Fiabilitate si Durabilitate - Fiability & Durability no 2(6)/ 2010 Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X 79 NUMERICAL VERSUS ANALYTICAL METHOD IN FINDIG STRESS STATE IN MECHANISMS ELEMENTS Assoc. Prof. Stelian ALACI, Suceava University, Lecturer Florina Carmen CIORNEI, Suceava University, Professor Dumitru AMARANDEI, Suceava University, Assoc. Prof. Constantin FILOTE, Suceava University, Assoc. Prof. Delia-Aurora CERLINCĂ, Suceava University, Lecturer Luminiţa IRIMESCU, Suceava University. Abstract: The finite element method is applied to find the stress field from the parts of a wobble plate mechanism. There are thus identified the most stressed component elements and the respective regions. For the two contact neighbourhoods where stress concentrators occur, the maximum contact pressure is found by analytical methods and afterwards compared to the numerical results. Keywords: finite element, gradients, derivatives equations. 1. Introduction The elements of a mechanical structure work together, most of them either by direct contact or by means of electric or magnetic fields, cases that are seldom met and especially in electric drives, armature cores etc. For the parts from the first category, the contact can be accomplished in two ways, [1], namely contact characterized by broad surfaces or conforming contact, as in the case of sliding bearings, or, secondly, Hertzian contact, where there is no initial contact surface, for instance, as in ball bearings, cams and gears. These Hertzian contacts are characterized by strong stress gradients and solutions are required to diminish the maximum contact pressure in order to avoid material failure. The stress state for a certain part, whit précised loads and under the assumptions of elastic strains is found using the relations from theory of elasticity. These equations, which are partial derivatives equations, need finding a particular solution to satisfy the imposed boundary and initial conditions, [2]. Alas, due to the form taken by the boundary conditions, only some elasticity problems present analytical solutions. The necessity of stress field estimation in mechanical parts for an optimum design imposed at a large scale level the numerical methods, [3]. These methods proved to be an extremely efficient but discrimination should be considered when using them. It is recommended that the numerical results of a certain problem to be compared, when possible, to the analytical result when the last exists, or to apply the numerical model to a simplified problem which presents a known analytical solution. The present paper aims to apply and emphasize the above aspects by using the exposed methodology for an actual case, namely the wobble plate mechanism. 2. Stress evaluation from mechanism finite element modelling The swash plate mechanism is in fact a spatial mechanism, [4], with frontal cam, for which a scheme is presented in Figure 1. The mechanism consists of a disk, 1, assembled on a shaft so as between the normal to the disk plane and the shaft axis the α angle appears. A plunger linked to the ground through the prismatic joint, contacts the disk. The stresses in the plate-follower contact region are infinite and decreasing them requires increasing the curvature radius, and the mechanism appears as shown in Figure 2. In this new representation the contact stresses between sphere and plate are particularly high, yet.