Optimization of Herringbone Grooved Thrust Air Bearings for Maximum Load Capacity

2021 ◽  
pp. 1-25
Author(s):  
Yunluo Yu ◽  
Guang Pu ◽  
Tianchu Jiang ◽  
Kyle Jiang
Keyword(s):  
Load Capacity ◽  
Maximum Load ◽  
Optimization Method ◽  
Numerical Results ◽  
Air Bearing ◽  
The Novel ◽  
Air Bearings ◽  
Thrust Bearings ◽  
Herringbone Grooves

Abstract Many studies in herringbone grooved thrust bearings are focused on searching for the optimal groove parameters to improve the load capacity, but few of them adopting different grooves in different sections. In this study, a novel optimization method of herringbone grooved thrust air bearings is proposed for maximum load capacity by seeking the optimal groove parameters in each section of the bearing independently. An example of an optimized thrust air bearing is presented, and its performance is compared with a non-optimized bearing and a conventionally optimized bearing without dividing grooves into sections. The resultant herringbone grooves are found to have different parameters in the inner and outer sections, which is uncommon in existing grooves. Numerical results show that the novel bearing has a higher load capacity than the non-optimized reference bearing and conventionally optimized bearing. The study shows that the new design can increase load capacity by 30.77%, verified by experiments.

An Accurate Solution of the Gas Lubricated, Flat Sector Thrust Bearing

1977 ◽  
Vol 99 (1) ◽  
pp. 82-88 ◽  
Author(s):  
I. Etsion ◽  
D. P. Fleming
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Thickness Distribution ◽  
Maximum Load ◽  
Accurate Solution ◽  
Operating Conditions ◽  
Thrust Bearings ◽  
Practical Design ◽  
Minimum Film Thickness

A flat sector shaped pad geometry for gas lubricated thrust bearings is analyzed considering both pitch and roll angles of the pad and the true film thickness distribution. Maximum load capacity is achieved when the pad is tilted so as to create a uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves. A comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

An Air Layer Modeling Approach for Air and Air/Vacuum Bearings

1997 ◽  
Vol 119 (3) ◽  
pp. 388-392
Author(s):  
J. M. Pitarresi ◽  
K. A. Haller
Keyword(s):  
Load Capacity ◽  
Load Resistance ◽  
High Load ◽  
Air Bearing ◽  
Air Bearings ◽  
Bearing Surface ◽  
Know How ◽  
Modeling Approach ◽  
Vibrational Characteristics ◽  
High Load Capacity

Air layer supported bearing pads, or “air bearings” as they are commonly called, are popular because of their high load capacity and low in-plane coefficient of friction, making them well suited for supporting moving, high accuracy manufacturing stages. Air/vacuum bearings enhance these capabilities by giving the bearing pad load resistance capacity in both the upward and downward directions. Consequently, it is desirable to know how to model the air layer between the bearing pad and the bearing surface. In this paper, a simple finite element modeling approach is presented for investigating the vibrational characteristics of an air layer supported bearing. It was found that by modeling the air layer as a bed of uniform springs who’s stiffness is determined by load-displacement tests of the bearing, a reasonable representation of the response can be obtained. For a bearing supported by air without vacuum, the dynamic response was very similar to that of a freely supported bearing. The addition of vacuum to an air bearing was found to significantly lower its fundamental frequency which could lead to unwanted resonance problems.

Design Optimization of Gas Foil Thrust Bearings for Maximum Load Capacity

2015 ◽  
Author(s):  
Tae Ho Kim ◽  
Tae Won Lee
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Drag Torque ◽  
Rotor Speed ◽  
Design Guideline ◽  
Film Pressure ◽  
Thrust Bearings ◽  
Minimum Film Thickness

