# A Study on the Electromagnetic-Temperature Coupled Analysis Method for In-Wheel Motors
## 1 Introduction  
The in-wheel motor (IWM) drive is one of the key technologies of the next generation 'pure electric drive' electric vehicle, which eliminates power transmission devices, such as the transmission and differential. It not only improves the transmission efficiency of the system but also makes the chassis structure simpler and more flexible, and each wheel motor can be controlled independently, which can meet the power demand of the vehicle well [1; 2; 3; 4]. As the core component of IWM driven electric vehicles, the structure and performance of the IWM directly affect the driving/braking performance of each driving wheel and the driving performance of the vehicle. It is necessary to analyze its performance accurately in the design. During operation, the coupling of electromagnetic, temperature, and other fields in the motor takes place [5; 6]. However, most of the current studies on IMMs adopt a decoupling simplification method to separate the coupled fields, which not only affects the accuracy of the solution results but also affects the design results and performance prediction. Therefore, it is necessary to study the coupling analysis method of theelectromagnetic and temperature fields of an IWM to improve the accuracy of the calculation and to accurately predict the performance of the IWM. In the coupling analysis of the electromagnetic and temperature field of an IWM, [PERSON] et al. studied the optimization of the magnetic circuit of the motor. The basic parameters, such as torque and loss, are calculated by the two-dimensional transient electromagnetic field of the optimized structure, and then the temperature distribution using the results of electromagnetic calculation was analyzed [7]. [PERSON] et al. simulated the electromagnetic and temperature characteristics of the motor. First, the electromagnetic field of the motor was analyzed by the finite element method, and the loss value of the motor was calculated. The loss value was taken as the main thermal source in the temperature field. The finite element analysis of the temperature distribution of the motor was carried out [8]. [PERSON] et al. analyzed the electromagnetic-thermal coupling of a three-phase induction motor. First, the parameters of the equivalent circuit of the motor were obtained by establishing the finite element model, and the loss was calculated as the heat source of thermal analysis. Then the lumped parameter temperature model was established. At the same time, the parameters of the lumped parameter thermal model grid were calculated accurately by using the finite element method, then the temperature rise of different components was calculated by the lumped parameter thermal network model, and fed back to the electromagnetic analysis. The parameters of the electromagnetic analysis were updated and calculated until convergence [9]. In summary, in reviewing the research on the electromagnetic and temperature fields of an IWM, we find most of them are unidirectional coupling analyses, that is, the final results of loss calculated by the electromagnetic field are taken as the initial condition of the temperature field, and the temperature distribution is analyzed with little consideration given to the influence of temperature on electromagnetic characteristics [10; 11; 12; 13; 14; 15]. In fact, the components of an IWM adopt different materials, and the change in temperature varies the material properties of each component, which can lead to change in important electromagnetic parameters and affect the electromagnetic characteristics. The change in electromagnetic characteristics can further affect the temperature characteristics of each component. This is a process of mutual influence and interaction. Different coupling methods used in the calculation may obtain different results. The analysis of the influence of different coupling methods on the calculation results deserves further discussion. In this paper, a 15 kW IWM is taken as the research object.