Coupled Electromagnetic-thermal Analysis of Segmented PM Consequent Pole Flux Sw

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(1.Department of Electrical and Computer Engineering,COMSATS University Islamabad,Abbottabad Campus,Abbottabad 22060,Pakistan;2.Department of Electrical Power Engineering,Universiti Tun Hussein Onn Malaysia,Parit Raja 86400,Malaysia)

Abstract:Compact stator structure of flux switching machines (FSMs) encompassing both permanent magnets (PMs) and armature winding slots (AWS) attract research interest whenever high power and density are the basic requirements.However,it also results in temperature rises owing to heat generation by electromagnetic power losses degrading the electromagnetic performance and affecting machine performance.In this study,a segmented permanent magnet (SPM) consequent pole FSM (SPM-CPFSM) is developed,which provides a stator cooling channel (duct) for improved heat dissipation to avoid demagnetization of PM as well as overheating.Furthermore,this study investigates detailed electromagnetic performance analysis and prediction of temperature variation in various machine parts owing to the heat generated by iron,copper,and magnet eddy current losses utilizing coupled electromagnetic-thermal analysis accounting for magnetic flux density variation.In comparison with the 2D analysis,the developed 3D coupled-field analysis more accurately predicts electromagnetic performance and temperature distribution.Analysis reveals that a cooling duct at the stator significantly assists in stator heat dissipation in the axial direction ensuring a safe operating condition of the PMs as well as machine parts to avoid overheating.

Keywords:AC machines,coupled field,consequent pole,permanent magnet,loss analysis,thermal analysis

1 Introduction1

Segmented permanent magnet (SPM) consequent pole flux switching machines (SPM-CPFSM) are considered worthy candidates for applications requiring high power and torque density for operation.The primary constituents of SPM-CPFSMs are NdFeB-PMs,armature winding,and silicon steel sheets.These SPM-CPFSMs encompass an SPM and armature winding in the stator leaving a steel stacked robust rotor made of silicon sheet stacked steel.Because a rotor is simple,it has low inertia[1]and is considered as a competent applicant for high speed operation.

The aforementioned machine parts are associated with temperature dependent properties,that is,their performance varies with temperature variation owing to heat generation.The primary source of heat generation is due to armature windings,which sandwich the SPM and both act as heat sources.This concentrated heat source ultimately increases permanent magnet (PM) temperature.The PM temperature rise alters the operating point and may cause irreversible demagnetization,degrading electromagnetic performance.Furthermore,the losses associated with the iron and magnet eddy current losses also significantly contribute to temperature rise.

Numerous techniques have been reported in literature for thermal analysis[2-4]utilizing finite element analysis (FEA) on the design for temperature distribution,however temperature rise is ignored.The author in Ref.[5] introduces an alternate parameter model using a multiple iterative simulation program to improve the accuracy,however owing to 2D and 3D multiple simulations,this method becomes inconvenient for designs with complex geometry.Axial segmented magnetic-thermal couple is introduced in Ref.[6] with a water-cooling jet in the stator shell however,despite axial segmentation,the proposed technique employing 2D and 3D approaches increases computational complexity.Temperature rise is accounted in Ref.[7] for a detailed investigation of the PM operating point,however this technique considered the loss calculation in the 2D model and extending it to a 3D thermal analysis for thermal distribution prediction.The aforesaid problems are curtailed utilizing a lumped parameter method for effective investigation of thermal distribution in terms of a differential heat-transfer method[8-9],however,this method considers individual component temperature distribution rather than the overall machine.The author in Ref.[10] investigates temperature distribution in a steady state where obtained iron and copper losses function as heat sources,however,in this method the losses are assumed to be evenly coupled therefore,genuine coupling among magnetic and thermal studies are lost.

