A Calculation Method to Investigate the Effects of Geometric Parameters and Operational Conditions on the Static Characteristics of Aerostatic Spherical Bearings

Abstract

In this paper, a calculation method based on matlab partial differential equations (PDE) tool is proposed to investigate the static characteristics of aerostatic spherical bearings. The Reynolds equation of aerostatic spherical bearings is transformed into a standard elliptic equation. The effects of geometric parameters and operational conditions on the film pressure, bearing film force, and stiffness are studied. The axial and radial eccentricities result in different film pressure distributions; the bearing film force and stiffness are significantly influenced by geometric parameters and operational conditions. The relative optimal parameters are confirmed based on the calculation results. A comparison between the numerical and experimental results is also presented. The highest relative error between the numerical results and the experimental data is 11.3%; the calculation results show good agreements with the experimental data, thus verifying the accuracy of the calculation method used in this paper.

Fluid Film Bearings and CFD Modeling: A Review

“…Aerostatic bearings are thus characterized because the lubricant fluid film is generated from the external pressurization of a compressible fluid-mainly air (Figure 3). Aerostatic bearings have more and more applications in ultra-precision machine tools due to their specific advantages, such as their low driving power and friction, high movement accuracy, thermal stability, and others [3].…”

“…The characteristics of aerostatic bearings are modified by varying the radial clearance C, the supply pressure P, and/or the supply orifice diameter d 0 (Figure 3); the bearing load capacity and the stiffness increase at high operation speeds [5,81]. Cui [3] transformed the Reynolds equation of a spherical gas bearing into a standard elliptic partial differential equation, which was solved by using the MATLAB PDE tool. Cui carried out a theoretical and experimental analysis of a spherical bearing lubricated with air and observed the following: Given C y d 0 , the radial force F r , the axial force F a , the radial stiffness K r , and axial stiffness K a increase for all ε as P increases.…”

Performance of textured spherical thrust hybrid bearing operating with shear thinning and piezoviscous lubricants

“…To obtain the appropriate mesh size, a mesh sensitivity analysis is performed. The spherical domain between the recess boundary and the boundary exposed to ambient is transformed into a two-dimensional plane 59 as shown in Figure 4(a) and is discretised using isoparametric four-node quadrilateral elements as shown in Figure 4(b). The recess area is not discretised 31,60 and the pressure within the recess is assumed to be equal to the recess boundary pressure.…”

A simplified FEM analysis on the static performance of aerostatic journal bearings with orifice restrictor

“…But the MATLAB PDE tool can only be used for solving some particular partial differential equations, for example, elliptic, hyperbolic, parabolic, and eigenvalue partial differential equations. In the previous studies, 20 Reynolds equation of aerostatic journal bearings was transformed into a standard elliptic equation successfully, and a calculation procedure based on MATLAB PDE tool was presented to study the load capacity and stiffness of aerostatic spherical bearings, which provides a guidance for the calculation of aerostatic journal bearings.…”