Coupled thermal electromagnetic numerical modelling of an effective heat dissipation process from an electricmotor; Sprzężony cieplno-elektromagnetyczny model numeryczny procesu efektywnego rozpraszania ciepła z silnika elektrycznego - Digital Library of

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Bartłomiej Melka

Coupled thermal electromagnetic numerical modelling of an effective heat dissipation process from an electric motor

Ph.D. Thesis

Institute of Thermal Technology

Faculty of Energy and Environmental Engineering Silesian University of Technology

Gliwice, Poland, 2019

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Author:

Bartłomiej Melka, M.Sc.

Silesian University of Technology

Faculty of Energy and Environmental Engineering Institute of Thermal Technology

S. Konarskiego 22, 44-100 Gliwice, Poland e-mail: Bartlomiej.Melka@polsl.pl

Supervisor:

Jacek Smołka, Ph.D., D.Sc.

Associate Professor at Silesian University of Technology Faculty of Energy and Environmental Engineering Institute of Thermal Technology

S. Konarskiego 22, 44-100 Gliwice, Poland e-mail: Jacek.Smolka@polsl.pl

Co-supervisor:

Janusz Hetma ´nczyk, Ph. D.

Faculty of Electrical Engineering

Department of Power Electronics, Electrical Drives and Robotics B. Krzywoustego 2, 44-100 Gliwice, Poland

e-mail: Janusz.Hetmanczyk@polsl.pl Polish title:

Sprz˛e˙zony cieplno - elektromagnetyczny model numeryczny procesu efektywnego rozpraszania ciepła z silnika elektrycznego

Reviewers:

Maciej Jaworski, Ph.D., D.Sc.

Associate Professor at Warsaw University of Technology Faculty of Power and Aeronautical Engineering

Institute of Heat Engineering

Nowowiejska 21/25, 00-665 Warsaw, Poland e-mail: Maciej.Jaworski@itc.pw.edu.pl Mariusz Rz ˛asa, Ph.D., D.Sc.

Associate Professor at Opole University of Technology Faculty of Mechanical Engineering

Department of Thermal Engineering and Industrial Facilities S. Mikołajczyka 5, 45-271 Opole, Poland

e-mail: M.Rzasa@po.opole.pl

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to my beloved wife Karolina

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Acknowledgements

I would like to sincerely thank my supervisor Jacek Smołka. I direct thanks especially for his support, professional guidelines in scientific writing and for many constructive ideas given, not only in the scientific field. During my PhD studies, he showed me the real perfec- tionism of the scientist. I admire his never expiring spirit of hard work.

I would also like to express my gratitude to my co-supervisor, Janusz Hetma ´nczyk for many pieces of advice in the electric field and for help and many ideas during the experimental research.

I thank Paweł Lasek for consultations, his useful advice in the electromagnetic modelling and for his support during the experimental research.

I would also like to thank Zbigniew Buli ´nski for his cooperation in velocity and thermal measurements during Experimental Campaign I. I would like to express my gratitude to Arkadiusz Ryfa for the advice given during the calibration procedure. Here, I express also thanks to Michał Palacz for teaching me the aspects of the infrared camera operation. Last but not least, I would like to thank Tadeusz Kruczek for the advice about the high emissivity covers.

I would also like to express my gratitude to my Family – mother Ewa, sister Maria, father Grzegorz and parents in law – Bo˙zena and Andrzej. I thank for their support during my PhD studies. In particular, I would like to thank my wife – Karolina to whom this dissertation is dedicated.

Finally, I wish to thank all the people (not listed here) who made this dissertation possible.

Financial assistance was provided by grant no. DEC-2011/03/D/ST8/04171 funded by the National Science Centre, Poland. This work was also partially supported by statutory research funds of the Faculty of Energy and Environmental Engineering of the Silesian Uni- versity of Technology within grant no. BKM-559/RIE6/2016.

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Nomenclature

Latin Symbols

g gravitational acceleration vector, m · s⁻²

G_b generation of turbulence kinetic energy due to buoyancy, kg · m⁻¹·s⁻³

G_k generation of turbulence kinetic energy due to mean velocity gradients, kg · m⁻¹·s⁻³ h specific enthalpy, J · kg⁻¹

HC coercivity of the permanent magnet, T I radiation intensity, W · m⁻²·sr⁻² I_S current density vector, J · m⁻²

k_{i j} thermal conductivity in the specific direction, W · m⁻¹·K⁻¹ k_{e f f} effective thermal conductivity, W · m⁻¹·K⁻¹

k_t turbulent thermal conductivity, W · m⁻¹·K⁻¹ k_{t ur b} turbulence kinetic energy, J · kg⁻¹

p pressure, Pa

r position vector

s direction vector

s_s scattering direction vector

t time, s

t_c temperature,^◦C

T temperature, K

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u velocity vector component parallel to the gravity direction, m · s⁻¹ V electric potential, V

v velocity vector, m · s⁻¹

w velocity vector component perpendicular to the gravity direction, m · s⁻¹ v^T transposed velocity vector, m · s⁻¹

Y_m fluctuating dilatation dissipation, kg · m⁻¹·s⁻³ Greek Symbols

ε turbulence dissipation rate, J · kg⁻¹·s⁻¹

∆PCu copper (winding) losses, W

∆PF e core (iron) losses, W

∆Pmech mechanical losses, W

µ dynamic viscosity, kg · s⁻¹·m⁻¹ µ_t turbulent viscosity, kg · s⁻¹·m⁻¹ ρ density, kg · m⁻³