Improvement of the load capacity of gas foil thrust bearings (GFTBs) is important to broadening their application in oil-free microturbomachinery (<250 kW) with high power density. Although GFTBs have the significant advantage of low friction without the use of lubrication systems compared to oil film thrust bearings, their inherently low load capacity has limited their application. The aim of the present study was to develop a design guideline for increasing the load capacity of GFTBs. The Reynolds equation for an isothermal isoviscous ideal gas was used to calculate the gas film pressure. To predict the ultimate load capacity of the GFTB, the pressure was averaged in the radial direction of the gas flow field used to deflect the foil structure. The load capacity, film pressure profile, and film thickness profile were predicted for a GFTB with an outer radius of 55 mm, inner radius of 30 mm, and eight foils each of arc length 45°. The predictions showed that the load capacity of the GFTB increased with increasing rotor speed and decreasing minimum film thickness, and was always lower than the analytically determined limit value for infinite rotor speed (obtained by simple algebraic equations). A parametric study in which the ramp extent (or inclined angle) was increased from 5° to 40°, and the ramp height from 0 to 0.320 mm, revealed that the GFTB had an optimal ramp extent of ∼22.5° and ramp height of ∼0.030 mm for maximum load capacity. Interestingly, the optimal values were also valid for a rigid-surface bearing. The predicted load capacities for a ramp extent of ∼22.5° and increasing ramp height from 0.030 to 0.320 mm were compared with experimental data obtained from a previous work. The predictions for a ramp height of 0.155 mm were in good agreement with the experimental data for all three test GFTBs with outer radii of 45, 50, and 55 mm, respectively. In addition, this paper shows that the predicted drag torque increases linearly with increasing rotor speed and decreasing minimum film thickness, and nonlinearly with decreasing ramp height. The drag torque significantly increased only for ramp heights below the optimal value. The predictions imply that the optimal ramp height improves the load capacity of the GFTB with little change in the drag torque.

scholarly journals EFFECT OF SURFACE ROUGHNESS ON STEADY PERFORMANCE OF HYDROSTATIC THRUST BEARINGS: RABINOWITSCH FLUID MODEL

2019 ◽  
Author(s):  
Udaya Pratap Singh
Keyword(s):  
Surface Roughness ◽  
Carrying Capacity ◽  
Load Capacity ◽  
Numerical Results ◽  
Integral Approach ◽  
Load Carrying Capacity ◽  
Film Pressure ◽  
Thrust Bearings ◽  
Longitudinal Roughness ◽  
Load Carrying

Purpose of the present theoretical investigation is to analyze the effects of surface roughness on the steady-state performance of stepped circular hydrostatic thrust bearings lubricated with non-Newtonian Rabinowitsch type fluids. Results for film pressure and load-carrying capacity have been plotted and analyzed on the basis of numerical results. To take the effects of surface roughness into account, Christensen theory of rough surface has been adopted. The expression for pressure gradient has been derived by means of the energy integral approach. This approach avoids the derivation of Reynolds’ equation. The numerical results for film pressure and load capacity have been obtained using Mathematica. It was observed that in comparison with smooth surfaces, dimensionless film pressure and load capacity is lower for longitudinal roughness and higher for circular roughness patterns with and the variations are significant. Load carrying capacity decreases with the increase of longitudinal roughness and, increases with the increase of circular roughness. Further, the effects of surface roughness and non-Newtonian lubricants are significant for larger values of inertia parameter. Because of the closeness of results to the experimental values, this study will be helpful in the design of circular hydrostatic thrust bearings.

Design Optimization of Gas Foil Thrust Bearings for Maximum Load Capacity1

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Tae Ho Kim ◽  
Moonsung Park ◽  
Tae Won Lee
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Ideal Gas ◽  
Outer Radius ◽  
Test Results ◽  
Rotor Speed ◽  
Design Guideline ◽  
Film Pressure ◽  
Thrust Bearings

The aim of the present study is to develop a design guideline to improve the load capacity of gas foil thrust bearings (GFTBs). The Reynolds equation for an isothermal isoviscous ideal gas calculates the gas film pressure. The film pressure averaged in the radial direction determines the ultimate load capacity. The load capacity, film pressure profile, and film thickness profile are predicted for a GFTB with an outer radius of 55 mm, inner radius of 30 mm, and eight foils each of arc length 45 deg. The predictions show that the load capacity of the GFTB increases with increasing rotor speed and decreasing minimum film thickness. A parametric study, in which the ramp extent (or inclined angle) is increased from 5 deg to 40 deg, and the ramp height from 0 to 320 μm, reveals that GFTBs have an optimal ramp extent of ∼22.5 deg and ramp height of 30 μm for maximum load capacity. A series of maximum load capacity measurements are conducted on four test GFTBs with ramp heights of 50, 150, 250, and 350 μm at the speeds of 12, 15, and 18 krpm. To estimate the maximum load capacity, the applied load is increased until the drag torque rises suddenly with a sharp peak. The test results show that the maximum load capacity generally increases for decreasing ramp height and for increasing rotor speed. The GFTB with a ramp height of 50 μm shows the largest maximum load capacity of 510 N, for example. Test results are in good agreement with model predictions.

