Page - 132 - in Hybrid Electric Vehicles

function—in order to“translate” the original multi-objective problem into a single-objective one which can be solved more easily. This function presents simplicity and thus the overall optimization complexity is reduced. Let the general form be CFj = βi⋅Qi, where βi is a 1 × i row matrix which contains the weight coefficients of the cost function and Qi is an i × 1 column matrix, which contains the values of any motor’s quantities under optimization. Numerous cost functions can be produced in this way by altering the weights and/or quantities according to the problem specifications and user’s requirements. Normally, a semi-exhaustive search has to be done first in order to explore weights search space for linear scalarization and, con- sequently, to identify efficient weight combinations. In the case examined here, we consider the motors’ weight (Mtot) and efficiency (η) as equally important quantities for optimization, thus the above cost function is formulated as CF = 0.5 Mtot + 0.5 (1 − η). Next, the optimization procedure is applied for the determination of numerous variables, such as stator slot configurations, the number of turns per phase, the thickness and the width of permanent magnets, etc. At each step of the proposed approach, a large amount of con- straints have to be met. Some of them are imposed in order to ensure the acceptable electro- magnetic behaviour of the motor. For example, the motor’s rotor yoke should be sufficient enough in order to ensure that no saturation will occur on this part of the machine. Likewise, the maximum acceptable flux density at other parts of the motor will also be set as prob- lem constraints. The estimation of various electromechanical quantities using FEM analysis is indispensable in order to find out if any of these constraints is violated. If this happens, the adopted variables and geometrical parameters of the investigated topology have to be modi- fied and the procedure returns to its initial step. Another significant constraint is the maximum allowable value of the current density. For a totally enclosed in-wheel motor this value cannot exceed 10 A/mm2 because there is no physi- cal air circulation and temperature alleviation. Thus, the determination of this parameter and motor’s thermal behaviour is essential in order to ensure high driving performance even under overload conditions, reduce the risk of magnets demagnetization and enhance the durabil- ity of insulation materials. Also, the implementation of a liquid cooling system for the motor is required. The research in recent literature revealed that the commonly used cooling sys- tem configurations are not suitable enough for this application. The oil-spray cooling method, which uses a radiator, is very energy consuming and increases the manufacturing complexity and the installation cost [34]. The implementation of ducting system and slot water jackets is difficult due to the limited space [35]. For the same reason, circumferential and axial water jackets are difficult to be applied, since the length of the motor is very short. Consequently, a more appropriate cooling system topology, which is effective enough despite the small cooling system surface, is developed and described thoroughly in the next Section. For each derived motor configuration, its thermal model and the thermal model of the proposed cooling system are constructed, the heat sources and the materials properties are specified, and the boundaries conditions and the temperature coefficients are determined. Finally, the temperature distribu- tion and the overall performance of the cooling system are estimated. Its parameters are calcu- lated by taking into account the optimal energy management of the HEV and the fact that the system’s energy consumption must be kept as low as possible. The aim of the incorporation of motor’s thermal analysis in the proposed methodology is to guarantee that motor designs Hybrid Electric Vehicles132