5HGXFWLRQRID ' HWDLOHG7KHUPDO 0RWRUkth.diva-portal.org/smash/get/diva2:1324136/FULLTEXT01.pdf · cal method thermal model for a permanent-magnet assisted synchronous reluctance machine

INDEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

,

Reduction of a Detailed Thermal Model Lumped Parameters Approach for an OSV Induction Motor

LUCA ROGGIO

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Reduction of a Detailed Thermal ModelLumped Parameters Approach for an OSV

Induction Motor

Luca Roggio

School of Electrical Engineering and Computer ScienceKTH, Royal Institute of TechnologyStockholm, SwedenSupervisor: Shafigh NateghExaminer: Oskar Wallmark

Abstract

This thesis work is dealing with a detailed thermal model for an open self ventilated inductionmachine with lumped parameters approach. The model is entirely built using as referencespublished articles. The thermal network is tested using both MATLAB for calculating theparameters and SimScape for simulations and validation. Thermal resistances and capacitiesare fully depending on the geometry and material of the analysed motor, although the use ofCFD simulation results has been needed to model accurately the speed of the air circulatingin the inner part of the motor. Using results from the temperature rise test performed onthe OSV motor, the LP model is validated and subsequently an attempt of reduction ofthe model’s order decreased the number of nodes from 78 to 24 with a reasonable loss ofaccuracy. During the reduction, a sensitivity analysis of the axial partition number and allthe resistances is presented. The goal of the model is to be suitable for control operation, hencethe inputs of the model are the duty cycle rotor speed and losses, copper iron and friction, astime variant arrays. The outputs are instead the temperature during the simulation time ofsensitive targets such as end windings, inner hotspot windings, rotor bars and bearings.

Sammanfattning

Detta examensarbete behandlar en detaljerad, lumped-parameter baserad, termisk modell aven oppen, sjalvventilerad asynkronmaskin. Den framtagna modellen ar helt baserad pa tidi-gare framtaget publicerat material. Det termiska natverket ar utvarderat med hjalp av Mat-lab (for att berakna modellparametrar) och Simscape (for att utfora sjalva simuleringen samttillhorande validering). De termiska resistanserna och kapacitanserna beror pa geometri – ochmaterialparameter kompletterat med parametrar framtagna med hjalp av CFD-simuleringarfor att representera det termiska utbytet pga. den cirkulerande luften i maskinens kylkanaleroch axiella andar. Den framtagna modellen har validerats mot temperaturmatningar fran ettexperimentellt test. Efter detta har forsok att reducera den framtagna modellens komplexitedgenom att minska antalet noder fran 78 till 24 utan att felet I predikterade temperaturerokat signifikant. Malet med den reducerade modellen ar att kunna implementera den I enregleralgoritm och dess indata ar darfor duty cycle, rotorvarvtal och forluster. Utdata franren reducerade modellen ar temperaturer pa kansliga motordetaljer sasom andlindningar,maximal temperaturer I statorsparen, rotorledarnas temperatur samt lagertemperaturer.

Acknowledgements

This thesis work represents the end of a difficult journey started in 2013. Although manypeople played an important role in my life during these five years, regarding these six monthsI would like to thank my supervisor Shafigh Nategh for the help received despite a busyschedule and believing in me, as well as the project manager Ola Algen for providing a com-fortable accommodation in Vasteras. The whole ABB experience has been training for myprofessional and human future. I would also like to say thank you to my examiner in KTHOskar Wallmark and my supervisor in Polytechnic of Turin Aldo Boglietti for following myproject step by step along its way. Moreover, a special thanks to Oskar who introduced meto ABB’s project believing I had the requirements to face all of this.

My words would never be enough to thank my family for their economical and moral sup-port. Friendship is one of the backbones in my life, so thank to Riccardo, my soul brother,Gabriele, mentor and true, reliable and inspiring friend, Martin and Georgios, my happy placein Sweden and Vincenzo, saving my boring Saturdays with pleasant and deep talks. Last butnot least, tack Nora to ascertain Virgil’s immortal words omnia vincit amor, being the lightduring this dark winter. I dedicate this all to the memory of a great man who could havebeen proud to share this result with me, my grandfather Ciccio, wherever he is watching overme.

List of Symbols

Abbreviations

CFD Computational Fluids DynamicsFEA Finite Element AnalysisOSV Open Self Ventilated

TEFC Total Enclosed Fan CooledLP Lumped ParametersDM Detailed ModelRM Reduced Model

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Contents

List of Symbols 6

1 Introduction 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.4 Method and Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Traction motors cooling layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Traction motors operating conditions . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Different thermal modeling methods . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Reduced size modeling methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.6 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Thermal modelling background theory 9

2.1 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Analogies with electrical network . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Thermal Network solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Network construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5.1 Nodalization process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5.2 Parameters calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19


3 Model Description 23

3.1 Motor general description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 Cooling system description . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Axial layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Windings model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Active motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5 Convection models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.5.1 Ducts heat transfer coefficient model . . . . . . . . . . . . . . . . . . . . 413.5.2 Airgap heat transfer coefficient model . . . . . . . . . . . . . . . . . . . 41

3.6 Housing modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Motor Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.6.2 End plates and bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.7 Inner parts modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.7.1 End windings coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.7.2 Short-circuit rotor ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.7.3 Inner air partitioned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


4 Detailed Model Validation 514.1 Temperature rise test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.3 Experimental data and simulation comparison . . . . . . . . . . . . . . . . . . . 564.4 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5 Model reduction 605.1 Primary DM model reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1.1 Axial partition number sensitivity analysis . . . . . . . . . . . . . . . . 615.1.2 Axial connections reduction . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.2 Resistances sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.3 Final model reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.4 Summary of the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6 Conclusions 736.0.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Chapter 1

Introduction

Electric drive systems have recently seen a massive and rapid increase in its usage and itspopularity is here to stay. The branch of the research is directed in developing sophisticatedand more accurate models to predict the temperature of every components in the electricalmachines. Every drive system is designed in order to run under specific condition set bythe user. The duty cycle has influence on the temperature rise of the system’s components-This aspect is so relevant because some parts are sensitive to high temperature values suchas insulation, magnets and winding. Accuracy and rapidity of and in receiving data couldprevent the machine to be damaged and save both money and energy.

1.1 Introduction

1.1.1 Problem Description

Thermal limit has always been an important constraint of the machine. The goal of designinga machine is to exploit its full potential. Going beyond the maximum reachable temperatureand the machine risks to decrease the lifetime, on the other hand, going lower representsa waste of material and hence economical resources. Moreover, temperature distribution isalso an important factor. If heat is homogeneously distributed, then the risk of temperaturehotspot is low, and the material is exploited equally. Otherwise, the degradation of someparts occurs before others and this still represents a waste. For those reasons, unnecessarysafety margins are always applied on the critical spots.

Temperature is crucial either in an early design optimization phase, in order to reach anoverall good efficiency and torque to power density, and for control purpose. The latter re-quires the thermal model to be fast and accurate for every simulation’s time step since itis known that temperature affects the performances of the drive system. The most preciseresults in terms of temperature are obtained through CFD and FEA simulations. Thus, thoseuse a remarkable amount of time and calculation power leading to accurate results. It wouldnot be possible to implement in a control system the previous method to have informationon the thermal status of the drive for every time step. Therefore, the purpose of a thermal

1

1 Introduction

model specifically designed for control is sacrificing accuracy and gaining speed. A good LPmodel is usually faster and predict temperature with a relative error of ± 5 - 10%.

In this report, a thermal lumped parameter model is going to be described in all of it detailspecifying assumptions and once built verifying its performance with two different data setsbelonging to two different experimental tests. The model has been based on an OSV inductionmachine designed by ABB. Since the model is parameterised in geometry and materials, it isgeneral enough to be applicable for investigating changes for several induction motor designswith the same cooling system.

1.1.2 Previous Work

This thesis is mainly inspired by the work of Gunnar Kylander PhD thesis [Kyl95] in 1995presenting a thermal resistance network model for a fan-cooled, caged induction machine with36 stator slots as well as the work of Shafigh Nategh 2013 [Nat13] with a LP mixed numeri-cal method thermal model for a permanent-magnet assisted synchronous reluctance machine(PMaSRM) equipped with a housing water jacket, building a very complicated but accuratemodel for the windings and testing several approaches. Finally, several other articles fromprof. Aldo Boglietti, prof. Andrea Cavagnino and prof. Dave Staton played a role in thisthesis work focusing on difficult modelling aspect for thermal calculations.

1.1.3 Objectives

The first goal is to build a fully analytical model, hence based only on geometrical and mate-rial data. From the latter, all the parameters are calculated and connected. The constructionof the thermal network starts from the active part of the motor, that is divided in four equalaxial partition by the assumption that the heat flux is radially directed mostly. The previousis connected to the ending parts: case, rotor ring, shaft, bearing and end windings. The pres-ence of air and the way the end parts exchange heat with it represents a challenge. Air insidethe motor indeed is hard to model, the all cooling is an open system and the help of CFDcalculations is needed to better understand how the velocity of the air affects temperaturesand heat exchange. The second goal is to reduce the size of the model with an optimizationalgoritm aiming not to loose excessively accuracy. This will allow the model to be suitablefor control purpose, the time of execution is drastically decreased now.

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1 Introduction

1.1.4 Method and Simulation Setup

The model has been developed step by step increasing gradually complexity. Details andmore complex equations have been added subsequently. All the parameters are written inMATLAB code on different scripts gathered by a main-script. Moreover, the latter providesall the information needed for the simulation: losses, time step settings, initial conditions andmore.

The network is built up on a specific tool for thermal calculation in SIMULINK called Sim-Scape, where thermal sources, resistances and capacitances are already programmed and readyto be used. Most of parameters are temperature dependent so during the simulation delayblocks are used in order to avoid algebraic loops. Once the simulation on SimScape is com-pleted, the temperature acquired is fed back to MATLAB environment and displayed througha script comparing it with the real measurements. The optimization process is subsequentlyimplemented first thinking out a block diagram and then writing the relative code on MAT-LAB. The code modifies directly the parameters on SIMSCAPE and it is writtend in orderto be generic: hence it is possible to use it for any model reduction process simply providinga list of parameters.

Figure 1.1: Typical motor for traction

1.2 Traction motors cooling layouts

When the topic is electrical machines, losses has always been a delicate issue. The design ofrotating electrical machines always considers the presence of a cooling system, without whomthe motor would not be able to reach its full potential. As a matter of fact, whether it regardsmechanical or electrical losses, heat production is an unwanted consequence and has to bedecreased through cooling. The presence of losses is massive during start up and breakingoperations and those increase proportionally to the load. The cooling layout continuouslytransfer heat to a medium. Cooling for rotating electrical machines is classified in the by the

3

1 Introduction

international standard norm IEC 34.6 and AS 1359.21. The focus is now directed to induc-tion motors. Typically, the cooling combines the effect of ventilation and natural convectionextending the surface of the external case with fins. The surface is ribbed also to enhancethe effect of external heat radiation exchange. Ventilation is realized by mounting a fan onthe shaft usually made up of the same material. The cooling layout that can be found moreoften is the TEFC, which stands for totally enclosed fan cooled. How one can guess from theacronym, the air inside has no way out and the heat is dissipated through the presence of anexternal fan mounted on the non-drive end part of the motor which blows air on the finnedexternal case surface. In small or medium electrical rotating machines, the rotor ring couldhave fins as well that augment air circulation in the internal part of the motor. Nevertheless,the operating point of the machine is crucial for the cooling system: the efficiency of therotor fan system, and in minor way rotor ring fins effect, highly depends on the speed. Foroperation below grid frequency (50 Hz) is inconvenient to have a rotor mounted fan systemand hence an external one is preferred. Noise could represent an unwanted effect, but it isbeyond the scope of this discussion. Larger machines have more elaborated cooling systems,those includes heat exchanger with circulating water that gives a higher efficiency. Water cancirculate inside the motor and commonly inside the windings itself. The machine analysed inthis report has an OSV system, which stands for open self ventilated. A fan is mounted onthe drive-end part of the shaft and both DE and NDE surface of the rotor are finned. Theasymmetry of this system has an important consequence: temperatures in the NDE parts areexpected to be higher than the ones in the DE. The following table 1.1 provides an overviewof the cooling systems with its respective acronyms.

Code Description

IC 01Open machineFan mounted on shaftOften called ’drip-proof’ motor

IC 410Enclosed machineSurface cooled by natural convection and radiationNo external fan

IC 41

Enclosed machineSmooth or finned casingExternal shaft-mounted fanOftern called TEFC motor

IC 416 AEnclosed machineSmooth or finned casingExternal motorized Axial fan supplied with machine

IC 43 REnclosed machineSmooth or finned casingExternal motorized radial fan supplied with machine

IC 61

Enclosed machineHeat exchanger fiddeTwo separate air circuitsShaft-mounted fansOften called CacA motor

Table 1.1: Cooling layouts IEC 34-1

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1 Introduction

1.3 Traction motors operating conditions

According to their design and range of operation, electrical machines are employed under sev-eral operating conditions. Those, also called duty service, are categorized under the standardsCEI 2-3 and IEC 34-1 and marked with the letter S followed by a number from 1 to 9. Inthis thesis work, the duty cycle plays an important role. As furtherly described in details,several time dependent vectors are fed to the model, both carrying information on rotor speedand losses over time. The knowledge of the work cycle is crucial: rotor speed influence thecooling in the machine while losses are represented by heat source generators. Nevertheless,for completeness the following table 1.2 provides an overview on the typical operating modesdescribed by the standards.

Name Service Picture

Continuous Service(S1)

The machine is operating at a constant load until itreaches the thermal equilibrium for a limited time.The temperature reached is the maximum allowed.

Limited duration Service(S2)

The machine is operating at a constant load until itreaches the thermal equilibrium for a limited time.The temperature reached is the maximum allowed.

