Taguchi-Based Preprocess Strategy for Fast Evaluating Worst Case Cogging Torque Due to PM Tolerance Interactions

The Taguchi method can be used with the finite element method (FEM) to evaluate the worst case cogging torque due to permanent magnet (PM) tolerances. However, the sampling number is huge due to interactions of various tolerances. To solve this issue, this article proposes a unique preprocess strategy based on the Taguchi method to significantly reduce the sampling number. By applying the proposed strategy to the 12-slot/10-pole (12S10P) machine, the sampling number is reduced significantly from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.2 \times 10^{28}$ </tex-math></inline-formula> to 381. Applied to machines with different slot and pole number combinations and compared with existing methods, the proposed strategy is more suitable for machines having small <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{pm}$ </tex-math></inline-formula>/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{T}$ </tex-math></inline-formula> (i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\le 10$ </tex-math></inline-formula>) and the number of critical PM tolerances (i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\le 4$ </tex-math></inline-formula>), where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{pm}$ </tex-math></inline-formula> is PM number and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{T}$ </tex-math></inline-formula> is the greatest common divisor of slot number (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{s}$ </tex-math></inline-formula>) and pole number (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2p$ </tex-math></inline-formula>). The measured results of the 12S10P machine agree well with the finite element predicted results by the proposed preprocess strategy.