| Because of high movement accuracy,nearly frictionless,low driving power,and long running life,aerostatic bearings have been widely used in ultra-precision machine tools and measuring instruments.The precision of machining and measurement is significantly influenced by the bearing load capacity,stiffness,damping and rotation accuracy.Compared with the conventional orifice restrictor,the stiffness,damping and rotation accuracy of aerostatic bearings can be improved by using porous materials as the bearing restrictor.However,due to the lack of systematic understanding of the microscopic pore characteristics of porous materials,high precision numerical simulation method,and rotation accuracy quantitative calculation method,it is difficult to accurately predict the static and dynamic properties of aerostatic porous bearings,which greatly limits the rapid development and application of aerostatic porous bearings.In this paper,theoretical analysis,numerical simulation and experimental testing are carried out to address the key foundational issues in the static and dynamic analysis of aerostatic porous bearings.The mapping relationship between the microscopic pore characteristics and macroscopic permeability of porous materials was established.Based on the fractal theory,the compressible gas conservation equation and the Darcy's law,the porous material permeability model was established.Combined with the image scanning technique,the pore fractal dimension and tortuosity fractal dimension of the porous material were determined by the box counting method.The influences of the scanning magnification and image pixels on the calculation results of fractal dimension were investigated.The pressure and flow tests were designed to verify the accuracy of the established fractal permeability model.The effects of pore characteristics and manufacturing technologies on the permeability of porous material were also conducted.The static characteristics of aerostatic porous bearings were studied.According to the permeability model and pore characteristics of porous materials,the internal fluid lubrication model of porous materials was established,which contained the inertial flow and velocity slip.Based on the law of mass conservation,combined with the governing equations of gas flow in the bearing film and the boundary conditions,the pressure distribution of aerostatic porous bearings can be solved by the finite volume method.The effects of material properties,geometric parameters and working conditions on the bearing capacity and stiffness were studied.The static characteristic test platform was established to verify the validity of the fluid lubrication model and accuracy of numerical solution.The dynamic characteristics of aerostatic porous bearings were investigated.A small disturbing analysis model was established based on the dynamic grid technique.The influences of disturbance amplitude,material permeability,gas supply pressure and axial eccentricity on dynamic stiffness and damping coefficient were investigated.The dynamic analysis model of the bearing system was established based on the generalized Maxwell constitutive model and the Newtonian dynamic equation.The effects of the supply pressure,the bearing load and the restrictor characteristics on the spectral characteristics of the bearing system were analyzed.Dynamic characteristics experiments were conducted to verify the validity of the dynamic analysis model.The quantitative solution and accurate measurement for the rotation error of aerostatic porous bearings were realized.The mathematical function of microscopic manufacturing error was established.The influences of different error types and error amplitude on the gas pressure distribution were studied.The fluid lubrication equation and Newton's second law were iteratively solved by two-way fluid-solid coupling method,the mechanism and dynamic evolution process of bearing rotation error were analyzed.The influence of manufacturing error on rotation error of aerostatic porous bearings was studied.An ultra-precision measuring platform was established based on the principle of inverse method,the measurement accuracy of bearing rotation error can achieve the nanometer level.According to the results of theoretical analysis,numerical calculation and experimental test,the relationship between the macroscopic permeability of porous materials and the microscopic pore characteristics can be accurately characterized,the accuracy of numerical simulation method can be improved effectively,the dynamic characteristics of aerostatic porous bearings can be predicted precisely,the mechanism and dynamic evolution process of bearing rotation error were revealed,which provide the theoretical basis and technical support for the design and development of ultra-precision and high performance aerostatic porous bearings. |
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