Periodic intermittentservice (S3)

The electrical machine run a cycle consisted of aconstant load period and rest that follows each otherin a fixed duty ratio. The temperature reached is themaximum allowed.

Periodic intermittent servicewith a start-up sequence (S4)

This operating is periodical like the previous,but the sequence is made up of a start-up, a constantload and rest after.

Periodic intermittent servicewith electric braking (S5)

Periodical duty service similar to the S4 service butadding after the constant load a breaking operation.

Continuous operationwith intermittent load (S6)

This cycle consists of a periodical alternating of aconstant load phase and a no-load phase without rest.

Periodical service uninterruptedwith electric braking (S7)

Operating service periodical with a sequence of start-up,constant load and breaking sequentially without any rest.

Continuous operation with periodicchanges in load and speed (S8)

Sequential, identical duty cycles run at constant loadand given speed, then run at other constant loads andspeeds. No rest periods.

Non-periodic variation inboth speed and load service (S9).

The mode can be guessed from the title. It is importantto specify the exact duty cycle in the motor plate.The former can have loads below, equal to or over thefull-load threshold.

Table 1.2: Standards Operating Conditions for Electrical Machines

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1 Introduction

1.4 Different thermal modeling methods

This paragraph is providing a small overview on the major approaches of thermal modellingtechniques used nowadays. Lumped parameters thermal modelling (LP) and numerical meth-ods are the most common. The former is based on the simplification that heat flow is a scalarinstead of a vector, hence one direction is preferable rather than the others. The problembecome one-dimensional simplifying the real three-dimensional case.

An LP Thermal model consists of an electrical circuit in which every type of componenthas its thermal equivalent basing on geometry, material data from the motor as well as dutycycle and losses calculation: for example, electrical resistances represents the thermal resis-tance heat flows face through a solid body. All the analogies are going to be described indetail in the report in section 2.3. The task of building a LP network is then choosing thecorrect model for every component and this could represent a challenge. In this report, everychoice in adopting one specific model rather than another is furtherly argued in chapter 3.Although it is important to specify that some parts such as windings, end coils and rotor isdifficult to extract accurate data from simulations. Generally, LP thermal models are val-idated with experimental measurements and the corresponding error can be below 12% atthe nominal speed and load according to the reference [Nat13]. This represents a drawback,but the advantage indeed is the calculation time. LP Models use less computational powercompared to the numerical methods and according to this, implemented in machine controlalgorithms. Numerical method combines finite elements analysis (FEA) with computationalfluid dynamics (CFD) for analysing the motor. FEA provides accurate results in modellingsolid parts of the electrical machinery but it needs convection and radiation heat transfercoefficients set as boundary conditions. Those are calculated basing on empirical correlationswhose input are temperatures value. In turn, boundary temperature requires CFD simula-tions to be evaluated and this is the main reason why CFD and FEA are used in parallel.Nevertheless, both methodologies require a massive computational time as well as a powerfulCPU unit. According to this, a partial FEA mixing LP, FEA and CFD results, is the newtrend in thermal modelling. As an example, the work led by S. Nategh in his doctoral thesis[Nat13] presents a model based on finite elements for the solid parts of the machine exceptfor the winding system modelled with LP approach. The complexity of the winding systemand the consequent mixed method exploit the advantage of LP and numerical methods withthe advantages of reducing calculation time without sacrificing the accuracy.

Considering the model described in this thesis work, LP approach is used taking great care inchoosing a suitable model for the windings, whose importance lies in the fact that predictingthe hotspot temperature is one of the most important target of the thermal analysis.

1.5 Reduced size modeling methods

The goal of model reduction is having results faster without excessively affecting the accuracy.As perceivable, reducing a model stepping from a detailed model (DM) to a reduced model

6

1 Introduction

(RM) involves loss of information. Anyhow, the goal is to prioritize the loss of informationto be less in some specific parts of the motor’s model or nodes named targets. The previousare crucial for different purposes. For example, winding hotspot temperature can be one ofthe targets because if a specific duty cycles an overload raise windings temperature to levelsthat can harm the lifetime of insulation system then it is important to have an accurate andfast prediction of temperature and eventually decrease it. Moreover, aiming to save target’stemperature accuracy can have as drawbacks loss of information in other nodes.

There are mainly two approaches in reducing a model, the first one act on the state spaceformulation of the problem expressed in equation 1.1

CaT (t) = GT (t) + P (t) (1.1)

that is going to described in detail in section 2.4, the second one consists into making multi-ple simulations varying the parameters of the model and reducing the model by knowing theinfluence of those on the targets.

The methodology adopted for this report is the second one. The main reason is becausethe SimScape ambient is visual: the network is built by dragging and drop elements fromthe library and initializing their values by MATLAB script. Hence, it is not possible to haveaccess to conductance (G) and capacities (Ca) matrix used in 1.1. Therefore, a future workproposal would be to transfer the network from Simulink and creating a script containing theprevious matrixes and use the first approach to reduce the model. Although it could still notbe possible because the first approach has as hypothesis temperature and time invariant Gand Ca matrix, while in the DM developed all the convection parameters are temperature andtime dependent.

Giving a quick overview of the first reduction methodology, it starts from equation 1.1 andexpressing it using the state space formulation:

T (t) = AT (t) +BU(t) (1.2)

Y0(t) = CT (t) (1.3)

A represent the state matrix, it is square with N dimension. U is a vector and contains allthe thermal excitations or well-known boundary conditions. Y0 contains q selected targetswhich are less than N nodes of A matrix, and finally C matrix has dimension q, N. Y0 is oftenconsidered equal as Y that is the RM output vector. System expressed by 1.3 is the startfor every type of reduction. Two very common methods are Eitelberg reduction and ModalIdentification reduction both described in details in reference [BVTP00].

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1 Introduction

1.6 Summary of the chapter

The content of this chapter consists of giving the reader an overview of the whole report.It starts with an introduction where the goals of the thesis are presented, specifically theimportance of the thermal models for control purpose and how providing fast and accurateresults means save money and energy. The model is based on already published material andhence the references of the LP-model structure are presented in a dedicated previous worksection. The goals of the thesis are then implementing a detailed model of an OSV inductionmotor and subsequently attempt to reduce the number of nodes and elements of the systemreducing the time needed for simulating it saving as much accuracy as possible. The chapterends providing a description of the typical cooling layout and operating conditions of anelectrical motor as well as different methods for thermal modelling and model reduction.

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Chapter 2

Thermal modelling backgroundtheory

2.1 Heat transfer

The theoretical background which represents the basis of thermal modelling is the physicsbehind the heat transfer. Heat is one of the two ways energy can be transferred by the inter-action of one body with its surrounding, the other one is work. Heat transfer is the thermalenergy transiting due to a temperature difference in space. The direction of this flow alwaysoccurs spontaneously, hence without any external source of work, from the higher temperaturesource to the lower. The former is also known as Clausius statement of the second principleof the thermodynamics: “Heat can never pass from a colder to a warmer body without someother change, connected therewith, occurring at the same time” [Cla56].

Heat can be transferred in three different ways: conduction, convection and radiation. Inmost of the cases, one of these modes prevails on the others so that one can assume thatthe heat is dissipated in one way only. In reality this represents an approximation of thereal physical phenomenon: two or even three modes can occur simultaneously when heat istransferred. In this thesis attention is focused on conduction and convection because thoseprevail over radiation. As it is possible to evince from table 2.1, conduction is related to solids,convection between surface and moving fluid and for radiation the exchange is independentof the body between the two surfaces exchange.

2.1.1 Conduction

Conduction is the mechanism of heat exchange through solid material. From a macroscopicpoint of view, the consequence of conduction is the temperature difference between two partsof a solid body. From a microscopic point of view indeed, conduction can be explained as the

9

2 Thermal modelling background theory

Conduction through a solidor stationary fluid

Convection from a surfaceto a moving fluid

Net radiation heat exchangebetween two surface

Table 2.1: This figures give a quick view of the three heat transfer modes, from the resource [al.07]

gathered impacts between neighbouring molecules. This process is known a diffusion. Theseparticles have a fixed position but either the possibility to vibrate and exchange kinetic energyby hitting the close molecules. Higher temperatures are associated to higher levels of energy.Conduction phenomenon is quantified and expressed by Fourier’s law in its differential form.

q = −k∇T (2.1)

q is the local heat flux density, k is the material conductivity and ∇T is the temperaturegradient. In a solid three-dimensional body, heat flows in all directions but the assumptionthat one direction is favoured is acceptable. Hence, the heat rate can be expressed by thefollowing in the x-direction.

qx = −kdTdx

(2.2)

Temperature has a linear distribution in the x direction as it is possible to see from figure 2.1while the heat flux qx is per unit area perpendicular to the direction of transfer. If the surfaceis constant, the reate of heat through a plane area is then the product of the heat rate qx bythe area A.

Figure 2.1: One-dimensional heat transfer by conduction

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2.1.2 Convection

This heat transfer mode is also due to diffusion between particles of the fluid from an exchangesurface to further, but it is mainly caused by the bulk motion of the fluid. The motion of the

Figure 2.2: Natural convection representation example

fluid is originated by buoyancy forces generated by the temperature gradient of the fluid itselfand hence the convection is called natural or free. On the other hand, convection is forcedwhen the flow is generated by external forces, such as fan, pumps or wind. The heat rate isexpressed in the form:

qconv = hconv(Ts − T∞) (2.3)

Where h is the heat exchange coefficient, Ts is the surface temperature and T∞ is the temper-ature of the fluid distant to heat surface enough that it is not affected by the heat convectioneffect. The h coefficient is always hard to calculate. Apart from very simplistic cases, thevelocities of the fluids considered lead to a turbulent flow regime and h can be evaluated onlythrough experimental evidence. Moreover, h is always temperature and speed dependent, soit changes constantly. It covers a wide range depending on several factors, with the aim ofhaving an idea of this value, the table 2.2 is useful.

Processh

(W/m2K)

Free convectionGases 2 - 25Liquids 50 - 1000Forced convectionGases 25 - 250Liquids 100 - 20000Convection with phase changeBoiling or condensation 2500 - 100000

Table 2.2: Typical values of the convection heat transfer coefficient from [Cla56]

11


2.1.3 Radiation

This heat transfer mode is generated by the mechanism of a body emitting photons carryingenergy. Radiation depends mainly on two factors: exchange surfaces of the two bodies and therespective temperatures. The following formula provides the value of heat exchanged betweena thermal source and a receiver body whose exchange area is A. The coefficient h takes intoaccount several factors as well as the degradation of the surface.

qrad = hr(T4s − T 4

surface) (2.4)

Where Ts is the thermal source temperature and Tsurface as intuible is the temperatureof the surface that is considered for heat radiation exchange. Although, the radiation heatexchange process tends to be rather small for electrical machines. The focus of the workduring the development of the model has been in modelling solid parts and convection withair. So complexity is reduced neglecting the presence of radiation heat exchange.

2.2 Heat Capacity

Most of the thermal model described in the literature neglect the presence of thermal capac-ity. As a matter of fact, the formers focus on predicting temperatures for stationary case.Nevertheless, the model in this report highlights the importance of heat capacities: time isfundamental during simulations carried on and hence the dynamic variations of temperaturesand heat fluxes are.

qacc = mcdT

dt(2.5)

The previous formula outlines that heat accumulated is equal to the product of the massof the object, the specific capacity and the derivative of the temperature over time. Mass andspecific capacity multiplied give the thermal capacity. Considering the balance of powers, thedifference of heat dissipated and produced is the heat accumulated.

0− hA(T − Ta) = mcdT

dt(2.6)

For a simplistic case when no heat is produced, the equilibrium and so the regime condition,is reached when the accumulated heat is equal to the dissipated one as it is expressed in formula2.6, where zero indicates that no power is produced by the source. In the former, Ta is theambient temperature, m is the mass and c is the specific heat capacity. The presence of thederivative term in the equation give the solution an exponential form whose time constantdepends on both thermal capacity and exchange coefficient and dissipative area.

T = Ta + (Ti − Ta)e−hAmc

t = f(Ta, Ti, h, A,mc, t) (2.7)

In equation 2.7, where Ti represents the initial condition, it is possible to see that for avalue of the time going to infinite, the negative exponential goes to zero and final value of thetemperature will be the ambient one, so T = Ta. Even if the case is simplicistic, it is possible

12


to evince how the capacity affect the dynamics of the problem but not the steady state value,that depends only on heat transfer and power generated if present.

2.3 Analogies with electrical network

A network is the aggregation of a certain number of nodes, every of each is connected to atleast another one. Considering all the physics analysed in the previous chapter, it is possibleto assume that a thermal node can generate heat, accumulate it and exchange with othernodes. Connections between two nodes are represented by thermal resistances, heat is accu-mulated by the presence of a thermal mass and is produced by a thermal source. Accordingto [Ass00], for every thermal component there is an electrical equivalent according to table 2.3.

Thermal Parameter Electrical Correspondency

Temperature T [K] Voltage V [V]Heat Flow Q [W] Current I [A]Thermal Resistance R [K/W] Resistance R [Ω]Thermal Conductance G [W/K] Conductance G [S]Thermal Mass or Capacity C [J/K] Capacitance C [F]Heat Flux q [W/m2] Current density J [A/m2]Thermal Conductivity λ [W/mK] Electrical Conductivity σ [S/m]

Table 2.3: Analogies between thermal quantities and the correspondent electrical ones

The solution of the network is then finding the temperature and the flow for every instant ofthe simulation and for every nodes or connection between. How is it possible to prove therelations outlined in table 2.3 and hence provide a formula to calculate the parameters neededto build the circuit? Starting the equation 2.8 representing a single object that is producing,accumulating and dissipating heat both for conduction and convection at the same time,

Pdt = mcdT + (T − Tref )hconvAdt+ (T − Tref )hcondA

∆xdt (2.8)

dividing by the dt element and considering the temperature reference equal to 0, the (ref)equation turns into the form expressed by 2.9. It is important to specify that the h coefficientis expressed in unit per length and it is constant because the object is assumed homogeneous.

