Investigation On The Static And Dynamic Characteristics And Optimization Design Of Aerostatic Radial Bearing With Porous Restrictor

Bearings are one of the basic mechanical parts.Their main functions are support and positioning,which has a fundamental impact on the performance of the entire working system.The aerostatic bearing relies on external gas supply and restrictor to form supporting gas film,and porous material is one of the restrictors.Compared with other aerostatic bearings,porous bearings have the advantages of relatively large load capacity,stable support,etc.To meet the requirements of special conditions such as extreme temperature,the carbon fiber reinforced carbon composites(C/C porous)is used to manufacture porous aerostatic radial bearings.Theoretical,numerical,and experimental investigation on the static and dynamic characteristics and the optimization design are carried out in this dissertation.The main research content and achievements are shown in the following.1.According to the flow characteristics inside the lubricating gap,the complete form of the Reynolds lubrication equation(RLE)is derived,which provides a theoretical basis for establishing flow models for different applications.For the aerodynamic lubrication under porous airtightness,the complete form of the RLE is simplified according to the velocity boundary condition;the film thickness equation is established;thus,its pressure equation is formulated.Based on the finite difference method,the 2D uniform mesh,the central difference scheme,the Dirichlet boundary condition for pressure,the relaxation iteration method and the root mean square of residuals as the convergence criterion are adopted to solve the pressure equation.These numerical techniques are used in the solutions for the following partial differential equations concerning mass,momentum and temperature transportation.2.The theoretical model and the solution method for the coupling of pressure,velocity,temperature and viscosity of aerodynamic bearing are established.The 3D temperature equation is integrated and averaged in the radial direction and thus the 2D temperature equation is deduced.With the analysis of grid Peclet number,it is found that the convection term in the temperature equation under eccentricity increases significantly in magnitude,therefore the second-order upwind scheme is adopted while the central difference scheme is applied to the diffusion term.With regards to boundary conditions of heat transfer at axial ends of the bearing,a virtual node method combined with flow direction and Dirichlet boundary conditions for temperature are proposed to achieve stable numerical calculation.Meanwhile,it is found that the pressure work in the viscous dissipation term cannot be neglected.Furthermore,with the help of the non-conservative form of pressure equation and the concept of segregated solution,the coupling solutions of pressure,velocity,temperature and viscosity are established.The aerodynamic bearing solver ABCP is programmed using C++ and the Graphical User Interface is built in MATLAB.The load capacity,pressure field and temperature field calculated by ABCP are in good agreement with Fluent.More importantly,ABCP achieves instant simulation.The results by ABCP show that the temperature rise increases the load capacity for aerodynamic bearings.3.Two theoretical models and solution methods of porous bearings are established.The modelling streategy is: the RLE destribes the film flow,the Darcy equation describes the Poiseuille flow in the porous body,the continuity equation enclosures the theoretical model.The first theoretical model is a 1D model,only considering the radial flow in the porous bushing,integrating the Darcy equation in the radial direction and using the continuity equation in the radial direction to obtain the pressure-velocity equation of the porous bushing from the inlet to the outlet,directly substituted into the RLE,the numerical solution method of the model is the same as that of the aerodynamic bearing.The second one is a 3D model.Considering the 3D flow in the porous bushing,the Darcy equation is substituted into the continuity equation to obtain the pressure Laplace equation in the porous body,and then the Darcy equation is used to modify the velocity boundary conditions on the bushing in the RLE.In the numerical solution of the 3D model,the nonuniform 3D grid and the variable step-size difference scheme are introduced,and a virtual node method for processing the pressure Neumann-Laplace equation is proposed.The porous bearing solver PBCP are programmed.PBCP and Fluent results are very close,but PBCP achieves instant simulation.The results by PBCP show that the load capacity under slip boundary condition almost equals to that under non-slip one.The load capacity under isothermal compressible flow is greater than that under incompressible flow.The load capacity decreases as the polytropic index increases.4.A multi-parameter and multi-objective optimization platform for porous bearings is established,named PBOP.The design ranges of the main parameters of gas bearings are summarized.The single factor analyses of the feeding parameter,the ratio of length to diameter,the ratio of clearance to diameter,the feeding pressure,and the gas viscosity are carried out using PBCP.It is concluded that the comprehensive effects of various design parameters have to be considered if better overall performance is needed.Thereafter,PBOP is established.First,using the Design of Experiments,namely optimized Latin Hypercube,combined with PBCP calculating the static characteristics,a sample set is created.Secondly,using a two-layer feedforward neural network,an approximate model between design parameters and static characteristics is established.PBOP provides LMBP and GD-BP network training methods.Finally,the genetic algorithm NSGA-II in PlatEMO is called to seek the Pareto frontier and Pareto set.The geometric parameters,the permeable parameters of porous bushing and the feeding parameters of gas are optimized in order to obtain the maximum load capacity and the minimum feeding power.The optimization results by PBOP show that for the given design ranges,there is a limit of the maximum load capacity,meanwhile,it corresponds to the most economical power consumption of feeding gas or the most economical cost of manufacturing.5.Using the dynamic grid in Fluent,the method to calculate dynamic characteristics of porous bearings is established.Fluent UDF is used to define the journal motion,and the smoothing method is applied to update the moving mesh of gas film.A coordinate transformation method is proposed to obtain the motion of perturbation and its corresponding force responses generated by the gas film.Afterward,the least-squares method is used to fit the linear overdetermined equations,and the dynamic characteristics under isothermal compressive flow are obtained.The results show that the stiffness and damping decrease with the increase of eccentricity.The stiffness and damping increase with the increase of feeding pressure.The force response lags behind the displacement under compressible flow,while they are synchronized under incompressible flow.The load capacity decreases with the increase of perturbation frequency.6.The C/C raw material and C/C porous bearing test benches are built.The results show that under the observation that the gas mass flow rate is proportional to the feeding pressure difference,the Darcy equation can be used to describe the flow in the porous body.However,due to the pores on the porous surface blocked by the machining process and the carbon fiber weaving direction inside the porous bushing,the permeability of the C/C porous bearing is lower than that of the raw material.Using nitrogen and carbon dioxide as lubricants,C/C porous bearings are observed to achieve aerostatic lubrication.Besides,the test bench is further improved,and the brass and ceramic bearings using water lubrication are tested.The results show that the load capacity produced by the hydrodynamic increases with the increase of rotating speed.