Integration of Shape Memory Alloys into Low-Damped Rotor-Bearing Systems: Modelling, Uncertainties and Experimental Validation

Rotor-bearing systems are key components in a variety of industrial equipment, as turbines, compressors, pumps etc. They are often subjected to strict requirements with respect to cost of energy and stability. Solutions that meet the requirements often involve: low friction between rotor and bearing, high damping of lateral vibrations and high load-carrying capacity. Gas bearings and passive magnetic bearings are examples with very low friction. However, both examples also have a drawback with respect to very low damping and therefore prone to instability. To increase damping it is relevant to use passive adaptive control through smart materials. Shape Memory Alloys (SMAs) are interesting candidates in that relation, because of their highly temperature sensitive stiffness and mechanical hysteresis, which can be used for damping purposes. The thesis focuses on three main aspects related to the feasibility of integrating SMAs into rotor-bearing systems. The first one involves modelling of the constitutive relations of the metals with emphasis on stabilized cyclic behaviour under controlled temperature conditions. Two well-established phenomenological thermo-mechanical models are employed, and modifications are made to two subparts dealing with the evolution of phase transformations. By using the modifications, it is possible to reproduce experimental observations with higher accuracy. Uncertainty analysis of material parameters is a general theme of the thesis in order to ensure physical validity and identifiability, and to call attention to the inherent uncertainties of model predictions. The second aspect concerns design and modelling of machine elements made from SMAs. Different actuation principles of SMAs are covered, and pseudoelastic elements in pre-tension are found to have the most promising properties. Different element geometries are investigated with focus on helical springs. Several spring models are presented, which use different levels of approximations to the mechanical stress state. The models are compared to experimental results covering different levels of temperature, deformation and loading rate. Generally, there is a good agreement between model predictions and experimental results. The last aspect involves dynamical systems integrated with SMAs to ensure passive adaptive control and damping enhancement. The main system consists of a rigid rotor supported by passive magnetic bearings. A holistic and multidisciplinary approach is used for modelling the system, linking the nonlinear SMA spring, the weakly nonlinear passive magnetic bearings, and the dynamic interaction between the rotor and bearing housings. Theoretical and experimental results show that it is possible to reduce rotor vibrations significantly by changing resonance frequencies through temperature control. At the same time, mode shapes are also controllable, and large vibrations are limited and reduced by hysteretic damping of the SMAs.