The thermal behaviour of the electric armature was the object of many investigations from the beginning of electric machines popularization in the industrial techniques. One of the earliest found paper investigating thermal phenomena occurring in the electric mo-tor was published in 1902 [18]. That paper investigated temperature changes of the railway motor during its work. The earliest investigation of the comparison between closed and ven-tilated electric motor from the thermal point of view was found in [19]. The earliest found thermal behaviour of the induction motor, the most popular type nowadays, was presented in [20]. All the cited papers from the early XX century were focused on the temperature mea-surements of an electric motor using methods available at that time and estimation of the hot spots occurring in this machine. However, the first found papers investigating the impor-tant aspects of the measuring techniques of the electric machine temperature and referenc-ing these measurements to current room temperature was published later in [21,22]. One of the earliest paper dealing with the temperature behaviour and its influence on the elec-tric motor during the overload condition was found in [23]. An investigation of the cooling effects of active electric machine components, including natural and forced convection and accompanying radiation effect was published in [24]. Probably the earliest paper describing the mathematical formulation of the temperature distribution in small electric motor, us-ing mostly empirical and semi-empirical formulas, was published in 1923 [25]. The simple transient thermal model of the ventilated railway motors based on empirical equations was presented in [26]. The wide spectrum of temperature rise for the series of train motors was recorded during experiments and then published in [27]. The earliest found paper reviewing the available technology to switch off motor before the overheating failure was published in [28]. The thermal measurement in the past was also used to estimate losses from the elec-tric motor using so-called calorimeelec-tric method [29]. Even the latest research papers concern the inverse thermal modelling to estimate the motor losses, e.g., in [30]. The thermal anal-ysis describing main heat transfer mechanisms with the geometrical aspects of the brushed motor was presented as one of the first papers [31].
One of the simplest and the most popular models to predict the temperature distribution in electric machines is the lumped parameter model (LPM) [32]. This technique was spread in the middle of XX century and is still the tool of the temperature estimation in the current research [33]. LPM in the thermal analysis of electric machines is also known as the thermal network [34]. State of the art complex thermal networks contain dozens of the elements -nodes [35]. The simplest LPM allows for calculating the temperature of the entire element, e.g., one temperature for winding, when it is based on the zero-dimensional model without
any spatial resolution. Moreover, it does not contain precise information about the coolant flow. The essential parameters used in the thermal networks, e.g., convective heat trans-fer coefficients, are assumed or calculated usually from the empirical equations, which are presented in the heat transfer literature for simplified body shapes. These equations were derived from the heat transfer field analysis, e.g., in [36]. The simplified thermal models based on the thermal network concept were presented in [37]. The electromagnetic analysis based on FEM is used for the power loss estimation implemented as the heat sources in the LPM thermal model as it was presented in [38]. The main advantage of thermal networks is their sufficient accuracy with short computational times. Moreover, the application of the thermal networks is still up to date even for the simple models equipped with the calibra-tion procedure [39,40]. In the complex multiphysics analyses investigating the mechanical motor failure, the thermal LPMs are suitable as the auxiliary thermal model for the hot spot estimation, e.g, as in [41]. In that paper, the magnet bearing failure was investigated and thermal analysis was one of the parts of the research.
A more complex and accurate method for an estimation of the temperature distribution is Computational Fluid Dynamics (CFD). In this method, many characteristic parameters, such as the heat transfer coefficient, can be calculated directly and locally within a selected computational domain. This is possible by extending the model geometry to space outside the machine and, consequently, by considering the heat generated inside the motor and then dissipated directly to the ambient air [42,43]. As a result, a more detailed analysis leads to more accurate heat dissipation predictions. In the literature, there are many studies that compare CFD and LPM with respect to experimental data [44]. One of the most important works about thermal modelling of the electric motor operation describes the CFD model formulation and the usage of the CFD field results in the LPM analysis [45]. In the literature, there are also studies based on the Finite Element Method (FEM), which is usually applied when researchers focus only on the thermal conduction in solids. One of the studies with thermal conduction analysis in the motor housing is the study of [46]. In the cited work, the authors assumed heat flux from the internal surface of the housing frame and analytically calculated the heat transfer coefficient. Consequently, the estimated temperature field of the finned housing was compared with the conducted experimental study. In works based on FEM methods investigating EV motors, simplifications such as neglecting radiation phe-nomena or treating fluid medium as a solid with convective boundary conditions is a way of getting reasonable solutions with the opportunity to model the transient phenomena with the motor power peaks, e.g., in [47]. Zhang et al. [48] presented a coupled analysis between the electromagnetic and thermal solvers based on FEM. However, the external heat transfer coefficient was calculated analytically, while radiation between internal elements was
as-sumed to be negligible. Coupling of the electromagnetic analysis using FEM with thermal networks was used to estimate temperature of the motor components in [49]. Coupled ther-mal and electromagnetic analysis of the motor working in high temperature applications was also presented in [50]. The temperature field in the coupled multiphysics analysis in a case of the superconducting motor for ship propulsions was presented in [51]. However, in that paper, the thermal model was not described in detail. The power loss generation and ther-mal behaviour investigated numerically and experimentally is well known for a large power machine which still is a current object of the studies [52].
