# Multi-Objective Optimization for Outer Rotor Low-Speed Permanent Magnet Motor
## 1 Introduction  
Outer rotor low-speed permanent magnet motors (LSPMMs) have extremely wide application prospects in the fields of industrial production, coal mine development, port lifting and ship propulsion [1, 2, 3]. The low-speed permanent magnet synchronous motor studied in this paper can be applied to the coal mine belt conveyor, replacing the traditional method of driving the asynchronous motor and the reducer used in the coal mine. For the LSPMM, it is usually run at the rated speed and rated torque point, that is, mainly at the rated load point. In the application of the coal mine belt conveyor, the LSPMM has a higher efficiency and a higher power factor than the induction motor, and the LSPMM can maintain good performance in a wide range of load changes [4]. In addition, compared with the inner rotor motor, the outer rotor LSPMM has a larger moment of inertia, less copper loss, a higher output power, a stronger power density, and the outer rotor LSPMM is more convenient to be made into a multi-level structure [5, 6]. For the LSPMM, electromagnetic performance is a very important performance index, which can reduce the motor long-term operating costs and result in a longer working life [7]. Temperature is also an important evaluation criterion for the LSPMM. If the temperature is too high, it will not only affect the safety of operation, but also reduce the motor service life. An excessive winding temperature may harm the insulation of the motor [8], and an excessive PM temperature will cause irreversible demagnetization of the PM [9]. Loss is an important factor affecting the motor temperature; the heat generated by various losses can significantly increase the temperature of the motor, and even when the total losses are the same, the differentproportions of losses will have a large impact on the motor temperature [10]. For the LSPMM, the stator winding copper loss accounts for the vast majority of the total loss, and the effect of copper loss on the motor maximum temperature is also the largest compared to other losses [11]. Therefore, when optimizing the motor, it is not only necessary to pursue excellent electromagnetic performance, but also to consider the influence of thermal load parameters on the temperature in electromagnetic performance. In the existing literature, the electromagnetic performance and temperature of the LSPMM have been optimized based on some multi-objective optimization methods. For the efficiency performance, five different rotor topologies (V-shape, U-shape, double V-shape, delta-shape, and double tangential-shape) were optimized by the particle swarm optimization (MPSO) algorithm, and their performance characteristics such as efficiency and anti-demagnetization ability were compared [12]. For the power density, the differential evolution algorithm was used to optimize the motor parameters in order to pursue a high power density, including the stator yoke thickness, the rotor yoke thickness and the motor relative magnet span [13]. For the torque performance, a new flux-assisted consequent pole spoke-type permanent magnet (PM) synchronous torque motor was proposed and the rotor design was optimized; the optimized motor had a higher torque-to-magnet-weight ratio and a wider constant power region. [14]. For the temperature characteristics, the motor was optimized for copper loss minimization in pursuit of a low temperature rise [15]. It can be seen that both the electromagnetic performance and temperature are very important for the optimal LSPMM design. For the LSPMM, electromagnetic performance is an important performance index, including the power factor, back EMF, torque density, etc. Optimizing the electromagnetic performance can greatly improve the motor working efficiency and reduce the motor cost, but the highest electromagnetic performance may lead to an increase in the motor temperature and reduce the motor working life [16]. The temperature also has a great influence on the motor.