International Journal of Aerospace Engineering

Volume 2016, Article ID 9725416, 9 pages

http://dx.doi.org/10.1155/2016/9725416

## Electromagnetic-Thermal Integrated Design Optimization for Hypersonic Vehicle Short-Time Duty PM Brushless DC Motor

School of Automation, Northwestern Polytechnical University, Xi’an 710072, China

Received 30 May 2016; Accepted 30 August 2016

Academic Editor: Linda L. Vahala

Copyright © 2016 Quanwu Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

High reliability is required for the permanent magnet brushless DC motor (PM-BLDCM) in an electrical pump of hypersonic vehicle. The PM-BLDCM is a short-time duty motor with high-power-density. Since thermal equilibrium is not reached for the PM-BLDCM, the temperature distribution is not uniform and there is a risk of local overheating. The winding is a main heat source and its insulation is thermally sensitive, so reducing the winding temperature rise is the key to the improvement of the reliability. In order to reduce the winding temperature rise, an electromagnetic-thermal integrated design optimization method is proposed. The method is based on electromagnetic analysis and thermal transient analysis. The requirements and constraints of electromagnetic and thermal design are considered in this method. The split ratio and the maximum flux density in stator lamination, which are highly relevant to the windings temperature rise, are optimized analytically. The analytical results are verified by finite element analysis (FEA) and experiments. The maximum error between the analytical and the FEA results is 4%. The errors between the analytical and measured windings temperature rise are less than 8%. It can be proved that the method can obtain the optimal design accurately to reduce the winding temperature rise.

#### 1. Introduction

There are many kinds of permanent magnet brushless DC motor (PM-BLDCM) in the engine of hypersonic vehicle to achieve fast, flexible, and precise thrust control [1–5]. These PM-BLDCMs have different load profiles, which can be classified by the standard of IEC 60034-1:2010 as ten kinds of duty types: S1 to S10 [6]. The short-time duty (S2) PM-BLDCM in hypersonic vehicle can be used in pumps, actuators, fans, and so on. Reliability and power-density are the fundamental requirements for the hypersonic vehicle PM-BLDCM [7–9]. Thermal equilibrium is not reached for short-time duty PM-BLDCM, so there is a risk of local overheating [10, 11]. Overheat can cause damage to those components which are sensitive to the temperature, especially, the winding insulation. As the temperature increases, the winding insulation lifetime is heavily reduced by the thermal-aging degradation effect [12–14]. Reliability of the short-time duty PM-BLDCM is directly affected by the winding temperature rise. Therefore, reducing the winding temperature rise is the key to the improvement of the PM-BLDCM’s reliability [15].

Both the electromagnetic and thermal designs need to be concerned for the PM-BLDCM. The electromagnetic and thermal design parameters are coupled. The electromagnetic-thermal integrated design needs to be adopted to reduce the winding temperature rise. There are different types of electromagnetic-thermal integrated design methods proposed in the literatures. Nevertheless, these methods can be divided into two main categories: numerical methods and analytical methods [12, 15–21]. The two methods have their own advantages and disadvantages. There are also some approaches which combine the two methods [16, 17]. The numerical methods, which are based on the finite element analyses (FEA) and computational fluid dynamics (CFD), can get the accurate results intuitively. However, the numerical methods have high requirements in terms of model setup and computational time [19, 20]. The analytical methods, which are based on the electromagnetic and thermal parametric model, provide a fast and accurate solution for the electromagnetic-thermal integrated design optimization [20, 21]. In preceding publications, the electromagnetic-thermal integrated design optimization is based on the thermal steady state. However, the winding temperature is directly affected by the thermal transients for the short-time duty PM-BLDCM. Therefore, in this paper, an analytical electromagnetic-thermal integrated design optimization method, which is based on the thermal transients, is studied for the short-time duty PM-BLDCM.

Some main design parameters are highly relevant to the electromagnetic and thermal performance, such as the stator outer diameter , the stator inner diameter , and the motor active axial length [16–21]. The winding temperature rise can be decreased by optimizing the parameters. In some existing papers, there are too many variables involved and the optimization is complex [15, 19–21]. According to motor design theory, the main design parameters are determined by the electric load and magnetic load, which can be converted to the maximum flux density in the stator lamination , the stator inner diameter , and copper loss [22]. When two of , , and are determined, the dimensions of the PM-BLDCM can be obtained. For low-speed PM-BLDCM, the copper loss is the only main loss, and so and are usually chosen to optimize [23–28]. For the high-power-density PM-BLDCM with high-speed, and are suitable for the optimization. In order to make data comparable, is usually expressed as split ratio, which is the ratio of the stator inner diameter to the outer diameter . In this paper, the electromagnetic and thermal parameters are converted to the functions of the split ratio and . Only two variables are involved, so the optimization can be highly simplified.

The split ratio is an important design parameter since it has a significant influence on temperature rise, torque, loss, efficiency, and cost [23–27]. There are many investigations on the optimization of the split ratio in some existing papers. Different split ratio optimization methods for electrically excited motors, surface mounted PM motors, interior PM motors, external rotor PM motors, and so forth are presented in [23–25]. These methods are aimed at low-speed motor and thermal limitation is achieved by limiting the copper loss. In [26], Tang et al. indicate that the split ratio has a significant influence on temperature rise of the short-time duty PM-BLDCM. In [27], Reichert et al. indicate that the local thermal situations should be considered, especially for the stator winding, which is one of the main heat sources; an analytical split ratio optimization method for low-speed PM-BLDCM is developed with global and local thermal limitations. In [23–27], the split ratio has been optimized for these PM-BLDCMs whose losses are dominated by the copper loss, whereas other losses can be neglected. Speed has a significant influence on the optimal split ratios [28]. For the high-power-density PM-BLDCM in this paper, the iron loss, the rotor eddy current loss, the rotor air friction loss, and the mechanical friction loss should be considered in the design optimization.

In this paper, an electromagnetic-thermal integrated design optimization method is proposed to reduce the winding temperature rise of the short-time duty PM-BLDCM. The analytical design model and electromagnetic torque equation are given in Section 2. The losses are calculated in Section 3. The thermal transient analysis and the optimal design determination method are presented in Section 4. Finally, the analytical optimization results are verified by FEA and experiments.

#### 2. Electromagnetic Torque Calculation

The PM-BLDCM intended to design is used in an electrical pump of hypersonic vehicle. High reliability and high-power-density are required. The PM-BLDCM operates for a short time in a flight. Some constraints for the PM-BLDCM are given as follows:(1)The motor is required to be able to operate 300 s per cycle with full load. The load profile is shown in Figure 1.(2)The rotational speed and torque under full load condition are 10000 r/min and 1.6 N·m, respectively.(3)Outer diameter and length of the motor are limited.(4)The operating altitude is 20 km.(5)The motor is cooled by natural cooling.(6)The maximum ambient temperature is 80°C.