13


P = CthdT

dt+ T

1

Rconv+ T

1

Rcond= Cth

dT

dt+ TGconv + TGcond (2.9)

G is the thermal conductance, the inverse of the thermal resistance. Now, since the equationis similar to the one representing a system with a current generator, a capacitor and two resis-tances, it is straightforward to assume that the thermal capacity is expressed as the productof the mass of the object by the specific thermal capacity, the resistance instead is expressedby 2.10 for conduction in solids and 2.11 for convection.

Rcond =1

Gcond=

∆x

hcondA(2.10)

Rconv =1

Gconv=

1

hconvA(2.11)

In reality the expression of the conduction resistance takes into account the fact that thearea along the heat path is not constant. The expression 2.10 is then valid for simple cases,such as a parallelepiped element. So, the general form of thermal resistance is outlined in 2.12and it will be used to calculate the resistance of simple thermal element through which theaxial layer of the motor will be divided into and from this the network is built. The resistanceis calculated along the path from 0 to its full length L.

R =

∫ L

0

1

A(x)hcond, dx (2.12)

2.4 Thermal Network solving

As previously mentioned, the solving a thermal network consist into finding the solution tothe problem expressed in 1.1. SimScape software uses the information from the visual builtnetwork to create a numerical linear system of the form 1.1. It is clear that the dimension ofthe system depends on the number of nodes and the complexity of the solution depends bothon the previous number and on the time varying form of the losses.

Let us proceed step by step. The Ca matrix is a diagonal matrix in the form of 2.15. Everynode has its own and those contribute to the dynamics of the system. Larger capacities leadto longer transient.

14


Ca =

C1 0 · · · 00 C2 · · · 0...

.... . .

...0 0 · · · CN

(2.13)

The losses vector, or power vector, is a 1 x N vector, expressed by 2.14, whose elementsare values of losses injected in every node. If one node does not produce losses but its tem-perature is still a target of the simulation, then the correspondent P value in the vector is0. In the simulation carried on during the thesis work losses are constant for all operatingpoints. This makes the simulation rather fast, but the model built in the next chapter andthe reduced and optimized version can simulate with time-varying losses. This circumstancecan extend the computational time of the simulation, but the results are more accurate andsimilar to the reality.

P =

P1(t)P2(t)

...PN (t)

(2.14)

The conductance matrix is expressed by 2.14 and every element of the matrix is calculated:

- In the diagonal the sum of inverse of the resistances connected to the node;

- In non diagonal position the negative of the inverse of the resistance connecting twonodes.

The matrix if sparse and hence some elements, if not connected, are null. The parameters ofthe matrix can be time variant also. For the former case, the solution is calculated by thesofware with numerical methods whose description is beyond the scope of this report.

G =

∑N

k=11

R1,k− 1

R1,2· · · − 1

R1,N

− 1R2,1

∑Nk=1

1R2,k

· · · − 1R2,N

......

. . ....

− 1RN,1

− 1RN,2

· · ·∑N

k=11

RN,k

(2.15)

15


2.5 Network construction

This section is dealing with presenting the techniques and approximation adopted in order tobuild the thermal network. The first part is called nodalization and the reasons behind thepartition in geometrical solid domains are analysed, while the second part is a description ofthe formula used to calculate the parameters.

2.5.1 Nodalization process

The term “nodalization” refers to the process of approximating a continuous physical systeminto a discrete one whose element composing it are called nodes. The complexity of the systemis directly proportional to the number of nodes: a system with more nodes usually reflectsreality better than a correspondent with less nodes. As an example, it is well known that finiteelement analysis (FEA) modelling provides better results than lumped parameters approachmodelling because of its nodes much higher numerosity. As a matter of fact, before everysimulation, programs using FEA approach divide solid objects into small three-dimensionaldomain and every of that is considered a node. This process is called meshing and nowadaysmore and more complicated algorithm are used to understand how to proper do it. Nodal-ization is understanding how many nodes and which shape represent the best solutions. Anexample of nodalization is shown in figure 2.3. A simple parallelepiped is divided into threeidentical cuboidal elements and every of those is a node. Every cuboid has its temperaturemean value and a thermal capacity.

Figure 2.3: Nodalization example and Resistances connection detail

Let us now assume that the temperature varies only with the length, hence it is constantin height and width of the solid body. While the distribution of temperature in the paral-lelepiped is a curve varying along the length (x) with a different value for every point becausethe system is continuous, in the nodalized system the temperature is reconstructed assumingthat the distribution is linear between the nodes and every node is placed in the center of

16


the cuboid with good approximation. Those are connected by resistances as it is possible toevince from figure 2.4.

Figure 2.4: Nodalization temperature distribution actual case and lumped approximation for examplein figure 2.3

Physical system, as motor lamination, have complex geometries. Assuming that the thick-ness is constant, how is the area divided in sub-domains in order to nodalized the system? Thisprocess is arbitrary, but several reasons can affect the division preferring one choice ratherthan another. For example, it is always convenient to place one node exactly in the positionof a thermal sensor because during the finalizing operation, simulation and experimental dataare easier to compare. From figure 2.5, here there is an example of how the presence of athermocouple force the choice of node placement.

Figure 2.5: Examples of geometrical partitions with and without the presence of thermocouple sensors

Placing the node in the geometrical midpoint is not always the best choice. Let us assumethat losses are proportional to the volume. In simple object like the cuboidal element in figure

17


2.3 choosing midpoint means having two perfect halves that has equal length, resistance andvolume. Each of the two halves has exactly shares a half of the losses produced by a singleelement and half resistance too. This conclusion is important because predicting a lineardistribution for the temperature over the body and an accurate prediction of the temperaturein the point of interest (the midpoint) are both satisfied. If the element considered is a hollowcylinder, the choice of the midpoint is more complicated. Choosing the midpoint to lay inthe mean radius distance implies that losses are not any more evenly distributed because thetwo volumes are different, as well as the resistances, whose are not equal for upper and lowerpart. The higher ratio between outer radius and inner radius is and the more choosing meanradius results an inaccurate approximation.

Figure 2.6: Visual detail of midpoint different midpoint choices

Although, for the model described in this report, since the ratio of industrial motor isbetween 1.2 and 1.3 per cent then it introduces an error that is negligible compared to theerror introduced by the convections model described in the next chapter. Midpoint is alsoimportant because capacitance and eventual losses generator, whether joule or iron, are con-nected as in figure 2.7.

Figure 2.7: Lumped capacity network example

18


2.5.2 Parameters calculation

This section provides an explanation of how resistances and capacitances are calculated forconvection case in solid bodies. The first assumption is that the material is homogeneous andkeep the same properties in every part of the machine. For simple elements with a constantcross-sectional area along its length, resistance is calculated according to the formula 2.10.Thermal capacity, as from equation 2.16, is simply the product of volume, density and specificheat and volum can be easly calculated as the product of length and area.

C = ρV c (2.16)

In this report the density of solid elements is assumed to be constant but in reality, it in-creases with heat. In general, all material properties are temperature dependent, as well asthe conductivity or specific heat capacity. Although, in the range of temperature variationsfor thermal simulations, it is reasonable assume these parameters constant. The previousformula for thermal capacity and resistance are valid for simple elements, like parallelepipedrotor bars, cylindrical shaft, axial thermal resistance connections. Nevertheless, the validityis lost when hollow-cylindrical elements, as in figure 2.8, in radial and tangential direction areconsidered, because the area is not constant but varies along the radius proportional to thepover of two.

Figure 2.8: Cylindrical element and equivalent network representation

Cavagnino A. has proposed simplified version of the Turner and Mellor model in his article[BCLP03], where the convection for a cylindrical body consists into two resistances. The first

19


connect the inner surface to the midpoint, that is the mean radius calculated as rmean = ri+ro2 ,

the second connect the midpoint to the external surface. The thermal capacity is connectedto the midpoint aswell. The general formula for a hollow cylinder is expressed by 2.21 andderived solving the general expression 2.12 integrating along the radius from the inner radiusri to the outer radius ro.

R =ln ro

ri

2πlλ(2.17)

So, formula 2.21 is applied for inner resistance calculation between mean radius and innerradius and for outer resistance calculation between outer radius and mean radius. For clarity,equations are explicit in formula 2.19:

Ri =ln rmean

ri

2πlλ(2.18)

Ro =ln ro

rmean

2πlλ(2.19)

Nevertheless, the hollow-cylinder equations described are not enough for dividing the motorin geometrical partitions and building the network. The lamination, both for stator androtor, cannot schematically be divided in hollow cylinders: elements such as ducts or slotalternates themselves with lamination cylindrical path. In this case, the simmetry of geometryis exploited to split the hollow-cylinder in several partitions, each one is represented by thedrawing in figure 2.9.

Figure 2.9: Cylindrical partition element representation

The network representing the cylindrical partition element is similar in structure to thefull hollow cylinder element presented in 2.8. Although the formula calculating the resistances

20


are different: since the angular extention of the cylinder is 2π radians, the cylindrical elementis a partition of the full element and then the 2π in 2.21 is substituted by θ that is the angleswept by this.

Ri =ln rmean

ri

θlλ(2.20)

Ro =ln ro

rmean

θlλ(2.21)

Considering the resistance from the midpoint to the lateral surface Rs where s stands for side,a further simplification can be done. Assuming that the temperature of the right surface hasthe same value than the correspondent left one, in terms of electrical equivalent it is possibleto put the two surface nodes at the same potential. Then the two Rs, since are equal, canbe sostituited with an equvalent Rs that is half of the value making a resistance parallel.Physically, it can be explained saying that the heat flowing in the tangential direction hasan exchange surface that is twice the value of a single lateral area of the cylindrical partitonelement. Finally, Rs is calculated as:

Rs =θrmean

λl(ro − ri)(2.22)

For the winding model, since the stator slot has a rectangular shape, the trapezoidal el-ement pictured in figure 2.10, is proposed to model the insulation and impregnation layers.Similar to the cylindrical partition, the vertical conduction thermal resistance is calculatedintegrating the area along the path and resulting in the formula:

R = yln xo

xi

lλ(xo − xi)(2.23)

Figure 2.10: Trapezoidal element representation

21



The content of this chapter consists of giving the reader an overview on the theoretical andphysical aspect related to the thesis. It starts by describing the fact that heat, a form of energy,move from a physical body through conduction, convection or radiation or it can either beaccumulated. The LP-approach consist of approximating the reality with an electrical circuitequivalent. The definition of the network starts from the nodalization of the physical system:the motor is divided in sub-elements to each of a thermal node is associated; nodes are thenconnected to each other. The nodalization is a crucial aspect for this thesis work: a trade-offbetween the number of elements and connection is the key for a good LP-model. Finally, theequation for the calculation of thermal resistances and capacities of basics elements such ascylinder partitions are presented.

22

Chapter 3

Model Description

3.1 Motor general description

This section regards the description of the motor in all its main features. The prototype con-sidered for the experimental in figure 3.2 validation dataset is an induction machine designedfor railways application. The motor is a 4-poles induction machine. The rotor type is squirrelcage with casted alluminium, stator and rotor are laminated. The DE correspond to the inletwhile the NDE to the outlet part. Ratings caracteristic are summarized in table 3.1.

Motor Parameter Value

RatingsVoltage 1100 VCurrent 160 APower 230 kWPF (cosφ) 0.82Speed 2163 rpmFrequency 73 HzPoles 4

Table 3.1: IM main characteristics

3.1.1 Cooling system description

The cooling system is forced ventilation: the prototype is an open-self ventilated. This is oneof the most complicated system to model for several reasons. Unlike the TEFC mode whereair does not recirculate with the external ambient, OSV air is continuously exchanged. Theefficiency of the latter is higher than the former’s one, air from the inlet is always at the ambi-ent temperature, assuming that the ambient temperature is somehow constant. Nevertheless,both temperature and air velocity along the air path can change. This has two consequences;the cooling system is asymmetrical: heat transfer coefficients are higher in the inlet parts anddecrease in the outlet. Secondly, heat transfer coefficients are calculated basing on correlation

23

3 Model Description

which need in input temperature and air speed in proximity of the exchanging surfaces con-sidered, hence CFD calculations are needed to adjust the relation between rotor speed andair speed. For completeness, figure 3.1 illustrate the air path in the motor: it goes from theinlet to the outlet passing through stator, rotor ducts and airgap.

Figure 3.1: Airflow path representation. Grey arrows represents the rotation of the shaft, blue arrowsairflow path and in ligh the presence of air in general

Figure 3.2: Prototype motor pictures with temperature rise set up

24

3 Model Description

3.2 Axial layer

From now and on, active motor is defined as rotor and stator lamination together with rotorbars, stator windings and shaft excluding short circuit ring, end windings and the rest of theshaft. For the detailed model, active motor is axially divided in four layers. Every partitionis then a cylinder thick the active length divided by the number of partitions. This parameterwill frequently appear in the report and its symbol is l. Dividing the active motor in severalparts makes the network to be either more complicated but as well more accurate. As anexample, losses are not fed in a single point but are split and distributed evenly and thisallows the model to better approximate the reality. Considered this, this section will focus onmodelling a sub-network for each axial partition and, exploiting symmetry, connecting all thepartitions in a wider network representing the active motor. Subsequently, the active motoris connected to the rest of the external parts modelled in following sections.

The starting point for the nodalization process and the building of the circuit after is thelamination design in figure 3.4 for the rotor and 3.3 for the stator. Those represents only aquarter of the entire drawing for simplicity: the design is axial-simmetrical. It is importantto specify that while all the data and parameters in table 3.2 are the same in the real motor,small details are not included in this report.

