Investigation of the influence coefficient method for balancing of flexible rotors systems
Several sophisticated procedures for balancing flexible rotors have been developed during the past two decades. For a variety of reasons, none of these methods has gained general acceptance by practicing balancing engineers. Some of these balancing techniques require a great deal of expertise from the operator. This thesis is dedicated to the research of flexible rotor balancing techniques, and aims to apply some advanced techniques to the field of high-speed rotor balancing. Significant progress in balancing methods for flexible rotors can be achieved by the improvement and optimization of existing balancing techniques. Experimental tests were conducted to demonstrate the ability of the influence coefficient method to achieve precise balance of flexible rotors. Various practical aspects of flexible- rotor balancing were investigated. Tests were made on a laboratory quality test rig having a 3.6 m long rotor representing a High Pressure Turbine (H.P.T) (10.1 kg)(43.767 cm), a Low Pressure Turbine (L.P.T) (43.922 kg) (113.698 cm) and a Generator Rotor (G. Rotor) (71.611kg) (146.413 cm) and covering a speed range up to 6000 rpm. A specific data acquisition system has been developed for use in a high-speed rotor balance facility. Special measurement requirements for this facility include order-tracked vibration measurements and phase angle data. The data acquisition system utilizes dual high-speed computer systems to share the tasks of measurement data processing, and results display. A study of balancing errors is systematically discussed in detail from the view point of increasing the balancing precision. The methods for controlling and reducing these errors are also discussed. Both the qualitative and quantitative analyses of balancing errors are performed as the guide to reduce the error and improve the balancing quality. The thesis also presents the theoretical background and the techniques necessary to the procedure to balance the flexible rotor. A trim balancing method was developed to expand the implementation of flexible rotor balancing. A computer program has been written which generates influence coefficient from measured motions and goes on to predict the correction mass. The vibration has been measured at several locations and speeds and the results have been used to (a) ensure that the vibration levels were not excessive as the rotor speed increased and (b) to calculate the balance correction weights using the traditional influence coefficient method and a least squares influence coefficient method. The procedure developed was verified using an experimental rotor rig. The successful application of the procedure to the balancing of this rotor demonstrates that balancing using Singular Value Decomposition, QR Factorization, and QR Factorization combined with SVD and new trim balancing method is not only a theoretical but also a practical possibility. The Moore-Penrose generalized inverse has been employed to solve the problem. The dynamic characteristics of the rotor rig, however, were somewhat limited and did not cover all the possibilities considered during the project. Therefore, a more complete numerical example was also successfully solved using the computer model of a rotor with characteristics similar to those of a real turbine by using a finite element software package called ANSYS.