An extension of the Hertz theory for three-dimensional coated bodies

This paper presents a work on extending the Hertz theory for circular and elliptical point contact problems involving coated bodies. The extended form of the Hertzian formulae are adopted to express maximum contact pressure, contact radius, and contact approach in terms of applied load, equivalent radius, and an extended equivalent modulus that properly considers the presence of a coating. The extended equivalent modulus is a function of Youngs moduli and Poissons ratios of the coating and the substrate, coating thickness, and a parameter, which is obtained through substantial numerical simulation. The extended Hertzian formulae are easy to use and give accurate predictions of contact characteristics.     

Using normal approximation for calculating the p-value in assessing process capability index Cpk

When a process is in a perfect state of statistical control, the process capability indices are widely used to measure the capability of the process to manufacture items within the required tolerance. Most evaluations on process capability indices focus on point estimates, which may result in unreliable assessments of process performance. The index C_pk has been used in various manufacturing industries to provide a quantitative measurement of the performance of the manufacturing. In this paper, based on the theory of statistical hypothesis testing, we propose a procedure on assessing C_pk index for practitioners to use in determining whether a given process as capable. Applying Hamakers approximation, the testing procedure can be adequately derived from a normal distribution approximation, which avoids the more complicated non-central t-distribution. The provided approach is easy to use and the decision making is more reliable.     

A methodology for extracting dimensional requirements for a product from customer needs

Dimensional requirements greatly influence the performance of a product, yet there is no systematic process for determining them. Often as a result, some dimensional requirements are overlooked at the design stage, which forces costly changes at a latter stage of product realisation (such as manufacture and assembly). A methodology is presented here which will assist extracting the dimensional requirements for a product from the customers needs. It is suitable for use in a Concurrent Engineering (CE) environment and incorporates some of the existing methodologies used in CE viz. quality function deployment, tree diagrams (The New Seven Tools) and Pughs concept selection method. It provides a systematic way of determining the dimensional requirements of a product and establishes clear links between customer needs and the dimensional requirements. These links will help the CE team to understand the product requirements and how they are to be satisfied through the dimensional aspects of a design.     

Alternative optimisation strategies and CAM software for multipass rough turning operations

The development of constrained optimisation analyses and strategies for selecting optimum cutting conditions in multipass rough turning operations based on minimum time per component criterion is outlined and discussed. It is shown that a combination of theoretical economic trends of single and multipass turning as well as numerical search methods are needed to arrive at the optimum solution. Numerical case studies supported the developed solution strategies and demonstrated the economic superiority of multipass strategies over single pass. Alternative approximate multipass optimisation strategies involving equal depth of cut per pass, single pass optimisation strategies and limited search techniques have also been developed and compared with the rigorous optimisation strategies. The approximate strategies have been shown to be useful, preferably for on-line applications such as canned cycles on CNC machine controllers, but recourse to the rigorous multipass strategies should be regarded as the reference for use in assessing alternative approximate strategies or for CAM support usage.Nomenclature d _i depth of cut for theith pass - d _opt optimum depth of cut - d _T total depth of cut to be removed - D _i workpiece diameter before theith pass - D _o,D _m initial and final workpiece diameter (afterm passes) - f _i feed for theith pass - f _max,f _min machine tool maximum and minimum feed - f _opt optimum cutting feed - f _sj, V_sj available feed and speed steps in a conventional machine tool - f _sgl, f_rec optimum and handbook recommended single pass cutting feeds - F _pmax maximum permissible cutting force - L workpiece length of cut - m continuous number of passes - m _H next higher integer number of passes from a givenm - m _HW upper limit to the optimum integer number of passesm _opt - m _L next lower integer number of passes from a givenm - m _LW lower limit to the optimum integer number of passesm _opt - m _o optimum (continuous) number of passes - m _opt optimum integer number of passes - N _a machine tool critical rotational speed whenP _a=P _max - N _max,N _min machine tool maximum and minimum rotational speed - n,n ₁,n ₂,K speed, feed and depth of cut exponents and constant in the extended Taylor's tool-life equation - P _a,P _max machine tool low speed and maximum power constraints - T _i tool-life using the cutting conditions for theith pass - T _L loading and unloading time per component - T _R tool replacement time - T _s tool resetting time per pass - T _T production time per component - T _TDi multi-passT _T equation with workpiece diameter effect - T _TDm, T_TDo multi-passT _T equations with constant diameterD _m andD _o, respectively - T _Topt overall optimum time per component - T _Tsgl optimum time per component for single pass turning - T _{T2re c} handbook recommended time per component - V _i cutting speed for theith pass - V _max,V _min machine tool maximum and minimum cutting speed - V _sgl,V _rec optimum and handbook recommended single pass cutting speeds - V _opt optimum cutting speed - a, E, W empirical constants in theP _a/F _pmax/P _max equations - , , feed, depth and speed exponents inF _pmax andP _max equations     

