Hydrostatic Journal Bearings Research Articles

Active control of multi-input hydraulic journal bearing system

Because of the advantages of high accuracy, high capacity, and low friction, the development of hydrostatic bearing for machine tool receives significant attention in the last decades. The mechanics and mechanical design of hydrostatic journal bearing with capillary restrictors has been discussed in literature. However, pragmatically, the undesired loading effects of cutting force tend to result in resonance and instability of the rotor and damage the shaft during operation. Therefore, multi-input, active flow control using state feedback design is proposed in this paper. To this purpose, the proportional pressure valves are added to the hydraulic system as active control devices, and the linearised models of the bearing and valve are discussed and identified. Simulation and experimental work is conducted to verify the proposed active control and parameter identification techniques. The results show that the unbalance responses of the rotor are reduced by the proposed state feedback controller, which is able to regulate the flow pressure effectively, thus enhancing the stability and accuracy of the hydraulic journal bearing.

Orifice compensated performance characteristics of hybrid hole-entry conical journal bearing

Influence of semi-cone angles on the performance of the non-recessed hybrid/hydrostatic hole-entry conical journal bearing compensated with orifice restrictor has been carried out analytically. The analysis comprises two rows of symmetric hole-entry contour in the circumferential direction of hybrid/hydrostatic conical journal bearing. An orifice restrictor is used in the hole-entry contour to allow the restricted flow in the clearance space of a journal and bearing. Well-known finite element method and Newton–Raphson method for restrictor have been used to solve the Reynolds equation, governing the fluid flow in the clearance space of a hybrid/hydrostatic conical journal and bearing. Further, the spherical coordinate system has been employed to solve Reynolds equation instead of cylindrical coordinate system. Performance characteristics in terms of stiffness coefficient, damping coefficient, bearing pressure, bearing flow, and minimum fluid film thickness have been discussed for variable external radial load ([Formula: see text]) = 0.25–1.5. The performance characteristics in terms of [Formula: see text], [Formula: see text], and [Formula: see text] is found to be quite significant for hybrid hole-entry conical journal bearing when compared with hydrostatic hole-entry conical journal bearing, which allows the designer to choose appropriate non-recessed hybrid hole-entry conical journal bearing.

On the Stiffness and Damping Coefficients of Constant Flow Valve Compensated Conical Hydrostatic Journal Bearing with Micropolar Lubricant

A theoretical analysis for performance characteristics of a conical multirecess hydrostatic journal bearing compensated with constant flow valve has been carried out considering micropolar lubricant. The numerical solution of the modified Reynolds equation for the conical bearing has been done using finite element method with necessary boundary conditions. The performance characteristics have been presented for various values of the restrictor design parameter, load, micropolar parameters, semi-cone angle and aspect ratio (L/D ratio) of the bearing at zero speed. It has been observed that the bearing develops large stiffness and damping coefficients with increase in restrictor design parameter, micropolar effect and semi-cone angle.

非対称給気圧力による静圧ジャーナル軸受の軸受性能向上

Hydrostatic gas journal bearings can contactlessly support rotors by gas pressure. They provide advantages such as high precision rotation, high speed rotation and low friction loss. However, the load capacity of gas bearings is very small in comparison with rolling contact bearings, so they have been mainly applied to small size rotating machinery. In order to support heavier rotors and unbalanced rotors, we have developed an asymmetric gas supply system for the bearing. The system is supplied different gas pressure to the bearing from multiple supply holes in accordance with rotational state of the rotor. A test rig was fabricated by authors and a rotating test was carried out to verify the advantageous. The test bearing has diameter of 60 mm and the length of 120 mm. The results of the numerical simulation using non-linear orbit method was compared with the test results. Each approaches showed that the asymmetric gas supply system can be reduced the rotor vibration compared with the conventional symmetric gas supply system.

A Simulation Study of Recessed Type Hydrostatic Journal Bearing

In this paper, a simulation model is established to study effects of the bearing system parameters on bearing performance. The static performance (such as load capacity, stiffness and flow) about various dimensions of multi-recess type hydrostatic journal bearings with constant-resistant restrictor compensation was investigated. The parameters studied includes length/diameter ratio, number of recess, recess length ratio, recess width ratio, initial ratio between recess pressure to supply pressure, and eccentricity.