Coupled electrothermal analysis was conducted by the authors in Ref.[11] to predict and validate thermal behavior and the effect of heat losses in water cooled coils for magnetic fluid hyperthermia purposes.Analysis revealed that circulating water in copper windings results in significant cooling of inductors.The authors in Ref.[12] utilized an Arrhenius model to estimate thermal profiles of liver tissue utilizing a multi slot coaxial antenna.The two proposed methodologies are used to calculate magnetic forces on ferromagnetic materials in a non-uniform magnetic field which can be employed in biomedical applications.The methods utilized for analysis are the equivalent dipole and Maxwell’s stress tensor methods.The forces are used to direct ferromagnetic particles resulting in heat generation.The authors in Ref.[13]performed thermal analysis to analyze short circuited winding positions and thermal deformation owing to excessive heat generation and thermal stress on magnetic poles of hydro-generators.The authors in Ref.[14] performed thermal analysis to investigate inter-turn short circuit faults in a permanent magnet synchronous machine using the finite element method(FEM).Factors that affect rise in short circuit current are also being researched in the manuscript.

In this study,coupled electromagnetic-thermal analysis is investigated based on 3D magnetic and thermal analysis for temperature distribution of SPM-CPFSM based on the loss distribution.This technique is based on two studies.First,3D magnetic studies are performed for electromagnetic performance and loss distribution.Second,using the losses as a heat source,develop a 3D thermal analysis for temperature distribution in SPM-CPFSM as well as at different machine parts.Therefore,electromagnetic studies are performed first and extended to the thermal studies.

The key innovation of this study includes the design of a SPM-CPFSM at a 46.52% reduced PM volume that suppress the overall PM cost by 46.48%and enhancing the flux modulation phenomena for higher torque density.Furthermore,coupledelectromagnetic thermal analysis based on the loss density of a transient magnetic study is chosen for accurately predicting temperature distribution at various machines parts which validated the effectiveness of the cooling duct in the SPM-CPFSM design.Analysis reveals that a cooling duct at the stator significantly assists in stator heat dissipation in the axial direction ensuring a safe operating condition for the PMs and machine parts to avoid overheating.

The remainder of the paper is organized as follows:Section 2 presents SPM-CPFSM construction,Section 3 illustrates the analysis scheme,Section 4 discusses coupled electromagnetic-thermal analysis and finally some conclusions are drawn in Section 5.

2 SPM-CPFSM construction

The proposed SPM-CPFSM is developed and the design parameters are displayed in Tab.1 whereas they are properly illustrated in Fig.1.A 2D cross-sectional view of the machine model is shown in Fig.2 where armature windings having two coil sets wound between PMs having different magnetization directions.The PMs near the air gap have a circumferential magnetization direction,namely CM-PMs where the PMs near the stator yoke enclosed between stators,flux barriers,and flux bridges have a radial magnetization pattern,namely RM-PMs.The RM-PMs are adjacent to armature winding and may overheat owing to excessive winding overheating.Therefore,it is important to investigate its temperature variation for safe operation.

Tab.1 Design parameters construction of SPM-CPFSM

Fig.1 Design parameters for SPM-CPFSM construction

Fig.2 2D cross-sectional view of SPM-CPFSM

It is obvious that segmented PMs are placed in an H shaped stator tooth leading to a geometry where leakage flux is eliminated and is converted to linkage flux.Furthermore,flux modulation of segmental PMs is improved where both PMs superimpose each other and with the help of flux barriers and flux bridges leads to a higher value of flux generation and MFD which ultimately improves overall machine performance in terms of torque capability,whereas an H-shaped stator tooth reduces the slotting effect between slots and PMs which in turn reduce torque ripples and peak to peak cogging torque.From Fig.1,it is also clear that an H-shaped stator tooth provides a cooling duct in the stator to reduce overall machine temperature and avoid PM demagnetization for improved electromagnetic performance. Flux modulation is achieved not only with stator teeth but also with the help of flux bridges leading to an improved magnetic flux circulation resulting in machine performance enhancement.

Owing to symmetrical machine construction being the same,electromagnetic flux is achieved from all machine coil sets and the same sinusoidal flux is generated from respective coils.Referring to Figs.3a and 3c we can see that maximum flux linkage is achieved whenever the rotor pole is aligned with any stator pole A1 at the respectived-axis position.Moreover,no flux is linked whenever the rotor pole is misaligned with stator teeth and is aligned with the stator slot at theq-axis as shown in Figs.3b and 3d.The rotor position varies from Fig.3a to Fig.3c,and in this duration,bipolar flux linkage is achieved.Fig.4 shows a typical single coil bipolar flux linkage over one complete periodic cycle.

