تجزیه و تحلیل عملکرد یاطاقان های اسپیندل با سرعت بالا

The methods adopted to derive the pressure distribution and precision of bearing rotation are fundamental issues in the arena of gas bearing design. The current study presents a detailed theoretical analysis of bearing performance, in which the gas flow within the bearing is initially expressed in the form of simplified dimensionless Navier Stokes equations. Adopting the assumption of mass flow continuity between the bearing clearance and the orifice, the nonlinear dimensionless Reynolds equation is then derived and subsequently discretized using the Newton method. Finally, the modified Reynolds equation is solved by means of the iterative rate cutting method. The current numerical models are valid for the analysis of the film pressure distribution, friction effects, loading capacity, rigidity, lubricating gas flow rate, and eccentricity ratios of a variety of static and dynamic pressure aerostatic bearings, including high-eccentricity ratio journals, high-speed non-circular journals, thrust bearings, and slider bearings, etc. The proposed analytical models provide a valuable means of analyzing the static and dynamic performance of a high-precision rotating gas bearing, and allow its design to be optimized accordingly.

Gas bearings are characterized by low noise under rotation and by their low frictional losses. As a result, they are frequently employed within precision instruments, where they yield zero friction when the instruments are used as null devices, and within high-speed electrical motors. Compared with traditional oil bearings, gas bearings have the advantages of lower heat generation, less contamination, and a higher precision. However, their major disadvantage is that they tend to be rather unstable, and this frequently restricts their permissible range of application. In 1961, Gross and Zachmanaglou [1] first developed, and then applied, perturbation solutions to steady, self-acting, infinitely long journal and plane wedge films. The proposed perturbation solutions are valid for all ranges of geometrical parameters, and yield highly precise results. In 1975, Majumdar [2] presented a theoretical method to derive the steady-state performance characteristics of stationary and rotating journals by considering a three-dimensional flow in the porous material of a bearing. It is known that the response of gas bearing supported systems is greatly influenced by the dynamic characteristics of the gas film, and that the important parameters are the film stiffness, the damping, and the stability range. As the majority of bearings are intended to operate in a stable manner, a detailed knowledge of their relative stability characteristics is of fundamental importance. Accordingly, Majumdar [3] constructed theoretical models for the stiffness and damping characteristics of an externally pressurized, rectangular, porous thrust bearing with a compressible lubricant. In 1985, Gero and Ettles [4] evaluated the relative precision of the FDM and FEM approaches when applied to a steady, isoviscous, incompressible lubrication problem. In their study, it was assumed that the solution of a complicated coupled problem could be derived by solving a sequential series of simple, uncoupled, steady problems. The results for two-dimensional bearings demonstrated that the relative errors of the FDM solutions were smaller than those associated with the FEM approach. Furthermore, it was shown that the FDM approach was more rapid than the FEM technique, with an average CPU time of 0.15 s as compared to 0.17 s for the FEM method. In 1992, Slocum [5] performed experimental studies to develop comprehensive design procedures for orifice-compensated gas journal bearings. More recently, the influence of surface roughness on bearing performance has been investigated [6] and [7]. The results have confirmed the commonly held belief that surface roughness has a negligible effect on the lubrication characteristics of gas bearings in the case of laminar flow. In 1996, Hughes et al. [8] analyzed a gas lubricated thrust bearing experimentally and presented detailed measurements of the flow in the idealized bearing. The pad surface temperature measurements confirmed that the bearing flow was locally isothermal. In 1994, Malik and Bert [9] considered the differential quadrature method (DQM), and applied it for the first time to the solution of steady-state oil and gas lubrication problems in self-acting hydrodynamic bearings. The quadrature solutions of the Reynolds equation for the case of incompressible lubrication were compared with the exact solutions of finite-length bearings. Furthermore, the quadrature solutions of the compressible Reynolds equation for finite-length plain journal bearings were compared with those obtained using the FED and FEM approaches. The CPU times associated with the quadrature solutions were compared with those of the trigonometric series and the finite element solutions for oil-lubricated plain slider and journal bearings. Additionally, the CPU times of the quadrature solutions were compared with those of the finite solutions for the case of a gas-lubricated journal bearings. In all cases, it was found that the DQM method was capable of yielding precise solutions to the lubrication problems, and that it was computationally more efficient than either the FED or the FEM method.

This study has investigated the performance of high-speed spindle aerostatic bearings and the effects of the gas supply pressure, orifice diameter, gas film thickness, and eccentricity ratio upon the load capacity, stiffness, and volume flow rate change of a journal bearing operating at different rotational velocities. A modified iterative method has been applied to determine the pressure in the journal bearing at δi=1, i.e. at the outlet of the throttle, and at δi=0, i.e. at all other locations along the inner bearing wall. It has been determined that choke flow is typically associated with large degrees of eccentricity, small orifice diameters, and with small clearances. Furthermore, this effect is also likely to appear when the pressure ratio is lower than 0.528. When using the SOR method, it is important to choose appropriate initial conditions, otherwise the solution may fail to converge, or it may even diverge. At the orifice, the pressure is solved by means of the flow equation, and when the thin film thickness is very thin, the pressure approaches a value of 1. However, if the calculative pressure exceeds 1, the system will become divergent. Consequently, the present study has adopted the so-called rate cutting method. The results have indicated that unlike the SOR method, the rate cutting method converges to a solution even when very thin film thicknesses are considered.