Nonlinear Thermoelastic Behavior of Structural Joints—Solution to a Missing Link for Prediction of Thermal Deformation of Machine Tools

The analysis of the process of heat transfer across the joints in machine tool structures reveals their non-linear thermoelastic behavior. Nonlinearity basically results from two distinctive causes. First, it is the material nonlinearity due to the fact, that the stiffness of the surface asperities takes a nonlinear, load-dependent form. The second cause is the nonlinearity resulting from the thermoelastic behavior of contacting elements, which experience a closed-loop interaction between the thermal field and the thermal deformation of structural elements in contact. This interaction affects the distribution of the contact pressure along the joint and causes a consequent redistribution of the thermal contact resistance. As a result, the final pattern of deformation depends on the final contact pressure distribution which is unknown in advance. The nonlinear thermoelastic behavior of the joint is inherent to the process of heat transfer across the interface. By considering this behavior of the joint, characterized by the time-dependent distribution of the thermal contact resistance along the interface, thermal deformation of the whole structure can be treated with thermally interacting structural elements taken into account. This was a missing link in predicting the thermal deformation. As a solution, a consecutive-iteration technique is proposed, which, with introduction of contact elements representing equivalent properties of the joint, allows us to portray the thermal deformation of the structure under transient and steady state conditions.