Effect of Elasticity on Capillary Compensated Flexible Multi-recess Hydrostatic Journal Bearing Operating with Micropolar Lubricant

This paper presents a theoretical study of the effects of bearing shell deformation upon the performance characteristics of a capillary compensated multi-recess hydrostatic journal bearing system operating with micropolar lubricant. The finite element method has been used to solve the modified Reynolds’ equation governing the micropolar lubricant flow in the bearing and the three dimensional elasticity equations governing the displacement field in the bearing shell. The elasto-hydrostatic performance characteristics of the bearing are presented for various values of micropolar parameters (l m and N 2) and for a wide range of the deformation coefficient $$\bar{C}_{d}$$ which takes into account the flexibility of the bearing shell. The computed results indicate that the influence of the bearing shell flexibility is quite significant on the performance characteristics of recessed hydrostatic journal bearing system operating with micropolar lubricant.

5축가공기를 활용한 내면 형상 가공용 최적 앵글헤드의 개발

In general, recent critical studies of five-axis machine have tended to center on the question of effective machining to realize complex shape parts. However, the hydrostatic bearing and journal bearing, both of which are involved in the complex process of dividing the processing of internal precision-shape machining, must be optimized. Although the angle head is designed to machine the internal shape as it approaches the inner diameter of the work piece, research on the angle head in five-axis machining has received only minimal attention in domestic industries. In this study, an angle head which is optimized for effective internal shape machining is developed. In pursuit of this purpose, 3D and 2D designs of the angle head for five-axis machining are devised. Reliability is secured through static performance tests and machining accuracy evaluations of the angle head in keeping with the machining accuracy standard of 0.2mm for hydrostatic bearings.

Investigation of velocity slip effect on steady state characteristics of finite hydrostatic double-layered porous oil journal bearing

Steady state characteristics of finite hydrostatic double layer porous oil journal bearing are investigated theoretically by incorporating tangential velocity slip at the porous-film interface given by Beavers–Joseph. The governing equations for flow in the porous medium and modified Reynolds equation in the film region are solved simultaneously using finite difference method. The effects of slip and design variables such as feeding parameter, bearing number, eccentricity ratio, slenderness ratio, and anisotropy of permeability have been investigated on bearing performance characteristics like load-carrying capacity, attitude angle, friction variable, and volume flowrate. The results are depicted in the form of graphs that can be utilized during design.

Dynamic Characteristics of Hydrostatic Active Journal Bearing of Four Oil Recesses

More and harsher operational environment of spindle puts forward higher requirements for the performance of bearings. It is no longer suitable for the traditional journal bearing to work in the conditions above. In order to meet the requirements of high speed and heavy haul operation, the article presents servo-valve active compensation to realize accurate control of spindle position accuracy and improve the behavior of hydrostatic journal bearings. By regarding the journal bearing as an automatic control system in the process of modeling, the dynamic equation and flow continuity equation for the proposed bearing were derived. The dynamic characteristics of the proposed journal bearings and the traditional journal bearings were studied in the operational environment of high speed and heavy duty. The numerical results indicate that the proposed hydrostatic active journal bearing has good performances, including good controllability and stability, fast response, high stiffness, strong resistance, etc., compared to traditional journal bearings. The use of active lubrication with servo-valve controller results in a significant amount of amplitude reduction and greatly improves the positional accuracy of the spindle. Therefore, it has the potential application in heavy-haul and high-speed machinery.

딤플이 크랭크 샤프트 핀 터너 유정압 베어링의 윤활특성에 미치는 영향에 관한 연구

Recently, surface texturing technologies have been widely used in lots of industries to increase the machinery efficiency. In this research, the lubrication characteristics of a crank shaft pin turner bearing with dimples were studied. When increasing the dimples, the load carrying capacity due to the increased pressure was increased because those have sealing effects. Also, the run-out error of the bearing was decreased. Therefore, it is important to consider the depth, the number and the distribution of dimples when designing the hydrostatic journal bearing.

A new method for calculating the static performance of hydrostatic journal bearing

A new analytical method is proposed to calculate the static performance of hydrostatic journal bearing. Analytical expressions of recess pressure and flow are deduced through analyzing flow continuity equation and utilizing Gauss–Legendre integral formula. To study the computational accuracy and the application range of the new method, recess pressure and flow of a four-pocket capillary compensated hydrostatic bearing under different eccentricity ratios and wrap angles of oil recess are calculated using three methods (the new method, the old analytical method and the finite difference method). The results indicate that new analytical method has the advantage of simplicity and high computational accuracy.

