Orifice Restrictors Research Articles

Effect of Wear on Symmetric Hole-Entry Hybrid Journal Bearing Compensated by Orifice Restrictor Under Turbulent Regime

This study examines the impact of wear and turbulent flow on symmetric hole-entry hybrid journal bearings with orifice restrictors. Dufranes’s abrasive model for wear effect and Constantinescu’s lubrication model for turbulent flow have been used. A modification has been made to the Reynolds equationand utilized the finite element method to solvealong withflow equation of an orifice restrictor. For selected wear depth parameter values and Reynolds numbers,computed results have been acquired. The minimum fluid film thickness increases for worn bearings when operating under a turbulent regime rather than a laminar regime. Further, the stiffness coefficient decreases for constant external load when worn/unworn bearings function in a turbulent regime.

Static and Dynamic Performances of Novel Aerostatic Bearings with Primary and Secondary Orifice Restrictors

Aerostatic bearings are crucial support components in ultra−precision manufacturing equipment. However, improvements in the load−carrying capability (LCC) of aerostatic bearings often lead to higher intensity nano−vibrations. This paper introduces a novel primary and secondary orifice restrictor (PSOR) designed to simultaneously enhance the LCC and mitigate nano−vibrations in aerostatic bearings. The static performance of complex turbulent flows occurring within the chamber of aerostatic bearings with PSORs was investigated. The dynamic performance of the turbulent flows was analyzed through 3D transient numerical simulation using the large eddy simulation method. The LCC and nano−vibration acceleration were measured experimentally, and the results indicated that the design of the secondary orifice diameter could enhance LCC and mitigate nano−vibrations, consistent with theoretical predictions. The accuracy of the proposed model was validated, confirming the effectiveness of PSOR. In the experiments, an aerostatic bearing with a secondary orifice diameter of 0.1 mm exhibited the lowest LCC and largest nano−vibration. Conversely, an aerostatic bearing with a secondary orifice diameter of 0.26 mm exhibited the highest LCC and weakest nano−vibration. This study provides insights into the formation mechanism of turbulent vortex and interaction mechanism among the primary orifice and secondary orifices in aerostatic bearings with a PSOR.

Performance of electro-rheological (ER) lubricant operated hybrid circular thrust pad bearing considering 3D surface irregularities

This paper describes the behaviour of ER lubricated hybrid circular thrust pad bearing (HCTB) having three-dimensional (3D) surface irregularities. Finite element analysis has been used to solve the Reynolds equation and the orifice restrictor equation to analyze the behaviour of hybrid circular thrust pad bearing with irregular surface. The use of ER lubricant and consideration of 3D surface irregularities results in improved load capacity, and damping coefficient, but reduces the stiffness coefficient of HCTB. The dynamic stiffness S̅ and damping C̅ coefficients gets altered around − 98% and 44.45% respectively due to the synergic effect of ER lubricant (V=800volt) and 3D surface irregularity (h̅a=0.2) in comparison to smooth surface (h̅a=0) HCTB lubricated with Newtonian Fluid (V=0volt).

Performance of a Spherical Hybrid Thrust Bearing Considering the Influence of Surface Irregularities and MR Lubricant Behavior

This article describes the finite element modeling of a spherical hybrid thrust bearing (SHTB), taking into account the influence of three-dimensional surface irregularities and magnetorheological (MR) lubricant behavior. The rheological behavior of MR lubricant was described using the Herschel–Bulkley model, and the yield shear stress relationship of MR fluid was expressed using the asymmetrical sigmoidal function. The finite-element method (FEM) is used to solve the governing Reynolds equation for an irregular surfaced SHTB configuration along with the orifice restrictor equation. The findings of the study indicate that the performance of the SHTB is improved by considering the three-dimensional (3-D) surface irregularities and operating with MR fluid at the expense of power loss due viscous friction. The percentage increase in the value of dynamic coefficients () and () due to the coupled effect of MR fluid and three-dimensional surface irregularity () on the spherical hybrid thrust bearing is of the order of 52.37% and 71.22%, respectively, at and

On the static performance characteristics of ER fluid lubricated asymmetric journal bearing