Parameter Complete name Value [mm]

rsi stator inner radius 147.5rso stator outer radius 227hsy stator yoke height 45.7hss stator slot height 33.8wss stator slot width 9.3rsh shaft radius 50rrdi rotor ducts inner radius 65rrdo rotor ducts outer radius 88hrd rotor duct height 23wrdu rotor duct upper width 25wrdl rotor duct lower width 15lrda rotor duct adiacent length 12rrbi rotor bars inner radius 117rrbo rotor bars outer radius 142hrb rotor bar height 25wrb rotor bar width 5.55rro rotor outer radius 147

Table 3.2: List of geometrical parameters used for resistances and capacities calculation

Another approximation adopted in the drawing is the number of ducts, rotor bars andstator slots which does not represent the actual ones. As a matter of fact, Qr, rotor bars

25

3 Model Description

number, is 62, more than the represented ones; Qs, that is stator slots number, is 48 and thenumber of rotor ducts Qrd is 15. Another fundamental parameter is the distance betweenrotor and stator, also known as airgap length lairgap, whose value is secreted for industrialdesign issue property of ABB. Concluding the geometrical description, for the future resistancecalculation:

- Stator teeth and slots are perfectly straight;

- Rotor ducts are assumed trapezoidal;

- Gaps between rotor ducts are straight and hence its geometry is rectangular;

- Rotor bars are rectangular;

- The angular proportion between rotor bars and the gap between is 1:1;

- Gaps between rotor bars are straight and hence its geometry is rectangular;

As far as are materials concerned, rotor cage and hence rotor bars are entirely made upof aluminium while lamination type is M600-50A, that is an electrical steel non-oriented fullyprocessed. All the materials in this model are assumed perfectly homogeneous except for thelamination which has different heat conductivity coefficients λ. Since the all system is axialsymmetrical, the spatial reference system used is cylindrical. Heat can flow radially, so thatparallel to the direction of the radii, tangentially, perpendicular to the direction of the radiiand axially. For radial and tangential direction, the heat conductivity is the same and thisvalue is higher compared to the axial one. This information can be found in [Pow] and it isremarkable since heat will have a preferred direction: instead of flowing axially, it “prefers”to go from the rotor to the stator and the case radially. For completeness, in table 3.3, a listwith all parameters used is provided.

Once geometry and material data are defined, the axial layer is nodalized according to figure3.5. The first node n1 represents the shaft and it is the start of the network. Going fromthe shaft to the end of the stator n1 is connected to n2. The previous represents a hollowcylinder, the first element of the rotor that is a yoke connecting the shaft to the ducts. Thenheat forking in two directions, one represented by the ducts and another represented by thelamination part connecting two adjacent ducts. While in figure n2 represent a unique element,a hollow cylinder, node n3 and n4 respectively for ducts and duct side connection representan alternation of equal elements. It is questionable to assume that a single node is needed forevery duct and duct side connection. Nevertheless, the symmetry helps in this case: since thethermal network works as an electrical one, all the resistances representing each duct or ductside connection are in parallel and since all resistances are equal, it is possible to have simplytwo nodes whose resistances connecting upper and lower yoke are calculated as the resistanceof a single element divided by the total number of ducts. This assumption is valid if thetemperature in all the ducts is the same and it is adopted as well as the equivalent for rotor

26

3 Model Description

Figure 3.3: This figure gives a graphical overview on all geometrical parameters belonging to thestator. The lamination design is simplified and hence some details are removed.

bars with respective side connection and slot with teeth. Moreover, n3 and n4 are connectedto each other because some of the heat might flow from the side connection and dissipatedin ducts air. Both n3 and n4 are then connected to n5, rotor middle yoke connecting ductsto bars and respectively connected to , n6 representing all the bars and n7 representing theconnection bar to bar. The previous are connected to the most external and thin rotor yokethat is node n8. The airgap n9 node connect the rotor to the stator made up of simply threenodes: n10, n11 and n12 respectively representing teeth, slots and stator external yoke.

27

3 Model Description

Figure 3.4: This figure gives a graphical overview on all geometrical parameters belonging to therotor. The lamination design is simplified and hence some details are removed.

Figure 3.5: This figure gives a graphical overview on how the axial partition is nodalized.

28

3 Model Description

Parameter Description Value Unit of measure

Conduction coefficient λ

rotor lamination axial direction 0.37 W / m Krotor lamination radial and tangential direction 28 W / m Kstator lamination axial direction 0.37 W / m Kstator lamination radial and tangential direction 28 W / m Krotor bars 237 W / m Kshaft 52 W / m K

Specific heat capacity c

rotor bars 896.9 J / kg Krotor lamination 460 J / kg Kstator lamination 460 J / kg Kshaft 460 J / kg K

Density ρ

rotor bars 2.7 kg / dm3

rotor lamination 7.65 kg / dm3

stator lamination 7.65 kg / dm3

shaft 7.8 kg / dm3

Table 3.3: Material coefficients used for axial layer thermal parameters calculation

Once the axial layer is nodalized, the network with resistances and capacities is built as infigure 3.6. The nomenclature for the nodes described in figure 3.5 is the same, hence node n1represents the shaft, node n2 rotor inner yoke and going on. Although some other nodes areadded and labeled with m-letter, m stands for midpoint. The pedix in mpedix gives informationon the position of the midpoint position: for example, m123 is the midpoint between n1, n2and n3. With this system, resistances and capacities are uniquely defined:

- For every i-th node ni there is one and only one capacity connected from the node tothe ground, that represents the temperature reference

- There is always one resistance from a node to node or node to midpoint. For examplethe first resistance in figure 3.6 from the bottom is the one connecting n1 to n2.

The capacity associated to the first node, that is the shaft element, is calculated as for all thecapacities in this report according to equation 2.16. The volume, is calculated consideringthat the shaft in the axial partition is a cylinder l thick and with area πr2si, that is a circulararea. The capacity instead associated to the second node, that is the rotor inner yoke, iscalculated as the product of layer thickness and the area of a ring, hence π(r2o − r2i ). Theresistances from node n2 to n1 and from node n2 to m123 are calulated according to formula2.19. The same procedure is applied for all parameters belonging to the nodalized hollowcylinder elements, such as nodes n5, n8 and n12. For node n4, the assumption adopted andpreviously mentioned is considering the elements connecting rotor ducts rectangular. Usingformula 2.10, resistance between n4 and midpoint m123 as well as resistance between n4 andmidpoint m345 are calculated considering the ∆x as half of the difference between the externaland internal radius (rrdo and rrdi) while the cross-sectional area is the product of the thicknesslrda and the axial layer thickness l. Moreover, it is fundamentally important to divide theeuqation 2.10 by the number of rotor ducts in this case because heat crossing those resistancesin reality is assumed to pass through all the elements: node na exploiting simmetry represents

29

3 Model Description

as a matter of fact all the rotor ducts connection side elements. Considering again the samerelation 2.10 and procedure as before, the resistance between node n4 and midpoint m34 iscalculated considering the heat path ∆x as half of the thickness lrda and the cross-sectionalarea is twice the product of the rotor duct heigth, hence the difference between the externaland internal radius (rrdo and rrdi), and the axial layer thickness l, finally dividing by thenumber of rotor ducts. The resistances between n3 and midpoints m123, m34 and m345 aresimply calculated with equation 2.11 considering respectively as convection exchange arealower, side and upper surface of rotor ducts multiplied bu the number of ducts.The heat transfer coefficient will be described in details laterin section 3.5 and it is the samefor all the three parameters. Instead, capacity associated to node n3 is calculated alwaysusing 2.16, where density ρ and specific capacity c are referred to dry air and the volume iscalculated as the product of the trapezoidal duct area and the axial layer thickness l. Nodesn6 and n10, and hence all the resistances related, are evaluated accordind to the model infigure 2.9. The n9 node representing the airgap is modelled like nodes n5, n2, n8 and n12 butthe resistances are calculated considering the relation 2.11, the heat transfer coefficient will bedescribed as well in section 3.5. Last node is n11, the windings node, that is described in detailin the next section: copper and insulations are distributed in layers to have more accuracyin predicting the hotspot. Actually n11 is not a unique node but represents a sub-modelcontaining several nodes.

30

3 Model Description

Figure 3.6: This figure shows how the thermal-electrical equivalent made up of resistances andcapacitances is connected in details.

31

3 Model Description

3.3 Windings model

Before starting with the description of the windings model itself, some information on thewindings system is provided. In figure 3.7, a scheme drawing of the coil shape it is shown.The coil consist of four rigid copper strand with rectangular section. This type of windings isknown as form-wound windings. The strands are gathered by the presence of the insulationand wrapped with mica tape. Every stator slot contains two coils and the rest of the slot isfilled with impregnation. The two straight orizontal sides in the scheme belong to the activepart of the motor while the rest, hence both sides of the end windings part, forms the endwindings coil, whose model is going to be outlined later.

Figure 3.7: Scheme of the windings coil shape

The scheme of the coil section is presented in figure 3.8. The two coils are drawn insidethe stator slot. Each coil has four strands and the first layer sorrounding the strands repre-sents the insulation, the outer instead the impregnation. In order to describe all the thermalresistances and capacitances, only six geometrical lengths are needed and expressed in table3.4. Considering the material indeed, the strands are made of pure copper while insulationand impregnation are assumed to have the same property of varnish at room temperature.Moreover, it is important to highlight that the impregnation process usually leaves some airbubbles trapped inside varnish. The presence of air alterates the thermal properties of theimpregnation: a new parameter is defined as impregnation goodness and it is expressed inpercent. For examole, if the impregnation goodness is 70% that means the ratio betweenvarnish and air inside the slot is respectively 70:30. The higher impregnation goodness is andthe better the electrical insulation. This value is not reported because of industrial designissue property of ABB. Moreover, the presence of air makes the thermal dissipation from thecopper in the windings to the stator throughout the slot worse. As a matter of fact, air heattransfer coefficient λair is lower than λvarnish. So, defining χ as the impregnation goodness(0.7), the equivalent impregnation heat transfer coefficient is calculated as:

λimpregnation = χλvarnish + (1− χ)λair (3.1)

Now, in literature windings has been modeled in several ways. In reference [NOMW15],

32

3 Model Description

several methods are presented for modelling wires: even if the motor presented in the articlehas litz wires, the segment layer modelling approach suits to the form-wound windings casein this report and hence it was chosen. It consist in nodalizing with simple geometrical shapethe section of the coil and build the network. The bottom coil in figure 3.8 shows how thesection is nodalized exploiting simmetry:

- There is one node for every copper strand;

- Because of high thermal conductivity, copper thermal resistances are neglected;

- Hence, strands are connected to each other through thermal resistance representing theinsulation layer;

- Strands are connected to the slot walls through insulation layer and then insulationlayer is connected to impregnation;

Copper strands can be of two types regarding their position in the coil: those can be innerstrands or outer strands. Inner strands are connected up and down respectively to upper andlower strads while on the sides to insulation and impregnation. Outer strands are connectedto only one strand, whether it is upper or lower sides and the rest of the connections is withinsulation and impregnation. Moreover, considering the upper strand in the lower coil in fig-ure 3.8, it is possible to notice that the connection with the insulation and impregnation layerboth sides and upper must be different because of the corner position: as a matter of fact theshape of insulation and impregnation layer is trapezoidal differently to the inner strand casewhere connections to insulation and impregnations sees only rectangular shaped elements.With these informations, the thermal network for a single coil is represented in figure 3.9.

33

3 Model Description

Figure 3.8: Coil section simplified scheme

Parameter Complete name Value [mm]

ws single strand width 7.1hs single strand height 2.95wcu total copper width 7.33hcu total copper height 12.72wc total coil width 8.77hc total coil height 14.16

Table 3.4: Stator coil geometrical parameters

Describing the coil network in figure 3.9, firstly the presence of thermal generator connectedevery strand nodes implies the fact that the joule losses are distributed along the copperelements. This ensure more accuracy in the system than feeding all the losses in one singlepoint and information regarding the windings hotspot is saved. It is easy to notice thatstrand nodes have only one side connection. The reason of this choice is that, similarly to theassumption made in the previous section for the axial layer, the temperature distribution isequal for both sides of the coil and it allows to reduce the number of thermal resistances bya half since those are in parallel and the equivalent is simply the resistance connecting thestrand to the slot side divided by two. There are three types of thermal resistances in thisnetwork:

34

3 Model Description

Parameter Description Value Unit of measure

Conduction coefficient λ

Insulation 0.2 W / m KImpregnation 0.2 W / m KDry air 0.0312 W / m KCopper 401 W / m K

Specific heat capacity c

Insulation 1700 J / kg KImpregnation 1700 J / kg KCopper 385 J / kg KDry air 1012 J / kg K

Density ρ

Insulation 1.4 kg / dm3

Impregnation 1.4 kg / dm3

Copper 8.933 kg / dm3

Dry air 0.932 ·10−3 kg / dm3

Table 3.5: Material coefficients used for windings model thermal parameters calculation

Figure 3.9: windings network

- Rss, thermal resistance between two strands

- Rins, thermal resistance representing the insulation between strand and impregnation

- Rimp, thermal resistance respresenting the impregnation and connecting the rest of thewindings network with the slot

While Rss is always the same, the other two parameters can vary in their formulation de-pending on the position of the strand, whether inner or outer, or if the connection is withvertical, with lower or upper part of the slot, or tangential, hence with the side part of theslot. Thermal resistance Rss is calaculated considering equation 2.10 where the conductivityis λinsulation, the ∆x is the distance between two strands and the cross-sectional area A is theproduct between the thickness of the axial partition l and the width of the strand ws. Rins iscalculated using then the equation 2.10 for inner strand case, the conduction coefficient is the

35

3 Model Description

same as Rss, the ∆x is half the difference between wc and ws while the cross-sectional area Ais the product between the thickness of the axial partition l and the height of the strand hs.The connection of outer strands with side, upper or lower surface of the slot is calculated withthe trapezoidal relation 2.23. The calculation of Rimp in the three cases is similar to the pa-rameter Rins only changing respectively the geometrical lengths and the conductive coefficientto λimpregnation. Finally, the windings network is completed connecting two coil networks invertical and all the sides connection are collapsed in a unique connection point with the sideof the slot: it is reasonable to say that some accuracy is lost but in reality the goal of thismodel is to preserve the temperature distribution only in vertical direction in proximity ofthe center of the strands. There is no practical interest in knowing the distribution on theedge of the slot side and the connection of this model with the axial layer is via a single node,that is midpoint m10,11 in figure 3.6.

