In rolling bearing analysis Hertzian contact theory is used to compute local contact stiffness. This theory does not have a closed form analytical solution and requires numerical calculations to obtain results. Using approximations of elliptical functions and with a mathematical study of Hertzian results, an empirical explicit formulation is proposed in this paper and allows us to obtain the dimensions, the displacement, and the contact stress with at least 0.003% precision and it can be applied to a large range of ellipticity of the contact surface.
In order to optimize the mechanical behavior of high speed rotors, it is useful to know the load-displacement law of the angular-contact ball bearing. The relationship between preload, speed, and contact angle is studied and a new analytical approach is proposed, giving explicitly and with good precision the contact angle versus preload and rotational speed for the special case of elastically preloaded high speed angular-contact ball bearing.
Uncertainty in product characteristics is ubiquitous in any engineering system at all the stages of product life-cycle. Considering uncertainty from different sources during the product design phase is critical to its reliable performance. This paper presents a framework integrating the uncertainty propagation through different product characteristics and its effect on product properties. The framework consists of three main parts: a descriptive model based on formal logic and characteristics properties model; a mathematical implementation through set theory and probabilistic approach; and an algorithm for design space evaluation and tolerancing. The application of framework is demonstrated through an industrial case study.
Variation Management during the Product & Process Development can profoundly impact the quality, the cost of the product and the number of scraps in mass production… Designers want tight tolerances to ensure product performance; manufacturers prefer loose tolerances to reduce manufacturing and assembly cost. To analyse compromise solutions, the primary aim is to establish an objective function. This paper presents a model for the key indicators assessment to the relevance of variation management: cost, and investigates which model used in decision analysis is the most appropriate to prioritize and aggregate the predetermined performance measures. The applications of this model are demonstrated through an industrial case study where tolerance allocation, product development, problem is firstly addressed. Once optimized tolerances are attained, inspection planning, process development, problem is approached to ensure the optimized awaited quality level for the least cost.
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