Fig.3 No-load flux linkage of SPM-CPFSM

The flux distribution shown in Fig.3 to achieve the phase flux linkage as shown in Fig.4 is obtained through transient magnetic study.In this study model,the number of turns is 180,the stack length is 25 mm,with a 1 mm mesh size,and the slot filling factor is 0.5 mm.

Fig.4 Typical no-load one phase flux linkage of SPM-CPFSM for a single periodic cycle

3 Analysis scheme

Certain issues and effects must be kept in mind whenever the electromagnetic performance of a machine is enhanced.A significant issue in this regard is temperature rise in the machine,as the excitation sources act as heat sources leading to increased temperature[7].Iron losses (Hysteresis and Joule losses),copper losses,and PM joule losses are primary losses which account for temperature rise.Hence,a magnetic loss study must be investigated to acquire different machine losses which may further be extended to evaluate temperature distribution in the machine.The loss study is coupled with an electromagnetic thermal study to calculate heat distribution in different design regions.This study presents 3D-FEA-based coupled electromagneticthermal analysis for investigating thermal distribution with coupled losses in a transient thermal analysis by using JMAG designer version 18.1.The detailed scheme for respective analysis is illustrated in Fig.5.

In the aforesaid losses,the physical phenomena show that the dominant loss associated with SPM-CPFSM is due to copper loss from the armature winding current flow.Furthermore,magnet eddy current loss from the SPM and iron loss at the rotor and stator also accompany copper losses in the temperature rise.Note that iron loss is caused owing to the change in magnetic flux and magnet eddy current loss is due to the SPM itself.Based on the aforementioned loss distribution leading to the rise in temperature issue,overall analysis is divided in the two sections,i.e.,joule loss analysis model (loss analysis) and temperature analysis model (thermal analysis study).Magnetic field analysis assists in accurate loss prediction and thermal analysis for precise temperature distribution as shown in Fig.5.Details of the associated losses are listed as follows.

Fig.5 Physical phenomena,model analysis,and analysis scheme steps

3.1 Copper loss in SPM-CPFSM

The primary heat source causing the temperature rise in the SPM-CPFSM design is a summation of copper,mechanical,and iron losses of both rotor and stator.For the SPM-CPFSM,the armature winding copper loss (Pcu) in the stator is expressed as[2]

whereJrmsis the armature applied current density,ρis copper resistivity,andVcuis the copper winding volume in the armature.

The copper loss is due to eddy current and ohm losses.Internal proximity,skin effect,and a time-varying magnetic field contribute to eddy current loss;whereas Ohm loss (I2R) is a resistive loss which varies with the variation in temperature and can be expressed as whereRTrefis copper resistance at an initial temperature reference of 20 ℃,Trefis the initial temperature andβis the temperature coefficient.

3.2 Magnet loss

The developed SPM-CPFSM is composed of PMs in segments.The losses incurred by both PM segments are eddy current and hysteresis losses which are due to a time varying magnetic field and flux distribution[15].This field variation is the result of a slot effect that causes variation in air-gap reluctance and originates additional magnetic field variation.This magnet loss is expressed as[16]

whereLPMis each PM length,WPMis each PM width,TPMis each PM thickness,Bis magnetic flux density,andfis applied current frequency.

Because a PM is highly sensitive to temperature rise and results in irreversible demagnetization at temperatures higher than the intrinsic PM operating condition provided by the supplier.Therefore,it is important to determine the magnetic flux density from the B-H curve.Provided by the magnet remanence and coercive force at the reference temperature,its variation with temperature is expressed as[17]

whereBr(Tref) andHc(Tref) are remanence and coercive force at the reference temperature (Tref),respectively.Br(T) andHc(T) are remanence and coercive force at the temperature (T),respectively.Moreover,bothγandαare temperature coefficients.

3.3 Core loss

The rotor and stator core of the SPM-CPFSM are formed from a stack of silicon steel sheet laminations.This loss is a combination of eddy current and hysteresis losses.It is worth mentioning that a sinusoidal alternating magnetic field has an excited core with the core loss directly proportional to the square of the applied armature current frequency and can be calculated as[15]

whereKhis the hysteresis loss coefficient,Keis the eddy current loss coefficient,fis the applied armature current frequency,Bmaxis the maximum magnetic flux density,andnis the material dependent exponent.