¯¯τ stress tensor, Pa Abbreviations

C F D Computational Fluid Dynamics

H T C Heat Transfer Coefficient, W · m⁻²·K⁻¹ LD A Laser Doppler Anemometry

P I V Particle Image Velocimetry

P M B LDC Permanent Magnet Brushless Direct Current

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Chapter 1 Introduction

1.1 General background and motivation

Nowadays, the main human concern is how to save Earth from continuous anthropogenic degradation. Environmental and political tendencies prompt the industry to reduce the usage of non-renewable energy sources. It leads, among others, to increase of the meaning of electrical power drives in transport and other branches of industry replacing at the same time internal combustion engines characterised by lower efficiency of energy conversion [1].

Choosing this strategy, the reduction of anthropogenic emission of CO2to the atmosphere would be achieved, while the electricity powering of electric vehicles (EV) will be secured by the renewable sources. In the world regions where primary source utilised for electricity generation is non-renewable, e.g. power plants fired by hard coal, this strategy could also be effective. It is possible mainly because, at some level, fossil fuel conversion is more efficient and more environmental friendly in larger units with advanced flue gas treatment systems.

However, the concept of spreading EVs usage on the large scale is now limited mostly by price and the current state of electric power storage technology. Nevertheless, power storage solutions for EV are still being developed. In the near future, we can expect more and more effective technologies available on the market [2,3,4,5]. In addition, challenge for broader spread of the EV concept is also the necessity of the electric grid integration with charging stations allowing for fast charging of the batteries. It is observed that the technology in this branch is also rapidly developing [6, 7]. Electric motors used as the main drive source in EVs should be powered from the direct current compatible with batteries. Therefore, in up- coming years, the increasing usage of electric motors driven directly from the direct current

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sources can be expected.

Two main technologies of electric motor construction are available for sources of the direct current and they are brush or brushless solutions. Electric motor with brushes can be characterised as the one with simpler construction and lower price [8], but this kind of solution also requires a systematic brush replacement and an additional maintenance procedure. The efficiency of the motors with brushes is also decreased by friction losses during the mechanical commutation process and often by higher electrical contact resistance between brushes and a mechanical commutator [9]. On the other hand, motors constructed in the brushless technology have to be equipped with an electronic commutator but they are free from the pointed disadvantages of brush technology [10]. Moreover, the main advantage of the brushless motor technology is its higher efficiency which is the rationale of the higher price of this product. The brushless motors can also be characterised by higher power density. Those reasons motivated the choice of permanent magnet brushless direct current (PM BLDC) motor to become the main subject to be studied in this thesis.

Thermal analysis should play an important role in an electric motor design process [11].

It allows to estimate the maximum temperature in the machine and find the location of a potential overheating. The overheating protection is especially important in the area of the motor windings [12]. The motor construction should also be protected from reaching temperature higher than allowable from the thermal stress point of view. In many works, the thermal analysis of the electric motor is treated as the key aspect of the motor designing, e.g., in [13]. Moreover, thermal analysis allows for reduction of the machine size while maintaining the safety margin and thus also allows for the decrease of the material costs. The thermal motor behaviour optimisation could also decrease the copper losses in the machine since the amount of the copper losses is connected to windings resistance and depends on its temperature. The lower temperature of the internal motor elements could also ensure maintaining the operating point beyond demagnetization of the permanent magnets [14] in motors such as PM BLDC. The enhanced high-temperature performance of rare-earth permanent magnets was also investigated in [15]. The temperature field in the similar motor type as PM BLDC, namely a switched reluctance motor, was investigated in [16,17]. The thermal motor analysis with the accompanying heat dissipation improvements could also allow to overload the machine more than in its previous design. Due to the presented facts, the thermal analysis should always be included in the electric motor design process. For this reason, the thermal analysis is the main object of the presented dissertation.

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1.2 Thermal analysis of electric motors in literature

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 motor 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 ventilated 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 measurements 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 important 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 electric 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, using 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 electric motor using so-called calorimetric method [29]. Even the latest research papers concern the inverse thermal modelling to estimate the motor losses, e.g., in [30]. The thermal analysis 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

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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 transfer 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 calibration 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 phenomena 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-

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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 thermal 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 thermal 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 technologies 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 machines 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 transport 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 reduction was compared with the water jacket application 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 covering 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 integration 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 dissipation 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 construction modification as it was proved in [66] where the concept of the core slot shape was

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changed. The construction change based on the passive method of heat dissipation intensification 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 thermal phenomena in [71]. Moreover, thermal 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 improvement 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 dissipation. 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

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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 inside and outside 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].

1.3 Aim of the research

The motivation and literature survey presented in the previous section shaped the goal of the thesis that is defined as the heat dissipation intensification concepts from PM BLDC small power motor which allow to decrease the windings temperature. The thesis verifies these concepts experimentally and numerically.

Therefore, the hypothesis of the dissertation is formulated as: "The combination of passive techniques for the heat dissipation improvement is an effective way to decrease the temperature of the windings in the PM BLDC small power motor, including application of high emissivity layer, extension of the external surface of the housing and application of the thermal filler (potting material)". The hypothesis was formulated on the basis of the literature review presented in the previous section.

