Aerostatic Spherical Bearing Design Study

Aerostatic bearing has specific advantages, such as high precision, no friction, etc. Aerostatic spherical bearing has a stated application in precision machining and precision testing with its advantages of supporting radial and axial load at the same time, three-degrees of freedom (d.o.f.), self-regulation ball center, etc. Aerostatic spherical bearing can reduce the difficulty to assemble, and be propitious to enhance the gyration precision of principal axis. In order to master the key technology of numerical simulation analysis, configuration design, manufacturing and assembly of aerostatic spherical bearing. This paper which is supported by the emphasis developing fund of China Academy of Engineering Physics (CAEP), "Study the Technology of Design and Manufacturing on High Precision Aerostatic Spindle", makes valuable explorations in the field of aerostatic spherical bearing.Based on the lubrication theory and the characteristic of configuration, the mathematical model of aerostatic spherical bearing was established from the general form of Reynolds equation. The dimensionless form of spherical bearing Reynolds equation was derived from the general form, and a method to iteratively solve the spherical bearings Reynolds Equation by using the MATLAB Partial Differential Equation (PDE) Toolbox as the solver was proposed. Some modules of MATLAB PDE Toolbox were modified, and software system was established to calculate the performance of spherical bearings. A set of spindle system based on aerostatic spherical bearing was designed and manufactured according to the results of numerical simulation.The problem of three-dimensional spherical surface gas lubrication was transformed into two-dimensional rectangular plane by coordinate transformation, and then the Reynolds Equation of spherical bearing was converted into standard form of elliptic partial differential equations, and the software system was established to calculate the performance of spherical bearings. The software system used an iterative idea to solve the pressure on the generetrix, and the pressure distributing of the whole plane was calculated through the equation of quality flux, then the load capacity and rigidity of spherical bearing was obtained by integral. Based on the study above, the bearing static performances with variety of air pressure, average gas gap, throttle bore aperture, throttle bore number, and the angle of spherical bearings versus z axis were respectively calculated. The result of numerical calculation suggest that the load capacity and rigidity of spherical bearing increases along with the augmentation of air pressure, decrease of average gas gap, and accretion of throttle bore number, the load capacity and rigidity of spherical bearing increases at the beginning and then gradually reduces at the end along with the augment of throttle bore aperture and the angle of spherical bearings versus z axis, so the maximum exists.The configuration parameters of spherical bearing were optimized according to the results of numerical simulation, and then a set of spindle system with variable ball center distance using the style of contraposition double hemisphere aerostatic spherical bearing was designed. After constructing the test-bed of aerostatic spindle prototype aeroplane, investigation was carried out to test the bearing static performances under variety of air pressure, average gas gap and beforehand eccentricity. The results indicated that the bearing radial and axial load capacity exceed 250N, and rigidity exceed 40N/μm in the case of 0.4MPa air pressure, 15μm average gas gap, 10μm beforehand eccentricity, 0.2mm throttle bore aperture, 8 aperture of double line throttle bore distributing, and 16 angle of spherical bearings versus z axis. This orderliness of experimental results is uniform to the numerical simulation, and gets the better consistency.Theoretical analysis, numerical simulation and experiment results on static performance show that the static mathematical model of aerostatic spherical bearing established in this paper is correct, the method of numerical calculation is creditable, the designing of spindle prototype aeroplane is basically logical, and the designing technology of aerostatic spherical bearings is basically grasped. The results of numerical simulation and experiment results provide dependable gist for improving the performance of aerostatic spherical bearing and greatly valuable preference for spherical bearing researchers and designers.