System Approach to the Thermal Behavior and Deformation of Machine Tool Structures in Response to the Effect of Fixed Joints

Abstract

Following the theory of nonlinear thermoelastic behavior of structural joints, developed recently by the authors, the conditions of heat transfer between contacting elements are analyzed. Two cases are considered: a hypothetical case in which no interactions take place at the joint, and a realistic one with the interactions in effect. Analysis of the structure response to the effect of the joint is carried out through the system theory, which is a new way to approach this problem. It is revealed that due to the interactions at the joint, the structure behaves thermally as a second order system, and not as a first order system. The latter would be the case if the nonlinear thermoelastic behavior of the joint were neglected. This finding, obtained in general terms, indicates that the thermal deformation of machine tool structures can vary nonmonotonically with time. This was verified through a computer simulated case study and was confirmed by existing experimental data.