Recovery of transversely-isotropic elastic material parameters in induction motor rotors

TL;DR

The paper tackles recovering five TI elastic constants of a rotor core from modal data by formulating an inverse eigenvalue problem for linear elasticity. It compares Hessian-based (SLSQP) and derivative-free (EKI) optimization on simulated spectra, finding EKI more reliable though computationally intensive. Key results show that, in the noiseless setting, three bending-mode pairs and one torsional mode enable accurate five-parameter recovery, while two bending pairs suffice for up to four parameters; Poisson ratio remains the most challenging. With multiplicative noise, data quantity improves robustness but achieving full five-parameter accuracy requires very low noise, highlighting practical limits and pointing to future work in computational acceleration and more realistic models.

Abstract

We propose numerical algorithms for recovering parameters in eigenvalue problems for linear elasticity of transversely isotropic materials. Specifically, the algorithms are used to recover the elastic constants of a rotor core. Numerical tests show that in the noiseless setup, two pairs of bending modes are sufficient for recovering one to four parameters accurately. To recover all five parameters that govern the elastic properties of electric engines accurately, we require three pairs of bending modes and one torsional mode. Moreover, we study the stability of the inversion method against multiplicative noise; for tests in which the data contained multiplicative noise of at most $1\%$, we find that all parameters can be recovered with an error less than $10\%$.

Figures (7)

• Figure 1: Sketch of an induction motor's rotor. The top picture shows an assembled rotor consisting of a shaft with pressure plates, short circuit rings with bars, and a rotor core, which are depicted individually from left to right in the bottom row.
• Figure 2: Illustration of mode types. Left: bending, Right: torsional.
• Figure 3: Illustrations of the optimization landscapes given three bending pairs and one torsional mode: The ordinates illustrate the values of the cost function \ref{['eq:minimisation_exact']}. In the left picture, the abscissa illustrates the physically reasonable values for $E_x \in [5\text{e}10,3\text{e}11]$. In the right picture, the abscissas cover the physically reasonable values of $E_z$ and $G_{xz}$. All other parameters are assumed to be known exactly.
• Figure 4: Relative errors for different noise levels, 2 bending pairs. Left: $(E_x,G_{xy})$; right: $(E_z,G_{xz})$.
• Figure 5: Relative errors for different noise levels, 3 bending pairs, 1 torsional mode. Left: $(E_x,G_{xy})$; right: $(E_z,G_{xz})$.