A Miniature Linear Slide With Air Bearings and Its Implementation in a Mesoscale Precision Turning Machine

2007 ◽  
Author(s):  
Seung-Kook Ro ◽  
Byung-Sub Kim ◽  
Jong-Kweon Park
Keyword(s):  
Permanent Magnets ◽  
Thrust Force ◽  
Load Capacity ◽  
Linear Motor ◽  
Air Bearing ◽  
Air Bearings ◽  
Vertical Stiffness ◽  
Single Crystal Diamond ◽  
Micro Turning ◽  
Single Crystal Diamond Tool

In this paper, we propose a new miniature air-bearing stage with a moving-magnet slotless linear motor. This stage was developed to achieve the precise positioning required for submicron-level machining and miniaturization by introducing air bearings and a linear motor sufficient for mesoscale precision machine tools. The linear motor contained two permanent magnets and was designed to generate a preload force for the vertical air bearings and a thrust force for the stage movement. The characteristics of the air bearings, which used porous pads, were analyzed with numerical methods, and a magnetic circuit model was derived for the linear motor to calculate the required preload and thrust forces. A prototype of a single-axis miniature stage with dimensions of 120 × 120 × 50 mm3 was designed and fabricated, and its performance was examined, including its vertical stiffness, load capacity, thrust force, and positioning resolution. Two fabricated stages were then used for the X and Z-axes of a mesoscale micro-turning machine combined with an air-bearing spindle to investigate the effectiveness of the proposed system. A mirror surface was machined from an aluminum alloy with a single-crystal diamond tool.

Optimal Control and Path Planning of a 3PRS Robot Using Indirect Variation Algorithm

Robotica ◽  
2019 ◽  
Vol 38 (5) ◽  
pp. 903-924 ◽  
Author(s):  
H. Tourajizadeh ◽  
O. Gholami
Keyword(s):  
Optimal Control ◽  
Lagrange Multipliers ◽  
Inverse Dynamics ◽  
Null Space ◽  
Load Capacity ◽  
Optimal Path ◽  
Maximum Load ◽  
Optimization Method ◽  
Matlab Simulation ◽  
Prismatic Joints

SUMMARYIn this paper, optimal control of a 3PRS robot is performed, and its related optimal path is extracted accordingly. This robot is a kind of parallel spatial robot with six DOFs which can be controlled using three active prismatic joints and three passive rotary ones. Carrying a load between two initial and final positions is the main application of this robot. Therefore, extracting the optimal path is a valuable study for maximizing the load capacity of the robot. First of all, the complete kinematic and kinetic modeling of the robot is extracted to control and optimize the robot. As the robot is categorized as a constrained robot, its kinematics is studied using a Jacobian matrix and its pseudo inverse whereas its kinetics is studied using Lagrange multipliers. The robot is then controlled using feedforward term of the inverse dynamics. Afterward, the extracted dynamics equation of the robot is transferred to state space to be employed for calculus of variations. Considering the constrained entity of the robot, null space of the robot is employed to eliminate the Lagrange multipliers to provide the applicability of indirect variation algorithm for the robot. As a result, not only are the optimal controlling signals calculated but also the corresponding optimal path of the robot between two boundary conditions is extracted. All the modeling, controlling, and optimization process are verified using MATLAB simulation. The profiles are then double-checked by comparing the results with SimMechanics. It is proved that with the aid of the proposed controlling and optimization method of this article, the robot can be controlled along its optimal path through which the maximum load can be carried.

Maximum Load Capacity Profiles for Gas Thrust Bearings Working Under High Compressibility Number Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 571-576 ◽  
Author(s):  
I. Iordanoff
Keyword(s):  
Load Capacity ◽  
Maximum Load ◽  
High Load ◽  
Two Dimensional ◽  
One Dimensional ◽  
Thrust Bearings ◽  
Constant Slope ◽  
Compressibility Effects ◽  
Composite Bearing ◽  
Commercial Equipment

To meet the requirements of new commercial equipment, performances of air thrust bearings always have to be improved. This work is concerned with the research of the converging profile that will give high load capacities. When compressibility effects increase (when the compressibility number Λ is over 50), a one-dimensional study shows that the best bearing is a composite bearing, i.e., one in which the leading portion has a constant slope followed by a surface parallel to the runner. For each compressibility number, entrance film thickness H1 and the transition angle θ1 define the best profile. In a two-dimensional study, for compressibility numbers from 10 to 1000, comparison in term of load capacity is made between tapered and composite profiles. It outlines the better load capacity of the composite bearings and confirms the good results obtained by Heshmat (1983) and Gray (1981) with such profiles.

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