1.4 Object of the research

The object of this study was a PM BLDC motor. Permanent magnets applied in the analysed motor were neodymium magnets characterised by a remanence of approx. 1.05 T. The rated power of the motor reached approx. 430 W, while its rated voltage was at the level of 24 V and rated current of 21.1 A. The rated mechanical torque of the motor reached 1.09 Nm, while its rated speed was 3780 rpm. The rated parameters classified investigated machine in the group of the small power motors. The studied machine was the object of the experimental and numerical investigation presented in the following chapters of the dissertation.

According to the introduced motivations, the chosen concepts of the heat dissipation intensification from the analysed motor are verified in the thesis. Therefore, in the current section,

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these concepts are described with the research object presentation for each variant.

Images of the disassembled motor construction are presented in Fig.1.2, while a simplified scheme of the investigated motor construction is also shown in Fig. 1.1in the bottom left corner. Fig. 1.1also contains the elements of the test rig and is described in the following chapter devoted to the experimental part of the thesis. The motor construction contains stator and motor elements. The stator core is in the internal front part of the motor. The three-phase windings are wounded on the six-tooth stator core, while the bobbin (plastic spacer) between the windings and core is placed. Along the stator core of length 0.05 m, the rotor core with fixed eight pairs of the neodymium magnets is located. In the rear part of the rotor, the additional ring with three magnets is placed to control the current rotor position. In Fig. 1.2(a), the front endcap of the motor is visible. The ball bearings are fixed to each endcap and position the rotor at the right place. The front and back of the internal stator construction are partially separated by Printed Circuit Board (PCB) plate visible in green colour in Fig. 1.2(b). On the PCB plate, the three copper paths are placed which connect each power phase wire with the windings. Moreover, on the internal part of the PCB plate, the hall effect sensor is placed to read the rotor position from the magnetic field of the mentioned ring with three magnets. The length of the motor reaches 0.14 m when measured between external surfaces of the endcaps. The width of the aluminium brackets reaches 0.2 m. Therefore, in all the tested cases, the brackets were the natural external surface extension.

During this study, three different concepts of heat dissipation improvement were investigated including emissivity modification of the housing walls, two radiators application and the thermal filler implementation in the motor housing. The first step, while preparing the motor for the experimental tests, was to mount the aluminium brackets to the motor that allowed for the motor stabilisation and its operation on the test rig. Therefore, these brackets were treated as an integral part of the motor and were also under the amendments during the realisation of the heat dissipation intensification methods described in the current chapter.

The concepts of heat dissipation improvement were based on passive methods. Firstly, the motor before any modifications was tested on the dedicated test rig and was referred to Variant A. This variant was the object of the previous studies published in [42,83] and the image of this variant is presented in Fig. 1.3(a). The first concept of heat dissipation improvement was based on covering external surfaces of the motor and motor brackets by a thin layer of material that was characterised by high emissivity and that improvement was denoted as Variant B shown in Fig.1.3(b). The high emissivity layer applied in Variant B was also applied in the next amendments. The second concept of heat dissipation improvement

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Shaft

Windings Stator Core NdFeB

Magnets

Rotor Core

GENERATOR Universal

Coupling

Star Connection to Set of Resistors 3 phase Electronic

Commutator

PCB Plate

DC Power Supply

Power Supply of Commutator

Plexiglass Cover Housing

Front Endcap

Back Endcap

Figure 1.1: Simplified scheme of the test rig during Experimental Campaign I

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Figure 1.2: Images of the disassembled motor construction: (a) rotor of the motor, (b) stator of the motor

was based on the aluminium radiators mounted on the external motor walls. This concept was realised in two configurations: the radiator with a higher number of smaller fins (Variant C) and the radiator with a lower number of bigger fins (Variant D) presented in Fig. 1.3(c) and Fig. 1.3(d), respectively. Both radiator types were mounted to the motor housing area which was approx. 0.015 m², while the external surface of the radiator in Variant C was 0.085 m²and the external area of the radiator in Variant D reached 0.1125 m².

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Figure 1.3: Images of the motor on the test rig in five variants: (a) Variant A: the motor be- fore modifications, (b) Variant B: external surfaces of the motor housing covered by graphite, (c) Variant C: the motor equipped with radiators with smaller fins, (d) Variant D: the mo- tor equipped with radiators with bigger fins and (e) Variant E: the motor with thermal filler around the windings

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All the described Variants from B to D were connected with the heat dissipation im- provement applied to the external part of the motor (external surfaces of the housing and brackets). However, the motor temperature reduction is a result of the winding tempera- ture reduction. For this reason, the last concept denoted as Variant E, that should lead to the temperature reduction in the region of the winding, was the application of the thermal filler in the free space within the motor housing, specifically in the stator region. During the modification of the motor leading to Variant E, the original hall effect sensor specifying the rotor position for the motor control system, placed within the motor, was damaged. There- fore, to reproduce a signal of the rotor position to the electronic commutation system, the in-house construction was prepared. This construction was mounted on the shaft in the rear part outside the motor. It reduced at some level the heat dissipation possibility via radiation from the rear bracket of the motor comparing to Variants from A to D. On the other hand, an additional rotating element used as the rotor position controller could increase the forced convection in this region. However, the assumption was made that potential influence of this controller replacement is not significant from the thermal point of view. Hence, the results of the specific variants can be compared between each other. The pictures describing Variants from A to E are presented in Fig. 1.3, while the last photography also denoted as Variant E shows the in-house construction of the rotor position controller described earlier.

