Calculation of the stress-strain state of a chord flywheel with spokes

Abstract

We shall examine a system consisting of n chords (spokes) on each side of the equatorial plane of the flywheel. It is assumed that the chords are secured rigidly at the points of intersection and do not rotate in relation to each other. Since the symmetry of the system of the chords is not violated during uniform rotation, all the chords are deformed in the same manner and, consequently, their intersection points are displayed only in the radial direction. In this formulation, the problem of the system of the chords can be reduced to the problem of a single multiple-supported bar (semichord) with the given direction of displacement in the supports (points of intersection with other chords) (Fig. 2a). The multiplesupported rod is loaded with inherent centrifugal forces and by force F at the outer end, which is determined from the conditions of compatibility of displacement of the rod and the rim. Thus, the rod is loaded by longitudinal--transverse bending with tensile loading. The solution of this problem in complete formulation is quite complicated, and it is therefore useful to initially examine several simplifications and, above all, assess the contribution of longitudinal bending to the stress state. For this purpose we shall examine the case in which the effect of longitudinal bending may be strongest, and investigate the problem of a flexible two-support rod which does not interact with the rim and is loaded with centrifugal forces from a uniformly distributed mass (Fig. 2b). The problems associated with loading of flexible rods have been examined in [6, 7]. The given problem differs from the above problem in the loading mode and the fact that the extensibility of the rod is taken into account to a certain extent. 2. Let it be that (x, to) are the coordinates of the element of the rod in the unde