Optimal design of one-dimensional porous slider bearings using the Brinkman model

On the basis of the Brinkman model, a theoretical study of the optimal load-carrying capacity and friction coefficient for one-dimensional curved porous slider bearings with the gap width varying slowly is presented. The modified Reynolds equation is obtained by applying Brinkman equations to guide oil motion through the porous matrix. By using the technique of calculus of variations, the optimization is performed over a class of step profiles. According to the analysis, the step height ratio and riser location of the optimal geometry are found to depend upon the permeability parameter of the porous matrix. Compared with the inclined-plane bearing case, the stepped porous slider bearing provides an enhancement in the load-carrying capacity as well as a reduction in the friction parameter. An illustrative design example is also included for engineering and industrial applications.     

Reliability-based design optimization of slider air bearings

This paper presents a design methodology for determining configurations of slider air bearings considering the randomness of the air-bearing surface (ABS) geometry by using the iSIGHT. A reliability-based design optimization (RBDO) problem is formulated to minimize the variations in the mean values of the flying heights from a target value while satisfying the desired probabilistic constraints keeping the pitch and roll angles within a suitable range. The reliability analysis is employed to estimate how the fabrication tolerances of individual slider parameters affect the final flying attitude tolerances. The proposed approach first solves the deterministic optimization problem. Then, beginning with this solution, the RBDO is continued with the reliability constraints affected by the random variables. Reliability constraints overriding the constraints of the deterministic optimization attempt to drive the design to a reliability solution with minimum increase in the objective. The simulation results of the RBDO are listed in comparison with the values of the initial design and the results of the deterministic optimization, respectively. To show the effectiveness of the proposed approach, the reliability analyses are simply carried out by using the mean value first-order second-moment (MVFO) method. The Monte Carlo simulation of the RBDO’s results is also performed to estimate the efficiency of the proposed approach. Those results are demonstrated to satisfy all the desired probabilistic constraints, where the target reliability level for constraints is defined as 0.8.     

Topological design sensitivity on the air bearing surface of head slider

In this study, a topological design sensitivity of the air bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.     

Multi-objective optimization of air bearings using hypercube-dividing method

The commonly used genetic algorithm (GA) in solving a multi-objective optimization problem (MOOP) is replaced by the hypercube-dividing method (HDM) in this air bearing optimization study. In the new method the dividing of hypercubes in the design space is conducted based on the size and Pareto rank of hypercube. A comparison of the HDM- and GA-based method for the MOOP is performed. The results show that the solution obtained by the HDM is improved with more selections and less computing load. The search in the HDM can also be confined to some useful resolution to improve its global search capability.     

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.     

The design of aerostatic bearings for application to nanometre resolution manufacturing machine systems

This paper addresses the design of aerostatic bearings for use within machines requiring nanometre precise translation or rotation. The major design parameters which affect aerostatic bearing performance are discussed. The supply pressure ratio and hence, the bearing clearance and the type and specific size of inlet flow control device are shown to require special consideration. Specific information on the tolerance of each of the parameters which have a direct effect on the nano-precision location of these bearings is given. In addition the paper addresses the manufacturing tolerances and manufacturing variations which can occur in practice and places limits on the magnitude that these sources of errors can contribute to the permissible manufacturing variations.     

A finite element model for rolling contact fatigue of refurbished bearings

Bearing refurbishing has become a popular method of extending the life of rolling element bearings. In the refurbishing process the raceways of the bearing may be ground to remove any surface damage prior to repolishing and reassembly with larger sized rolling elements. In the current study a continuum damage mechanics finite element model was developed to quantify the damage in original and refurbished bearings. After calculating the damage accumulation for a set number of contact cycles with the original bearing geometry, refurbishing is simulated by removing a layer of the original surface. The refurbished microstructural model is then subjected to additional computational contact cycles until a fatigue crack reaches the surface, signifying failure. This model preserves the fatigue damage accumulated prior to refurbishing and evaluates its influence on the refurbished bearing fatigue life. All refurbished bearing surfaces showed a significant amount of life after refurbishing with L₁₀ lives from the point of refurbishment, varying from 20% to 94% of the original L₁₀ life. The results indicate that the remaining life of the refurbished bearing population is inversely related to the time before refurbishing and is proportional to the depth of the regrinding. Results obtained from this investigation are in good agreement when compared to the Lundberg-Palmgren bearing life equation modified for analyzing the life of a refurbished bearing.     

