Design and Manufacturing of IPM Synchronous Motor for Field Weakening Operation

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Degree project in

Design and Manufacturing of IPM Synchronous Motor for Field Weakening Operation

Jonas Finnman and Erik Eketorp

Stockholm, Sweden 2013 Electrical Machines and Drives

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Design and Manufacturing of Internal Permanent Magnet Synchronous Motor for Field Weakening

Operation

JONAS FINNMAN AND ERIK EKETORP

EJ210X Master Thesis Project at the School of Electrical Engineering

Royal Institute of Technology Stockholm, Sweden, May 2013 Supervisor: Johan Clarholm, Mats Leksell

and Oskar Wallmark Examiner: Oskar Wallmark

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Abstract

Rotor designs for permanent magnet synchronous machines suitable for field weakening operation have been evaluated for use with an existing drive system. The designs have been simulated with the FEM-based software Finite Element Method Magnetics (FEMM). Based on the results two different internal magnet rotors have been constructed and tested. Both designs significantly improved the speed range while maintaining or improving magnet utilisation. The implementation of field weakening algorithms in drive electronics is complex and need thorough optimisation for stable operation. Internal permanent magnet rotors are a good alternative to surface mounted designs and enables a wider speed range through improved field weakening capabilities.

Keywords: PMSM, field weakening, rotor manufacturing, FEMM

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Referat

Olika rotordesigner lämpliga för fältförsvagningsdrift har utretts angå- ende lämplighet i ett befintligt drivsystem. Rotorerna har modellerats och simulerats med den FEM-baserade programvaran Finite Element Method Magnetics (FEMM). Utifrån resultaten har två olika rotordesigner med interna magneter konstruerats och testats. Båda modeller- na har ökat varvtalsområdet avsevärt samtidigt som magneternas ut- nyttjningsgrad vidhållits eller förbättrats. Implementering av fältför- svagningsalgoritmer i drivelektroniken är ett komplext område och i behov av genomgående optimering för att systemet skall bli stabilt.

Interna permanentmagnetsrotorer är ett bra alternativ till den ytmon- terade motsvarigheten och möjliggör ett större varvtalsområde genom förbättrade fältförsvagningsegenskaper.

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Acknowledgment

This master thesis was written as an investigation regarding field weakening implementation in existing drive systems, for Allied Motion, Stockholm, Sweden. We would like to thank our supervisor Johan Clarholm for his amazing support and knowledge of the subject, during the entire project. Björn Hedlund for his never ending enthusiasm that permeated the work. Further on we thank Peter Östergren, Thomas Garpebo, Robert Pettersson and Ulf Gustafsson, for their assistance that enabled completion of the project and all other involved at Allied Motion.

At KTH Royal Institute of Technology we would like to thank our supervi- sors/examinator Mats Leksell and Oskar Wallmark for all their advice and encour- agement during the project. Alija Cosic for granting Allied Motion employees a tour at the electric machine laboratory. Mikael and Patrik Hellgren for their consultation regarding balancing of the rotors.

Several companies have supported our work. Firstly we would like to thank Surahammars Bruk for donating 10 kg of electric steel to the construction of the rotors. Secondly Gustav Nyström at SAMAB (Spånga Allmontage AB) for taking the time to assist us with laser cutting and adjustments of the CAD-drawings. Lastly Göran Karlsson at Ge-Kå Finmekaniska Verkstad AB for quickly manufacturing special parts needed during construction and testing.

Additionally we would like to thank David Meeker, for creating the very capable and free software FEMM, who also took the time to answer questions.

Finally we would like to thank our understanding partners and families for all their moral support the last couple of months.

Erik Eketorp Jonas Finnman

A sunny day in Stockholm, May 2013

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Introduction

In this chapter the background to the project will be discussed, followed by definition of the objectives in this thesis. Finally, different synchronous electric machine types will be discussed in the light of the objectives.

