model,and changes the stiffness values of the corresponding torsion springs k2 to make the arbitrary transition between the fixed boundary and simply-supported boundary.The experimental data were used to fit the values of k2,the results from arbitrary boundary method were compared with the results obtained by the conventional algorithm and simply-supported large deformation method.It is found that the results obtained by the arbitrary boundary method are closest to the experimental results.It seems that the membrane boundary is not a constant boundary,and the value of k2 will change with the change of the supply pressure.The establishment of arbitrary boundary conditions is of great practical importance for the accurate calculation of the static flow rater and the understanding of the actual working conditions of the single-action membrane restrictor.4.The hydrostatic support compensated with single-action membrane restrictor has instability problem.The source of instability is the coupling of two nonlinear systems.The nonlinear dynamics analysis of the single-action membrane restrictor was carried out,the reference mass of membrane is found for the use of first-order model.By comparing the first-order and second-order systems,it was found that reducing the membrane mass and reducing the membrane dimensionless stiffness can eliminate the oscillation of membrane restrictor at the stable point.For the hydrostatic lead screw,there exists an optimal dimensionless stiffness k=4/3 for the design of the single-action membrane restrictor.The static dynamic characteristics of the hydrostatic lead screw under various conditions were analyzed and found that the static equilibrium point of the hydrostatic screw is difficult to find when the membrane dimensionless stiffness is lower than 4/3.The negative static stiffness does not mean that the hydrostatic screw is unstable,only when k<4/3,the hydrostatic screw is unstable under a specific load.The hydrostatic screw can be simplified as closed type hydrostatic thrust bearing,and when it is unstable,the open type hydrostatic bearing will also be unstable.The stability analysis of the open hydrostatic support was carried out,and the instability was found to be related to the size of the restictor and bearing,the membrane dimensionless stiffness and the magnitude of the external load.A nonlinear control law exists that allows the system to maintain infinite static stiffness over a wide range of loads.The trajectory tracking nonlinear control law for open hydrostatic support is explored,simulation results verify the effectiveness of the nonlinear control law.