Optimum Design of an Abrasive Disk

The minimum weight design of an axisymmetric rotating abrasive disk in the presence of a side tool load is obtained under the strength and stiffness constraints. The PARS (Programs for Analysis and Resizing of Structures) system which employs an optimization procedure based on a mathematical programming method using the Sequence of Unconstrained Minimization Technique (SUMT) is used. The derivatives of the inertia load vector which depends upon the resized dimension (thickness) of the disk are obtained analytically. They are needed in the computation of the derivatives of stresses and displacements, which are also obtained analytically. Due to symmetry, only half of the abrasive disk is modelled using general plate finite elements having bending and extensional stiffnesses. It is shown that by permitting tapered radial thickness distribution, a lighter and much stronger design can be achieved as compared to disks of uniform thickness.