1.1 Background

The most commonly used electric machine has long been the induction machine because of it’s well-known control and low manufacturing cost [1]. However, in applications where size and efficiency is important the permanent magnet synchronous machine (PMSM) can have advantages [2] [3]. The speed range of electric machines is basically limited to the available voltage and magnetisation magnitude. The utilisation of high voltages to increase the speed range comes with other problems, such as the insulation of the windings and the cost of higher grade components in the power supply. The other alternative is to decrease the magnetisation of the rotor.

This has traditionally been a problem for permanent magnet machines since they unlike an induction machine have a constant magnetisation.

In many applications for electric machines as well as combustion engines a wide speed range is desirable. Typical examples are in traction applications, i.e. cars and trains, where the necessary starting tractive effort is high whereas at high speeds the tractive effort is low. Traditionally this has been accomplished with gearing or gearboxes, enabling a motor to run a vehicle at different speeds without increased power output. Gearboxes however, have several drawbacks such as an increase in weight, dimension and cost. All mechanical parts also requires periodic maintenance and can lead to failure of the entire vehicle.

In the recent decades the concept of field weakening has emerged, where an opposing magnetic field is applied to the permanent magnets, thereby reducing the magnetisation. This can effectively increase the speed range within the same voltage range without adding any mechanical parts.

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Chapter 1. Introduction

1.2 Objective

Allied Motion is a worldwide spanning manufacturer of electric machines, gearboxes and drive electronics for different applications. Every division of Allied Motion is specialised in a specific component of the drive systems, which enables them to customise solutions to meet the demands of the customer. In their broad product portfolio electric machines are a central part. This project has investigated the possibility of field weakening operation in an existing drive system.

In this master thesis an existing PMSM drive system was the starting point, where the standard rotor had surface mounted magnets. Allied Motion was inter- ested in investigating the possibility of a modular drive system, where a rotor swap would adapt the system to another application. As a complement to the original design a high speed rotor was desired, therefore field weakening operation was necessary. The objective was to design rotors and build prototypes, thereby having the possibility of comparing the simulated results to real world data. Additionally the new rotor designs should be implemented in the existing drive electronics.

1.3 Different synchronous machines

In figure 1.1a, 1.1b and 1.1c the Surface mounted Permanent Magnet Synchronous Machine (SPMSM), Interior Permanent Magnet Synchronous Machine (IPMSM) and Reluctance Synchronous Machine (RSM) can be seen.

(a) SPMSM (b) IPMSM (c) RSM

Figure 1.1: Different rotor types.

The SPMSM has its magnets mounted on the outer surface of the rotor side by side. This design is common due to an cheap and simple manufacturing process.

Since the magnets often are placed side by side and follows the contour of the rotor, the harmonics is low.

The field weakening capabilities are limited because of the low d-axis inductance.

The IPMSM has its magnets buried inside the rotor steel, and exists in many different shapes and forms. Due to the removal of electrical steel in the rotor to fit the magnets, the inductance will vary along the circumference. Generally an

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1.3. Different synchronous machines

IPMSM perform better than a SPMSM in field weakening applications because of saliency and the increase of d-axis inductance.

The RSM does not have any magnets in the rotor but air, thereby only producing reluctance torque. A high saliency ratio is important to utilise the size of the motor.

A RSM is because of its lack of magnets cheaper to manufacture but often has a lower torque per length and weight.

Among the different rotor types internal permanent magnet rotors would serve the project’s objectives best.

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Chapter 2

Theoretic framework

In this chapter important concepts like maximum torque per ampere (MTPA), con- stant power speed range (CPSR) and torque density will be defined as well as a discussion regarding demagnetisation of permanent magnets.

2.1 Field weakening operation of IPMSM

In an IPMSM it is difficult, as opposed to the separately excited DC machine (section 7.5), to control the magnetising current. The three phase currents must be transformed into a stator current vector I_s, in a synchronous reference frame according to section 7.1. This vector will have two components in quadrature from each other, ¯Is = I_d+ jI_q. With such a reference frame it is possible to control the flux producing (and reducing) current I_d and the torque producing current I_q separately. This possibility together with the fact that the field from I_d, Ψ_I_dwill interact with the permanent magnet field Ψ_m, field weakening can be implemented by injecting a current in the negative d-direction. This will result in a reduced field according to (2.1).

