A Reduced Model of Higher Order Composite Rotor using Balanced Realization Technique

Abstract

A tangential force to whirl orbit is introduced due to internal damping of rotors, which is also proportional to spin speed and causes instability after certain speed. Literature shows that the improvement in the stability range can be achieved by using fibre reinforced composites or layered rotors which are light yet strong and exhibit better damping properties. In this work, a unidirectional long fibre reinforced composite rotor is considered, where both fibre and matrix materials are assumed to be visco elastic. Viscoelastic behaviour is modelled by using internal variable approach like An elastic Displacement Field (ADF) and constitutive relationship is formed. This is further converted to operator based constitutive relationship. Euler-Bernoulli beam theory is adopted to obtain the equation of motion through operator based approach; subsequently finite element method is employed to discretize the rotor shaft continuum. The rotor-disc system is analysed considering simply supported boundary condition at its two ends. Due to consideration of visco elastic properties of fibre (Graphite) and matrix (Epoxy), the order of equation of motion increases depending upon the number of an elastic fields that are used to delineate the constitute property of material. State space transformation is used to convert the higher order equation motion to first order differential equation, which is numerically more efficient to solve. By this transformation, the system matrix size increases drastically resulting again to a complex system with huge number of states. The main aim of this paper is to incorporate balanced model order reduction method, which is implemented to reduce the size of the system matrix to considerable amount. It is demonstrated that balance realization approach support reduction process by guaranteeing that the transformation matrix for all lessened mode is controllable and observable. The advantage of implementing this procedure is to handle the issues caused because of skew-symmetric matrices that are originated because of the addition of material internal damping and gyroscopic effects. Under these conditions, a relative study is performed between full model and reduced model considering various parameters such as Campbell Diagram, Decay rate and modal damping factor. Good agreement amongst reduced and full system predicts the usefulness of the investigation.