Abstract：With the advancement of pump-driven systems for liquid rockets, pump-driven motors are increasingly designed to be lightweight, highly reliable, and capable of short-term high-power output. However, the maximum power of these motor systems is constrained by voltage limitations and thermal boundaries, making significant power increases challenging. Traditional motor design methods often incorporate redundancy for maximum power rather than directly optimizing for the extreme power point. This paper introduces the concept of short-term extreme output power and establishes a design methodology for the extreme power point. Given the significant losses associated with this operating point, a novel cooling structure is proposed to effectively dissipate the heat generated by substantial copper losses. Through electromagnetic-thermal coupling analysis and experimental validation, the reliability and effectiveness of the proposed design methodology and cooling structure are demonstrated. A mathematical model of the motor is first established to analyze the variation of output power with current under the voltage limit circle. As the current increases, the output power initially rises and then declines, exhibiting a maximum point. By employing the Lagrange multiplier method to solve for this maximum power point, it is found that only a minimal magnetic flux is required to meet the output requirements, significantly reducing the cost of permanent magnets. However, this extreme point is often impractical in real-world applications because, from the rated power point to the extreme power point, copper losses increase by 3.45 times, exceeding the thermal limits of the winding insulation materials. To adjust the extreme power point, the motor's tolerance to copper losses can be enhanced through improved cooling methods, or copper losses can be minimized. The primary factor influencing the motor's extreme output power under copper loss constraints is the stator resistance. This paper proposes a novel cooling configuration that incorporates flow channels in the stator slots and introduces a low-temperature cooling medium. This cooling approach not only reduces stator resistance but also designs an efficient heat transfer path by placing the cooling medium in close proximity to the windings, thereby enhancing cooling effectiveness. Consequently, from the perspectives of motor parameters and cooling capacity, this cooling configuration optimizes the motor's extreme power output. The ultimate realization of the theoretical maximum power point depends on the design of the flow channels. A model for motor losses and cooling capacity is established, summarizing the principles of flow channel construction. Under a fixed temperature rise, the heat dissipation increases with the contact perimeter of the flow channel and decreases with the cross-sectional area. However, in the selection of flow channel shapes, the contact perimeter and area are not independent parameters. Once the contact perimeter is determined, an upper limit for the area can be derived, and vice versa. Cooling topologies of X, Y, Z, and V types are proposed. Among these, the maximum temperatures for T-type, X-type, and Y-type channel structures are 177.1 K, 187.0 K, and 175.3 K, respectively, while the V-type structure achieves a significantly lower maximum temperature of 137.9 K. Further optimization of the V-type structure reduces the maximum temperature to 136.2 K, with an optimal V-angle of 97.8°. For short-term extreme power output motors, such as those used in rocket electric pumps, the cooling capacity can be evaluated by the maximum power achieved under constraints of limited time, temperature rise, and voltage. This maximum power represents the motor's extreme output capability. By establishing an electromagnetic-thermal coupling model, the temperature rise of the motor under different currents within a specified time is calculated to determine the maximum allowable current under the permitted temperature rise. Validation of the extreme power point and electromagnetic-thermal coupling model for a Y-type winding under specific parameters shows that, at a liquid nitrogen flow rate of 1.25 cm/s, a three-phase winding current of 5.9 A, and stator copper losses of 397 W, the experimental temperature rise is approximately 23.6% higher than the simulation results. This discrepancy may arise from the use of average temperatures from the previous time step to define copper losses in the simulation, leading to an underestimation of local high-temperature points. By maintaining constant liquid nitrogen pump pressure and varying the current, the temperature rise curves of the winding under different currents are obtained. At an operating time of 200 s and a temperature rise of 273 K, the extreme operating point at a liquid nitrogen flow rate of 1.25 cm/s is I1=5.9 A. The liquid flow rate significantly affects the cooling capacity, with the maximum allowable current density and copper losses under the temperature field boundary within 200 s varying with flow rate: at 0.58 cm/s, the current density can reach 43 A/mm2, while at 3.83 cm/s, it can reach 70 A/mm2, demonstrating superior cooling performance. The maximum allowable copper loss in the experiment is 397 W, with a 4.3% error compared to the simulation result of 414.88 W.
陈博宇, 曹继伟, 刘钰清, 宋禹辰, 李立毅. 火箭用高功率密度深冷电动泵极限输出功率设计方法研究[J]. 电工技术学报, 2025, 40(22): 7238-7249.
Chen Boyu, Cao Jiwei, Liu Yuqing, Song Yuchen, Li Liyi. Design Method for Maximum Output Power of Rocket High-Power Density Cryogenic Electric Pumps. Transactions of China Electrotechnical Society, 2025, 40(22): 7238-7249.
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