The last tested configuration combined Variants B, D and E. This configuration was denoted as Variant E+D.

1.5 Outline

The dissertation was divided into five chapters that can be summarised as follows:

Chapter1is the current one.

Chapter2describes experimental activities conducted during the study. The presented measurement procedures are described as two experimental campaigns. The first one focuses on the measurement of the air velocity within and around the analyses motor and on the simultaneous temperature measurements. In that experimental campaign, a set of constant temperature anemometers, Laser Doppler Anemometry technique and a set of cal- ibrated thermocouples were used to analyse Variant A. The second experimental campaign was focused only on the thermal measurements using calibrated thermocouples of the different passive heat dissipation intensification concepts verifying all the variants presented in Chapter1.4.

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Chapter3 contains description of the formulated numerical models. In that chapter, two thermal models are presented. Each of them corresponds to the performed experimental campaigns. In both developed models, one of the Reynolds-Averaged Navier–Stokes (RANS) turbulence models is used during the calculation procedure. Moreover, two models investigating thermal radiation phenomena are tested. In the windings and core region, the anisotropic thermal conductivity is applied and described in the chapter. For this reason, the values of directional thermal conductivity were determined using a separate model. The set of boundary conditions for each model were also introduced. The electromagnetic model and its coupling procedure with second thermal model is also described.

Chapter4discusses the results of the experimental campaigns and the numerical model presented in the previous chapters. Firstly, for each model and experimental campaign, the validation procedure of the numerical results is introduced for the temperature field. In the presented sections, the validation of velocity field located outside and inside the investigated machine is also described.

Chapter5summarises the dissertation. The general overview of the thesis is summed up and final remarks are presented. The conclusions about the validation procedure are drawn.

The most effective investigated method of the heat dissipation intensification is pointed out and recommended. Moreover, the advantages and disadvantages of all investigated methods are highlighted. The chapter contains also suggestions for further works which could be conducted within the discussed research area.

The numbered chapters are followed by Bibliography presented in the order of citations occurring in the dissertation. Next, the list of figures is presented. Subsequently, the thesis introduces an abstract in English and Polish.

It is also worth noting that the dissertation is partially based on the papers registered in the Scopus database. For this reason, some fragments presented in the dissertation can also be found in those papers [42,82,83,84]. Therefore, the last two of these papers were published in journals indexed in JCR. In those papers, I am denoted as a corresponding author.

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Chapter 2 Experimental research

In this chapter, two independent experimental campaigns are presented. For each campaign, the motor mounting with the test rig components and measuring devices are presented and described. Moreover, all the investigated operating points in each campaign are introduced.

In Experimental Campaign I, the machine under investigation was a low-power electric motor tested only in Variant A which was the primary variant described in Chapter1.4. The main aim of this campaign was a validation procedure of the thermal model, presented in the next chapters, by measurement of both: velocity and temperature in selected positions for all the investigated operating points.

The second campaign, denoted as Experimental Campaign II, focused only on thermal measurements without velocity recordings, but all the presented concepts of heat dissipation enhancements were tested. Therefore, Experimental Campaign II included all variants, i.e., from Variant A to Variant E+D presented in Chapter1.4. However, the number of operating points for each variant in this campaign was limited when compared to Experimental Campaign I.

The detailed description and differences of each test rig configuration for each campaign are presented in the following sections.

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2.1 Experimental Campaign I

2.1.1 Motor description and test rig components

The test rig consisted of two the same PM BLDC motors connected to each other by a universal coupling. A simplified scheme of the constructed test rig is presented in Fig.1.1in the previous chapter. The first motor was working in the motor mode (on the left-hand side in Fig.1.1), while the second one was operating in the generator mode. In consequence, the second motor was used as the load for the first machine. The research object was the first machine working in the motor mode. Therefore, all the measurements were recorded only within this machine.

As it was mentioned in Chapter1.4, the motor was mounted on the test rig using aluminium brackets. The natural rubber distances were used to fix brackets as well as to limit heat conduction towards the aluminium base. The described components of the test rig were covered by an acrylic glass (plexiglass) cover. That component was applied to reduce velocity fluctuations coming from the laboratory space, which could disturb the experimental records. The plexiglass cover was schematically pointed by red colour frame in Fig. 1.1 presented in the previous chapter. The cover was a square-shaped channel open from the bottom and closed at the top. Its image is presented in Fig. 2.1. In this figure, the boundary conditions presented in the following chapters are also depicted. In addition, an 8-mm-hole was drilled in the top wall to enable the outflow of the air moving by the natural convection mechanism. The above mentioned components were the main parts of the test rig and all of them were taken into consideration in the formulated CFD model described in the following chapters.

The additional components of the test rig were located beyond the acrylic glass cover and were used as power supply and power output from the described machines. Those components are also schematically presented in Fig. 1.1above the red dotted rectangle. The DC power supply was connected to the motor through an electronic commutator. The control of electronic commutator was powered by a second separate power supply. In the test rig, the electronic commutator consisting of MOSFET transistors was used as a control system for the PM BLDC motor which allowed for supplying the motor by the converted three-phase current. The system of resistors was used to dissipate electric power produced by the generator. The mentioned devices were connected by a set of wires and connectors.