Heat transfer intensification from electric motors was the object of many studies in re-cent years and it is still current relevant topic. The review paper concerning cooling tech-nologies and heat analysis of PM BLDC machines is presented in [49]. The review paper investigating the systems improving technologies of the heat dissipation from electric ma-chines is also presented in [53,54]. An interesting work was presented by Jungreuthmayer et al. [55], where thermal analysis was conducted for a water-cooled electric motor. A concept of using water jacket as the heat dissipation intensification is one of the most popular and effective solution in industrial practice and well described in the literature when water trans-port system is available and reasonable [56,53,57]. The solution with the oil coolant flowing within the hollow shaft was described in [58] and its effect on the motor temperature reduc-tion was compared with the water jacket applicareduc-tion and air cooling. The thermal analysis of the permanent magnet motor in the planetary gearbox drive system with oil coolant flowing was also investigated in [59]. An investigation of the cooling system with centrifugal im-peller in a brushed motor was presented in [60]. A detailed investigation of the heat transfer intensifications method applied to the high power switched reluctance motor and cover-ing the fan implementation was presented in [61]. In that paper, a coupled electromagnetic and thermal analysis was discussed. One of the state-of-the-art concepts of heat transfer intensification from motor windings by using spray cooling medium applied directly on the conductors were presented in [62,63,64]. These concepts were investigated experimentally and numerically. To intensify the temperature reduction effect, the combined techniques are often applied. One of the combined methods is connecting water jacket with an internal ventilation system and in the case of the high-speed motor, this combination was tested and described in [65]. However, spray cooling or external water cooling systems or impellers in-tegration with motor is not often suitable for small power machines which are constructed with using passive systems of heat dissipation. For this reason, systems of the heat dissipa-tion improvement using passive elements as radiators and thermal fillers are analysed in this dissertation. The effect of windings temperature reduction can be reached by the motor con-struction modification as it was proved in [66] where the concept of the core slot shape was
changed. The construction change based on the passive method of heat dissipation intensi-fication is also an application of the potting materials or in other words thermal fillers. These materials were investigated in studies such as [67,68,69,70]. In the cited papers of Polikar-pova, thermal behaviour and the potting material application in, e.g., the axial flux electrical machines were investigated. This machine type was also the object of the study of the ther-mal phenomena in [71]. Moreover, therther-mal improvement of the large axial machine with a combined method of heat dissipation concepts was described in [72]. The potting material application was considered in the large motor dedicated to work in the food and beverage industry and that was described in [73]. Materials with higher thermal conductivity are more effective as thermal fillers. Therefore, the potting element could contain additional particles and components within the internal structure of this element [74]. In the transient analyses of the thermal motor behaviour, the effective solution of the temporary heat dissipation im-provement is the application of the Phase Change Material (PCM). In this application, the material changes its phase from solid to liquid during the heat accumulation process and in the opposite way when the accumulated heat is released. The PCM implementation in the motor construction allows for increasing the heat capacitance during the high current flow that occurs very often when a motor starts or is temporarily overloaded. This concept was verified numerically, e.g, in [75]. Moreover, an application of the PCM as the way of heat transfer improvement is also noted in the solution of heat pipes. In heat pipes, the phase change of internal structure occurs. The phase change of the medium, namely the vaporiza-tion process, occurs in the hot region, while the pipe filler condensates in the cold region.
The medium circulation is accelerated using gravitational forces or capillary effect. There-fore, with the heat pipes application, the motor work can be also characterised as a steady state. Application of heat pipes filled with phase change material in the windings region and its effect were examined experimentally and numerically in [76,77]. This concept was also investigated numerically in the case of the motor applied in EV such as electric motorcycle [78]. The combination of the mentioned ideas as fan and water jacket implementation with accompanying heat pipes was investigated, on the case of the motor in EV, numerically and experimentally in [79]. In the cited paper, the cooling strategy was realised using combined methods with the dedicated control system.
The literature does not offer many publications concerning validated models of heat transfer from small power electric motors in which natural convention with accompanying radiation from the external surface of the housing is the main mode of power losses dissi-pation. The literature presents investigations based on validated models of objects which nature is similar to electric motors but the studies are based rather on different heat source than motors. The case in which natural convection from a small heat source in the closed
cavity was investigated numerically and next validated experimentally was presented in [80].
Nevertheless, electric motors dissipate their power losses by i.a. partially forced convection resulting from motion of rotating elements. Therefore, studies showing the flow field in-side and outin-side the motor casing are not prevalent in the literature. One of the examples in which water velocity field was the investigated object of measurements, is the work of Aubert et al. [81], where the velocity measurements were conducted in a water-filled axial machine.
Numerical results of the air velocity field within and outside the motor were validated in works connected with this dissertation [82,83].