3.4 Active motor

The thermal network for the active motor, previously defined as rotor and lamination packtogether with bar, ducts and windings along all the active length is built starting from theaxial partition network and windings network. Several axial partitions are then connectedthrough thermal resistances. The exact number is decided a priori. From thermal modellingliterature (reference Shafigh and gunnar), the number of axial partitions is usually 3 but,in this thesis, work the axial partition number chosen is 4. The reason behind the choiceis simple: knowing that the model is going to be subsequently reduced, preparing a setupwith more axial partition than needed shall provide results for a sensitive analysis varyingindeed the axial partition number. Hence, in later chapters, the axial partition number willbe reduced from 4 to 1.

Thermal resistances between partitions are fundamental: their presence allows the heat toflow axially. In the real case most of the heat has a preferred path is the radial direction.Although, thermal axial connections together with the presence of feasible results from CFDcalculations combined with the right model for heat convections make it possible to observea temperature distribution going from lower values in the DE part and finishing with highervalues in the NDE parts.

Connecting axial partitions, further thermal capacities are not included since those are al-ready took into account in the axial network. Air in the ducts and airgap are the onlythermal elements or nodes not connected, the reason will be outlined in section (reference).In order to have an figurative idea of this process, figure 3.10 is provided.

Once the axial partitions are connected, active motor is then linked to the outer case,one link per every axial partition, to the shaft, external rotor ring and wnd windings coil.Those in turn exchange heat through convection with sorrounding air circulating inside themotor.

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3 Model Description

Figure 3.10: Active motor: axial connections concept

Now, let us examine each connection in details. The reference figure is again the networkpresented in picture 3.6. Node n1 representing the shaft is connected to the correspoindingthrough a thermal resistance using the equation 2.10, with conduction coefficient λshaft intable 3.3, ∆x heat path of l and cross sectional area A the surface of the shaft, hence πr2shaft.Considering nodes n2, n5, n8 and n12, the correspondent connections are thermal resistancesagain using 2.10, with conduction coefficient λlamination, l as heat path and the cross-sectionalarea A is the surface of the hollow cylinder, so π(r2o − r2i ) with ro external radius and riinternal radius. The procedure to calculate the rest of the parameters is straightforward: theheat path ∆x is always l, only λ and the cross-sectional area vary. Nodes n4 and n6 have arectangular cross sectional area with conduction coefficient respectively λlamination and λal.Nodes n7 and n10 has A cross-sectional area calculated as the front surface of the cylindricalpartitionelement described in figure 2.9 with conduction coefficient λlamination. Finally, sincenode n11 represents the windings model and considering the network in figure 3.9, the onlyaxial connection are represented by the thermal resistances linking each strand to its corre-sponding. Then, using equation 2.10, the conduction coefficient is λcopper, the cross-sectionalarea A is the product of width and heigth of a single strand and the heat path ∆x is again l.

37

3 Model Description

3.5 Convection models

As previously seen in detail, convection is the heat transfer process involving the presenceof a fluid in a non-stationary condition. It can be either natural or forced depending onthe cause and subsequently type of the fluid movement. Considering the thermal resistanceequivalent outlined in formula 2.11, the aim of this section is presenting the models used forthe evaluation of the heat transfer coefficient hconvection whose importance is fundamental.As a matter of fact, it depends on several factors: local fluid velocity, the relative velocitybetween the surface and the fluid in the case of the airgap and temperature. The latterinfluences the property of the fluid, in this case air. Nevertheless, these models are simplyempirical dimensionless formulations. The SimScape software tool allows the presence ofsimple function blocks getting as input local temperature and air speed, rotor speed andparametrized surface and give back as output the heat transfer coefficient for conductionh. In general, those empirical formulation starts by calculating Nusselt number Nu. The

Figure 3.11: Convection model function scheme

previous is used to calculate h according to:

h =Nuk

L(3.2)

Where L is the characteristic length of the surface expressed in [m], k is the fluid thermalconductivity expressed in [W/mK]. Furthermore, three numbers are used to calculate Nu:

- Reynolds number Re, calculated as Re =ρvL

µwith ρ fluid density, v fluid velocity and

µ fluid dynamic viscosity;

- Prandtl number Pr, calculated as Pr =cpµ

kwith cp fluid specific heat capacity expressed

in [J/kgK];

- Grashof number Gr, whose calculation is not expressed since it will not be used in thisreport;

38

3 Model Description

Distinguishing natural and forced convection the formulations for the two Nusselt’s case areexpressed in (reference). Usually, letters a, b and c are constants given in the correlation anddiffers case by case.

Nu = a(GrPr)b (3.3)

Nu = a(Re)b(Pr)c (3.4)

The magnitude of Reynolds is used to understand if the flow is laminar or turbulent in aforced convection system.This information is crucial for choosing the specific correlation. Thepresence of the product instead Gr · Pr is for natural convection. All this information areexpressed with more details in reference [SC06]. Moreover, before presenting the model, it isimportant to outline the relation used to evaluate correctly all fluid properties.

To start, the fluid considered is air as it is outlined in the introduction during the descriptionof the cooling system, air parameters are temperature dependent. From the online source[Too], a table with a temperature range from 0 to 250 celsius degrees is considered. An exam-ple of air characteristics list a limited temperature range is provided in table 3.6. Since it hasnot been defined before, with µ symbol, it is meant the fluid kinematic viscosity, expressed in[m2/s].

Subsequently, considering that after the experimental tests air inside machine was not

T (K) cp (J/kgK) λ (W/mK) µ (kg/sm) ν (m2/s) ρ (kg/m3) Pr

273 1006 0,02418 0,00001724 1,35216E-05 1,275 0,7173274 1006 0,02426 0,00001729 1,36072E-05 1,271 0,7171275 1006 0,02433 0,00001734 1,36934E-05 1,266 0,7170276 1006 0,02441 0,00001739 1,37803E-05 1,262 0,7169277 1006 0,02448 0,00001744 1,38677E-05 1,258 0,7168278 1006 0,02456 0,00001749 1,39557E-05 1,253 0,7167279 1006 0,02463 0,00001754 1,40444E-05 1,249 0,7165280 1006 0,02471 0,00001759 1,41336E-05 1,245 0,7164

Table 3.6: Air properties table example, range between 0 to 7 Celsius degrees

covering all the temperature range, this is reduced to 20 to 120 celsius degrees. This opera-tion allows more accuracy for the evaluation of the fluid parameters corresponding functionsthrough MATLAB Fitting Toolbox. The results are summed up as follows in 3.7:

As previously mentioned, understanding how air circulates inside the motor with the aim ofcooling it is a complicated issue. This thesis work has been carried on in parallel with twoother topic regarding CFD simulations on the same motor. Thanks to the resuts of thosesimulation, it has been possible to evaluate a linear function of air local velocity in the airgapaxial direction and both rotor and stator ducts. Obviously, this is an important approxima-tion for several reasons: air has two distributions as it is possible to see in figure 3.12, it is

39

3 Model Description

Parameter name Symbol Unit of measure Temperature relation

Specific heat capacity cp [J/kgK] 0.075T + 9.839 · 102

Conduction coefficient λ [W/mm K] 7.059 · 10−5T + 0.005Dynamic viscosity ν [kg/s mm] 4.566 · 10−8T + 4.903 · 10−6

Kinematic viscosity µ [mm2/s] 1.039 · 10−7T − 1.528 · 10−5

Density ρ [kg/mm3]−1.254 · 10−9T 3 + 3.879 · 10−6T 2+−0.004T + 2.266

Prandlt Pr adimensional−3.890 · 10−10T 3 + 1.2570 · 10−6T 2++0.001T + 1.105

Table 3.7: Air parameters temperature relation

different point by point in every section and every section has a different distribution alongthe axial length. Nevertheless, since the variation in of axial speed in air gap and ducts isnegligible, it has been decided to carry two simulations, one per two different and constantrotor speed values and subsequently evaluated three function depending only on rotor speed.

Figure 3.12: CFD Simulations for air velocity distribution inside the motor

The results of the simulations are summed up in table 3.8). Every value associated to adifferent area, whether ducts or airgap, represents the mean value along the axial length andin the section area. Finally, using the same approach for air temperature-dependent param-eters, three linear correlation are calculated fitting the CFD speed results and used for heattransfer models.

40

3 Model Description

Rotor speed ωr [rpm] Stator ducts speed [m/s] Rotor ducts speed [m/s] Airgap speed [m/s]

1000 8.1750 10.664 2.28912500 20.924 27.567 6.9802

Table 3.8: CFD speeds results

3.5.1 Ducts heat transfer coefficient model

The calculation of the heat transfer coefficient for the ducts in both cases uses formula 3.2,where for L is used instead the axial partition length l since each layer has its coefficient.The Nusselt number is calculated considering two different cases: when the flow is turbulentand when laminar. The discriminant is the Reynolds number, if below 3000 then the flow isconsidered laminar, over 3000 and until 106 is then turbulent. The upper bound is consideredbecause the model suits until 106 Reynolds value, if it exceeds then it is not suitable. Al-though from the simulation this threshold is never outmatched. Using correlation presentedin [NZW+19] for rectangular section and laminar flow, Nusselt is calculated according toequation 3.5:

Nu = 7.49− 17.02(HDU/WDU ) + 22.34(HDU/WDU )2+

− 9.94(HDU/WDU )3 +0.065RePrDH/L

1 + 0.04(RePrDH/L)2/3

(3.5)

Where HDU and WDU are respectively height and width of the duct. The width for the rotor,since the geometry is trapezoidal is considered as the mean between upper and lower width.Instead, DH is the hydraulic diameter of the channel and it is calculated as:

DH =4A

P(3.6)

where A is the duct area and P the correspondent perimeter. When the flow is turbulent, theformula 3.7 used is proposed by professor Cavagnino from reference [Gni09]. Although thisrelation is only for annular tubes, it is suitbale in this case because from CFD results it canbe seen that air flow in the duct section is flowing with a circular distribution, in the rest ofthe surface air is almost standstill.

Nu =(f/8)RePr

1 + 12.7√f/8(Pr2/3 − 1)

[1 + (DH

L)2/3] (3.7)

The parameter f is called friction factor and it is calculated by the relation 3.8:

f = (1.8 log10Re− 1.5)−2 (3.8)

3.5.2 Airgap heat transfer coefficient model

This model is slightly more complicated then the previous described because takes into ac-count the simultanous presence of the local rotational air speed due to the rotor movement

41

3 Model Description

ωr and the axial air velocity v. Two relations are used to calculate Nusselt and hence h heattransfer coefficient as well as two different Reynolds number are evaluated, one for axial ve-locity Rea = vDHν and one for rotational speed Rer = ωrr

2r/ν. Moreover, it is important to

remeber that for the airgap case, L in formula 3.2 the distance between stator teeth and rotoris used, well known as airgap length. So, as proposed in reference [NZW+19] by S. Nategh, atlow motor rotational speeds, when Rer < 4e4 and Rea < 6.5e5, the relation 3.9 is used; whilefor higher rotational speed, hence 1.4e4 < Rer < 2.7e6, the relation suggested to use is 3.10.

Nu = 0.022(1 + (DHωr

πrrv)2)0.8714Re0.8Pr0.5 (3.9)

Nu = Nuz + 0.068(ωr/v)2Nuz (3.10)

Where rr is rotor outer radius, ωr is rotor speed, Nuz is the axial Nusselt number calculatedas

Nuz = 0.023Re0.8a Pr0.5 (3.11)

With all the information described, it is possible to define the resistances in the axial networkin figure 3.6, specifically the three resistances connecting the node n4 to midpoints m123,m34 and m345. The equation used is the one for convection resistance expressed in 2.11, h iscalculated used the rotor ducts model and the exchange surface considered are respectivelylower, side and upper rotor ducts. The side surface is multiplied by two, because the heatexchange is verified through both sides and all the surfaces are multiplied bu the numberof rotor ducts Qrd sice the node n4 represents all rotor ducts and not simply one. Similartechnique is used to model resistances connecting n9 that is the airgap node with midpointm89 hence the surface of the rotor and midpoint m9,10,11 hence stator teeth bottom surface.

3.6 Housing modelling

The active motor nodalized and modelled is then connected to the correspondet models forhousing and inner parts. These sections are dedicated to the description of each part in detailsand how those are connected. Considering figure 3.13, that is a section of a simplified motordesign along the axial direction, it shows that the active motor is connected to the housing,simplified as a cylinder. The housing cylinder is closed in in the back and in the front with twoexternal plate, each of has a bore where two bearings are placed. Bearings are then connectedto the part of the shaft. The four extension drop-shaped from stator slot represents the sectionof the end windings coil while the excess material connected to the rotor represents the shortcircuit ring for both DE and NDE part of the motor. Finally, all the previously describedelements are connected to the air inside the motor that in turn is partitioned in differentparts, one with each thermal mass. Consider now each part individually.

42

3 Model Description

Figure 3.13: Axial section of lamination, housing and inner parts

3.6.1 Motor Case

The housing or case of the motor is going to be modeled as a cylinder whose internal surfacecontains slots: once the stator lamination is inserted inside, the slots of the housing becomea further way for air to flow from the inlet part of the motor to the outlet. Those are knownas stator ducts. Considering figure 3.15, on the right the housing section is presented. Thenumber of the ducts is Qsd 15 and the proportion of the angle swept by the ducts and theremaining case is 1:1. Although this is an approximation since the real design of the case hasasymmetrical stator ducts even if the number is kept the same. The internal radius ri is thevalue of the stator outer radius already presented in 3.2 while the outer radius ro is 257.25mm. The height of the duct hsd is 12.5 mm. Any specification regarding the material areexpressed in table 3.9 that is made up of cast iron, as well as end plates.