The performance of a hole entry journal bearing with an asymmetrical arrangement of holes is examined in this paper using the finite element method. The lubricant utilised is electrorheological (ER) fluid, and orifice restrictors were used to control flow in each hole. Examined performance variables include lubrication pressure, lubricant film thickness, and bearing flow. The outcomes are contrasted with the Newtonian case. By altering the electric voltage, ER fluid has been used to provide very precise control of lubricant viscosity. When ER fluid driven bearings are compared to Newtonian lubricated bearings, higher pressure values are attained. Variable voltage was used to control the viscosity. At 400 V and 1200 V for W = 1.2, the increase in maximum pressure for the asymmetric hole entry design using ER fluid as the lubricant is calculated to be 8.3 % and 13.8 %, respectively. For the same amount of W, the percentage reduction in bearing flow is 2.5 % and 15.7 % at 400 and 1200 V, respectively.

Novel 3-D printed aerostatic bearings for the improvement of stability: Theoretical predictions and experimental measurements

Aerostatic bearings are extensively used in the ultra-precision equipment machines. However, vortex phenomenon in the recess will induce micro-vibrations on the bearing surface, which is known to be harmful for manufacturing accuracy and greatly limit the scope of application. According to the formation mechanism of the vortex phenomenon, this paper proposes some novel orifice structures for aerostatic bearings to achieve the purpose of suppressing the vortex occurrence by changing the airflow characteristics in the recess. The theoretical load capacity and pressure vibration of four aerostatic bearings with different orifice structures are obtained by using 3-D computational fluid dynamics (CFD) models. Due to the complexity of the orifice structures, the orifice restrictors are manufactured by 3-D printing technology. Test rigs are built to measure the load capacity, pressure distribution and micro-vibration. And experimental measurement data agrees well with theoretical calculation results. Both the theoretical and experimental results show that the arc hole bearing (AHB) has the best stability and the weakest vibration amplitude, among all the four aerostatic bearings, while the load capacity remains unchanged.

Investigations of the static and dynamic characteristics of the precision hydrostatic spindle with mid-thrust bearing under different loads

This paper investigates the static and dynamic characteristics of the precision hydrostatic spindle with a mid-thrust bearing under different working conditions. Firstly, the paper establishes the fluid governing equations of the coupled journal and thrust bearings based on orifice restrictors; and the dynamic and static Reynolds equations are solved using the perturbation and finite difference methods to obtain the steady and transient pressure distribution functions. Then the stiffness and damping characteristics of matrixes of the spindle are obtained by integrating the steady and transient pressure. Furthermore, by establishing the motion equation for the spindle rotor with five degrees of freedom, the quasi-static equilibrium position and stability criterion of the rotor under different working conditions are determined. Finally, the relationships between the dynamic and static characteristics of the spindle and cutting force, rotational speed, and cutting distance are simulated and analyzed. The simulation results show the patterns of variation in performance indices such as stiffness, damping, quasi-static position, and stability of the spindle under different working conditions, which provides important design information to be taken into consideration concerning the precision hydrostatic spindle.

Development of Pump-Drive Turbine Module with Hydrostatic Bearing for Supercritical CO2 Power Cycle Application

The turbomachinery used in the sCO2 power cycle requires a high stable rotor-bearing system because they are usually designed to operate in extremely high-pressure and temperature conditions. In this paper, we present a pump-drive turbine module applying hydrostatic bearing using liquid CO2 as the lubricant for a 250 kW supercritical CO2 power cycle. This design is quite favorable because stable operation is possible due to the high stiffness and damping of the hydrostatic bearing, and the oil purity system is not necessary when using liquid CO2 as the lubricant. The pump-drive turbine module was designed to operate at 21,000 rpm with the rated power of 143 kW. The high-pressure liquid CO2 was supplied to the bearing, and the orifice restrictor was used for the flow control device. We selected the orifice diameter providing the maximum bearing stiffness and also conducted a rotordynamic performance prediction based on the designed pump-drive turbine module. The predicted Campbell diagram indicates that a wide range of operation is possible because there is no critical speed below the rated speed. In addition, an operation test was conducted for the manufactured pump-drive turbine module in the supercritical CO2 cycle test loop. During the operation, the pressurized CO2 of the 70 bar was supplied to the bearing for the lubrication and the shaft vibration was monitored. The successful operation was possible up to the rated speed and the test results showed that shaft vibration is controlled at the level of 2 μm for the entire speed range.

