Determination method of scaling laws based on least square method and applied to rectangular thin plates and rotor-bearing systems

Abstract

In this study, we investigate the dynamic scaling laws of geometrically similitude models and systems for predicting their vibration characteristics accurately. A determination method of scaling laws based on least square method for calculating weighted powers of scaling factors is proposed for the first time. Taking geometric parameters as input (design) parameters and vibration characteristics parameters as output parameters, the weighted powers of scaling factors are calculated by least squares similitude method (LSSM) with several design models, and then scaling factors of the output parameters are obtained by combining weighted powers and corresponding scaling factors. Applicability of the LSSM is verified in the following two cases with rectangular plate and rotor-bearing system that the stiffness of supports is taken into account. The vibration characteristics are calculated by using finite element method in MATLAB and compared with simulation analysis software ANSYS. As a result, stable weighted powers and good predictions are obtained for two cases.

Keywords:

• LSSM
• scaling laws
• rectangular thin plate
• weighted powers
• rotor-bearing system

Additional information

Funding

This work was supported by National Science Foundation of China [grant numbers 11572082 and 11872148]; the Fundamental Research Funds for Central Universities of China [grant numbers N160312001 and N170308028]; and the Excellent Talents Support Program in Institutions of Higher learning in Liaoning Province of China [grant numbers LJQ 2015038].