Forced Response Vibration Analysis of the Turbine Blade with Coupling between the Normal and Tangential Direction

Alireza Mahmoodi ,Hamid Ahmadian

doi:10.1155/2022/2413022

Abstract

This paper is about the nonlinear dynamic of turbine blades due to the friction between blades. This paper investigates the coupling effect in an experimental turbine blade model. In this contact model, coupling between friction in tangential and normal directions and energy dissipation in the lateral direction are considered simultaneously, which has not been considered elsewhere in the contact model of the turbine blade. The mathematical model of the blade under-platform damper model is derived, and to solve nonlinear equations, the multi-harmonic balance method is used. The contact force is calculated by the alternative frequency time-domain method in this solution method. To solve nonlinear derived algebraic equations, a continuation algorithm is applied. It is shown that considering the coupling phenomenon causes the results to be different from the situation in which this physical phenomenon is ignored. To validate the algorithm of the solution, numerical results of previous references in the turbine-blade field are regenerated. Experimental analysis on the under-platform damper and turbine blade model is done to investigate the coupling effect. It is shown that the contact model with consideration with coupling effect between tangential and normal direction can predict experimental results (amplitude and frequency of resonance) most of the other contact models used in the turbine field. To accurately determine the amplitude and frequency of resonance, it is necessary to consider the coupling effect.

Highlights

Contact in the normal direction in turbine blade analysis is usually considered as stable contact, in the literature review there are several references [11, 12] that consider this hysteresis effect and its dissipation energy by compensation coefficient or by viscous finite element [5]
Ey calculated the vibration of the turbine blade by numerical integration and reducing the vibration level due to the snubbing effect is showed. ey show that combination parameters of the system and excitation force in some frequencies can increase frequency response, not resonance frequencies
One of the big challenges in accurately modeling contact surfaces is considering the normal lift-up due to the tangential motion because all surfaces have the roughness that causes this motion. e literature review survey about contact models used to simulate contact force in the blade-turbine field shows that none of them considered this effect in their simulation, while the importance of this effect to accurately predict contact force has recently been demonstrated in references [17]

Summary

Forced Vibration of the System

Force vibration of each nonlinear system has an equation of motion according to the following equation [38]:. Using the model provided by MohammadAli et al [2], precisian simulation from contact force was provided in this study In this model, the normal force and tangential force variation are expressed by the following relations [2]: fx CQ fmy ΔT, ΔT |Ω|sgn(x)⎛⎝1 − exp⎛⎝CnQCwk1C−nP(11−−mm) sgn(x) x0 − x􏼁⎞⎠⎞⎠ + ΔT0. It is worth mentioning that these relations expressed nonlinear force in the time domain, while frequency descriptions are used in the harmonic balance method. To solve this problem, the AFT method is used. E MHB method to solve the nonlinear equation method is used In this method (MHB) where the excitation force is harmonic, the response is assumed according to the following equation [36].

Evaluation of force law Frequency

Experimental Analysis

Conclusion