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

This paper puts forward a simplified FEM based on MATLAB PDE tool to investigate the static performance of aerostatic journal bearings. The pressure distribution equation is transformed into a standard elliptic equation, the boundary conditions and coefficients of the transformed equation are also confirmed by contrasting it with the standard elliptic equation. Then the effects of bearings structural parameters and external supply pressure on the film pressure distribution, load capacity and static stiffness are studied. The film pressure distribution changes significantly with the eccentricity ratio, and an eccentricity range corresponding to the optimal stiffness is also confirmed. Finally, an experimental platform with reversal structure is applied to reduce the measurement error, the maximum relative error between the results of simulation and experimental result is 11.54%.

Improving the stiffness of the aerostatic thrust bearing by using a restrictor with multi-orifice series

To improve the stiffness of the orifice-type aerostatic bearing, a new construction of orifice restrictor with multiple orifices in series was proposed to enhance the restriction effect. The restriction effects of the restrictors with multiple orifices in series were studied numerically. Based on a circular aerostatic thrust bearing with a central feedhole, the effect of the bearing stiffness improved by the restrictors with multiple orifices in series was studied. The results show that the aerostatic bearing with the restrictors with multiple sub-orifices in series shows higher maximal bearing stiffness than the bearing with traditional simple orifice restrictor. For example, the maximal stiffness for aerostatic bearing with the restrictor of four sub-orifices in series is 57 N/µm, which is ∼11% larger than that of the bearing with simple orifice. With this construction, the restriction effect of the orifice restrictor can be enhanced by increasing the number of the sub-orifices, instead of decreasing the aperture of the orifice. This approach avoids the difficulty of manufacturing the orifice restrictor with too small aperture for achieving a high restriction effect. The feasibility of the restrictor with multiple sub-orifices in series proposed in this paper was verified with experimental studies.

Modelling and Simulation of Aerostatic Thrust Bearings

This paper demonstrates the modelling and simulation comparison of the static characteristics of a porous, orifice, and multiple type aerostatic thrust bearings on the basis of load-carrying capacity(LCC) and stiffness. The equations Navier-Stokes (N-S) are used to solve the internal distribution of pressure in computational fluid dynamics(CFD) simulation environment. An axisymmetric model, which minimizes the computational time and increases efficiency, is used to evaluate the static characteristics of a porous, orifice, and multiple restrictors of aerostatic bearings. Our numerical analysis and empirical results show the agreement with the significant effect of material and geometrical parameters on the LCC and stiffness. The thickness of the air film is less than 10μm, the multiple orifice restrictors have more LCC than porous and orifice restrictor. The porous restrictor's stiffness is larger than orifice and multiple restrictors. The LCC of porous and orifice is notably smaller than multiple orifice restrictors. Additionally, it is analyzed that LCC of porous, orifice, and multiple orifice restrictors can be improved with an increase in the supply of air pressure.

Externally Pressurized Thrust Spherical Bearing Performance Under Variable Lubricant Viscosity (Un-recessed Clearance Type)

