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On the Use of the Cumulative Distribution Function for Large-Scale Tolerance Analyses Applied to Electric Machine Design

Department of Electrical Drives and Power Electronics, Johannes Kepler University Linz, 4040 Linz, Austria
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Received: 11 July 2020 / Revised: 8 August 2020 / Accepted: 15 September 2020 / Published: 22 September 2020
(This article belongs to the Special Issue Applied Statistics in Engineering)
In the field of electrical machine design, excellent performance for multiple objectives, like efficiency or torque density, can be reached by using contemporary optimization techniques. Unfortunately, highly optimized designs are prone to be rather sensitive regarding uncertainties in the design parameters. This paper introduces an approach to rate the sensitivity of designs with a large number of tolerance-affected parameters using cumulative distribution functions (CDFs) based on finite element analysis results. The accuracy of the CDFs is estimated using the Dvoretzky–Kiefer–Wolfowitz inequality, as well as the bootstrapping method. The advantage of the presented technique is that computational time can be kept low, even for complex problems. As a demanding test case, the effect of imperfect permanent magnets on the cogging torque of a Vernier machine with 192 tolerance-affected parameters is investigated. Results reveal that for this problem, a reliable statement about the robustness can already be made with 1000 finite element calculations. View Full-Text
Keywords: bootstrapping; cogging torque; cumulative distribution function; electric machine; quantile; reliability; robust design; tolerances bootstrapping; cogging torque; cumulative distribution function; electric machine; quantile; reliability; robust design; tolerances
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MDPI and ACS Style

Marth, E.; Bramerdorfer, G. On the Use of the Cumulative Distribution Function for Large-Scale Tolerance Analyses Applied to Electric Machine Design. Stats 2020, 3, 412-426. https://0-doi-org.brum.beds.ac.uk/10.3390/stats3030026

AMA Style

Marth E, Bramerdorfer G. On the Use of the Cumulative Distribution Function for Large-Scale Tolerance Analyses Applied to Electric Machine Design. Stats. 2020; 3(3):412-426. https://0-doi-org.brum.beds.ac.uk/10.3390/stats3030026

Chicago/Turabian Style

Marth, Edmund, and Gerd Bramerdorfer. 2020. "On the Use of the Cumulative Distribution Function for Large-Scale Tolerance Analyses Applied to Electric Machine Design" Stats 3, no. 3: 412-426. https://0-doi-org.brum.beds.ac.uk/10.3390/stats3030026

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