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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Tribology International, Volume 66, October 2013, Pages 83–92
Conical hydrostatic bearings with two different compensating devices have been proposed in this paper, which are classified as variable slot compensated hydrostatic bearing (VSHB) and fixed slot compensated hydrostatic bearing (FSHB), respectively. The mathematical models for them have been built with perturbation theory and solved by finite element method (FEM). Static loading experiment has been carried out to validate the research methodology. Then the static and dynamic characteristics of the proposed bearings have been comparatively studied. Results show that the VSHB exhibits a better radial performance of load carrying capacity and stiffness, but a worse radial damping performance, compared with FSHB under the same geometric and operational conditions.
Conical hydrostatic bearings have been successfully used in various engineering applications, such as precision machine tools, for the advantage of being capable of carrying both axial and radial load. They have been widely and deeply studied in available literature. Prabhu and Ganesan  and Chandra et al.  studied multirecess conical hydrostatic thrust bearings theoretically taking into account the effect of rotational lubricant inertia. Nowak and Wierzcholski  analytically solved the non-Newtonian lubrication problem for conical journal bearing of finite width. Then Abdel-Rahman  analytically studied the non-isothermal flow of non-Newtonian lubricant through the gap of a conical bearing when an external magnetic field was applied on the basis of Nowak and Wierzcholski's work. Khalil et al.  theoretically investigated the effect of turbulent lubrication on the performance of externally pressurized conical thrust bearings with an algebraic Reynolds stress model and revealed that the turbulent flow solution gave higher dimensionless pressure, load and torque than the laminar flow solution. Yoshimoto et al.  and  studied two types of water lubricated hydrostatic conical bearings with spiral grooves by numerical and experimental methods, and found that the compliant surface bearing had a larger load capacity in a relatively large bearing clearance than the rigid surface bearing, and the proposed bearings were very stable at high speed. Sinha et al.  analyzed the thermal effect on a porous constant gap conical hydrostatic bearing under rotation and found the load capacity was reduced by the highly porous surface. Yang and Jeng  also analyzed the thermal effect on conical–cylindrical bearing performance and revealed that pressure increased both film viscosity and temperature. Abdel-Rahman  built a theoretical model of flow in a thin film between immobile conical surfaces, with quantity, location and dimensions of the feeders taken into account. Guo et al.  presented a theoretical and experimental study to recognize the dynamic performance of a hydrostatic deep/shallow pocket hybrid conical bearing compensated by flat capillary restrictors, which exhibited an advantage of high load capacity and high stability under small eccentricity. Sharma et al.  theoretically studied the influence of cone angle on the performance of four-pocket conical hydrostatic journal bearing system and concluded that the lubricant flow rate of conical journal bearing was significantly reduced vis-a-vis the corresponding similar circular hydrostatic journal bearing. They also studied the influence of wear on the performance of multirecess conical bearing and found that the direct fluid film stiffness coefficients, damping coefficients and stability threshold speed margin reduced as the bearing was worn . Sharma and Rajput  revealed that micropolar lubricant offers better performance than Newtonian lubricant through theoretical study of conical hydrostatic bearings with different conical angle. Most studies reported in literature treat the conical bearing as either a thrust bearing or a journal bearing, although it can be both. For a hydrostatic bearing, restrictors or compensating devices are basic elements to regulate the fluid flow into the recess so that it can maintain a fluid film force carrying external load. Restrictors may become the most effective impacting factor on the bearing performance if the hydrostatic bearing is used under low speed condition. Hydrostatic bearings with diversity of restrictors have been widely studied , , ,  and . Slot restrictor is one of the commonly used restrictors. Sharma et al.  studied the slot-entry hydrostatic/hybrid journal bearing using finite element method and revealed that asymmetric slot-entry journal bearings provided an improved stability threshold speed margin compared with those compensated by capillary, orifice and constant flow valve restrictors. Elastic effect, thermal effect and non-Newtonian lubricant effect were found having a great influence on the performance of slot-entry journal bearings ,  and . Garg et al.  and  theoretically investigate the performance of slot-entry hybrid journal bearings considering combined influences of thermal effects and non-Newtonian lubricant, and compared the results with hole-entry bearing. Results indicate the direct stiffness coefficients, damping coefficients and stability parameters of slot-entry bearing are not as good as hole-entry bearing under the given operation and geometry parameters. Sharma et al.  pointed out that the slot-entry hybrid journal bearing operating with micropolar lubricant had an increase of minimum fluid film thickness and a reduction of friction coefficient as compared with corresponding similar slot-entry bearing operating with Newtonian lubricant. Generally slot restrictor is a fixed one, whose restriction parameters do not change. Kane et al.  proposed a so-called self-compensating hydrostatic bearing, and its restrictor is essentially a slot formed by the rotor part and the stator part, which can change when the rotor moves in the radial direction. In this paper, conical hydrostatic rotary bearings with two types of compensating slot have been comparatively studied. The bearings compensated by fixed slot are named fixed-slot compensated hydrostatic bearing (FSHB), and the others which are compensated by variable slot are named variable-slot compensated hydrostatic bearing (VSHB). Perturbation method was applied to model the bearings and finite element method (FEM) was used to calculate the static and dynamic characteristics. The influence of conical angle on the bearing performance has been studied. Both the performances in the axial and the radial directions have been discussed and the influence of the variable slot has been investigated.
نتیجه گیری انگلیسی
Conical multirecess hydrostatic bearings compensated with fixed slot and variable slot were theoretically studied with FEM. The performance of load carrying capacity, fluid flow rate, stiffness and damping coefficients were comparatively discussed. The main conclusions of the simulation results could be summarized as below: (1) VSHB and FSHB exhibit the same axial performance; and VSHB has a better radial performance than FSHB in load carrying capacity and stiffness. However, its damping coefficients in the radial direction are somewhat lower than that of FSHB. (2) The semi-conical angle has a great influence on the performances of the studied hydrostatic bearings. The bearings with large conical angle of 60° exhibit the best axial load carrying capacity, axial stiffness and damping characteristics. The bearings with conical angle of 30° exhibit the largest radial load carrying capacity. (3) The studied hydrostatic bearings with semi-conical angle of 60° needs the least lubricant flow rate under the same geometric parameters and operation conditions, so that they consume the least pump power. The fluid flow rate through VSHB is less than that through FSHB as the rotor is off center in the radial direction. (4) The radial stiffness of VSHB is more than triple of that of FSHB. From the view point of radial stiffness, a VSHB with a little semi-conical angle is apt to be used under light external load, while that with a large semi-conical angle is suitable for heavy load application. The radial damping coefficients of VSHB is a little lower than that of FSHB, so FSHB seems more stable under radial velocity perturbation.