Conductive coefficient λhousing 168 [W / m K]Specific heat capacity chousing 833 [J / kg K]Density ρhousing 2.79 [kg / dm3]

Table 3.9: Material parameters for the housing

The housing cylinder exceed the axial length of 126.55 mm in the back and 177 mm in

43

3 Model Description

the front. So the whole case is divided in 4 partitions, each connected to the axial partitionbelow. All of these are then axially connected to each others and then susequently to theelement representing the front and the back extension of the case. In turn, the extensionswill be connectedt to the end plates. For a better understanding, the figure 3.14 provides agraphical quick overview.

Figure 3.14: Scheme for the whole housing network connected to the active motor

The construction of the axial network start with the nodalization. Considering the figure3.15, in the section on the right and next to the geometrical labels, it is possible to evince thechoice of nodes placement. Node nducts represents all the ducts, the node ntooth represents allthe housing teeth connecting physically the lamination to the housing and then nyoke repre-sents the yoke of the housing cylinder. Again in figure 3.15 but on the left, the network isshown, with mi midpoints are defined to help describing each parameter. Node ntooth can beconsidered as a cylindrical partition element, described in the second chapter, so the resis-tances connecting ntooth to midpoints m1, m2 and m3 are easly calculated considering modelin figure 2.9 with parameters in equation 2.21. Node nyoke is a hollow cylinder element andthen reistances from nyoke to m3 and to the external air are calculated according to equations2.19. Differently, node nduct represents air, hence the capacity is the total mass of all the ductsby the specific capacity of dry air, while the resistances connecting nduct to midpoints m1,m2 and m3 are connection resistances and then expressed with the formula 2.11. The heattransfer coefficient hsd for stator ducts is calculated with the model presented in the previoussection using 3.5 or 3.7 depending on the case. The surface A linked to each resistance isinstead calculated considering the surface of bottom, side and top the duct as well as alreadydone for the rotor ducts. It is fundamental to remember that when necessary the resistancesare divided by the number of ducts Qsd in order to respect the simmetry.

44

3 Model Description

Figure 3.15: Housing section, parameters and network

The axial connections with all the housing active partitions are through node nyoke tonyoke using 2.10, conductive coefficient from table 3.9, heat path ∆x is the axial partitionthickness l and cross-sectional area A is π(r2o − r2i ). Finally, with similar equations, housingDE and NDE extention are calculated. The only difference is in the heat path ∆x that isrespectively 126.55 mm in the back and 177 mm in the front. The capacity is connected tothe middle of the extentions then the resistance is actually split in two with half ∆x per achand again using formula 2.10.

3.6.2 End plates and bearings

The last two elements that has to be modelled concerning the housing are the end plates andthe bearings. Since the focus of the model is on investigating the temperature on sensitiveparts such as windings, it has been possible to model the end plates using two simple hollowcylinder-shaped element. As a matter of fact the complex shape of the end plates in the realmotor, which it is reminded from figure 3.1 and 3.2 those are different because the DE platehas holes for the inflowing air on the side surface while the NDE ha holes for the outflow airon the front surface and it is less thicker, it does not influence the system. From this assertionend plates are more important in representing thermal mass rather then resistances modellingtheir complicated shape. For this reason, the simplification to hollow cylinders is feasible.

45

3 Model Description

Moreover, both of the plates are equal in dimensions and material specification. Hence, theouter radius ro is 257.25 mm, hence equal to the housing cylinder outer radius in the previoussection, the thickness is 23.45 mm and the inner radius, which correspond to the bearing outerradius is then 62.5 mm. It is modelled then with two resistances and a capacitance connectedto the midpoint. These parameteres are calculated according to the hollow cylindrical modeldescribed in the second chapter and whose equations are 2.19. The top part of the networkis connected to the housing DE or NDE extention while the bottom is linked to the bearingmodel.

For the bearing model, the reference [BCS08] has been used. These correspond to an equivalentinterface air gap and the sensitive parameter is then the thickness of the gap. A. Cavagninoet al. has proposed a correlation depending on the power of the machine: bigger motorslead to the choice of bigger and more resistent bearings, hence the equivalent interface gap ishigher. Using equation 2.10 with ∆x the equivalent thickness, λair for conduction coefficient,the cross-sectional area A is simply 2πrmeanl where rmean is the mean radius between theinternal end plate radius and the shaft radius while l is the thickness of the end plate. Thethermal mass or heat capacity is calculated as the product of the mass by the specific heatcapacity of the housing. The mass of the bearing from the specification of the motor is 1.09kg.

3.7 Inner parts modelling

The expression ”inner parts” used in this report is meant to describe all the componentsconnected to the active motor and exchanging heat by convection with inner air. In thissection the inner air partitions system is described as well as all the connection between theelements providing a final scheme of the whole model in blocks.

3.7.1 End windings coil

According to the model already presented in reference [NZW+19] by S. Nategh et al. the endwinding coil is modeled using the lumped parameters approach: considering figure 3.17, theassumption is that heat from the windings inside the slot to the end windings coil flows acrossthe copper from both sides of the two slots connected by the same coil, then goes throughthe insulation layer and then it faces air inside the motor, hence heat is dissipated throughconvection. Rew1/2 models half of the resistance of the copper in the end coil, whose lengthLew is from the drawings 200 mm, then it is calculated according to:

Rew1/2 =Lew/2

λcopperAstrandQstrand(3.12)

46

3 Model Description

Where Astrand is the area of a sigle strand calculated as width by heigth since the form-woundwindings system has 8 rectangular copper strand, four each coil and two coils per stator slot.Re−ins is then the reistance of the insulation layer that is wrapped by a mica tape and whoserelation is:

Re−ins =Lins/2

2λinsLew(Wcoil +Hcoil)(3.13)

Where Lins is the insulation thickness and 2Lew(Wcoil +Hcoil) is the cross-sectional area forthe heat path. Finally, Re−air is calculated with the relation 2.11, with convection surface2Lew(Wcoil + Hcoil) and the heat transfer coefficient is calculated with the relation 3.2, withL as the end windings’ coil length, k considered as λair and the Nusselt number is calculatedthrough the correlation for a cylinder in cross flow presented by Churchill and Bernstein:

Nu = 0.3 +0.62Re1/2Pr1/3

[1 + (0.4/Pr)2/3]1/4[1 + (

Re

282000)5/8]4/5 (3.14)

Anyhow, the network described in figure 3.16 represents a single coil. The passage from asingle network to the equivalent for the holistic end windings system is evaluated consideringan electrical parallel reduced system.

Figure 3.16: End windings single coil network

Considering figure 3.17, the first assumption is that heat is gathered in a unique flow,from all the stator coils to the external end windings coil and finally connected to inner air.Each single coil is modelled with the previous equivalent and considering that every coil hastwo ends, from the lamination stator block come out half of the number of stator slots Qs,then Qs/2 network systems are in parallel. The ”electrical” parallel is shown in figure 3.17for simplicity only for two networks. In conclusion, the final end windings model, all theresistances calculated for the single network are corrected simply dividing by Qs/2. The finalequivalent is then split into three equal resistances simulating three different heat flows: fromthe windings to the thermal air element up, center and down position respect to the end coil.

47

3 Model Description

The thermal capacity is calculated considering the sum of both insulation and total coppervolume, connected to the node between the coil extention copper resistance and insulationresistance for measuring reasons explained in the next chapter.

Figure 3.17: End windings all coils equivalent network

3.7.2 Short-circuit rotor ring

Exactly like the end winding case, the aluminum inside each rotor slot is welded to a uniquering. This has of course a complicated shape in the real design but it has been simplified witha hollow cylinder structure. the outer radius ro is 142.145 mm, the inner radius is ri 105.54mm and the thickness lr is 24.53 mm. then the network starts with a conduction resistanceexpressed by the formula 2.10 with π(r2o−r2i ) as cross-sectional area, ring thickness as the heatpath and λal for conduction coefficient. The previous resistance is then split in two halves andin the midpoint the capccity for the short circuit ring is connected, by formula 2.16 whosevolume is π(r2o − r2i )lr. Concluding the network, to the external conduction resistance is thenconnected the convection resistance to the local air element. It is calculated with formula2.11, where h heat transfer coefficient calculated according to the relation 3.15:

h = k1(1 + k2vk3) (3.15)

Where k1, k2 and k3 corresponds respectively to 15, 0.4 and 0.9 and v is local air speed. Thiscorrelation is frequenly use and proposed in reference [SC06], it is named Shubert correlation

48

3 Model Description

and its use is suitable for all surface where air velocity is quasi-stationary. This correlationis going to be used frequently for other parts during the model description. The exchangesurface is the sum of both front surface π(r2o − r2i ), outer side surface 2πrolr and inner sidesurface 2πrilr. Although it is important to consider two things: the front surface is finnedand in order to enhance the convection it has been considered 20% more the original value,moreover, the local air speed fed to the shubert correlation is obtained turning the rotor speedfrom rpm to m/s. The short circuit is moving together with the rotor and the finned surfacemoves the air around with the same speed.

3.7.3 Inner air partitioned

This section is the final section of the chapter and concludes it. In fifure 3.18, it is possibleto have a graphical overview of the model scheme. EW, Ring, Shaft, Bearing and End platecontains in the inside the thermal capacity representing each element. Then, those are con-nected between themselves through thermal conductive resistances while the connection withthe black dots represents the conduction heat exchange.

Figure 3.18: Full model blocks scheme with inner air connection

Inner air is partitioned in 4 elements for the DE side and other 4 for the NDE side. Eachof those is modelled as a thermal capacity calculated with formula 2.16, where both densityρair and specific heat capacity cair are constant hence not temperature dependent; volume Vis instead calculated considering that the inside of the motor both DE and NDE consist in

49

3 Model Description

hollow cylinder air volume partitions. Furthermore, each block contains a thermal generatorwhich allows the possibility to set the temperature from an external array: as a matter offact, inner air could not be modelled only with a thermal capacity for the OSV cooling systembecause the flow from the inlet to the outlet produce a continuous air circulation motion sothat the temperature is lower than the TEFC cooling case for example, where there is no aircirculation due to external fan but at least only convective motions.


The content of this chapter consists of giving the reader an overview on the constructionof the DM network. It starts by presenting the motor by a general description in all itsgeometrical and material aspects focusing on the cooling system. Then the network startswith the active motor, where all the lamination is subdivided in 4 axial partitions. The activemotor is then connected to external elements such as end windings coil, external shaft, shortcircuit ring and case. Case is then connected to closing elements such as end plated andbearings. Air inside the motor represents an important aspect of the whole system and henceboth convection models and how air is partitioned inside the motor are explained carefully.Another important aspect is choosing the suitable form-wound windings thermal network: itallows to save the information regarding temperature of the hottest spot in the slot, situatedin the bottom copper strand.

50

Chapter 4

Detailed Model Validation

In this chapter, the detailed model built before is validated through experimental evidence.The experiment at issue is a thermal rise test done in ABB Machine department’s testingroom. Once the setup is explained and all data are presented, the SimScape environment isprepared for the simulation as well explaining in detail all the choices and assumptions made.Finally, simulation’s results are compared to experimental data agreeing that the model givesfeasible results and it is ready for the reduction process.

Figure 4.1: Pictures from the setup temperature rise test

4.1 Temperature rise test

The temperature test in question, whose pictures 4.1 refers to, consisted in running the 4-poleinduction motor at the ratings specification, then a supply voltage of 1100V and a current of160 A rotating clockwise. The speed has been kept lower than the rating of 2163 rpm, but itis constant or slightly decreasing for the whole test as it is possible to evince from the graph

51

4 Detailed Model Validation

in figure 4.2. The test started at 8:40 and ended up at 12:40. During the 4 hours of test, dataare collected every 30 minutes, so the first measured set of data is acquired at 9:10, the second9:40 and so on. It is specified that the machine is totally at rest before the test and for thefuture simulation set up all the components have the initial condition equal to the ambienttemperature that instead is monitored during the test and starts with 24.6C.

0.5 1 1.5 2 2.5 3 3.5 4

time [h]

1905

1910

1915

1920

1925

1930

Roto

r speed [rp

m]

Rotor speed

Figure 4.2: Duty cycle operated bu the motor during the test

As it is possible to see some in figure 4.1 pictured in black, the test counted well 18temperatures probes and thermocouples. Among all these, only 7 were considered and theexplanation for this is going to be outlined later. On table 4.1 the dataset used for validationis outlined. Although, it is of fundamental importance to explain the placements of the sensor.The position of the termocouple has a massive impact on the results: different positions leadto different temperature values. Before the test, the position of all the sensor has been clearlydefined in order to prepare the SimScape ambient subsequently for the simulation.

TimeDE shortcircuit ring

NDE shortcircuit ring

End windingsDE

End windingsNDE

DE bearing Inlet air Outlet air

8:40 Start of heat-run test9:10 110.5 144.5 137.5 150.7 61.9 24.6 60.59:40 129 173 162.3 182.2 72.8 27.6 71.110:10 137.8 185.2 174 197.2 78 28.7 76.210:40 141.5 190.7 179.3 201.9 79.9 28.8 78.211:10 143.2 193 181.5 205.8 81 28.2 79.111:40 144.2 194 182.2 205.6 82.8 30.1 79.712:40 144.6 194.3 182.6 206.8 82.6 32.4 80.3

Table 4.1: Temperatures data from sensors acquired during the temperature rise test

The first and second dataset considered refers to the DE and NDE short circuit ring tem-

52


perature measurement. In order to accomplish this test, a ad hoc rotor has been used: theshaft and the rotor has been drilled so it is possible to insert several probe wires. Sensor 1 and2 are then shown in figure 4.3. The position on top or bottom is not affecting the temperatureresults since the rotor is not standstill but moving. Both termocouples are placed in the exactmiddle of the short circuit ring from DE side and NDE side.

