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In this paper we study the thermal system of a DC motor, based on the generalized network proposed by [7]; To carry out the analysis of variables such as the heat in the motor core, the thermal resistance and the thermal capacitance of the motor. These variables are used in two objective functions to perform a multiobjective optimization of the system and find the respective Pareto Front and Pareto set with the optimum values reached by the optimization algorithms. The selected optimization algorithms are evMODAD, which is part of the Genetic Algorithm family and Normal Normalized Constraint (NNC).

Electric motors represent the main driving force for the movement of the different moving parts of a robot [1], where high energy efficiency is required to move objects of all types and sizes, as well as to overcome the Weight and inertia of the same robot components. Electric motors are widely used to perform the movement of moving parts in humanoid robots, which must perform diverse tasks inside and outside industries and homes. This autonomy requires that the robot can handle high mechanical loads in each of the engines involved in the complete movement to carry out the required action. Given this fact, it is that the electric motors used in humanoid robots must be able to deliver as much energy as possible, consuming a greater amount of current in a given time interval [2]. One of the main problems that arise when increasing the energy efficiency in an electric motor that is going to be used for practical applications in humanoid robots is the relation angular velocity & internal temperature of the electric motor; Since these, represented algebraically, provide functions that oppose each other and are related by the same variables that affect both in some way. Multiobjective optimization methods have been carried out widely to generate the most optimal design in synchronous and induction motors [3], [4], resulting in suitable design parameters about the characteristics of each engine and respective practical applications to work in the field.

Many of these studies have incorporated external cooling systems to the engines that require to withstand a greater external mechanical load and that therefore increase the heat of the motors when carrying out a work. Studies of this type can be seen in [5] where a system of capsulation of the chassis of two electric motors is used to minimize the amount of heat that is generated in the chassis of both motors and in this way to be able to deliver a greater amount of current and the copper winding of the motors, increasing the running current of the motor and therefore its revolutions per minute. This special encapsulation is also seen in [6], where coolant is circulated through the conduits of the encapsulation that surrounds the external part of the motor stator using a cooling system that has a radiator and a Flow control system. In this research it is proposed to study the thermal system of a DC motor based on the generalized network to generate two working objectives that oppose each other and to carry out a multi-objective optimization by means of the algorithms EvaMODA and NNC to find their respective Pareto front and Pareto set owith respect to the obtained

The proposed optimization problem represents the study of the thermal system of a DC motor based on the thermal circuit in Figure 1 according to [8] and the generalized network; Which is a uniform way of studying any dynamic system. This study will allow us to analyze the model of a simple thermal system that represents the equivalent thermal model of a DC motor, where we find a function that presents it in an equivalent way by analyzing its differential equation to obtain the equivalent to the function in the time domain from the frequency domain.