Experimental and Modal Determination of the State-Space Model Parameters of a Uni-Axial Shaker System for Virtual Vibration Testing

Authors: Jonathan Martino, Kristof Harri

Abstract:

In some cases, the increase in computing resources makes simulation methods more affordable. The increase in processing speed also allows real time analysis or even more rapid tests analysis offering a real tool for test prediction and design process optimization. Vibration tests are no exception to this trend. The so called ‘Virtual Vibration Testing’ offers solution among others to study the influence of specific loads, to better anticipate the boundary conditions between the exciter and the structure under test, to study the influence of small changes in the structure under test, etc. This article will first present a virtual vibration test modeling with a main focus on the shaker model and will afterwards present the experimental parameters determination. The classical way of modeling a shaker is to consider the shaker as a simple mechanical structure augmented by an electrical circuit that makes the shaker move. The shaker is modeled as a two or three degrees of freedom lumped parameters model while the electrical circuit takes the coil impedance and the dynamic back-electromagnetic force into account. The establishment of the equations of this model, describing the dynamics of the shaker, is presented in this article and is strongly related to the internal physical quantities of the shaker. Those quantities will be reduced into global parameters which will be estimated through experiments. Different experiments will be carried out in order to design an easy and practical method for the identification of the shaker parameters leading to a fully functional shaker model. An experimental modal analysis will also be carried out to extract the modal parameters of the shaker and to combine them with the electrical measurements. Finally, this article will conclude with an experimental validation of the model.

Keywords: lumped parameters model, shaker modeling, shaker parameters, state-space, virtual vibration