Creating of the mathematical model of a resilient support spring type element and its transfer function from the input and output impulse responses

Abstract

Developing of the transfer function of the spring type element of the resilient bearing support by creating adequate mathematical models of processes for particular frequency intervals from signals obtained as impulse responses of the spring at its input and output measured in the stand under impact at the input is analysed in the article. Impulse responses are investigated by the Fourier method by separating components of particular frequencies. Mathematical models of the processes at the spring input and output are developed as the sum of models-formants corresponding to particular frequency ranges. Formants themselves are modeled by the sum of damped sine waves. Parameters of the model are estimated by the iterative Levenberg method. The mathematical model developed further is used for diagnostics of support bearings that are insulated from the external body by these resilient elements.