Ψ_d= Ψ_m− Ψ_I_d = Ψ_m− L_dId (2.1) There are several factors that limit the magnitude of field weakening. Generally the maximum current in the windings must be limited due to heating caused by the resistive losses in the stator according to (2.2). To achieve stable control of the field weakening, the maximum voltage must not exceed the available voltage, according to (2.3).

I_max =^qI_d²+ I_q² (2.2)

Umax =^qU_d²+ U_q² (2.3)

The permanent magnet synchronous machine’s equivalent circuits for d- and q-axis can be seen in figure 2.1b [4].

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Chapter 2. Theoretic framework

Lq

L_s

+

−

dψq

dt

+

− uq

i_q Rs

+−

ωsLdid

+−

ω_sψ_m

(a) q-axis equivalent.

L_d L_s

+

−

dψ_d dt

+

− u_d

i_d Rs

+−

ω_sψ_q

(b) d-axis equivalent.

Figure 2.1: Equivalent circuits of a salient pole PMSM.

If U_dand U_q are calculated from a simplification of the equivalent circuits, (2.3) becomes (2.4).

U_max= ω s

(L_dI_d+ Ψ_m)²+ (L_qI_q)²)

(2.4)

2.1.1 Infinite speed field weakening

To obtain infinite speed equation (2.5) should be met.

Ψ_m = L_dI_max (2.5)

If equation (2.4) is rewritten as (2.6) it can be validated by setting I_q = 0 and Ψ_m = −L_d I_d the obtained value of ω_max = ∞. Infinite speed is only achievable under ideal conditions where friction and the inertia of the rotor not are taken into consideration.

ωmax= Umax

q

(L_dI_d+ Ψ_m)²+ (L_qI_q)²

(2.6)

2.2 Maximum torque per ampere operation (MTPA)

In the context of electrical machines Maximum Torque Per Ampere is a way to operate a machine with the highest possible ratio between the output torque and losses regardless of geometry or type of electric machine.

The torque produced by an IPMSM can be calculated according to (2.7) and consists of two parts, the magnet torque and the reluctance torque.

T = Ψ_mI_q

| {z }

Magnet torque

+ (L_d− L_q)I_dI_q

| {z }

Reluctance torque

(2.7)

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2.2. Maximum torque per ampere operation (MTPA)

For a surface mounted permanent magnet synchronous machine (SPMSM) the in- ductances in d- and q-direction is equal, i.e. L_d= L_q, and thus the reluctance torque is zero. If (2.7) is examined it is visible that the MTPA operation is obtained with only q-current, i.e. I_s= I_q for 0 < I_s≤ I_max.

For an IPMSM the magnets will be buried in the rotor steel. Magnets have similar permeability to air. Thus the placing of magnets in the rotor will greatly affect the saliency ratio, defined as (2.8).

ξ = L_q Ld

(2.8) If angle γ is defined as the angle between the stator current I_s and I_q as shown in figure 2.2, (2.9) and (2.10) are obtained.

I_d

Iq

I_s

γ

Figure 2.2: d − q current plane.

Iq= I_scos(γ) (2.9)

Id= − I_ssin(γ) (2.10)

By combining (2.7) with (2.9) and (2.10) the resulting torque becomes (2.11) T = Ψ_mI_scos(γ) + (L_q− L_d)I_s²cos(γ) sin(γ) (2.11) If the partial derivative is taken on (2.11) with respect to the angle γ and put to zero, i.e. ^∂T_∂γ = 0, (2.12) for the MTPA angle is obtained.

γ₁ = arcsin

Ψ_m+^qΨ²_m+ 4I_s²(L_d− L_q)²cos(γ)² 2I_s(L_d− L_q)

(2.12) The expression (2.13) for I_d is then acquired.