Figure 4.3: Rotor block and shaft simplified scheme for sensors position defining

The third and fourth dataset instead belongs to the end windings and in this case sensorplacement is slightly more complicated. Starting from the description of the sensor in a singlecoil and considering figure 4.4, there are two termocouples placed in the midpoints where thecoil is bented. A further layer of mica tape is wrapped around the two coils and again infigure 4.4, the section in the top of the picture shows that each termocouple is between theadditional mica tape and the windings system. This information is going to be important forthe simulation sensor placing. As a matter of fact, the choice of the windings model describedin the third chapter is suitable with the actual sensor placement.

The fifth sensor provides information on the temperature of the bearing on the DE side.As for the rotor case, a specific bearing has been used during the test: a bore was drilledallowing the presence of the termocouple exaclty in the juction between the shaft and thebearing. The last two dataset monitor the temperature of the intaking air and of the florcoming out from the outlet holes. These information are going to be used to have a distri-bution of the temperature closer to the real case. As a matter of fact, air is aspirated atambient condition but as soon as it stream across the inlet holes it becomes hot and becomeshotter flowing along the motor. With this two data it is possible to replicate the distributionof air inside the motor with the variation of time and hence have good extimation for all theparameters which are temperature dependent.

53


Figure 4.4: Stator coil PT100 sensor placement DE and NDE side

This section ends outlining the losses values, in table 4.2. those four values are calculatedassuming that the power is constant during the simulation. Since the test is a temperaturerise, this hypothesis is valid and having a fixed values allows the simulations to run quicker.Losses, together with the duty cicle, represents the input for the model: every instant of thesimulation will be characterized by a specific value of rotor speed and losses. Althoug, this isstill an approximation because the extimation of losses is always an issue for the temperatureprediciton. The variation is both time and space dependent and its behavior is not linear forthe iron losses case: for calculating more accurate values FEA-based software are needed andit still will not be enough because other than information about the speed, even supply modeis crucial. Anyway, this lies outside the scope of the thesis but is related more to controlissue and that is why the reason of a temperature rise test and consequantly stationary lossesvalues helps to deal with issues related to the model only.

4.2 Simulation setup

This section is going to describe the settings used for the simulation. The first operation wasto create a time vector which is going to be the base of all the time-variant input. This issimply an array from 0 to 14400 seconds, hence 4 hours of simulation analysed in step of one

54


Simulation losses

Stator lossesJoule losses [W] 7641Iron losses [W] 6724

Rotor lossesJoule losses [W] 3602Iron losses [W] 1899

Table 4.2: Losses extimated values for the temperature rise test

second. Although, since the phenomenon regarding temperature changes have time constantsrelatively high, then the choice of 1 second of timestep can be furtherly reduced to one ora couple of minutes. Nevertheless, since this model is going to be used for further controlapplication and then losses as input can vary in a fraction of time even smaller than a second,the setting has been kept. Considering the intial temperature values, the SimScape environ-ment has the possibility to change it in all the capacity belonging to the model and in thetemperature, sources placed outside the model representing the outside air. As far as motorthermal capacities are concerned, all the initial values are set to 24.6C, that is the initialtemperature value for the ambient considering that the machine before the test was fully onrest. It is important to add that the previous setting is not crucial in the temperature risetest: the test take place in several hours with constant losses values and speed. If the dutycycle has been the one representing a train operation, speed and losses would have variedand the temperature would have had ripple or up and down trend. The input of the initialcondition for every machine part is important because high temperature values will lead toan urgency in decreasing the faster or an impossibility in feeding the duty cycle compared tolower temperature starting condition.

As previously said, losses are one of the input of the simulation and the value used for thevalidation process are outlined in table 4.2. Now it is going to be briefly explained how lossesare distributed in the model. First of all, it is important to remember that in the electrical-thermal equivalent, losses are fed from an ideal current generator connected to the midpointof the node, hence in the point where the thermal capacity itself is connected. Consideringthe value of iron losses, whether for rotor or stator lamination, the assumption is that thoseare equally distributed. Hence, the total value is divided by the number of axial partitionand then, since the section is constant along each axial partiton, losses are scaled accordingto the surface. For example, node n12 in figure 3.5 represents the stator yoke whose surfaceis π(r2o − r2i ) where ro is the outer radius and ri is the inner radius. Now, the whole statorlamination surface is the sum of the yoke surface and the teeth surface. So, the value of ironlosses fed to the stator yoke element in an axial partition is calculated as:

Pn12 =Piron

4

Ayoke

Ayoke +Ateeth(4.1)

Similarly, losses are distributed in all the other nodes according to this procedure. Thedistribution for the joule losses, both for rotor and stator consist in a first apportionmentbetween the parts in the active motor and the end parts. Then, joule stator losses are

55


distributed considering the coil: the copper section is constant for all the strands in thecoil and for all the coils. The discriminant factor is then the total length of the coil so thatthe sum of twice the active length and twice the length of the outer part, that is 200 mmaswell for each DE and NDE side. Then the portion of losses fed to the end windings partis given by equation 4.2 while the rest is divided by four and subsequently by the number ofstrand and fed to each strand node in the coil model outlined in the previous chapter.

Pew,DE−NDE = Pjoule

louter

2(louter + lactive)(4.2)

The rotor joule losses are distributed in the end parts scaling the total value by the volumethat is the sum of the two short circuit ring and all the bars volume. Another detail thatallowed to acquire more accuracy is including in the model the temperature-variance of thejoule losses. As a matter of fact, values outlined in table 4.2 are referred to a constant ma-terial reference temperature, that in this specific case was 20C. According to the fact thatthe temperature is proportional to the product of losses and resistance θ ∝ P · R, since itis assumed that the resistance is not changing, if the temperature is increasing then lossesare increasing. The temperature raise in stator copper and rotor aluminium is considerableand so losses increases because the resisivity augment proportional to (1 + α∆θ) where αis the temperature coefficient of resistivity and ∆θ is the difference of temperature betweenthe reference value and the actual temperature of the solid element considered.Temperaturecoefficient of resistivity αcu is 0.0039 [K−1] while for the aluminium αal is 0.00404 [K−1].

Pcorrected = Pinitial · (1 + α∆θ) (4.3)

The temperature of air inside the machine affect as seen in the model description chapter allthe convection parameters. To every inner air node or air node in the active motor, henceairgap, rotor and stator ducts, is connected a thermal capacity. Although, since air is flowingand it is not stationary as it could be in a TEFC motor, then the extimation of temperatureis hard during the test. Although, experience and evidence suggest that the hypothesis ofa linear-decreasing temperature distribution for inner air along the motor length is feasible.Considering table 4.1, the values for inlet air flow is always below the outlet one. Then, toeach air node is also connected a temperature source whose constant value depends on theposition of the node.

4.3 Experimental data and simulation comparison

In this section, the experimental data are compared with the respective simulated tempera-tures. The results are then commented in details.

Considering figures 4.7, 4.6 and 4.5 the first thing evinceable is that the continuous linesrepresenting the simulated data has an exponential growthas it was predictable, since all theinput are stationary or oscillating around a constant value. Althoug, as it is more evident

56


in figure 4.6, the short circuit ring temperature is more sensitive to the change of the speedsince some edges are accentuated when the duty cycle is changing, hence every 30 minutes.For this type of test, more experimental data would have been needed: the sampling rateof one measure every half hour is too low to have a good comparison and check if the totalthermal capacity is modelled correctly. Nevertheless, once the thermal transitory is expiredbetween the second and the third hour of simulation, temperature information regarding thesteady state are reliable considering it as the last measured data and comparing it with thelast simulated data.

With the last assumption, a table with the relative percentage error is outlined in table4.3. Considering the time spent to build the model and the fact that LP approach is fullybased on geometrical and material parameters, it was not possible to expect an error belowthe threshold of 5%. The error’s set of values occurs in the range between 5% and 10% andthis result is reasonable without the use of any corrective coefficient. Better results are possi-ble to reach in several ways: improoving the accuracy of the convective models, more preciseprediction of the temperature distribution of inner air and more.

Relative percentage error [%]

End windings coil DE 6.8End windings coil NDE 6.5Short circuit ring DE 7.8Short circuit ring NDE 7.5Bearing inner ring DE 2.7

Table 4.3: Percentage error relative to the steady state data compared with simulations results

Although, since the second goal of the thesis is the attempt of reduction of the detailedmodel, then the level of accuray gained is sufficient. Considering that the actual goal is havingfast temperature prediction for control purpose, then more precision is expected to be lostduring the reduction and hence there is no need to strees excessively the focus on DM’s errorbelow 5%.

One last consideration, unfortunaltely for technical problems during the test, the NDE innerbearing temperature dataset has been neglected for the comparison of the validation becausethose values were too close to the DE inner bearing dataset and the OSV cooling system isexpected to have a broader difference between inlet and outlet side.

57


0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

0

50

100

150

200

250

Te

mp

era

ture

[°

C]

End Windings

DE simulated

DE measured points

NDE simulated

NDE measured points

Figure 4.5: End windings temperature simulated and experiemental data comparison

0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

20

40

60

80

100

120

140

160

180

200

Te

mp

era

ture

[°

C]

Short circuit ring

DE simulated

DE measured points

NDE simulated

NDE measured points

Figure 4.6: Short circuit ring temperature simulated and experiemental data comparison

58


0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

20

30

40

50

60

70

80

90

Te

mp

era

ture

[°

C]

DE bearing inner ring

simulated

measured points

Figure 4.7: Bearings temperature simulated and experiemental data comparison


The content of this chapter shows the results of the validation of the detailed model built inthe previous section. In order to achieve this, the results of the simulation are compared withthe correspondent measured data. The experiment carried on is a simple temperature risetest where the induction motor is runt at maximum speed allowed and with the rated currentfor 4 hours until it fully reaches the thermal steady state. Once the temperature rise test isexplained in detail, like explaining the position of all the scopes, the simulation settings areoutlined: losses and speed. The results are finally presented with three MATLAB graphs anda final table with the error in percentage is shown.

59

Chapter 5

Model reduction

This chapter is going to deal with the reduction of the detailed model described and validatedin the previous chapters. From now and on, the reference for the reduction is the detailedmodel: simulations result from the subsequent reduced-model versions are compared to theones from the detailed model assuming its behaviour simulates perfectly the real motor. Thegoal of the reduction is then maintaining the accuracy of the detailed model reducing thenumber of nodes or connections.

In this report, by node it is defined every element to which a thermal capacity is associ-ated and that can be connected to one or more nodes through thermal resistances. Thenumber of nodes define the order of the model. The DM has 78 nodes, in this counting, thenumber of nodes belonging to the windings slot partition is not included because the reductionis focused on keeping the structure of multiple form-wound presented in the description of themode that allows to have accurate prediction on the windings hotspot. So, the DM is a 78-order model meaning that the thermal system has 78 variables and solving it implies findingthe temperature versus time for every instant of the simulation. The computational time in-crease with the number of nodes but on the other side a high-order system is represents betterthe reality and has more accuracy. The reduction performed in this thesis work goes from 78to 24 nodes, computational time and accuracy are tracked and analysed for every reductionstep. Although, it is necessary to make a remark before starting: in order to effectively trackthe time of simulation, the whole matrix system described in the second chapter (formula1.1) has to be transferred to pure code. In general, for this purpose the use of Python or Csuits to the task. Using the code, all the geometrical and material data are stored, from thoseparameters are calculated and hence matrix generated taking into consideration the structureof the network. Feeding as input losses and duty cycle, the simulation results are calculated.Nevertheless, the approach is based both on MATLAB coding and SimScape environmentwhich makes simulations times longer. The network is visualized, and it is possible to acquireinformation on the temperature in whenever a scope box is placed. This approach is usefulto build a network from the start but once finalized it is more convenient to write the codefor the matrixes and use pure code. Since that is the case of this thesis work, the going fromSimScape to code could represent a future work option.

60

5 Model reduction

5.1 Primary DM model reduction

Hence, a primary reduction has been performed considering that the number of axial layerscan be reduced as well as the number of connections between those, that is reasonably highconsidering that every node in the axial network is connected to its correspondent in the nextone.

5.1.1 Axial partition number sensitivity analysis

Every axial partition counts 11 thermal nodes; hence it is straightforward that reducing oneaxial partition means subtracting this number of nodes to the total. Nevertheless, consider-ing that the axial partition process does not regards only the axial lamination but even thehousing axial partition described in chapter III counting 3 nodes each (case yoke, case teethand stator duct), reducing the number of axial layer means loosing 3 additional thermal nodesto the system. The axial partition reduction for the simulation set up point of view meansfirstly to change the length of the axial partiton l outlined during model description. Then onSimScape one or more axial partitons are manually removed in order to reach the new axialpartitons number looked for. The axial connection between the layers are then redistributed.Let us consider going from 4 axial partitons to 3 and the number of axial partitions callingn the number of axial partitons for simplicity. It is straightforward that the conduction re-sistances connecting the correspondent nodes in two axial network or between inlet or outletaxial networs and inner parts are calculated with formula 2.10. While cross-sectional area andconduction coefficient are kept constant during the reduction of the number of axial layer,the heat path ∆x is changing. As a matter of fact, between inlet or outlet and the outsideit is always a half of the total motor length divided by the number of axial partitions, whichis l

2n ; between the partitions, ∆x is always l · n−1n . In the case of 4 axial partitions l in theresistances is scaled by a factor of 3

4 , in the case of 3 by 23 .

Following the results of the simulation are presented considering that the detailed modelis reduced from 4 to 2 axial partitons. As it can be seen in all the three figures 5.1, 5.2and 5.3 some accuracy is lost progressively. The temperature value increases from the leastvalue with four partitions to the highest with two partitions. While it was predictable thatthe accuracy was reduced decreasing the number of axial partition, nothing could be said inadvance about the shifting of the values, if ascending or descending. The maximum deviationsfrom the DM to the 2 axial partition model are gathered and presented in table 5.1. All thefigures are zoomed because the difference would not be evident considering the whole 4 hourssimulation time, whose input and temperature variables are the same presented and used forthe validation of the model. This reduction start from 78 nodes in the DM progressively goingto 64 (n = 3) and 50 (n = 2).