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Outlet

Inlet

Calculated HTC

& measured ambient temperature

Figure 2.1: Image of the test rig covered by acrylic glass cover with schematically depicted boundary conditions applied in a numerical model

2.1.2 Measuring devices

During Experimental Campaign I, the temperature was measured using 22 calibrated T- type thermocouples. The thermocouple calibration was performed using a Fluke 9100S unit with an accuracy of ± 0.3^◦C. The calibration procedure was conducted for all the thermocouples at the same time in the range between 25^◦C and 100^◦C. The image of thermocouples within the calibration unit during this procedure is presented in Fig. 2.2. The set of T-type thermocouples were connected by the National Instruments module to the computer software of the same producer. The LabVIEW software was used for the measurement records.

The positions of thermocouples mounted within the motor are schematically presented in Fig. 2.3using red dots. In addition, these dots are tagged with letter T and numbers for a particular sensor.

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The thermocouples that were used during the measurements numbered and schematically shown in Fig.2.3according to the following manner:

• inside the front part of the motor fixed to the winding directly to winding surfaces #T1 -#T4 and #T6;

• inside the front part of the motor fixed to the iron core at the end of the tooth #T5;

• between core and housing #T7,

• inside the back part of the motor #T8-#T11,

• on the external part of the motor housing #T12-#T17,

• above the analysed motors at heights of 15, 25, 38 and 48 cm from the upper housing wall, respectively #18 - #21.

Figure 2.2: Calibration unit with thermocouples during the calibration procedure

The constant temperature anemometry (CTA) technique was used to conduct measurements of the air velocity outside the machine. The CTA measuring equipment was produced by the Strata Mechanics Research Institute [85]. This type of device consists of thin heated wire or wires. The CTA measurement relies on the indirect measure of the velocity.

During the measurement, the heat losses from the hot wire occurring in the fluid flow are recorded and, in consequence, the specific component of the velocity is estimated. This effect is achieved by keeping the sensor resistance as constant using servo amplifier connected with the Wheatstone bridge. The detailed description of the CTA technique can be found in

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Shaft Windings

Stator Core NdFeB

Magnets

Rotor Core

T1 T2

T6 T3

T4 T5

T7 T8

T9 T10

T11

A1 A2 A3 A4 A5 A6 A7

A8 A9 A10 A11 A12 A13 A14

A15 A16 A17 A18 A19 A20 A21

A22 A23 A24 A25 A26 A27 A28

GENERATOR Coupling

LDA 2 LDA 1 A A-A

LDA 2 LDA 1

A

0.047 m 0.04 m

T10

T9 T8

T11

Figure 2.3: Scheme of the studied motor with thermocouple and anemometer positions.

[86]. In the experiment, the parallel-array probes were used. The vertical component of the velocity vector outside the motor was measured by a set of seven constant temperature anemometers at four height levels. The positions of these sensors are indicated in Fig. 2.3 as green square markers with letter A and numbers presented in green colour. The vertical plane, where the points were located, crossed the axis of the machine. Therefore, the velocity field was measured above both machines. The calculated errors were estimated on the basis of the standard deviation from the conducted records. Their values are presented within Section4.1that is devoted to the results discussion.

The velocity field within the motor housing in its rear part was measured using a Laser Doppler Anemometry (LDA) system or in other words Laser Doppler Velocimetry. The LDA technique is based on the optical measuring system in a semi-transparent medium basing on the Doppler effect in a laser beam to measure the velocity. The experimental investigation focuses on the transparent medium flow, i.e., the air needs additional seeding. In this thesis, smoke was used as the seed. The quality of the measurement was dependent on the seeding quality of the measuring space. The seeding was implemented before the LDA recording ses- sion and its quality varied during the single measurement in the neighbouring points. The main LDA system component was the FlowExplorer unit in which laser and optics sensors were mounted. Auxiliary equipment used in the LDA system allowed for powering the main unit and converting the recorded signal to the computer dedicated software. Moreover, auxiliary equipment allowed for positioning the main unit which was fixed to the gantry. The

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equipment produced by Dantec Dynamics was rented to conduct the measurements.

The LDA system was used to measure velocity components in two directions: horizontal and vertical. The velocity measurements within the housing were performed in two sections.

The first section was on the height of the shaft axis. This section contained the distance from the housing wall to the shaft. Its height is marked by a blue triangle with the label LDA1 in Fig.

2.3. The second section, where the velocity measurements were also conducted, included the distance from the wall to the centre of the motor. The height of this section is marked by a blue triangle with the label LDA2 in Fig.2.3. The distance between each recorded point was 1 mm. In the measured region, the motor shaft was covered by a thin layer of the non- reflecting graphite cover. It allowed for the measurement recording without laser reflections from the shafts.

The Particle Image Velocimetry (PIV) technique was also planned to be used during the study to measure the velocity field above the motor. However, the low quality of the recorded measurements did not allow to get reasonable results. During the PIV measurements, a procedure with the smoke seeding application and accompanied by the laser plane allowed for the flow visualisation by classic photography. Therefore, in Chapter4, where the results are discussed, the selected images of the flow are presented in the chosen instants of time.

The electric measurements were carried out using a Sanwa PC5000a digital multimeter, Chauvin Arnoux E3N current probes and a Tektronix MSO 3014 oscilloscope. The rotational speed of the machine was read from the oscilloscope connected to the electronic commutator which passed the signal from the hall sensor placed within the motor. Additionally, signal converters and recording systems were necessary for each device group to enable the data acquisition. The described test rig was also presented in detail in [83].