I_d^{M T P A}= Ψ_m 2(L_d− L_q) −

v u u t

Ψ_m

2(L_d− L_q)

2

+ I_q² (2.13)

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2.3 Field weakening range

The motor should operate according to the MTPA trajectory as long as possible, i.e.

until either the current or voltage reaches its maximum value. When the maximum voltage has been reached, field weakening operation begins. To obtain the optimal field weakening angle γ₂, (2.4), equations (2.9) and (2.10) should be solved whilst keeping the total current below I_max according to (2.2). The resulting I_d is shown in (2.14).

I_d^{F W} = −Ψ_m L_d + 1

L_d s

V_max²

ω² − (L_qI_q) (2.14) An example of the different regions can be seen in figure 2.3. Note that the MTPA curve in this example lies within the third quadrant of the I_d− I_q-plane. This is true as long as the saliency ratio is greater than 1.

−20 −15 −10 −5 0

0 5 10 15 20

I_d [A]

Iq [A]

MTPA region Field weakening region Constant current circles

Figure 2.3: Example of currents in MTPA and field weakening regions.

To obtain the full field weakening performance the flux linkage in the different phases for different d-currents needs to be obtained. Due to symmetry of all three- phase machines, only the flux linkage from one phase is needed. From (2.15) it is possible to see the relationship between phase current, linked flux and phase voltage.

Ua= dΨ_a

dt + R_sia= dΨ_a dθ

dθ

dt + R_sia= dΨ_a

dθ ω + Rsia (2.15) The maximum available DC-voltage is then compared to U_a according to equa- tion (2.16). The maximum speed for that phase current is where U_a(1)= U_DC/√

3.

U_a(1) ≤ U_DC

√3 (2.16)

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2.4. Constant power speed range (CPSR)

2.4 Constant power speed range (CPSR)

Figure 7.7 revealed a flat power output above rated speed. This is not possible to obtain due to limitations in the inverter and changing power factor. The constant power speed range is defined as the speed interval in which the power output is greater or equal to the rated power.

2.5 Torque density definition

A major cost in the manufacturing of a PMSM is the permanent magnets. Due to this the ratio between magnet volume and torque production is a major design parameter. Torque density in this project is defined according to (2.17).

Torque density = Tn

Vmagnet

(2.17)

2.6 Demagnetisation of magnets

Different magnet materials can be exposed to different magnitudes of opposing magnetic fields before demagnetisation occurs [4]. Another factor that can lead to demagnetisation is high temperatures. There is a cumulative effect between temperature and opposing fields. NdFeB magnets are normally used for high performance PMSM machines due to their ratio between high remanent magnetisation and tolerance to temperatures.

All machines run the risk of short circuit, resulting in a larger current than rated. According to Lenz law the current created by the rotation of the magnets will counteract its source, i.e. the magnetic field from the short circuit current will be in phase with the negative d-axis. From figure 2.4 the ”knee point” of the magnets for different temperatures can be seen. Exceeding this point leads to permanent demagnetisation.

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Figure 2.4: Demagnetisation curve for the magnets used in this project, where N36 is the rating of the magnets and the magnet’s coating [5].

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Chapter 3

Models and simulations

The design of an electrical machine is an iterative process. Starting with a general design, it is then optimised for different applications. In this project the existing drive system was to be adapted to an improved speed range with field weakening operation.

3.1 Introduction

The original machine was an eight-pole full pitched design. The existing rotor had surface mounted magnets, which produces a high torque in steady state operation.

While surface mounted are the most common, and probably the least complicated from a manufacturing point of view, the field weakening capability is worse compared to internal designs [6]. Another drawback is that they have large eddy-current losses [7]. This in turn, makes surface mounted design a non-optimal choice for the higher speeds achieved with field weakening operation. According to [7], internal designs reduce the eddy current losses. This project chose to investigate tangential internal (T1 and T2), radial internal and V-shaped internal design as alternative rotors in the existing drive system.

