Mechanical parameters detection in stepped shafts using the FEM based IET

This study suggests a simple, convenient and non-destructive method for investigation of the Young\'s modulus detection in stepped shafts which only utilizes the first-order resonant frequency in flexural mode and dimensions of structures. The method is based on the impulse excitation technique (IET) to pick up the fundamental resonant frequencies. The standard Young\'s modulus detection formulas for rectangular and circular cross-sections are well investigated in literatures. However, the Young\'s modulus of stepped shafts can not be directly detected using the formula for a beam with rectangular or circular cross-section. A response surface method (RSM) is introduced to design numerical simulation experiments to build up experimental formula to detect Young\'s modulus of stepped shafts. The numerical simulation performed by finite element method (FEM) to obtain enough simulation data for RSM analysis. After analysis and calculation, the relationship of flexural resonant frequencies, dimensions of stepped shafts and Young\'s modulus is obtained. Numerical simulations and experimental investigations show that the IET method can be used to investigate Young\'s modulus in stepped shafts, and the FEM simulation and RSM based IET formula proposed in this paper is applicable to calculate the Young\'s modulus in stepped shaft. The method can be further developed to detect mechanical parameters of more complicated structures using the combination of FEM simulation and RSM.