Concept evaluation and contact problems in simple rotordynamical systems

Sammanfattning: Rotating machines serves an important role in many different applications. Extensive research has been made, manly during the last century, in order to develop these systems and understand the dynamics. The theory of rotordynamics differs in many fundamental aspects from structural dynamics and is therefore usually treated as an own research area. In rotordynamical applications there exist several qualitatively different concepts. For example super- and subcritical machines supported on different types of bearings like ball-, roller- or journal bearings etc. At the early stage of the product development, the problem is often to find a general tool which can be used for dynamical evaluation of these concepts. Many concepts also contain significant nonlinearities which need to be studied separately. One such nonlinearity is a clearance which arises between a fixed support and an axially movable bearing assembly. Another nonlinear effect is the loss of contact which can occur in preloaded spherical roller thrust bearings. The aim is hence to present a method to dynamically evaluate different rotordynamical concepts, describe nonlinear effects due to these contact problems and suggest suitable design parameters. For the concept evaluation a linear model which captured the gyroscopic effect is proposed, while the contact problems are handled with nonlinear models (usually piecewise linear). The governing equations of motion are solved analytically in the linear case but needs to be simulated in the nonlinear cases. However, in some special cases it is possible to find steady state solutions even for the contact problems. Simulations of design spaces, Poincaré maps, bifurcation diagrams, Lyapunov exponents, contact forces etc. have been used to study the systems. In order to evaluate different concept, design spaces spanned by a requirement variable and three design parameters are plotted. These are four dimensional plots where the variations of the requirement variables are visualised by colours. This is done both for the unbalance response and an impact in order to include both the homogenous and particular solution. In the clearance problem bifurcation diagrams and Poincaré maps indicates that multi-, quasi- or chaotic motions are possible which in many cases include impacts. When stabilising rods are applied the unstable areas (positive maximum Lyapunov exponent) are reduced. In the case with the spherical roller thrust bearings nonperiodic motions are found. The stability shows strong dependency on the amount of preload. A method to dynamically evaluate rotordynamical concepts is suggested. Some especially interesting ranges of the design parameters which give low vibrations are presented. It has further been shown that strong nonlinear dynamics which may lead to failure can be expected in systems with clearance between the stator and bearing assembly. One way to get rid of such unwanted vibrations is to apply stabilising rods. It is than important to choose the right parameters since otherwise worse conditions may occur. In systems supported by preloaded spherical roller thrust bearings it is important that the preloading is high enough. Otherwise jump phenomenon and nonperiodic motions can arise. An expression of the limit preload of going in or out of full contact has been derived which can be used to choose a suitable preloading.