Static analysis of hydrostatic conical bearings using flow resistance network method

Purpose – This paper aims to study the static characteristics of the hydrostatic conical journal bearings by utilizing single-action membrane restrictors to compensate the working pressures of recesses. Design/methodology/approach – The flow resistance network method is used to analyze the influences of load capacity and static stiffness of bearing with the design parameters, including the number of recesses, radial eccentricity ratio, axial displacement ratio, restriction constant, membrane compliance, length-diameter ratio, circumferential land width ratio, axial land width ratio and half of cone angle. Findings – This study shows the infinite stiffness of the oil produced in the first and second recesses while single-action membrane restriction constant of 2 and 3, respectively, as well as in the fourth recess while single-action membrane restriction constant of 0.01 and 0.1, respectively. Research limitations/implications – This article provides the hydrostatic conical bearings in static and unbiased states for analyses of design parameters. The analyses ignore dynamic pressure effect and do not use the Reynolds equation, and assuming that each oil recesses pressure is constant. Practical implications – The influences of the design parameters including the number of recesses, membrane restriction, membrane compliance, length-diameter ratio, half of con-angle, circumferential land width ratio, and axial land width ratio are discussed to the load capacity and static stiffness of conical bearing. Originality/value – Based on the characteristics of the conical bearing through analysis, this article suggests the front bearing with hard membrane restrictor (capillary) and the back bearing with soft membrane restrictor are the most appropriate for axial stiffness.

Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

The water-lubricated bearings have been paid attention for their advantages to reduce the power loss and temperature rise and increase load capacity at high speed. To fully study the complete dynamic coefficients of two water-lubricated, hydrostatic journal bearings used to support a rigid rotor, a four-degree-of-freedom model considering the translational and tilting motion is presented. The effects of tilting ratio, rotary speed, and eccentricity ratio on the static and dynamic performances of the bearings are investigated. The bulk turbulent Reynolds equation is adopted. The finite difference method and a linear perturbation method are used to calculate the zeroth- and first-order pressure fields to obtain the static and dynamic coefficients. The results suggest that when the tilting ratio is smaller than 0.4 or the eccentricity ratio is smaller than 0.1, the static and dynamic characteristics are relatively insensitive to the tilting and eccentricity ratios; however, for larger tilting or eccentricity ratios, the tilting and eccentric effects should be fully considered. Meanwhile, the rotary speed significantly affects the performance of the hydrostatic, water-lubricated bearings.

A method for measuring the hydrodynamic effect on the bearing land

The concept of dynamic pressure ratio (γ) is put forward in this paper to measure the hydrodynamic effect on bearing land. The Reynolds equation and flow continuity equation have been solved using finite difference method, overrelaxation method and underrelaxation method. Taking the four-pocket capillary compensated hydrostatic journal bearing as an example, variations of dynamic pressure ratio(γ) with eccentricity ratio (ε)and rotating speed(N) are studied. The simulation results indicate that, as eccentricity ratio and rotating speed increase, dynamic pressure ratio will increase. With eccentricity ratio lower than 0.5, dynamic pressure ratio is smaller than 5% at three rotating speeds. However, when eccentricity ratio is higher than 0.5, dynamic pressure ratio will rise fast with increasing eccentricity ratio .

Hydrostatic Support Design of Cooling Copper Roller with Inner Pressure Feedback in Forming Amorphous Ribbon

Cooling copper roller is the key technology and equipment to amorphous ribbon forming. Rolling bearing support is difficult to obtain high rotation accuracy. A new inner pressure feedback hydrostatic journal bearing is proposed with different recess area. The load capacity and film stiffness mathematical model of hydrostatic journal bearing are established. The Inner pressure feedback hydrostatic journal bearing with different recess area at the diameter of 200mm is designed and manufactured for amorphous ribbon cooling copper roller support structure. The operation tests demonstrate that the rotation accuracy of the cooling copper roller shaft is less than 2μm, which in accordance with the requirements of amorphous ribbon production process.

A Comparative Elastohydrostatic Analysis of CFV- and Capillary-Compensated Multirecess Hydrostatic/Hybrid Journal Bearing Operating with Micropolar Lubricant

A comparative study on the performance characteristics of the flexible multirecess hydrostatic journal bearing system with constant flow valve and capillary restrictors has been presented considering the effect of micropolar parameters. The modified Reynolds equation for the flow of micropolar lubricant through the bearing has been solved using finite element method, and the resulting elastic deformation in the bearing shell has been determined iteratively. The results indicate that the micropolar parameters of the lubricant affect the performance of the flexible multirecess hydrostatic journal bearing system quite significantly.

