Abstract:  A pre-transmission liquid-cooled permanent-magnet retarder（PMR） was proposed to solve the problems of braking torque heat-fade for conventional PMRs. The calculation models of static and transient air-gap magnetic field were established considering the influences of magnetic flux leakage in the retarders based on the magnetic equivalent circuit（MEC）and piecewise function method. The braking torque model of the PMR was obtained and verified by finite element analysis method based on the transient air-gap magnetic field model. An iterative model of braking torque considering the influences of temperature was established based on the established braking torque model and the electro-thermal coupling theory. The bench test results show that the calculated values of the braking torque model are in good agreement with the braking torque-speed characteristic test. The torque values calculated by the iterative model of braking torque considering the temperature effects are in good agreement with the continuous braking test results， and the errors are less than 7%. 

Key words: pre-transmission retarder, gap flux density, liquid cooling, electro-thermal coupling, braking torque

摘要： 针对传统液冷缓速器制动力矩热衰减的问题，提出了一种变速器前置式永磁液冷缓速器。基于等效磁路法和分段函数法建立了考虑缓速器漏磁影响的静/瞬态气隙磁场的计算模型，基于瞬态气隙磁场模型得到了永磁液冷缓速器制动力矩模型，并通过有限元分析方法进行了验证。基于建立的制动力矩模型并根据电热耦合理论，建立了考虑温度影响的涡流制动力矩迭代计算模型。台架试验结果表明：制动力矩模型计算值与制动力矩-转速特性试验吻合良好；考虑温度影响的制动力矩的迭代模型计算的力矩值与持续制动试验结果吻合良好，误差在7%以内。

关键词: 前置缓速器, 气隙磁通密度, 液冷, 电热耦合, 制动力矩