A preload analytical method for ball bearings utilising bearing skidding criterion

The performance of ball bearings is greatly affected by the applied preload. This paper suggests a preload analytical method that accurately determines the optimum preload for different speed ranges. Mathematical models of ball bearings were used to calculate the proper preload. According to Hirano's criterion, the critical preload between the skidding and rolling of ball bearings is calculated as the optimum preload. Experimental results confirmed that the optimum suggested preload instilled the ball bearings with excellent temperature behaviour. This paper provides a foundation for the future development of an optimum preload technique for high-speed ball bearings.     

A new 3-DOF Z-tilts micropositioning system using electromagnetic actuators and air bearings

A new 3-DOF Z-tilts (z, pitch, and roll motion) micropositioning system has been developed. It uses electromagnetic actuators and air bearings. An electromagnetic actuator produces an attraction force between the air bearing and the base plate. An air bearing has the role of suspension and guidance, with a clearance of several tens of micrometers in the z-direction. Therefore, this system has design features of guiding 3-DOF XYθ motion without limiting the plane motion and playing the role of a z-directional position actuator. With the control of current, the equilibrium position between magnetic attraction force and air bearing thrust force can be controlled with inherently infinite resolutions. The theoretical background of an electromagnetic actuator is explained. Then, an air bearing is analyzed in the point of z-directional positioning mechanism. The air bearing can be modeled as a second-order system with parameter variation—stiffness and damping vary with respect to the z-directional displacement. Therefore, a simple robust control algorithm is applied to improve the control performance. With the aid of robust control, this system provides 25 nm positioning resolution over the total range of 40 μm along the z-direction and, accordingly, 0.29 μrad resolution over the total range of 460 μrad in pitch and roll motion.     

A revised design of circular hydrostatic bearings for optimal pumping power

A modification of the circular flat externally pressurized thrust bearing is presented in this paper. This involves the addition of a central step in the bottom of the rotating pad for the purpose of restricting the lubricant flow and minimizing the pumping power required for continuous operation. The performance of such a bearing configuration under static loads is analysed and the key design parameters are discussed, grouped and presented in a design chart. In addition to the minimization of pumping power, the proposed configuration provides higher thrust loads and enables the bearing to withstand radial loads, an advantage which could not be achieved in other hydrostatic thrust bearing configurations. The bearing is also able to restore concentricity due to the lateral damping provided by the squeezed lubricant film in the clearance between the step and the recess.     

基于Autodesk Inventor的三维参数化设计方法

应用三维Autodesk Inventor软件,以机械振动装置中板簧组件为例,介绍了零件的造型建模过程、零件的虚拟动画装配及判断虚拟装配中各零件之间是否相互干涉,从而对干涉的零件进行修改和结构调整的设计过程.体现了Autodesk Inventor软件在三维参数化设计中的强大功能及现代设计的优越性.     

The design and manufacturing of porous scaffolds for tissue engineering using rapid prototyping

This research paper addresses the issue of developing an efficient methodology to design and manufacture a complex scaffold structure of desired porosity required for tissue engineering applications using a novel approach based on fused deposition modelling (FDM) rapid prototyping (RP) technology. The scaffold provides a temporary biomechanical structure for cell growth and proliferation to produce the required body parts. Conventional techniques of scaffold fabrication (such as fibre bonding, solvent casting and melt moulding) generate scaffolds with unpredictable pore sizes due to their limitations in flexibility and control of pore volume and distribution. Moreover, such scaffolds have poor mechanical strength and structural stability. The paper describes an FDM pre-processor that ensures the fabrication of scaffolds of desired porosity and inter-connectivity on the FDM system.     

Process optimal design in non-steady forming of porous metals by the finite element method

A new approach to process optimal design in non-steady forming of porous metals is presented. In this approach, the optimal design problem involving diverse objective functions and design variables is formulated on the basis of the finite element process model, and a derivative-based approach is adopted as the solution technique. The process model, the formulation for process optimal design, the schemes for the evaluation of the design sensitivity, and an iterative procedure for optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach is demonstrated through application to a selected design problem.     