4 Coupled electromagnetic-thermal analysis

The heat generated in the developed SPM-CPFSM is due to foregoing machine losses which are associated with armature winding and PMs in the stator,therefore,the generated heat can be easily dissipated to the surrounding air through the built-in cooling duct in the stator.This heat dissipation significantly helps solve the temperature rise issue to enhance electromagnetic performance and output.The rise in temperature issues can be further solved by reducing the machine losses that act as heat sources and accurate thermal design for improved heat dissipation.

In coupled electromagnetic-thermal analysis,two different model types:Loss analysis and thermal analysis are coupled with each other to map the machine loss generated in magnetic field analysis as a heat source and model thermal analysis based on magnetic studies during a load condition with the overall flow chart as shown in Fig.6.

Fig.6 Overall flow chart for coupled electromagnetic-thermal analysis

Initially,SPM-CPFSM parts are designed to perform 2D transient magnetic studies.Once the 2D performance is confirmed,the model is extended to 3D analysis for precise electromagnetic performance analysis as well as loss calculation for mapping loss density.Once the loss is obtained,it is used as a heat source in the following thermal analysis.Losses obtained from the magnetic loss study account for the temperature rise obtained from the thermal study when it is coupled with the loss study.In this coupled analysis,a proper mesh setting,boundary conditions,material settings,and study properties are set.This setting involves heat flow based on the convection method though a heat equivalent circuit (HEC).To provide a clear idea of the methodology and coupled analysis for thermal study,flow charts are provided to understand each step.

Thermal analysis is performed by developing an HEC,which depends upon design topology of a machine and is illustrated in Fig.7,whereas material properties such as density and thermal conductivity must be assigned to newly created materials listed in Tab.2[1,6].The HEC is of significant importance as it forms the basis of heat transfer for different machine parts with their surroundings through the process of convection.It is also utilized for heat dissipation generated from the rotor shaft.Miscellaneous machine parts,such as the rotor bearing,shaft,and shell are also taken into consideration by the HEC if it is not included in the machine geometry.Heat transfer boundaries (HTB) are then applied to different HEC types in which different contact faces are selected between different machine parts and airgap.Heat transfer through convection is modeled through a contact thermal resistance (CTR) set between the facing components of the machine.

Fig.7 Heat equivalent circuit of the proposed SPM-CPFSM

Tab.2 Material properties used in thermal analysis

Note that thermal analysis performed in FEA is based on the HEC concept.Based on the flow chart steps,coupled electromagnetic-thermal analysis is performed in the proposed SPM-CPFSM with a detailed investigation as follows.

4.1 2D/3D electromagnetic performance

Initially,electromagnetic performance is determined based on 2D-FEA with key performance metrics of average torque (Tavg),cogging torque (Tcog),torque ripple (Trip),open-circuit phase flux linkages(φp-p),total harmonic distortion of flux (φTHD),back-EMF (BEMF),average power (Pavg),rotor iron losses (RIL),stator iron loss (SIL),and total core losses(TCL).Furthermore,TavgandTripcharacteristics are investigated based on variation of applied current density,phase angle of the applied current,and wide speed range. Once the 2D electromagnetic performance is accomplished,the developed SPM-CPFSM is extended to the 3D model (as shown in Fig.8) for precise analysis.Comparison of the electromagnetic performance between the 2D and 3D FEA results are shown in Figs.9-11,whereas back-EMF at 1 200 r/min is shown in Fig.12.Clearly,in comparison with 2D,the 3D FEA results are more accurate by considering the flux in the axial direction.Note that in the 2D FEA,TcogandTripare dominant and can be suppressed utilizing various rotor pole and PM shaping[18-19].This results in low vibration and acoustic noise owing to the elimination of higher frequency content[20].

Fig.8 SPM-CPFSM

Fig.9 Open-circuit phase flux linkage of SPM-CPFSM

Fig.10 Cogging torque of SPM-CPFSM

Fig.11 Instantaneous torque of SPM-CPFSM

Fig.12 Back-EMF of proposed design

Furthermore,torque characteristics are investigated based on variation in applied current density,applied current phase,and speed as shown in Figs.13 and 14.Analysis reveals that the developed SPM-CPFSM is feasible for speed applications.Moreover,higher average torque and lower torque ripples are obtained in a current phase angle between 0°and 5°.