2.1.3 Measurement procedure

During Experimental Campaign I, the temperature, velocity and electrical measurements were executed for three rotational speeds at four different loads of the generator side. The load was modified by changing a connection of four resistor sets per phase presented in Fig.

1.1on the right-hand side. This allowed for the examination of 11 different operating states presented in Tab. 2.1. The operating points in Experimental Campaign I were numbered using Roman numerals.

The main aim of the measurement procedure was to record the temperature and velocity

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Table 2.1: Operating points tested on the test rig during Experimental Campaign I

Operating Generator Power Av. RMS Rev. ∆PCu, ∆PFe, ∆Pmech, Point No. load, supply current of speed,

voltage, the phases,

Ω V A rpm W W W

I 0.25 9.43 10.70 1415 7.95 3.16 1.27

II 0.25 24.44 20.50 3489 33.52 11.57 3.12

III 0.33 9.16 8.98 1415 5.38 3.16 1.27

IV 0.33 16.66 14.20 2501 14.58 7.02 2.24

V 0.33 23.88 17.83 3572 24.57 11.99 3.20

VI 0.50 8.60 6.68 1415 2.94 3.08 1.24

VII 0.50 15.83 10.73 2501 8.05 7.02 2.24

VIII 0.50 22.77 14.13 3572 14.74 11.99 3.20

IX 1.00 8.05 4.07 1389 1.08 3.08 1.24

X 1.00 14.44 6.45 2501 2.78 7.02 2.24

XI 1.00 20.83 8.74 3489 5.27 11.57 3.12

values by the presented measuring devices. Moreover, the other aim of the measurement procedure was the power loss estimation.

Therefore, in the mentioned Tab.2.1, the calculated losses are also presented. The copper losses ∆PCuwere calculated according to the multiplication of square current in A and resistance of windings in Ω. In the resistance definition, the electric resistance of the windings was estimated taking into account the temperature measured for each load. The core losses

∆PFe, also known as iron losses, were calculated from the characteristics collected during the idle state measurements. They were dependent on the rotational speed. The mechanical losses ∆Pmech were first covered in the mentioned characteristic built on the base the idle state measurements. However, in the next step, they were separated. The mechanical losses

∆Pmech were calculated using a methodology presented by the bearing manufacturer [87].

All the measurements were performed when the thermal steady state has been reached.

The estimated losses were implemented in the numerical models that were presented in the following chapters. In general, they were defined as the volumetric heat sources in the motor components where those losses appeared.

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2.2 Experimental Campaign II

2.2.1 Motor description and test rig components

The experimental part at this stage of the research was realized on a modified test rig when compared to Experimental Campaign I. A torque sensor was mounted between the motor and the generator to compute the motor output power. The measurement of the machine torque was a significant improvement in the test rig. Similarly to Experimental Cam- paign I, the rotational speed of the machine was read from the oscilloscope connected to the electronic commutator which passed the signal from the hall effect sensor placed within the motor on the PCB plate. However, this time, the information about rotational speed and torque were used to compute the effective motor power. This was not possible in Ex- perimental Campaign I without torque sensor. Experimental Campaign II was conducted without plexiglass cover because its main aim was to perform only thermal measurements, i.e., without the velocity measurements. Moreover, the described application of the heat dissipation enhancement was investigated using the infrared camera which was possible to conduct only without acrylic cover. Eight thermocouples were mounted within the motor, while the remaining fourteen thermocouples were fixed to measure the temperature of the motor housing and brackets or to control the temperature of specific elements of the test rig.

The thermocouples specific locations are introduced in the next subchapter. All the considered variants of the motor passive cooling enhancements which were described in Section 1.4as Variants from A to E+D, were investigated during Experimental Campaign II.

2.2.2 Measuring devices

As it was previously mentioned, Experimental Campaign II concentrated on thermal measurements conducted for all the variants representing concepts of the heat dissipation enhancement. To investigate thermal motor behaviour during Experimental Campaign II, only thermocouples were implemented in the study. The investigation of all the variants of the considered machine was conducted with the relocation of the temperature sensors, presented in the following paragraphs, after the process of the thermal filler implementation. However, the corresponding positions of the sensors comparing to the previous manner were proposed to present the temperature field within the motor. In the following paragraphs, the detailed temperature sensor positions are introduced.

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Shaft

Windings Stator Core NdFeB

Magnets

Rotor Core

T4 T1

T2

Couplings A

A A-A

Torque Sensor Shaft

Rotor Core

T4 T1

T2 T9

T3

T5

T6

T6 T7

T7

T9

Star Connection to Set of Resistors 3 phase Electronic

Commutator Powered by DC Power Supply

, F1

F2 , F1

,F3

, F3, F5 F5

F2

F4

F4 , F6

, F6

F7

T3

Generator

Figure 2.4: Scheme of the test rig with thermocouple positions within the motor during Ex- perimental Campaign II

The thermocouples that were used during the measurements in Variants from A to D were numbered and schematically shown in Fig. 2.4 using red colour dots with "T" tags according to the following order:

• inside the front part of the motor fixed to the winding #T1 -#T4,

• inside the front part of the motor in the air between windings #T5,

• inside the front part of the motor fixed to the iron core at the end of the tooth #T6,

• inside the front part of the motor between windings and plastic separating windings from core #T7;

• on the cable of power supply #T8,

• between core and housing #T9,

• on the rear bracket of the motor #T10,

• on the external part of the motor housing #T11-#T16,

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• ambient temperature #T17-#T18.