A numerical analysis method based on flow continuity for hydrodynamic journal bearings

A numerical method of hydrodynamic bearing analysis is presented which is simple in concept, yet capable of development to handle complex situations such as dynamic misalignment. It is similar to the finite difference solution of Reynolds equation, but incorporates a more realistic modelling of cavitation. The approach to a numerical solution is direct, and should facilitate a better ‘feel’ for the way in which the physical processes are modelled. Results produced with this analysis are compared with other published data for aligned crankshaft bearings and misaligned sterntube bearings.     

A linear air bearing stage with active magnetic preloads for ultraprecise straight motion

In this paper, we propose a linear motion stage designed with magnetically preloaded air bearings. The magnetic actuators for preloading air bearings were combined with permanent magnets and coils to adjust the air bearing clearance by actively controlling the magnetic force. The system was designed to achieve a simplified configuration of air bearing stage while providing ultraprecise straight motion by actively compensating for the motion errors. The porous aerostatic bearings and magnetic preload actuators were designed and analyzed numerically for a single-axis prototype linear stage driven by a coreless linear motor. A magnetic circuit model was derived for the magnetic actuators. The static stiffness and load capacity of the air bearing stage in the vertical (magnetically preloaded) direction were experimentally measured and compared with the results from the numerical analysis. Motion control laws for three degrees of freedom (i.e., vertical, pitch, and roll motions) were obtained with a high linearity and independence for each axis. The active compensation of three motion errors, the vertical, pitch and roll motion errors were performed through curve-fitting the three errors measured with combination of capacitive gap sensors and a laser interferometer. The errors were reduced from 1.09 to 0.11 μm for the vertical straightness error, from 9.42 to 0.18 arcsec for the pitch motion, and from 2.42 to 0.18 arcsec for the roll motion as level of measured repeatability.     

A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings

Inertia effects in porous material, as well as velocity slip at the porous bearing surface, have hindered the use of simple mathematical models for the analyses of porous aerostatic bearings. Experimental evidence indicated that velocity slip at the porous surface did not obey the Beavers model, but could be approximated by an added equivalent clearance. This experimentally determined clearance value did not bear any direct relationship with the surface roughness of the test specimen. Good agreement between theoretical and experimental results of static load capacity of a porous ceramic test bearing, however, demonstrated the use of this equivalent clearance method, in conjunction with a proposed approximation to correct for inertia effects, as an effective modification to the simple one-dimensional model by Sheinberg.     

变结构体参数设计的一种新方法

变结构体参数化设计一直是参数化设计中的难题,在研究现有变结构体参数化设计中的主要方法一变结构变参数设计和模块化变参数设计的基础上,提出了一种基于样条化变参数设计的新设计方法,分析比较了这三种设计方法的优缺点.研究表明,基于样条化变参数设计方法具有数据储存量小、只需生成某一类型的参数设计样板即可实现一类零件的变结构体变参数设计的优点,用VC++6.0开发环境编制了实现程序,验证了样条化变参数设计方法的可行性.     

A contemporary adaptive air suspension using LQR control for passenger vehicles

Long rides on irregular roads and infrastructure problems like uncomfortable seating have a very bad impact on human body. The passengers suffer not only physical pain but also stress related problems. Airsprings gain more popularity in passenger vehicles with an increase in demand for ride comfort. Ride comfort and vehicle handling, being the two critical factors of a suspension system often contradict each other. This led to an extensive research on active automobile suspension systems. The authors of this article propose an innovative design of adaptive air suspension system with LQR control strategy. The proposed LQR controller is tuned by Particle Swarm Optimization. A dynamic model of an air suspension system used in passenger vehicles was designed and simulated for both passive and adaptive systems in MATLAB. An experimental evaluation was done to check the performance of the adaptive air suspension system on a vibration shaker table. Air suspension is a non-linear system and thus the authors have derived a stiffness equation for the same with minimal assumptions. A comparative analysis between the most commonly used PID controller and proposed LQR controller was performed over bumps, potholes and ISO standard random roads in MATLAB. Simulation results showed that adaptive air suspension system improves the ride comfort by reducing the maximum displacement amplitude of the vehicle over random roads by 31% while ensuring the stability of the vehicle by reducing the settling time by 85%. The experimental results of an adaptive air suspension system subjected to random vibrations of frequencies between 5 Hz to 20 Hz, exhibited a reduction of sprung mass acceleration by about 30% demonstrating that the proposed controller is effective for random vibration inputs.