Improved finite difference method for pressure distribution of aerostatic bearing

An improved finite difference method （FDM）is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses （less than 2 Win）are considered, the improved calculation method still yields a result and converges fast.

Numerical Simulation and Experimental Verification of the Stiffness and Stability of Thrust Pad Aerostatic Bearings

Many researchers concentrate on improving the stiffness and stability of aerostatic bearings, however the contradiction between stiffness and stability is still existed. Therefore, orifice, multiple, and porous restrictors are designed to illustrate the influence of restrictor characteristics on the stability and stiffness of the aerostatic circular pad bearings. Because both the stiffness and stability of aerostatic bearings are determined by the internal pressure distribution, the full Navier?Stokes(N?S) equations are applied to solve internal pressure distribution in bearing film by using computational fluid dynamics(CFD) method. Simulation results present that the stiffness and stability of aerostatic circular pad bearings are influenced significantly by geometrical and material parameters, such as film thickness, orifice diameters, and viscous resistance coe cient. Verified by the experimental data, the micro vibration of orifice restrictor is almost the same as multiple restrictors with amplitude of 0.02 m/s~2, but it is much stronger than the porous restrictors with acceleration of 0.006 m/s~2. The optimal stiffness of multiple restrictors increased by 46%, compared to only 30.2 N/μm of orifice restrictor, and the porous restrictors had obvious advantage in the small film thickness less than 6 μm where the optimal stiffness increased to 38.3 N/μm. The numerical and experimental results provide guidance for improving the stiffness and stability of aerostatic bearings.

Modeling of disturbance torque in an aerostatic bearings-based nano-satellite simulator

The disturbance torque of aerostatic bearings is in the same order of the reaction wheel, which causes difficulty in evaluation of the designed attitude control strategy of a nano-satellite based on the aerostatic bearing. Two approaches are proposed to model the disturbance torque. Firstly, the gravity induced moment,the vortex torque, and the damping moment are modeled separately. However, the vortex torque and the damping moment are coupled with each other as both of them are caused by the viscosity. In the second approach, the coupling effect is considered. A nano-satellite is constructed based on aerostatic bearing. The time history of the free rotation rate from an initial speed is measured by the gyro, which is further used to calculate the rotation angle and acceleration. The static vortex torque is measured via the removable micro-torque measurement system. Based on these data, the model parameters are identified and modeling errors are presented. Results show that the second model is more precise.The root mean squire error is less than 0.5×10^（-4） N·m and the relative error of the static vortex torque is 0.16%.

Spectral properties and identification of aerostatic bearings

Modified rotor kit Bently Nevada was used for dynamic characteristics measurements of new developed aerostatic bearings.Mathematical model of these bearings is considered as linear.Model was identified with the help of harmonic force excitation independently from the speed of journal rotation.The stiffness and damping matrices were identified for different air inlet pressures.The calculated spectral properties allow to determine the stability boundary for suitable variation of model parameters.

Entrance Effect on Load Capacity of Orifice Compensated Aerostatic Bearing with Feeding Pocket

The current research of the aerostatic thrust bearing mainly focuses on the porous material bearing and inherent compensated air bearing, which aims at obtaining small physical dimension and large load capacity. Although porous material bearing appears larger load capacity, materials anisotropy itself and void content distortion caused in heat-treating, and machining processes add greater complexity to internal flow transfer process. Inherent compensated air bearing has the advantages of simple structure and good stability, but its load capacity and static stiffness is not worth somewhat. In this paper, based on hydrostatic lubrication theory, finite volume method is presented for taking entrance effects into account in computing pressure distribution, load capacity and mass flow rates of circular aerostatic thrust bearings. Technical analysis, numerical simulations and laboratory demonstration tests of influence of pocket diameter and pocket depth on loading capacity of aerostatic thrust bearing are carried out on simple orifice compensated air bearings with feeding pockets. The static parameters, such as air consumption and pressure distributions, are measured as a function of supply pressure and air gap height for several different orifices and pockets size. Entrance effects are described in term of typical throttling types, and the effect of pocket diameter and pocket depth on load capacity is systematically described respectively. The proposed research results uncover the causation of throttling action of the orifice compensated air bearing with feed pocket and further develop and improve the design theory of air bearing.

Dynamic characteristics of ultra-precision aerostatic bearings

With high acceleration and ultra-precision requirements, the design of aerostatic bearings has been gradually focused on their dynamic performances. In this paper, the dynamic stiffness and damping coefficients of aerostatic bearings are investigated. Due to compressibility of the gas, the dynamic characteristics of aerostatic bear- ings show nonlinear frequency dependence. Particularly, their nonlinear dynamic behaviors are quite remarkable for ultra-precision aerostatic bearings with small air gap heights and high supply pressure.

Design, Development and Geometric Error Analysis of an Aerostatic Rotary Table

Rotary tables are equipments in precision machinery applied in five-axis Machine Tools and CMM （Coordinate Measuring Machines）, offering rotational （C-axis） and tilting motion （A-axis）, allowing the obtaining of several configurations for manufacturing or inspection of parts with complex geometries. The demand for high accuracy, high efficiency and fewer errors in the positioning of the part in precision machines increases every day, thus ensuring their high confidence and the use of aerostatic bearings enable constructive innovations to the equipment. In this context, this work presents the mechanical design, the development and error analysis of a prototype of an aerostatic rotary table. This study emphasizes the analysis of a prototype that uses the air as a working principle for reducing friction between moving parts, increasing the mechanical efficiency, and its influence of motion error is also discussed based on the experimental results. For the geometrical errors analysis, experimental tests were realized in laboratory using a DBB （Double Ballbar）. The tests are performed with only one axis moving, observing the behavior of the system for different feedrate at the C-axis.