In a previous study handling this subject, a series of six papers has been published covering the fitted type (equal radii of this sort of bearings) with its configurations in details. The present study handles the same subject investigating the clearance type of this sort of bearings starting with the un-recessed one. The clearance type of bearings, where the sphere radius is smaller than that of the seat, provides plenty of complications and great divergence in its behavior compared with the fitted one. The study investigates theoretically the bearing behavior under the lubricant viscosity variation in the presence of the centripetal inertia due to the shaft rotation and the surface roughness. Solutions have been derived for the un-recessed clearance type of bearings with hemispherical and partial hemispherical seats in addition to its two special cases using capillary tube and orifice restrictors. Unlike other studies, using the conventional integration (i.e., without using the Sommerfeld substitution), only one equation with one form for the pressure gradient is derived to cover the positive and negative eccentricity ratios. Expressions for the pressure distribution, temperature distribution in turn the temperature rise, load carrying capacity; volume flow rate, frictional torque, friction factor, power losses and stiffness factor are obtained. The study shows the combined effects of the viscosity variation, the centripetal inertia and the surface roughness on the bearing performance. The optimum design (with constant viscosity) based on the minimum power losses, minimum flow rate and the optimal restrictor dimensions, in a previous study is checked where it is found out that designing this type of bearings on such basis only is not sufficient in despite of the bearing consistency. A natural dynamic phenomenon ignored in the previous study is revealed and briefly touched.

Comparative characteristics of hydrostatic conical hole-entry journal bearing with CFV, orifice and capillary restrictors

ABSTRACTThe present comparison is mainly based on the type of restrictor employed in the conical journal bearing with hole-entry in hydrostatic mode. It suggests efficient restrictor to be used in the subjected conical journal bearing. To find the characteristics, Reynolds's equation is applied to the fluid present in the space between conical journal and bearing, the flow equations for various restrictors have been presented using FEM. Different parametric characteristics have been obtained for the range of eccentricity ratio () = 0.1–0.7. The outcome of the comparative characteristics depict the significant variations in the restrictor-based conical hole-entry journal bearing performances in hydrostatic mode which may be useful for the bearing designer to precisely design the conical hole-entry journal bearing. Comparatively, the constant flow valve fitted hydrostatic conical journal bearing with hole-entry may be recommended based on the present study.

A Study on Active Closed-Loop Gap Control for Hydrostatic Bearing

In this paper, a hydrostatic bearing controlled by servo-valve for precise closed-loop oil-film gap control is developed. Due to the increasing demands of larger dimension, heavier load and higher precision for current and future machine tools, the development of hydrostatic bearing has become a more and more important issue over the past decades. Nowadays, the most commonly used active pressure feedback restrictor for hydrostatic bearing is membrane type, in which a thin and flexible metal sheet serves as the key component to meter the hydraulic oil flow precisely. However, the membrane type pressure feedback restrictor is not quite suitable for extremely heavy load. Therefore, an alternative to design the active restrictor for hydrostatic bearing using servo-valve is presented in this paper. Different controllers are also designed and compared in this paper. There are two significant features regarding the proposed design. The first one is the introduced orifice restrictor inside the servo-valve which avoids the influence of possible oil temperature variation. The second feature is the introduced closed-loop oil-film gap control scheme that widens the application range effectively. Finally, a test rig of servo-valve controlled hydrostatic bearing is implemented and the experimental results prove the validity of the hydrostatic bearing with the proposed servo-valve and the closed-loop gap control scheme.

Analysis and experimental verification of dynamic characteristics of air spindle considering varying stiffness and damping of radial bearings

The dynamics of a radial bearing and aerostatic spindle system in an ultraprecision fly-cutting machine cause mid-spatial waviness errors, which have a significant effect on surface topographies. Air bearings, which are externally pressurized, comprise two journal bearings and two thrust bearings with orifice restrictors. The dynamic coefficients of the radial bearings are obtained by adopting the perturbation and finite difference methods with the MATLAB® software. In addition, the influences of the spindle speed and tilt angle on the dynamics of the radial bearings are investigated in detail. The simulation results show that the rotating speed has a little impact on stiffness but having a great impact on damping, and the theoretical values of static stiffness are almost the same as the experimental values. The dynamic responses of the spindle system supported by pressurized air film are obtained, and the simulation analysis of spindle responses under cutting forces is also well matched to the experiment results.

Elastohydrostatic simulation of thrust bearing Compensated with orifice restrictor operation with non-Newtonian lubricant

In the present work influence of elastohydrostaic lubrication on orifice compensated bearing has been shown. The thrust pad has been modeled by using three-dimensional mesh and lubrication domain has been modeled by using two dimensional mesh. The analysis of Reynold equation is coupled with the analysis of solution of equilibrium equation of thrust pad domain. The Present results shows that elasticity of thrust pad results a significant decrement in the fluid film Elasticity and it results an increase in fluid film stiffness. In the present case Circular, Elliptical, square and rectangular shape of recess has been taken from the analysis.