An important decision is the total amount of magnet material a design will have. This is a compromise between cost, maximum torque and field weakening performance. A decrease in total amount of magnet material will lower the flux, thereby increasing the speed but decrease the maximum torque and vice versa.

It was decided that the new designs should have equal or less magnets than the original.

3.2 The original surface mounted design

As a starting point the stator and original surface mounted rotor was dismantled, measured and modelled. Measurements were taken for the stator slots, stator back, length of the rotor stack, air gap width and position of the stack on the shaft. A 2-dimensional estimation of the magnet area radially was performed. This data was

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Chapter 3. Models and simulations

then used to model the original rotor and stator, where the latter was used for all designs.

The core loss simulations for 1500 rpm resulted in a loss of 6.00 W.

3.2.1 Field weakening capabilities

The field weakening performance of the original surface mounted rotor was simulated and can be seen in figure 3.1.

0 500 1000 1500 2000 2500 3000

0 1 2 3 4 5

T [Nm]

nrot [rpm]

0 500 1000 1500 2000 2500 30000

200 400 600 800 1000

P [W]

Simulated torque Simulated power

Figure 3.1: Torque and power in the field weakening region for the surface mounted original design.

3.3 General design parameters

A very important design parameter is the air gap width. Every tenth of a millimeter reduction of the air gap gives an increase in torque. The disadvantage is that a small air gap demands high mechanical precision. There is often a small difference between the measurements of the cut laminate, compared to the CAD-drawing which is called tolerance. Another factor is that bearings can have a little play, which allows radial movement. Lastly operating temperature has an effect due to expansion in the materials, reducing the effective air gap. These factors combined together with high speeds can lead to mechanical failure if the air gap is small.

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3.4. The tangential design

The existing surface mounted rotor had an air gap of approximately 1 mm. In a surface mounted design there are three uncertainties, the cutting of the laminates, the variations in magnet dimensions and the adhesion of the magnets to the surface (glue). A worst case scenario is that all deviations adds up and induce mechanical failure. An internal design will only have one uncertainty, the cutting of the laminates. The variation in magnet dimensions must be taken into account by adding a tolerance to the magnet slots. Adhesion is not necessary since the magnets are buried. With only one uncertainty instead of three, the air gap can be reduced. In this project an air gap of 0.7 mm was chosen.

3.4 The tangential design

The tangential design featured eight cuboid shaped magnets buried ”tangentially”

into the rotor, as seen in figure 3.2. The variables that were optimised were the magnet width, height and internal depth from the air gap.

Figure 3.2: Drawing of the tangential model.

Simulations gave increased torque with a decrease of the internal depth. There- fore a minimum distance of approximately 0.8 mm between the edges of the magnet and the surface was decided, to maximise torque and still maintain a mechanical endurance.

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To determine the optimal dimensions of the magnet, a series of simulations was performed. One of the variables was fixed (e.g. height) and the other varied (width) in small steps. When all the variations in width for a specific height were complete, the height was varied one small step and the procedure repeated. The result can be seen in table 3.10a, the torque density was calculated according to (2.17). The distance from the edges of the magnet to the air gap was kept constant for all widths.

13 15 17 1

2.5 4 0

1 2 3 4

Width [mm]

Height [mm]

Torque [Nm]

(a) Torque versus dimensions.

13 15 17 1

2.5 4 0

0.1 0.2 0.3 0.4

Width [mm]

Height [mm]

Torque density [Nm/cm3 ]

(b) Torque density versus dimensions

Figure 3.3

From the results in table 3.10a it is visible that an increase in width (perpendicular to the magnetisation direction) is more important than an increase in height (parallel to the magnetisation direction). This is reasonable, since an increase in height shouldn’t affect the total flux as much as an increase in width, due to the limited remanent magnetisation that can be achieved.

Due to time constraints, the available magnets in this project were limited to what the local magnet retailer had in stock. The choices were between 16x3x5 mm (T1) and 15x2.5x15 mm (T2). Since the former wasn’t a dimension that was simulated, simulations were performed with a resulting torque and torque density of 3.09 Nm and 0.134 Nm/cm³ respectively. Both dimensions were chosen for further investigations.