As it was mentioned, in the case of measurements in Variant E and Variant E+D, some of the thermocouples had to be relocated. Therefore, the thermocouples for these variants were numbered and schematically shown in Fig.2.4using blue colour dots with "F" tags (like filler) according to the following order:

• between core and housing #F1,

• inside the front part of the motor fixed to the winding #F2 -#F5 and #F7,

• inside the front part of the motor between windings and plastic spacer between windings from the core #F6,

• on the external part of the motor housing #F8 and #F12,

• on the cable of power supply #F9,

• on the front bracket of the motor #F10,

• on the back bracket of the motor #F11,

• ambient temperature #F13.

For the test series prepared for Variant D, E and E+D, the measurements were conducted with a reduced number of thermocouples. The recorded measurements from the thermocouples were averaged from minimum 120 recordings with frequency 1 Hz after reaching the steady state on the experimental rig.

2.2.3 Measurement procedure

The copper (conductor) losses were estimated using the averaged RMS values of the measured current per phase which was squared and the temperature-dependent resistance of the motor conductor. The copper losses were also divided between an internal component of the motor conductors: within power plug, on the copper paths mounted on the PCB connecting the plug with the motor windings. The mechanical losses were estimated as a function of the rotational velocity, while the rated point was taken from the motor data sheet. The

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Table 2.2: Operating points tested on the test rig during Experimental Campaign II

Operating Generator Power supply Av. RMS current Torque, Rev. Output

Point No. load, voltage, of the phases, speed, power,

Ω V A Nm rpm W

1 0.25 24.44 21.33 1.08 3495.00 395.28

2 0.25 17.49 17.23 0.94 2500.50 246.14

3 0.25 9.49 11.13 0.63 1382.85 91.23

4 0.33 23.88 18.53 0.98 3510.00 360.22

5 0.33 16.78 14.57 0.78 2499.00 204.12

6 0.33 9.12 9.20 0.49 1401.60 71.92

core losses were estimated on the basis of the mentioned energy balance without copper and mechanical losses and for the same points were averaged.

All the investigated operating points were presented in Tab. 2.2. The operating points in Experimental Campaign II were numbered using Arabic numerals to vary from operating points presented in Experimental Campaign I. The loads and voltages presented in the current section were tested for Variants from A to E and also for E+D that were discussed in Chapter1.4.

Moreover, for each concept of heat dissipation intensification, an additional state with generator load on the level of 0.25 Ω was investigated with the higher motor power voltage.

It also resulted in higher speed and effective power, giving additional overload operating point. Each point was achieved when reaching the same temperature of the windings above the ambient temperature as in Operating Point #1 (in Tab. 2.2) before modifications (Vari- ant A). Therefore, during the study, forty thermal steady states of the working machine were measured.

In Table2.3, the losses estimated during Experimental Campaign II are presented. The power losses of the motor for the presented operational points were estimated on the basis of energy balance between the motor supply power and the effective output power. The motor supply power was calculated comparing the primary power source and subtracting the losses occurring in the commutation system and in cable connecting commutator with the motor.

The copper losses ∆PCu were calculated according to the multiplication of square current and resistance of windings. In the resistance definition, the electric resistance of the windings was estimated taking into account the temperature measured for each load. The windings temperature varied more than during Experimental Campaign I because the conditions

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Table 2.3: Losses estimated during Experimental Campaign II

Operating ∆PCu, ∆PFe, ∆Pmech,

Point No. W W W

1 34.22 19.08 2.93

2 22.29 12.46 2.09

3 8.41 1.87 1.16

4 26.69 17.90 2.94

5 15.47 13.83 2.09

6 5.76 1.92 1.17

of measurements recorded without plexiglass cover and with torque sensor were slightly different. In Experimental Campaign II, the mechanical losses ∆Pmech were estimated by the function of the mechanical losses dependent on rotational velocity. This function was cre- ated on the basis of a series of the idle state measurements. The core losses ∆PFe were estimated by using the value of the motor effective power. The difference between the motor effective power and sum of copper and mechanical losses allowed to estimate the value of the iron losses. Therefore, the core losses were estimated on the basis of the mentioned energy balance without copper and mechanical losses. All the measurements were performed until the thermal steady state had been reached.

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Chapter 3 Numerical model

In the following chapter, two thermal models based on the CFD technique are presented.

These models predicted thermal behaviour of the motor during the two experimental test campaigns described in the previous chapter. The first thermal model, entitled as Thermal Model I, reflected conditions occurring during Experimental Campaign I. The second thermal model, Thermal Model II, was developed to investigate the suggested variants of heat dissipation improvements from the analysed electric motor. Moreover, Thermal Model II was built to mimic conditions from Experimental Campaign II. The specifics of each CFD model are described in the first two sections. The similarities and differences between the two models are clearly presented in those sections.

In the next section, the electromagnetic (EMAG) model and its application are presented.

The main aim of these models was to estimate the power loss independently from the experiment tests. The EMAG model was developed in two configurations including 2-D and 3-D computational domains. Moreover, the last section describes the coupling between EMAG models and Thermal Model II. The description of the EMAG models accompanied by the governing equations is presented within section discussing the coupled model. In this dissertation part, it is shown that thermal models can be developed independently from the experimental results. In consequence, the motor power losses can also be estimated numerically.

