Hard disc drive air bearing design: modified DIRECT algorithm and its application to slider air bearing surface optimization

Hard disk drives continue to increase in areal data density. This requires air bearing sliders with lower and lower flying heights (FH). Also the uniformity of the FH and the flatness of the roll profile with radius become more critical as the FH gets lower. By using modern optimization techniques, it is possible to optimize slider air bearing surface (ABS) designs according to multiple design goals. In this paper, we discuss two modifications to the DIRECT algorithm: one to handle tolerance and one to deal with hidden constraints. Some numerical experiments were carried out using these modifications and the modified DIRECT algorithm was applied to slider ABS optimization. The results show that these two modifications can improve the efficiency of the DIRECT algorithm and they also provide more flexibility in slider ABS optimization.     

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.     

Shape optimum design of slider bearings using inverse method

This study aims to develop an algorithm for designing the optimum shape of slider bearing and pressure distribution using an inverse method. The proposed algorithm only needs to obtain the load and moment conditions in order to simultaneously estimate the slider bearing shape and the pressure distribution. The algorithm is developed from the Reynolds integral, and from force and moment balance equations. The least-squares error method, variational method, Gauss–Seidel method and Newton–Raphson method are employed to calculate the optimum shape of slider bearing. Simulation results reveal that as the degree of the shape polynomial function increases, there are corresponding gains in the maximum pressure, load and torque are, and a corresponding decline in the minimum film thickness. On the other hand, the lower the degree of the objective shape polynomial function is, the more accurate the estimated slider bearing shape and pressure distribution are. With increases in degree of polynomial and number of grid points, the errors in the estimated slider bearing shape and pressure distribution can be reduced. The initial guessed values of the coefficients for the estimated slider bearing shape (C_j), the position of the maximum pressure (X_m) and the outlet film thickness (H₀) have notable effects upon the estimated results for the present algorithm. Moreover, the greatest error of initial guessed value is that of C_j, followed by X_m, and then H₀. The estimated pressure distributions are more accurate than the estimated values for film thickness. Consequently, the present algorithm is capable of providing accurate results for slider bearing shape and pressure distribution.     

Film height optimization of dynamically loaded hydrodynamic slider bearings

A method is presented to determine the optimal surface shape distribution for a hydrodynamic slider bearing. This is the surface shape distribution that is able to carry a prescribed load while maintaining a maximum separation between the surfaces. This method is first derived for a bearing with constant load and sliding speed. It is subsequently extended for a bearing with periodic load and sliding speed. Results for slider bearings with different shapes, loads and speeds are presented. It is shown that the numerical procedure developed in this paper is numerically more efficient than a reference optimization method.     

Hydrodynamic lubrication of rough slider bearings with couple stress fluids

The combined effects of couple stresses and surface roughness on the performance characteristics of hydrodynamic lubrication of slider bearings with various film shapes, such as plane slider, exponential, secant and hyperbolic, are studied. A stochastic random variable with non-zero mean, variance and skewness is used to mathematically model the surface roughness of the slider bearing’s. The Stokes couple stress fluid model is used to characterize the rheological behavior of the lubricant with polymer additives. The modified expressions for the bearing characteristics, namely pressure, load carrying capacity, center of pressure, frictional force are obtained for the general lubrication film shape on the basis of Stokes microcontinuum theory for couple stress fluids. Results are computed numerically for various film shapes under consideration. It is observed that, for all the lubricant film shapes under consideration, the negatively skewed surface roughness increases the load carrying capacity, frictional force and temperature rise, while it reduces the coefficient of friction. On the contrary, the reverse trend is observed for positively skewed surface roughness. Further, these effects are more pronounced for the couple stress fluids.     

