# Development of a Thermal Analysis Tool for Linear Machines
## 1 Introduction  
In the last few years, thermal optimization has become a really important stage in electrical machine design. The thermal sizing of electrical machines was previously based on several rules of thumb and rudimentary variables. If the maximum allowable temperatures were surpassed, the designers would increase the size of the machines to enhance heat dissipation. Hence, increased cost and volume had to be accepted as the only solution to overheating issues [1]. Thanks to the latest thermal analysis tools, the designers are able to make precise predictions of the working temperatures at different parts of the machines. Thus, both the cost and thermal operating point of the machines can also be optimized in the design stage. There are currently two main types of tools for the thermal analysis of electrical machines, numerical and analytical. The numerical tools divide the analyzed geometries into small samples. Then, the behavior of each sample is obtained with the physical formulations that describe the phenomenons that are taking place in each of them. These methods allow the analysis of complex geometries. However, they are quite demanding to set up, and the required computation time is significant, especially when complex geometries are analyzed [1; 2; 3; 4]. Computational Fluid Dynamics (CFD) techniques are one of the most common numerical methods for the thermal analysis of electrical machines. In this case, the tools compute fluid flows and heat transfer between solids and fluids [5]. It is hard to calculate the heat transfer coefficient analytically in regions with complex geometries, such as the end windings or the airgap. Thus, CFD simulations are often used to predict the operating temperatures of electrical machines [5; 6; 7; 8; 9; 10; 11]. However, as this technique requires high computational capabilities, the geometries of electrical machines are often simplified by means of symmetries and periodicities [5]. Nonetheless, the usage of these tools is essential for obtaining detailed results of especial heat exchange region configurations. For example, the influence of the end winding porosity in the heat transfer of the end region of a totally enclosed and fan cooled machine is analyzed in Reference [10]. The results show that increasing the porosity of the end windings from 3.7% to 15.2% can reduce the thermal resistance between the end windings and external the frame in 28%. Without a CFD tool, it would not be possible to predict such an improvement. Due to long computation times of CFD simulations, they are often adopted to predict the heat transfer coefficient of the housing with the ambient, in order to use this value in FEM or LP thermal analysis tools [5; 9; 12]. Thermal FEM tools operate similarly to CFD packages. In this case, numerical methods are used to calculate the conductive heat transfer between solids, instead of convection in fluids [1]. As these are numerical tools, any kind of geometry can be modeled with them, allowing precise calculations no matter the shape of the model [1; 2; 3; 4]. However, the convective heat transfer cannot be evaluated in these simulations. It has to be set by the user as a boundary condition [1; 3; 4]. For example, a 3D thermal FEM package is used in Reference [13; 14] to predict the operating temperature of a double-sided linear induction motor. The results are very accurate, but the authors had to estimate the value of the convective heat transfer coefficients. This is why thermal FEM simulations are commonly combined with CFD tools, but this solution generates very heavy computational loads. In this aspect, the analytical methods can be precise enough and much faster than their numerical counterparts [1; 3; 4; 15; 16]. The most common analytical approach for the analysis of the thermal behavior of electrical machines is the usage of Lumped Parameter (LP) thermal circuits [17; 18; 19]. In these models, the different heat flux paths are modeled with thermal resistors and capacitors [1].