A Three-Dimensional Parametric Study and Numerical/Experimental Flow Visualization of a Six-Pocket Hydrostatic Journal Bearing

This article presents a numerical investigation and some experimental results supporting evidence on the flow structure and the pressure distribution in a hydrostatic journal bearing with six equidistant pockets. The parametric studies are of both operational and geometric nature. The operational ones include shaft's angular speed and inlet pressure. The geometric ones include pocket depth, eccentricity, clearance and restrictor diameter. The latter two are instrumental in changing the ratio of the restrictor to clearance hydraulic resistance (R). The flow regime in the bearing is kept in the laminar range (Rebrg < 60). It was found that for the deep pocket the pressure is uniformly distributed across its circumferential length, whereas for the shallow pocket it increases in a ramp fashion along the direction of rotation. The oil injected through the restrictor forms a penetrating jet that constitutes the driver of the upstream and downstream vortical cells that eventually interact with the Couette effect generated by the rotating shaft. This latter effect deforms both the upstream and downstream vortical cells, causing the downstream one to elongate and occupy a large portion of the pocket center. A direct consequence is the formation of a central vortical cell located at the mouth of the restrictor. It has become evident that the flow in the restrictor has to be modeled when simulating the flow in the pockets, because it represents an influential boundary condition that significantly alters the structure of the flow in the pocket itself. A novel modeling feature is the introduction of large sink-type reservoirs upstream of the restrictors. This allows prescription of the same pressure at the inlet of these ‘sinks’, thus simulating a common and constant pressure manifold for all restrictors. For high speeds of rotation the pressure on the lands between the pockets is dominated by hydrodynamic effects, which cause pressures higher than the hydrostatic pressure in the convergent zone. This situation has important consequences on the overall flow structure in pockets adjacent to these large hydrodynamic pressures, as the flow may be completely shut off at the circumferential and partially at the axial exits of the pocket. The change in the resistance R is associated with the change in the hydrodynamic to hydrostatic pressure component dominance in the bearing. Some validating qualitative experimental results concerning the numerical simulation of the flow in the pockets and associated feed mass flows are also presented.

Analysis of Hybrid (Hydrodynamic/Hydrostatic) Journal Bearing

The Hybrid (hydrodynamic/ hydrostatic) journal bearing system has found wide spread application in high speed rotating machines such as compressors, gas turbines, steam turbines, etc. The present studies include solution of Reynolds equation for hydrodynamic journal bearing with infinitely long approximation (ILA), infinitely short bearing approximation (ISA) and finite journal bearing approximation. Further Finite Journal bearing approximation considers two dimensional solution of Reynolds equation with natural boundary condition, which cannot be solved by analytical method. So, here the solutions for finite journal bearing have been done with finite difference method (a MATLAB® code is prepared for finite difference method) to get bearing performance parameters such as load capacity, Sommerfeld no., etc.

Modeling of Gas Thermal Effect Based on Energy Equipartition Principle

In the present article, a gas thermal effect is modeled based on the energy equipartition principle. Two new independent state equations for an ideal gas are developed that provide a new way to analyze thermal effects in gas lubrication. Furthermore, the energy equation is derived for gas lubrication and the analysis of thermal effects is carried out on a gas spiral thrust bearing and a gas hydrostatic journal bearing. The results show that gas temperature increases significantly in the lubricated region at high speed for both the thrust and hydrostatic journal bearings, and the thermal effect positively influences the load capacity of the thrust bearing. The gas expansion effect makes the gas temperature decrease in the hydrostatic journal bearing, and the gas temperature decreases with an increase in the inlet pressure.

Experimental Study on Journal Gas Bearing with Axial Slot for a Miniature Air Turboexpander

A new type of hydrostatic journal gas bearing with axial slot of tangential gas entry for miniature air turboexpander is firstly developed in this paper. This bearing configuration is presented and constructed to fit manufacture simplicity. The experimental investigations are carried out to reveal the relationship between bearing parameters and instability threshold speed. It is feasible to increase the stability of hydrostatic journal gas bearing by adopting this kind of configuration with axial slot of tangential gas entry. Some valuable tested results are obtained to reveal the optimum slot height and radial clearance for this miniature air turboexpander.