61

5 Model reduction

Temperature deviation ∆T [C]Short circuit ring DE 2.59Short circuit ring NDE 2.85End windings coil DE 0.70End windings coil NDE 2.15Bearing inner ring DE 0.7

Table 5.1: Temperature deviations form 4 axial layers DM to 2 axial partition RM

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8

time [h]

170

180

190

200

210

220

230

240

Tem

pera

ture

[°

C]

End Windings

DE 4 partitions sim

NDE 4 partitions sim

DE 3 partitions sim


DE 2 partitions sim


Figure 5.1: Sensitive analysis simulation results for the end windings coil both DE and NDE reducingthe DM from 4 to 2 axial partitions

62

5 Model reduction

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8

time [h]

140

150

160

170

180

190T

em

pe

ratu

re [

°C

]

Short circuit ring

DE 4 partitions sim


DE 3 partitions sim


DE 2 partitions sim


Figure 5.2: Sensitive analysis simulation results for the short circuit ring both DE and NDE reducingthe DM from 4 to 2 axial partitions

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8

time [h]

76

78

80

82

84

86

88

Te

mp

era

ture

[°

C]


4 partitions sim

2 partitions sim

3 partitions sim

Figure 5.3: Sensitive analysis simulation results for the DE inner bearing reducing the DM from 4to 2 axial partitions

63

5 Model reduction

5.1.2 Axial connections reduction

As outlined in details in the description of the model, all the nodes belonging to each axiallayer are connected to their correspondent. Since there is no connection between air nodesbecause the temperature is independent, it is possible to classify these connections in ther-mal resistances gathering two lamination elements, two copper elements, hence each windingsstrand axial connection, or two aluminium elements, hence rotor bars axial connection. Con-sidering that the thermal conductivity of copper and aluminium is four order of magnitudehigher than the thermal conductivity of the lamination in the axial direction, then the heat-flow passing through the lamination is negligible compared to the one crossing copper oraluminium. The axial connections reduction performed in this subsection consist of removingthe connection between lamination nodes in the already reduced two-axial-partitions modelso that heat from an axial partition to the next one is flowing only trough copper path for thestator and aluminium path for the rotor. Moreover, considering the rotor, heat goes acrossthe axial shaft connections. The number of nodes reducing the connections between axialpartitions remains unaffected but the conductance matrix G of the system expressed in 1.1becomes more sparse and the solution is evaluated faster by the solver.

Although, some of the accuray is lost in this case too: the simulated temperature variablesare affected by the fact that the structure of the network is modified and the axial connec-tions remained resistances are less than the previous case forcing the heatflow to redistribute.Simulations results are expressed in figures 5.4, 5.5 and 5.6 and the temperature deviationsin C are explicit in table 5.2.


Table 5.2: Temperature deviations form 4 axial layers DM to 2 axial partition and axial connectionreduced RM

Also by this modification, the temperatures increase their values overall shifting furtherlyaway from the values performed by the DM set as reference. Nevertheless, this reduction hasless impact compared to decreasing the number of axial partitions and it clear comparing thedevaitions from table 5.1 to 5.2.

64

5 Model reduction

0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

0

50

100

150

200

250

Te

mp

era

ture

[°

C]

End Windings

DE 4 partitions sim


DE 2 partitions a.r. sim

NDE 2 partitions a.r. sim

Figure 5.4: Simulation results for the end windings coil both DE and NDE comparing the DM witha RM 2 axial partitions and less axial connections

0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

20

40

60

80

100

120

140

160

180

200

Te

mp

era

ture

[°

C]

Short circuit ring

DE 4 partitions sim


DE 2 partitions a.r. sim

NDE 2 partitions a.r. sim

Figure 5.5: Simulation results for the short circuit ring both DE and NDE comparing the DM witha RM 2 axial partitions and less axial connections

65

5 Model reduction

0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

20

30

40

50

60

70

80

90

Tem

pera

ture

[°

C]


4 partitions sim

2 partitions a.r. sim

Figure 5.6: Simulation results for the DE inner bearing comparing the DM with a RM 2 axialpartitions and less axial connections

5.2 Resistances sensitivity analysis

In order to furtherly reduce the model, a resistance sensitivity analysis has been done aimingto better understand the behaviour of the detailed model. This consisted in choosing first sixtarget for the reduction, temperature values for:

- Bearing inner ring DE

- Bearing inner ring NDE

- Rotor bars DE

- Rotor bars NDE

- Windings hotspot strand DE

- Windings hotspot NDE

The SimScape probe for the rotor bars has been placed in node n7 for the axial networkpresented during the model description, DE stands for belonging to the DE axial partitionand the same nomenclature is used for the NDE side. Considering the winding hotspotinstead, the SimScape probe is placed in the last copper strand node for the windings networkpresented again in the model description chapter. With the OSV cooling system, the windingsmaximum temperature is often situated in the bottom of the stator slot, considering that therotor has always higher temperature compared to the stator values. Changing the target from

66

5 Model reduction

short circuit ring to bars and from end windings coils to windings hotspot in the stator slotis a decision taken with the goal of preserve the behaviour of the model not only in the endparts of the motor but even in the axial network. Moreover, a good prediction of the hotspottemperature and hence understanding the suitability of a specific duty cycle performed bythe machine can prevent the unwanted loss of insulation life. So, a MATLAB script makingmultiple simulation of the model is created following the block diagram in figure 5.7.

Figure 5.7

The list of feasible parameters fed to the algorithm is the list of all resistances used tobuild the network. The program starts by making a simulation of the network with theparameters unchanged and then two nested for loops change the value of the resistance, oneby one, tracking the temperature of the targets and comparing with the reference simulationvalues. The highest influence between the six targets is then saved in a list containing thename of the parameter and the influence value in per cent. This means that if a specificparameter in table (reference) has a certain value of influence, this belongs to the elementmost affected by the change of the parameter and hence it is not excluded that the influenceon other parameters could be lower. It has been decided to move in this direction because itis obvious that the modified parameters with the lowest stored influence affect less the rest ofthe target’s temperatures. The advantage of this procedure is that there is no need to displayall the influence values of the target but only the highest, the drawback is that consideringthe structure of the script, it is not possible to know which target is affected the most butgenerically only its influence. Following, a list gathering the 15 parameters influencing thenetwork the most is shown in table 5.3. Actually, the whole list counts 47 resistances. Thevalues with lowest influence are not displayed because those are in the order of 10−4. Knowing

67

5 Model reduction

that some parameters has such this negligible effect on the network is an important resultand it is going to be used for the final reduction process.

Parameter name Target least influence [%]

Rotor ring convection 11.8EW coil thermal resistance (copper) 11.4Shaft to inner air convection 6.3Rotor ducts convection 5.6Inner shaft thermal resistance (back) 3.6Stator tooth tangential thermal resistance 3.3EW coil thermal resistance (insulation) 2.6Stator yoke outer thermal resistance 2.0Stator-case contact thermal resistance 1.5Stator yoke inner thermal resistance 1.3Inner shaft thermal resistance (front) 1.3Stator tooth radial thermal resistance 1.2Airgap convection 1.1Bearing outer contact thermal resistance 1.1Bearing inner contact thermal resistance 1.0

Table 5.3: Sensitivity analysis thermal resistances results

5.3 Final model reduction

The final reduced model has 24 nodes, compared to the initial model with 78 nodes. Thereduction is made up of three steps. To start, considering the resuslts of the thermal resis-tances sensitivity analysis, it is known that the modification of the parameters with the lowestinfluence in the list of 47 has infuence on the target in the order of 10−4%, that is negligible.All this parameters belong to the thermal conductive connection from the housing extention,end plate and bearing inner ring. Moreover, according to this analysis the convection betweenthose element with inner air does not affect the results.

Figure 5.8

68

5 Model reduction

Hence, considering that two nodes connected in series like in picture 5.8 can be reducedin one if:

- The new capacity C ′ is the sum of the previous two C1 + C2

- The new resistance is the sum of all the previous resistances R1 +R1−2 +R2 and thensplit in two distributed in R′1 and R′2

With this reduction the nodes in the network belonging to the exterior of the active motordecreases its number of 3 per each DE and NDE side, reducing the whole number of 6 nodes.

The second step consisted of furtherly reduce the axial parititon number to a mono-axiallayer active motor network, redistributing the axial connection properly as already seen inthis chapter making the system decrease of overall 11 nodes.

The final step consisted in replacing the inner air system made up of 4 partitions with aunique inner air node, one per each side DE and NDE. As a matter of fact, while all theconductive resistances are temperature dependent and the temperature reference is the clos-est air node to the considered element, the calculation of the heat transfer coefficients h forconduction is not affected by the choice of the air node temperature dependency: whether itis the closest or another one in the same side. Hence, the four air nodes previously outlinedin the model description are substitued by a unique one scaling correcting the temperaturearray for the simulation and using a thermal capacity that gathers all air inside each motorside. In order to visualize this change figure 5.9 is provided below. This reduction attemptreduce the total number of thermal node of 3 nodes per side, hence a total of less 6 nodes.

Figure 5.9

Finally, the simulation results are outlined in figures 5.10, 5.11 and 5.12. Since these are

69

5 Model reduction

the last simulation presented in the report, both end coil and hotspot windings temperaturesas well as rotor bars and short circuit ring temperatures are shown in the graphs. Here again,the comparison has been made between the final reduced model counting 24 nodes to the DMwith 78 nodes instead. As it can be seen, the final RM overextimate the temperature and thedeviation are presented in table 5.4.


Table 5.4: Temperature deviations form 4 axial layers DM to final RM simulation results

One last table is shown in 5.5 with the different simulation times of the model and outliningagain the number of nodes for every case described in this report. As already said, thesimulation time is indicative: a portion of the whole simulation running time is spent to openSimScape and it ca affect the results. Althoug, in order to have a good reference as finalresults, every time is calculated as the average of 10 simulations, each of it is carried cleaningMATLAB chache files generated after every round.

Model name Numer of nodes Average simulation time [s]

Detailed model 78 84.63-axial partition mode 64 54.82-axial partition mode 50 40.9Axial connection reduced model 50 35.3Final reduced model 24 18.9

Table 5.5: Nodes and simulation times comparison for the several analized models

70

5 Model reduction

0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

0

50

100

150

200

250

300

Tem

pera

ture

[°

C]

Windings

DM hotspot

DM DE end windings

DM NDE end windings

FM hotspot

FM DE end windings

FM NDE end windings

Figure 5.10

0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

20

40

60

80

100

120

140

160

180

200

Te

mp

era

ture

[°

C]

Rotor

DM rotor bars

DM DE ring

DM NDE ring

FM rotor bars

FM DE ring

FM NDE ring

Figure 5.11

71

5 Model reduction

0 0.5 1 1.5 2 2.5 3 3.5 4

time [h]

20

30

40

50

60

70

80

90

Te

mp

era

ture

[°

C]


Detailed model

Final model

Figure 5.12


The content of this chapter shows the step going from the detailed model with 78 nodes to areduced version with 24 nodes. The reduction is divided in two parts. The primary reductionconsists into going from 4 to 2 axial partitions providing a sensitive analysis of the numberof axial partitions and subsequently reducing the number of axial connections between twolayers. After, a sensitivity analysis of all the resistances is provided and basing on the resultsof the previous, the secondary reduction reduces the number of nodes gathering the nodesconnected with least influence parameters. Moreover, the number of air nodes is reduced toone per part, both DE and NDE sides, and the axial partition number is reduced to one.The reduced models progressively presented are finally compared in temperature error on thetargets point, simulation speed and number of nodes. All the results are outlined in a finaltable.

72

Chapter 6

Conclusions

This thesis work dealt with one of the two most crucial aspect of the machine together withthe electromagnetic noise: thermal calculations. Starting from geometrical and material pa-rameters the whole model has been built and then tested. Although the LP modelling toachieve accurate results especially for designing purposes is going to be substituted with themore accurate FEA and mixed FEA modelling approach. Nevertheless, it is not possible touse those methods for control purposes, a god compromise between time spent on the DMbuilt on SimScape and the accuracy gained has been reached. The subsequent reduction ofthe model was satisfying also: the number of initial nodes has been reduced of 60 % makingan important impact on the computational time for each simulation decreased of 77 %.

However, in order to be sure of the overall accuracy of the model, further thermal test couldhave been useful for the validation of the model. As a matter of fact, while the results con-cerning the steady state values are satisfying, the dynamic behaviour is estimated with moreuncertainty. For example, a test running the motor at different operating conditions varyingboth speed and torque acquiring the temperature signals concerning different parts in the mo-tor with higher sampling could have been compared with the correspondent simulation resultsand check the validity of the overall thermal capacities system. Although, in the previous casea better estimation of the losses was needed and hence this thesis work had necessarily to becombined with some other students thesis work.

The importance on having thermal results regarding the windings is related to understandingof the feasibility of a specific duty cycle. Overloading the machine can lead to decreasing thelife of the windings insulation and hence higher probability of future failures or shutdown inthe traction system. Every thermal modelling approach has a degree of uncertainty so thatthe estimation of the right windings’ temperature is always crucial for both design and controlapplications.

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6 Conclusions

6.0.1 Future work

As previously explained, a possible scenario for the future work on the model consist in firstlyin going from the SimScape visual network to defining the matrix of the system through cod-ing in Python or C. The next possible step is expanding the project including the possibilityto have different cooling systems. This means testing new motors and modelling on SimScapegoing after from the network to the matrix system. A hypothetical thermal control tool couldstart from geometrical and material parameters creating the conductance and capacitancematrixes according to the selected cooling system.

However, it is still possible to work on furtherly reducing the model presented in the re-port other than implementing new ones with different cooling systems. 24 nodes is a goodresult for a first reduction attempt but using the reduction methods presented in the firstchapter aiming to 12 or less nodes. Concerning the OSV cooling system, a system for theestimation of the air temperature in different point inside the machine can be implementedstarting on the total losses value.

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