Possibility of surface force effect in slider air bearings of 100 Gbit/in hard disks

The recording density has been increasing in a high rate of 60% per year in the last 10 years. In the next several years it is expected that the recording density will be 100 Gbit/in² and then 1000 Gbit/in². It is said that a spacing of about 5 nm will be necessary for 100 Gbit/in². For two solid surfaces with such a small spacing, it is expected reasonably that the surface force will come into action. In this paper, numerical analysis was conducted to explore the possibility of the surface force for the slider air bearing working with respect to the glide avalanche. The numerical results show that surface force reduces the stiffness of the slider air bearing and the load carrying capacity as well. It is worth noting that, although the decrease in the load carrying capacity may not be significant, the reduction in the stiffness may be critical for many cases. The reduction in the stiffness of slider air bearings due to the surface force may be one of the most important mechanisms of the glide avalanche. The predicted take-off height to overcome the surface force is about several nano-meters. Increasing the pitch angle tends to decreases the take-off height. A lubricant film of about 1 nm will reduce the risk of the glide avalanche in some extent, but increasing the film thickness has little effect.     

Optimal film shape for two-dimensional slider bearings lubricated with couple stress fluids

The shape of a slider bearing is one of the major geometric conditions influencing the performance of the bearing. The aim of this study is to design the optimum shapes of the surfaces of sliders to meet the load and center of pressure demands specified by the designers. The design strategy uses COMSOL Multiphysics software package to solve the modified Reynolds equation derived on the basis of stokes microcontinuum theory. The sequential quadratic programming (SQP) is used to optimize the shape of the slider bearing. Results show that designers seeking to effectively reduce friction should consider a reducing the aspect ratio since it is the most significant parameter affecting optimal friction. In addition, slider bearings should be optimized with a polynomial profile of order 6 to reduce the computational effort and yield a solution that is very close to the solution of higher order polynomials.     

An analytical approach for analysis and optimisation of slider bearings with infinite width parallel textures

This paper introduces an analytical approach to study the textured surfaces in hydrodynamic lubrication regime. For this purpose, a method of integrating the Reynolds equation for slider bearings with surface discontinuities is presented. By introducing appropriate dimensionless parameters, analytical relations for various texture profiles in both indented and projected forms are delivered. These relations express the nature of mathematical dependence between textured bearing performance measures and geometrical/operational parameters. An optimisation procedure is employed to achieve the optimum texturing parameters promoting maximum load capacity, load capacity to lubricant flow rate ratio and minimum friction coefficient for asymmetric partially textured slider bearings.     

Effect of Surface Roughness on Hydrodynamic Lubrication of Slider Bearings

The effect of surface roughness on the performance of hydrodynamic slider bearings is studied. A generalized form of surface roughness characterized by a stochastic random variable with non-zero mean, variance and skewness is assumed to define the bearing surface topography. Various film shapes such as: plane slider, exponential, secant and hyperbolic are considered. The results are obtained for the general lubricant film shape in integral form which are numerically computed for the shapes under consideration. The results are presented both graphically as well as in tabular form. The performance of a rough bearing can be considered in terms of an identical smooth bearing with an equivalent film thickness. It is observed, for the lubricant film shapes under consideration, that the increasing positive values of α, σ and ε decrease the load carrying capacity, frictional force and temperature rise while it increases the coefficient of friction. Increasing positive values of α and ε shift the center of pressure towards the outlet edge. For negative values of α, the increasing value reverses the trend of the effect on performance characteristics which is in conformity with the physical aspects of the problem. A similar trend is observed in case of the effect of negative values of ε. Thus, a negatively skewed surface roughness modifies the performance of the slider bearings whereas the performance of a bearing suffers on account of positively skewed surface roughness. Moreover, it is noticed that in the case of exponential and hyperbolic slider bearings the effect of increasing values of σ is more pronounced whereas in case of plane slider and secant shaped slider this effect is marginal.     