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3.1 Thermal Model I

In order to simulate the phenomena occurring during Experimental Campaign I, which was executed on the test rig described in Section2.1, Thermal Model I was proposed. Accord- ing to the description of Experimental Campaign I, the motor was tested only in Variant A as presented in Section1.4. Therefore, the first CFD model was also developed in one geometrical configuration which reflected the conditions present during Experimental Campaign I.

The numerical investigation was realised in the ANSYS software environment. The geometry was prepared using Design Modeler and Space Claim programs, while Ansys Mesher was used to discretise the computational domain. The generated mesh was imported to Fluent that was as a solver in the CFD calculations [88].

3.1.1 CFD numerical domain

The computational domain was defined including solid components of the motor, air within investigated machine and air outside the machine. The fluid outside the machine was limited by the Plexiglass cover as described in Section2.1. The solid elements of the motor domain consisted of motor housing, two endcaps, two aluminium brackets, stator core, plastic elements (bobbin), windings, printed circuit board (PCB) plate, copper paths on the PCB, shaft, rotor core, neodymium magnets, coupling and a part of the generator shaft.

The solid motor elements of the numerical domain are presented in the semi-transparent view in Fig. 3.1. The green colour was used to present the PCB plate which separates the front and back parts of the motor. Moreover, in this figure, the copper elements are presented using orange colour. On the six-tooth stator core, the solids represented windings are shown.

Moreover, on the PCB plate, the cooper paths are also visible as they are highlighted by the mentioned orange colour.

The generator domain was limited to its external surfaces due to the fact that the generator was not treated as the object of study. Therefore, the internal elements of the generator were not included in the numerical domain. Such an approach allowed to reduce the number of numerical mesh divisions which is described in the next section. The image of the numerical domain is presented in Fig. 3.2. The solid parts of the motor construction are shown in the figure in grey colour. As it is visible in the figure, the above mentioned external surfaces of the generator are located in front of the motor. Moreover, the power and control wires were not included in the numerical domain for the sake of model simplification. As it was mentioned, the numerical domain also covers air around the investigated motor. This

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external air was limited to the internal walls of the acrylic glass cover described in Section 2.1. In Fig. 3.2, air under the acrylic glass cover is presented in a transparent mode. The internal motor structure was consistent with the motor construction described in Section 1.4.

Figure 3.1: Motor components of Thermal Model I presented in the semi-transparent view

3.1.2 Numerical mesh

On the basis of the domain presented in the previous section, the numerical mesh was prepared. All the domain fluid and solid elements were divided into smaller grid elements allowing for the domain discretization.

The final numerical mesh generated within the computational domain included more than 8 million elements. Due to the domain complexity, the mesh consisted of hybrid elements connecting tetrahedrons, quadrilateral pyramids, triangular prisms and hexahedrons.

Moreover, due to the geometry complexity, it was decided to use non-conformal mesh between solid and fluid elements. It allowed building mesh in the connection regions between the small dimension elements, e.g., air gap and bigger solid elements, e.g., stator core.

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Outlet

Inlet Motor elements

Generator surfaces Coupling

Figure 3.2: Computational domain of Thermal Model I

Due to the domain complexity, the process of numerical mesh creation was a challenging task. Therefore, the mesh independency test was conducted only for two different meshes which were coarser and finer comparing to the one finally selected. The region, where the number of elements varied during the test, was located in the vicinity of surface connecting surrounding air with external motor elements. Moreover, the tested region of the mesh influence was within the back part of motor where the LDA measurements were recorded. The finer mesh consisted of 10 million elements. Finally, the selected mesh, as presented above, reached 8 million elements and showed similar results as for the finer mesh.

The visualisation of the final mesh is presented in Fig. 3.3 on a vertical cross-section cutting the main motor components across the shaft axis. In the figure, on the left-hand side,

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the cross-section through all fluid and solid domain is presented. In Fig.3.3(a), the mesh in a cross-section through the whole domain is presented. On the right-hand side of the figure, three zooms of the mentioned cross-section are presented with the mesh without air domain around the investigated machine. In Fig. 3.3(b), the zoomed view of half of the motor is presented. This view is consistent with the yellow frame marked in Fig.3.3(a). In Fig.3.3(c), the internal elements of the motor are zoomed and their image is presented in Fig. 3.3(b) using a red frame. The last zoomed view illustrates the air gap between stator and rotor in Fig.3.3(d). This image is pointed out using a green frame in Fig.3.3(c). Using orange colour, the windings were pointed out and the remaining solid elements are in grey colour. The fluid was presented using blue colour. On the right-hand side of the figure, the numerical mesh without an external air is illustrated, while two zoom views are shown in colour frames. In the figure, the mesh details are displayed on the side of the motor. However, the generator side is not included in this view but the mesh resolution in the generator vicinity was similar to on the motor side. The semi-transparent view through solid motor elements is presented in Fig.3.1.

(a)

(b)

(c) (d)

Figure 3.3: Mesh of Thermal Model I displayed in the vertical cross-section of the motor in four views: (a) whole domain with air around motor within the acrylic cover, (b) motor elements with external surfaces, (c) internal motor elements, (d) zoom to the air gap

Coupled thermal electromagnetic numerical modelling of an effective heat dissipation process from an electricmotor; Sprzężony cieplno-elektromagnetyczny model numeryczny procesu efektywnego rozpraszania ciepła z silnika elektrycznego - Digital Library of

Bartłomiej Melka