The Effect of Surface-Active Phospholipids on the Lubrication of Osteoarthritic Sheep Knee Joints: Friction

The synovial fluid aspirate from human joints that have experienced serious traumatic injury has been shown to have lower concentrations of phospholipids when compared with healthy joints. Previous studies provide evidence that synovial fluid constituents, specifically dipalmitoyl phosphatidylcholine (L-DPPC), are highly surface active, capable of rapidly depositing a layer of phospholipids onto glass. Such research has demonstrated that the adsorbed surface layers of synovial surfactant are excellent lubricants in vitro, significantly reducing the coefficient of friction under physiological loading in human knee joints. This study aimed to investigate the effect of concentration of L-DPPC lubricant solutions on the coefficient of friction of worn articular cartilage on steel. A pin-on-disc apparatus was used to measure the coefficient of friction of sheep-knee articular cartilage on steel under unidirectional sliding at physiological conditions of load and speed. Concentrations of L-DPPC solution between 100 times less and 100 times more than is normally present in synovial fluid were tested. All specimens were tested following a period of unlubricated induced wear. Trials were carried out at ambient temperature and between 33–37°C (representative of in vivo joint temperature). Friction measurement results demonstrated a reduction in the coefficient of friction of worn articular cartilage against steel with increasing concentrations of L-DPPC in lubricant solution.     

Selecting distribution centre location using an improved fuzzy MCDM approach

A distribution centre (DC) is usually supplied by manufacturing factories and in turn it supplies the consumers. To reduce transportation costs and enhance operation efficiency, selecting a suitable DC location has become a very important issue for both manufacturing and distribution industries. Recently, Chen [1] proposed a fuzzy MCDM (multiple criteria decision-making) approach to selecting the location of a distribution centre. Despite its merits, two limitations were found in his works, i.e. follows: (1) the final fuzzy evaluation value P _i was treated as a triangular fuzzy number. This is not correct because it may not produce a triangular shape and (2) the difference of two final fuzzy evaluation values, i.e. P _i –P _j , was regarded as a triangular fuzzy number. This is also incorrect. Obviously, P _i –P _j may not produce triangular shape because P _i and P _j may not be triangular fuzzy numbers. To resolve the above limitations and enhance the applicability of the fuzzy MCDM to the DC location selection problem, an improved fuzzy MCDM approach is proposed. In this work, the membership functions of P _i and P _i –P _j are developed to construct an improved fuzzy preference relation, which is further employed with the Chen ranking procedure to complete the proposed method. Finally, a numerical example demonstrates the feasibility of the proposed method.     

Computation of a turbulent natural convection in a rectangular cavity with the low-reynolds-number differential stress and flux model

A numerical study of a natural convection in a rectangular cavity with the low-Reynoldsnumber differential stress and flux model is presented. The primary emphasis of the study is placed on the investigation of the accuracy and numerical stability of the low-Reynolds-number differential stress and flux model for a natural convection problem. The turbulence model considered in the study is that developed by Peeters and Henkes (1992) and further refined by Dol and Hanjalic (2001), and this model is applied to the prediction of a natural convection in a rectangular cavity together with the two-layer model, the shear stress transport model and the time-scale bound model, all with an algebraic heat flux model. The computed results are compared with the experimental data commonly used for the validation of the turbulence models. It is shown that the low-Reynolds-number differential stress and flux model predicts well the mean velocity and temperature, the vertical velocity fluctuation, the Reynolds shear stress, the horizontal turbulent heat flux, the local Nusselt number and the wall shear stress, but slightly under-predicts the vertical turbulent heat flux. The performance of the model is comparable to that of the low-Reynolds-number differential stress and flux model except for the over-prediction of the horizontal turbulent heat flux. The two-layer model predicts poorly the mean vertical velocity component and under-predicts the wall shear stress and the local Nusselt number. The shear stress transport model predicts well the mean velocity, but the general performance of the shear stress transport model is nearly the same as that of the two-layer model, under-predicting the local Nusselt number and the turbulent quantities.