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.

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 [

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 [

Some main design parameters are highly relevant to the electromagnetic and thermal performance, such as the stator outer diameter

The split ratio is an important design parameter since it has a significant influence on temperature rise, torque, loss, efficiency, and cost [

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

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:

The motor is required to be able to operate 300 s per cycle with full load. The load profile is shown in Figure

The rotational speed and torque under full load condition are 10000 r/min and 1.6 N·m, respectively.

Outer diameter and length of the motor are limited.

The operating altitude is 20 km.

The motor is cooled by natural cooling.

The maximum ambient temperature is 80°C.

Load profile of the PM-BLDCM.

The operation time of the PM-BLDCM is far less than the time deenergized and at rest. There is enough time for it to reestablish motor temperatures within 2°C of the coolant temperature [

Air density at altitude of 20 km is 0.0889 kg/m^{3}, which is 1/14 that of 0 km. At high altitudes, due to the thin air, the convection cooling capacity is reduced.

Some designs of the PM-BLDCM prototype, such as 120° electrical conduction, inner rotor, surface mounted magnets, air-gap width, slots number, poles number, outer stator diameter, and axial length, have been designed previously before optimization. Some requirements and design parameters are shown in Table

Main parameters of the prototype motor.

Items | Values |
---|---|

Rated speed (r/min) | 10000 |

Outer stator diameter (mm) | 80 |

Poles number | 4 |

Rated torque (N·m) | 1.6 |

Active axial length (mm) | 30 |

Slots number | 12 |

The configuration and main geometric parameters of the PM-BLDCM are shown in Figure

Configuration and geometric parameters of the PM-BLDCM.

The split ratio is given as

The stator tooth width

According to the geometric relationships and the expressions of

The cross-sectional area of a conductor is given as

The back-EMF of a single conductor is given as

The phase back-EMF can be obtained as

The electromagnetic torque is given as

Losses are the heat source that causes increase of motor temperature. Losses of the high-power-density PM-BLDCM mainly include the copper loss, the iron loss, the rotor eddy current loss, the mechanical friction loss, and the rotor air friction loss [

When the winding temperature of the PM-BLDCM is ambient temperature

According to (

The iron loss in the stator lamination is given as

Based on the analytical design model, the expressions of

Eddy current loss in the permanent magnets, the sleeve, and the rotor yoke is caused by the space MMF harmonics and time MMF harmonics. The eddy current loss mainly locates in the permanent magnets and the sleeve, and the loss in the rotor yoke can be ignored [

The mechanical friction loss is caused by running of the bearing, and its expression can be expressed as [

The rotor air friction loss is generated by the friction between rotor and air. According to [

The rotor air friction loss is close related to the radius of the rotor

In various components of the PM-BLDCM, the winding and permanent magnet are the main heat sources and their reliabilities are sensitive to temperature. In order to increase the reliability of the PM-BLDCM, high temperature materials are adopted besides decreasing the motor temperature. The grade of the enamel insulated wires intended to adopt is_{2}Co_{17}, and its grade is

The air-gap thermal resistance is larger than other thermal resistances in the stator. Furthermore, the air-gap thermal resistance increases with air density decreases. Therefore, the effect of the rotor temperature on the winding temperature can be ignored at the high altitude. The winding temperature rise is mainly determined by the copper and iron losses. The winding temperature rise can be calculated by the following equation:

The heat transfer coefficient of the PM-BLDCM is the sum of the natural convection and radiation heat transfer coefficients. The natural convection heat transfer coefficient decreases with altitude rises. In order to improve the cooling capacity of the PM-BLDCM at high altitude, the radiation heat transfer coefficient needs to be raised by increasing the emissivity of the motor surface.

The electromagnetic torque is the sum of the resistance torque and the output torque. The electromagnetic torque can be expressed as

Combining (

Based on (

The winding transient temperature rise is given as

The ratio of different losses in total losses and thermal time constant can be changed by adjusting

Variation of the winding temperature rise with split ratio and

Using (

On the other hand, it should be noted that the optimal

The analytical results are verified by FEA and experiments. The verification purpose is to prove that the analytical optimal design is accurate and the optimization method can minimize the winding temperature rise.

In FEA verification, the air density at altitude 20 km and the ambient temperature of 80°C were considered. Different designs, which include the optimal design, are chosen to simulate. As shown in Figure

Analytical contour of the winding temperature rise and the points used for FEA verifications.

The analytical and FEA predicted winding temperature rises of the different designs are shown in Table

Analytical and FEA results of different designs (

Designs | | | | |
---|---|---|---|---|

C1 | 0.43 | 1.1 | 75.4 | 73.0 |

C2 | 0.43 | 1.3 | 67.6 | 66.9 |

C3 | 0.43 | 1.5 | 63.8 | 63.0 |

C4, R3 | 0.43 | 1.7 | 62.0 | 60.6 |

R1 | 0.25 | 1.7 | 85.4 | 82.0 |

R2 | 0.35 | 1.7 | 65.5 | 63.0 |

R4 | 0.55 | 1.7 | 69.5 | 68.3 |

R5 | 0.65 | 1.7 | 98.9 | 97.9 |

FEA verifications of the designs C1, C2, C3, and C4.

FEA verifications of designs R1, R2, R3, R4, and R5.

3D thermal field of the design C4 (R3) at

As shown in Figure

Prototype and measuring instruments. (a) Prototype, controller, and dynamometer. (b) Dynamometer controller, power analyzer, and LCR tester.

The winding temperature rise was measured by the resistance method [

Process of the resistance measurement.

Using these measured resistances, the winding temperature rises are calculated by the following equation:

The measured winding temperature rises, together with analytical and FEA winding temperature rise, are given in Table

The analytical, FEA, and measured winding temperature rise of MP1, MP2, and MP3.

Items | MP1 | MP2 | MP3 |
---|---|---|---|

Analytical (°C) | 21.4 | 42.0 | 61.9 |

FEA (°C) | 20.4 | 40.1 | 59.0 |

Measured (°C) | 22.7 | 40.8 | 57.4 |

Experimental verification of the winding temperature rise.

In order to improve the reliability of the short-time PM-BLDCM in hypersonic vehicle, an electromagnetic-thermal integrated design optimization method is proposed. This method can satisfy both the requirements and constraints of thermal and electromagnetic design aspects. The method is based on electromagnetic analysis and thermal transient analysis. The electromagnetic and thermal design parameters are represented as functions of split ratio and

The authors declare that there are no competing interests.

This work was supported by the National Natural Science Foundation of China (Grant no. 51507143), Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20136102120055), and the Industry Science and Technology Research Foundation of Shaanxi Province, China (Grant no. 2015GY090).