Predicting unbalance asymmetric rotor vibration behavior based on sensitivity analysis and using Response Surface Methodology method considering parallel misalignment

Abstract

Mass unbalance, shaft misalignment, rotor asymmetry, and force due to rotor weight are the main causes of vibrations in rotary machines especially when the shaft is not symmetric. Although extensive researches have been carried out to determine the effect of each on the increase of vibration levels far, there has been no clear study on the simultaneous existence of all these parameters and their interactions. In this research, the model is a rotor composed of a rigid disk and a flexible asymmetric shaft. The general equations of motion are first derived by considering the effect of high order large deformation in bending. The equations are discretized using the Rayleigh–Ritz method. The obtained equations are nonlinear coupled differential equations that are solved using the numerical method. Sensitivity analysis has been utilized to identify the percentage of the contribution of each parameter to the increase of vibration. Then a DOE-based Response Surface Methodology (RSM) is applied to present a model to predict the vibration behavior of the system with good accuracy. Genetic algorithm is also used to optimize the effective parameters and to verify the results. A 3D model of the asymmetric rotor is carried out in experimental studies to attain more precise responses. The research shows that rotor asymmetry alone and also its combination with gravitational force has much more effects on the vibration amplitude. These effects are observed at frequencies both once and twice the rotational speed in spectral data, in comparison with other factors. The mass unbalance also plays a significant role in frequency equal to the rotational speed. In the end, the achieved results are validated with experimental simulations.

Indifference Computer Experiment for Mathematical Identification of Two Variables

“…The theory and method of differential equations have always been one of the keys to the development of modern science and technology and also one of the key issues of mathematical research. However, most differential equations cannot be solved analytically, and even some differential equations that can be solved require very high skills; differential equations are a compilation of tricks [1]. Therefore, while people are looking for analytic solutions, discussing and studying the analytical features of the solutions have also become one of people's research methods.…”

Vibration Behavior of Misaligned Rotor with the Asymmetric Shaft Using Theory of Timoshenko Beam

“…Jamshidi and Jafari [31] and [32] studied accurate models using asymmetric shaft with misalignment and under unbalance forces in rotating coordinates verified by developing an experimental test. They also utilized Timoshenko theory to improve the accuracy of the results.…”