Investigation on the static and dynamic characteristics of 3-DOF aerostatic thrust bearings with orifice restrictor

This paper studies the static and dynamic characteristics of 3-DOF aerostatic thrust bearings with orifice restrictor. The coupled perturbation Reynolds equations are solved simultaneously for the first time to obtain the dynamic stiffness and damping coefficients considering the interaction between these equations. The perturbation mass flow rate is considered in determining the numerical convergence of the solution. The developed model demonstrates the nonlinear relationship between air film thickness and pressure. The effect of air film thickness, tilt angles, rotating speed and perturbation frequency ratio on load capacity, load moments, volume flow rate, dynamic stiffness and damping coefficients are evaluated. The results from the developed model provide guidance for design of aerostatic thrust bearing with required static and dynamic performance.

Performance comparison between aerostatic bearings with orifice and porous restrictors based on parameter optimization

ABSTRACT The performance of aerostatic bearing mainly depends on the throttling effect of its restrictor. The orifice and porous material are the most common restrictors, which have their own advantages and suitable working conditions. At present, there are many studies on the performance comparison of bearings with the two types of restrictors, but almost all of them are carried out on the premise of the determined restrictor parameters, the results of the comparison will vary greatly due to the different restrictor parameters. In order to avoid this problem, the CFD software was used to simulate the flow field in the film based on the theory of gas lubrication. The dynamic and static characteristics of the two kinds of bearings were obtained, and the optimal restrictor parameters were optimized. Based on parameter optimization, the bearing performances were analysed and compared. The study reveals that for the single-restrictor aerostatic bearing, the use of porous restrictor can make the bearing obtain superior dynamic and static performances; For the multi-restrictor aerostatic bearing, the use of the orifice restrictor can make the bearing obtain quite high stiffness, but the use of the porous restrictor can enable the bearing to achieve a considerably high load capacity.

Design optimization of high-precision aerostatic equipment based on orifice restriction

The aerostatic lubrication model with orifice restriction is built based on finite difference method. The model is solved by combination of flux-error feedback and optimization of grids parameter. The stiffness of aerostatic bearing can be improved by reducing the diameter of the orifice, but the optimum working gas gap is reduced and the processing difficulty of surface throttle is improved. The experiments of load and stiffness are carried out on the slider (50 × 50 mm) with the diameter of orifice at 50 µm. The experimental results and theoretical calculation are in good agreement; thus, the model is verified. The structural parameter of two, three, and four orifice gas-bearings is optimized, respectively, based on the proposed model, and the optimum positions of the orifices are obtained. According to the results, the aerostatic bearing guideways, made up of optical material (K9), are manufactured by some optical ways, and the lubrication of the small gas gap is guaranteed; meanwhile, the straightness accuracy of the aerostatic bearing guideways is 0.1 µm/200 mm. The analysis result verifies that the calculation method and the aerostatic lubrication model are significant to the design of high-precision aerostatic equipment.

Numerical analysis of the dynamic performance of aerostatic thrust bearings with different restrictors

This study utilizes a dynamic mesh technology to investigate the dynamic performance of aerostatic thrust bearings with orifice restrictor, multiple restrictors, and porous restrictor. An experiment, which investigates the bearing static load capacity, was carried out to verify the calculation accuracy of dynamic mesh technology. Further, the impact of incentive amplitude, incentive frequency, axial eccentricity ratio, and non-flatness on the bearing dynamic performance was also studied. The results show incentive amplitude effect can be ignored at the condition of amplitude less than 5% film thickness, while the relationship between dynamic characteristics and incentive frequency presented a strong nonlinear relationship in the whole frequency range. The change law of dynamic stiffness and damping coefficient for porous restrictor was quite different from orifice restrictor and multiple restrictors. The bearing dynamic performance increased significantly with the growth of axial eccentricity ratio, and the surface non-flatness enhanced dynamic performance of aerostatic thrust bearings.