3.4.1 Field weakening capabilities T1

The first analyzed design was the tangential design, shown in figure 3.4. The total magnet volume was 23 cm³.

Because of the saliency (L_q > L_d) this motor had, as opposed to the motor in section 3.5.1, a MTPA trajectory in the third quadrant of the I_d− I_q-plane. Subse- quently it will utilise the reluctance torque with negative d-currents. The different operation points is shown in figure 3.5a. The first operation point corresponds to MTPA with maximum stator current. The result is also illustrated in figure 3.6.

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Figure 3.4: T1 design.

2500 3000 3500 4000 4500

0 5 10 15 20

n_rot [rpm]

Absolute value of currents [A] I_d

Iq

(a) Currents with corresponding maximum speed for the T1 design.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 0

5 10 15 20 25 30 35

Harmonic order

Voltage [V]

Spectra over induced phase voltages at n=2750 rpm With air pockets Without air pockets

(b) Frequency spectra for the two designs.

Figure 3.5

From figure 3.6 it is visible that the tangential design performed better in field weakening operation compared to the radial design in section 3.5.1, although with a lower nominal torque.

3.4.2 Air pockets

One way to increase the d-axis inductance, thereby improving the field weakening capabilities, is to add air extensions. Since the reluctance in air is greater than in electrical steel, less flux will flow through these areas. This way the flux leakage paths can have the same area for a greater interal depth. An example of this can

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0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0

1 2 3 4

T [Nm]

nrot [rpm]

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000 250 500 750 1000

P [W]

Figure 3.6: Torque and power in the field weakening region for the T1 design.

be seen in figure 3.7a and 3.7b.

A comparison between the two designs and their field weakening capabilities showed that the maximum speed increased from 4800 to 5140 rpm when air pockets were added.

Aside from the improved field weakening capabilities, the harmonics were ef- fected by having the magnets buried deeper. This can be seen in figure 3.5b. The total harmonic distortion was reduced from 35.7% to 27.9%. Moreover the domi- nant harmonic component in the design with air was the third harmonic which will, in a three phase system, form a zero sequence. Without a connection to ground such a current cannot exist and is therefore of minimal importance in this kind of application.

3.4.3 Field weakening capabilities T2

The T1 design had good field weakening capabilities with a maximum speed of approximately 5000 rpm, but with suboptimal torque density. The T2 design with a total magnet volume and torque density of 18.0 cm³ and 0.165 N/cm³ respectively, was evaluated as an alternative. Another factor was also considered, that field weakening capability generally becomes better with the internal depth of the magnets, due to the increased inductance along the d-axis. A drawback with both design T1 and T2 was a small internal depth. Therefore the alternative design with

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(a) Without air pockets (b) With air pockets

Figure 3.7: Flux with/without air pockets.

air pockets was investigated to optimise the performance for the T2 design, shown in figure 3.7b.

From figure 3.8 an increased field weakening region compared to the T1 design can be seen. With 80% of the magnet volume 96 % of the nominal torque could be achieved, thereby increasing the torque density. The currents for the different operating points were very similar to those observed for the T1 design in figure 3.5a.

The core losses were simulated for the T2 design and were approximately 6.60 W at 2500 rpm.

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0 1000 2000 3000 4000 5000 6000

0 1 2 3 4

T [Nm]

nrot [rpm]

0 1000 2000 3000 4000 5000 60000

250 500 750 1000

P [W]

Figure 3.8: Torque and power in the field weakening region for the T2 design.

3.5 The radial design

The radial design featured eight cuboid shaped magnets buried ”radially” into the rotor, as seen in figure 3.9. The variables that needed to be optimised were as in the case with the tangential design, the magnet width, height and internal depth.

A minimum distance of approximately 0.8 mm between the edges of the magnet and the surface was once again settled for, to maximise torque and still maintain a mechanical endurance.

