Solving Eddy Currents in Solid Rotor Induction Motors through the Collocation Method

Abstract

With the integration of electric vehicle technology into our daily lives, researchers have increasingly focused on the development of various electric motor types and efficiency calculations. Given the rising production costs of permanent magnets, researchers have explored alternative induction motor designs suitable for high-speed systems. Solid rotor induction motors (SRIM) stand out due to their simple structures, ease of production, and exceptional vibration-free operation at high speeds. It is crucial to derive analytical solutions for optimizing Solid Rotor Induction Motor (SRIM) structures. This study explores the viability of utilizing the collocation method, a type of weighted residuals approach, for the modeling of SRIM structures. Collocation polynomials of various orders were employed to model the Maxwell equations, and the results were compared with analytical solutions. The findings demonstrate that the collocation method effectively solves electromagnetic systems, and employing 12 or more collocation points yields results within acceptable limits, with an RMSE of less than 1e-5.

Keywords

• Solid rotor induction motor
• collocation method
• approximate solution
• eddy currents

Kütlesel Rotorlu İndüksiyon Motorlarında Oluşan Eddy Akımlarının Kollokasyon Yöntemi Kullanılarak Çözümü

Abstract

Elektrikli araç teknolojisinin hayatımıza girmesi ile birlikte farklı türde elektrik motorlarının gelişimi ve verimlilik hesaplamaları araştırmacılar tarafından ilgi görmektedir. Kalıcı mıknatısların üretim maliyetlerinin artması nedeni ile, yüksek hızlı çalışan sistemlerde kullanılmak üzere çeşitli indüksiyon motor tasarımları mevcuttur. Kütlesel rotorlu indüksiyon motorları (KRIM) basit yapıları, üretim kolaylığı, yüksek hızda titreşimsiz çalışması gibi nedenlerden dolayı öne çıkan motor türlerindendir. KRIM yapılarının optimizasyon süreçlerinde analitik çözümlerin elde edilebilmesi büyük önem taşımaktadır. Bu çalışmada, KRIM tasarımlarında, ağırlıklı kalanlar yöntemlerinden biri olan kollokasyon yönteminin kullanılabilirliği araştırılmıştır. Çalışmada Maxwell denklemleri farklı mertebede kollokasyon polinomları tarafından modellenerek analitik çözümler ile kıyaslanmıştır. Çalışmada, kollokasyon yönteminin elektromanyetik sistemlerin çözümü için kullanışlı olduğu, 12 ve üzeri kollokasyon noktası kullanılması durumunda kabul edilebilir (RMSE<1e-5) sonuçların elde edilebileceği gösterilmiştir.

Keywords

• Kütlesel rotorlu indüksiyon motoru
• kollokasyon yöntemi
• yaklaşık çözüm
• girdap akımları

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