Prediction of natural frequencies of turbine blades for turbocharger application. An investigation of the finite element method, mathematical modelling and frequency survey methods applied to turbocharger blade vibration in order to predict natural frequencies of turbocharger blades.

Abstract

Methods of determining natural frequencies of the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs for various environmental conditions were investigated by application of Finite Element Analysis and beam theory. Modelling and simulation methods were developed ; the first method composed of 15 finite element simulations ; the second composed of 15 finite element simulations and a set of experimental frequency survey results; the third composed of 5 simulations , an incorporated mathematical model and a set of experimental frequency survey results. Each of these methods was designed to allow prediction of resonant frequency changes across a range of exhaust gas temperature and shaft rotational speed. For the new modelling and simulation methods, an analysis template and a plotting tool were developed using Microsoft Excel and MATLAB software. A graph showing a frequency-temperature-speed variations and a Campbell Diagram that incorporates material stiffening and softening effects across a range of rotational speeds was designed, and applied to the D76D88, B76D88, A86E93, C86G90, C86L90 and C125L89 turbine wheel designs. New design methodologies for turbine wheels were formulated and validated, showing a good agreement with a range of data points from frequency survey, strain-gauge telemetry and laser tip-timing test results. The results from the new design method were compared with existing single compensation factor methodology, and showed a great improvement in accuracy of prediction of modal vibration. A new nomenclature for the mode shapes of a turbocharger’s blade was proposed, designed and demonstrated to allow direct identification of associated mode shape. It is concluded that Finite Element Analysis combined with the frequency survey is capable of predicting changes in turbine natural frequencies and, when incorporated into the existing turbine design methodology, resulted in a major improvement in the accuracy of the predictions of vibration frequency.