Computer Analysis and Optimal Design of Mechine Elemennts

The subject machine elements is traditional a research field where standards have a significant influence on the design, i.e. the keyway in a shaft has a given shape and size dictated by a standard. This is important for the interaction between different elements produced at different locations, other examples of standardized components are bolts and gears. The standard designs are typically very good, many years of experience have gone into the design process. The design consists in most cases of straight lines and circular arches, not including e.g. the involute shape of gears. The standard cutting rack for the involute gear is however made from straight lines and circular arches. The optimization objective is strength and the focus is on fatigue. The designs are improved by lowering the stress concentrations that controls the strength. In the lecture the following components are discussed; bolts-plate connections, shaft- hub connections and gears. Overall the different components are improved by shape optimization using the finite element method for analysis. The optimality criteria states that the designs are optimal when the stress along the boundary is constant if possible. For bolts it is shown how design changes, that does not influence the function, can greatly improve the strength. The function is unchanged because even though the thread design is modified it can still be combined with the standard design. For gears the contacting surface has the involute shape and should not be changed, instead the design changes are made to the gear root where there is no contact and therefore total design freedom. The final machine elements that are presented are shaft-hub connections, i.e. keyways and splines, also for these elements design changes that does not influence the function are shown to have a large impact on the fatigue strength. For machine elements it is important that all design changes made by shape op- timization are practical, i.e. that the shape can be communicated to the users and subsequent produced. It is therefore essential that the parametrization of the shape to be designed is simple. In most of the cases presented a super elliptical parametriza- tion is used, sometimes in the standard form but typically also distorted such that slope constraints at the end point of the design domain can be meet.