Head slider designs using approximation methods

This paper presents an approach to optimally design the air bearing surface (ABS) of the head slider by using the approximation methods. The reduced basis concept is used to reduce the number of design variables. In the numerical calculation, the progressive quadratic response surface modeling (PQRSM) is used to handle the non-smooth and discontinuous cost function. A multi-criteria optimization problem is formulated to enhance the flying performances over the entire recording band during the steady state and track seek operations. The optimal solutions of the sliders, whose target flying heights are 12 nm and 9 nm, are automatically obtained. The flying heights during the steady state operation become closer to the target values and the flying height variations during the track seek operation are smaller than those for the initial one. The pitch and roll angles are also kept within suitable ranges over the recording band.     

A design model for circular porous air bearings using the 1D generalized flow method

Although the working principles of porous air bearings have been known for many years, most calculation procedures still involve specialized 3D CFD techniques which are not very useful to design engineers who initially require first-order engineering models for feasibility studies. This paper presents a simple design model for a circular porous air bearing based on well-established 1D generalized flow theory. Understanding porous air bearing mechanics is relatively easy with the proposed design model because it captures the essential physical phenomena governing the airflow. Moreover, the 1D model has a very simple architecture that allows easy design synthesis and requires minimal computational requirements. Comparison with experimental data shows accuracy comparable to specialized 3D techniques.     

Refined simulation of friction power loss in crank shaft slider bearings considering wear in the mixed lubrication regime

Friction reduction is a fundamental factor in decreasing fuel consumption of internal combustion engines. During the design stage of the engine the simulation of friction in the crank mechanism plays a vital role to develop optimum solutions. Due to the interaction of oil and elastic structures with rough surfaces in slider bearings, complex simulation models have to be used for representing the relevant physical behavior. The following article is focused on crank shaft slider bearings of large engines.The article describes a procedure evaluated by measurements showing how to model wear profiles of slider bearings to reach a high quality friction forecast. A fundamental influencing factor of bearing friction is given by the mixed lubrication regime and it is considered in the simulation model as part of asperity contact friction and hydrodynamic friction. Further effects result from the compliance in radial and width directions of the bearing structure and the wear of the bearing surface. Furthermore, the specific operating conditions of the slider bearing such as load, temperature, shaft speed and oil characteristics are essential and have to be taken into account.The objective of this investigation is to propose the wear profile of the bearing surface for the simulation model to be treated iteratively, where simulation results for the amount of mixed lubrication are successively assessed. For this purpose an iterative procedure is introduced and validated by measurements on a slider bearing test rig.The applied simulation method is based on elastic multi-body systems; the lubrication film contact is calculated based on Reynolds differential equation via the pressure balance calculated iteratively in the time domain. The model accounting for the mixed lubrication regime is based on the theory of Greenwood and Tripp.     

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.     

A Hybrid Search Algorithm for Porous Air Bearings Optimization

The study deals with the development of a hybrid search algorithm for efficient optimization of porous air bearings. Both the compressible Reynolds equation and Darcy's law are linearized and solved iteratively by a successive-over-relaxation method for modeling parallel-surface porous bearings. Three factors affecting the computational efficiency of the numerical model are highlighted and discussed. The hybrid optimization is performed by adopting genetic algorithm (GA) for initial search and accelerated by simplex method (SM) for refined solution. A simple and useful variable transformation is presented and used to convert the unconstrained SM to a constrained method. In this study, the hybrid search algorithm for a multi-variable design exhibits better efficiency compared with the search efficiency by using the SM. The proposed hybrid method also eliminates the need of several trials with random initial guesses to ensure high probability of global optimization. This study presents a new approach for optimizing the performance of porous air bearings and other tribological components.     

基于神经网络的车辆空气悬架系统阻尼优化

在研究膜式空气弹簧结构参数和受力状况关系的基础上,建立了空气悬架车辆的柔性双质量振动模型,并对模型进行了仿真计算和分析.采用径向基函数神经网络,对空气悬架系统阻尼进行了不同负载工况下的多级优化.结果表明,空气悬架系统阻尼最优值随着载荷的减少而降低,优化阻尼后的车辆,在保证悬架行程的情况下,同时提高了平顺性和轮胎接地性能.     