Quantitative electromagnetic performance comparison of the aforementioned key metrics are listed in Tab.3 and the loss density distribution as shown in Fig.15.It is worth mentioning that these loss densities are used as a heat source for precise mapping of the loss to temperature distribution in the thermal analysis.A comprehensive overview and detailed discussion regarding comparison with conventional design and the analytical modeling of SPM-CPFSM can be addressed in Refs.[21-23].

Fig.13 SPM-CPFSM torque characteristic

Fig.14 SPM-CPFSM torque-speed characteristics

Fig.15 Loss density distribution

Tab.3 2D/3D FEA base quantitative electromagnetic performance analysis

Note that electromagnetic performance as shown in Figs.9-15 is obtained through transient magnetic study.In this magnetic study model,the number of turns is 180,current density is 15 A/mm2,speed is 1 200 r/min,stack length is 25 mm,with a 1 mm mesh size,and slot filling factor is 0.5 mm,whereas temperature distribution as shown in Fig.16 is obtained through coupling the loss density calculation of magnetic studies to the transient thermal study.

Once detailed electromagnetic performance and loss distribution are confirmed,the model is extended to thermal analysis for temperature distribution in the overall machine as well as in each part of the machine in the preceeding section.

4.2 Temperature distribution

Thermal analysis is performed by steps and settings already discussed in previous sections.The temperature distribution achieved from the analysis of the overall machine is shown in Fig.16.The analysis shows that the results of coupled electromagnetic thermal analysis provides temperature distribution over all machine parts which are very close to each other with a minimum temperature at the rotor core and a maximum temperature at the stator coils.A peak temperature of 46 ℃ was recorded at the stator whereas a temperature of 22 ℃ was recorded at the rotor.The temperature range at the stator core was nearly 41 ℃,whereas 42 ℃ temperature was found in the CM-PMs and RM-PMs.

Fig.16 Temperature distribution

Analysis reveals that no part of the machine,especially the stator core,coils,and PMs are exposed to excessive heat beyond allowable limits owing to the cooling duct in the stator located between the RM-PMs and CM-PMs.Moreover,it also ensures that the operating conditions of the PMs are not affected and are safe from thermal demagnetization.The heat generated at the PMs is dissipated through the cooling duct between both PM segments.It is worth mentioning that the same cooling duct can be used for alternate cooling methods such as water cooling in the future.

In addition,comparison of conventional FSMs without a cooling duct[10,24]shows that the temperature distribution in the stator of the proposed design is reduced with the addition of a cooling duct.Comparison reveals that conventional design without a cooling duct shows a stator temperature of 50 ℃,whereas the proposed design with a cooling duct exhibits a maximum of 44 ℃ in the winding portion of the stator slot.Details of temperature distribution at each part of conventional FSMs without a cooling duct and the proposed SPM-CPFSM with a cooling duct are listed in Tab.4.

Tab.4 Temperature distribution in conventional FSMs without cooling ducts and proposed SPM-CPFSM with cooling duct

Furthermore,the aforementioned comparison is based on magnetic-thermal coupled analysis (proposed design) and un-coupled analysis (conventional design)where loss distribution is evenly considered.This analysis unveils that a cooling duct assists in heat distribution in the axial direction whereas coupled analysis results in accurate temperature distribution prediction.

5 Conclusions

In this study an SPM-CPFSM with a built-in cooling duct is developed for improved heat dissipation to avoid thermal demagnetization and overheating of SPMs and ensure safe operating conditions.For this purpose,coupled electromagneticthermal analysis is performed for detailed electromagnetic performance analysis and temperature distribution in various machine parts owing to the heat generated by copper,iron,and magnet eddy current losses.Analysis leads to the conclusion that in comparison with the 2D-FEA,the developed 3D coupled-field analysis more accurately predicts electromagnetic performance and temperature distribution.Furthermore,the stator cooling duct assists in heat dissipation in the axial direction ensuring safe operating conditions for the PMs as well as machine parts to avoid overheating.It is worth mentioning that RM-PMs adjacent to the armature winding operate without overheating and avoid demagnetization owing to the built-in colling duct in the stator core adjacent to the RM-PMs.