The deformation of bodies in contact (with special reference to those used in work-holding fixtures)

This thesis presents the analytical studies of the behaviour of the bodies in contact, particularly with reference to those used in work-holding fixture systems under the action of a static loading. The analyses lead to the development of formulae to predict the deformation of three different systems which commonly occur in practice. For the case of a spherical locator in contact with a flat work-piece, the limit of elasticity is reached so early that the work-piece always deform plastically. Hardness and Meyer constant play important roles in determining the diameter of the indentation and hence the total deformation of the system at the contact zone. The theoretical predictions are in agreement with the experimental values. Shawski's empirical formulae do not follow the experimental results very well, particularly for hard work-pieces, his formula gives negative deformations. For the case of a flat locator in contact with rough surface work-pieces of varying hardness, the asperities deform plastically while the material supporting them deforms elastically. The peak heights of the asperities are assumed to be isotropic and represented by the normal probability distribution. The deformation of the asperities can be evaluated accurately by the theory of Williamson up to q/M = .1 where q and M are the applied pressure and the Meyer hardness of the work-piece respectively. Our theoretical predictions for the deformations of the rough work-pieces indented by a flat locator show better agreement with the empirical formulae of Shawki than the theoretical curves proposed in his article. The compression of a cylinder by two narrow bands of pressure of distribution [formula here] (β is a real number) is found. The displacement of a semi-infinite solid under the same band of pressure is similarly derived. These results are combined with the deformation of the asperities to produce the approach of two hard planes compressing a rough turned cylinder of the same material. The asperities deform plastically while the material of the cylinder supporting the asperities and the planes deform elastically. The analysis ceases to apply when the cylinder and the planes start deforming plastically. This study may be used as an approximation for the evaluation of the approach of two Vee locators compressing a rough cylinder investigated by Shawki