Performance analysis of Pareto optimal bearings subject to surface error variations

A Pareto optimization study was carried out on a flat pad aerostatic bearing design. Some of the Pareto optimal configurations were then subjected to surface profiling errors including tilt, concavity, convexity and waviness and key performance parameters such as load capacity, stiffness and flow rate determined. From these studies it was concluded that multi-orifice aerostatic flat pad bearings are highly sensitive to surface profile variations and these surface profile variations are inherent limitations of the current manufacturing techniques. A technique to account for the sensitivity to manufacturing tolerance within air bearing optimization studies is also proposed.     

Experimental Comparison of Load/Unload Slider Dynamics For Two Different Pico-Slider Designs

A comparison of Laser-Doppler vibrometry (LDV) and acoustic emission (AE) data is presented for two different slider designs during load/unload (L/UL). The behavior of the slider is measured for three different vertical load/unload velocities using a transparent glass disk with the slider flying at the bottom surface of the disk. The LDV laser spot can be positioned on the slider alrbearing surface during the complete load/unload process with the help of a so-called “periscope.” A characteristic velocity peak during unloading is observed that is caused by the slider pull-off force.     

Multidisciplinary design optimization of a structurally nonlinear aircraft wing via parametric modeling

In this study, the optimization of an aircraft wing design was conducted using multidisciplinary design optimization (MDO), which integrates aerodynamic and structural analysis in considering nonlinear structural behavior. Automation is an absolute necessity to make the MDO framework practical for actual engineering optimization problems. The objective of this research was to develop a fully automated MDO framework in which the entire process is automated through a parametric-modeling approach. The computational fluid dynamics (CFD) grid was generated automatically from parametric modeling using CATIA and Gridgen, followed by automatic flow analysis using FLUENT. The computational structure mechanics (CSM) grid was generated automatically by the parametric methods of CATIA and MSC/Patran. The structure was analyzed by ABAQUS considering the deformation nonlinearity, and the aerodynamic load was transferred from the CFD grid to the CSM grid using the volume spline method. The response surface method was applied for optimization, which helped achieve the global optimum. The developed MDO framework was applied to a wing optimization problem in which the objective was wing weight and the constraints were the lift-drag ratio, wing deflection, and structural stress level. The aspect ratio, taper ratio, quarter-chord sweep angle, skin thickness, and spar flange area were the design variables. The optimization design result demonstrated a successful application of the fully automatic MDO framework.     

A Divide-and-Conquer Parallel Computing Scheme for the Optimization Analysis of Tribological Systems

The trend of using commercial products and open source packages to construct a scalable computer cluster for distributed computing to minimize the execution time of numerical optimization has long been expected. However, in the tribology field progress has been slow due to the complexity of parallel coding and the lack of easy-to-implement parallel algorithms. This study presents an optimization analysis of constrained problems by using a divide-and-conquer scheme suitable for parallel computation. A porous air bearing model of moderate computational load is used to illustrate the optimization procedure. In the optimization process, the design space is subdivided and each of the subdivisions is dealt with by Taguchi's Design of Experiments to achieve the local optimum. The global optimum is then determined when all the local optima are obtained. Two task-assignment strategies in the cluster computing are implemented and discussed. Reasonable speedup and parallel efficiency were obtained for the highly uneven task-load calculations. The approach does not require the knowledge of parallel programming techniques associated with message passing libraries. The presented scheme has high portability, low cost of evaluation process, and algorithm-machine scalability, which should be an easy-to-implement and efficient tool for many tribological studies.     

An Experimental Study of Fretting and Galling in Dental Couplings

Specimens of materials used in dental couplings were tested in a simplified wear test machine which duplicated as closely as possible the actual wear conditions existing in operating couplings. The wear patterns that were obtained by tests of short duration on this machine duplicated those found in service. The results of tests covering the variables load, speed, duration, amplitude of reciprocating motion, surface finish and hardness are presented, together with brief discussions of the effects of these variables.