The same simulations were performed for the radial design as for the tangential, to observe the variation of the torque. The following results seen in table 3.10 were obtained.

Apparently the same trend could be seen in the radial case as with the tangential.

Increases in the magnetisation direction resulted in worse torque density while an increase perpendicular to the magnetisation direction had a positive effect. Due to the limited choice of magnets 15x2.5 mm was chosen for further investigations.

3.5.1 Field weakening capabilities

With magnet dimensions chosen the field weakening capabilities of the radial design was investigated. The total magnet volume and torque density for this design was 18 cm³ and 0.225 Nm/cm³ respectively. To examine the field weakening performance

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3.5. The radial design

Figure 3.9: Drawing of the radial model.

the motor was analysed during different operation points of the field weakening region, i.e. different combinations of I_dand I_qwhilst also satisfying the voltage and current limitations (2.2) and (2.4). The different currents with the corresponding torque and maximum speed for those operation points is shown in figure 3.11.

Note that the first operation point was the MTPA-operation which optimised the reluctance torque from (7.3) for the maximum allowed stator current.

The results for torque/power versus speed in figure 3.12 shows that the field weakening capabilities of the radial design were suboptimal. It was decided that further investigation into this design would not be performed. A possible explanation was that the design had little steel where fields opposing the flux from the magnets could be induced. Nominal torque and torque density were high.

Of theoretical interest were the core losses, which were approximately 8.27 W at 1750 rpm.

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13 15 17 1

2.5 4 0

1 2 3 4 5 6

Width [mm]

Height [mm]

Torque [Nm]

(a) Torque versus dimensions.

13 15 17 1

2.5 4 0

0.1 0.2 0.3 0.4

Width [mm]

Height [mm]

Torque density [Nm/cm3 ]

(b) Torque density versus dimensions

Figure 3.10

1800 1900 2000 2100 2200

0 3 6 9 12 15 18 21

nrot [rpm]

Absolute value currents [A]

Iq

Id

Figure 3.11: Currents with corresponding maximum speed for the radial design.

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3.5. The radial design

0 500 1000 1500 2000 2500

0 1 2 3 3.5

T [Nm]

n_rot [rpm]

0 500 1000 1500 2000 25000

200 400 600 700

P [W]

Figure 3.12: Torque and power in the field weakening region for the radial design.

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3.6 The V-shaped design

The V design featured 16 cuboid shaped magnets buried in a ”V-shape” into the rotor, as seen in figure 3.13. In this design there were additional variables to optimise apart from the magnet dimensions and internal depth. The spacing and angle between the magnets can have a large impact on the performance. Since there are many variables and they are hard to isolate and vary one by one, this report will focus on optimisation for one magnet size. The magnets that could be obtained had the dimensions 10x1.9x5 mm. With the magnet dimensions fixed the internal

Figure 3.13: Drawing of the V-design.

depth, spacing and angle were left to determine. The internal depth was as in the previous cases set to 0.8 mm from the edges of the magnets to the surface. The angle was varied while maintaining the internal depth. The results showed a torque that varied between 3.08-3.10 Nm for the angles 40 − 55^◦.

Since the torque almost was unaffected by the angle of the magnets, an angle of 50^◦ was chosen due to mechanical tolerances.

3.6.1 Demagnetisation

The highest risk of demagnetisation occurs during full field weakening operation, i.e. full negative d-current. During this scenario the flux was as shown in figure

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3.6. The V-shaped design

3.14a. The corresponding flux densities can be obtained from 3.14b.

(a) (b)

Figure 3.14: Flux during maximum field weakening operation.

A zoomed-in view of one of the magnets is presented in figure 3.15. An area in the edge of the magnet had a flux density less than 0.3 T. This will definitively lead to demagnetisation of the magnets according to figure 2.4.

Figure 3.15: Zoomed-in view of one magnet.

Part of the problem was the very high flux densities along the edges of the magnet. The simplest way of solving these kinds of problems is to increase the

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internal depth. This is obviously not a good solution to the problem, since this will result in a lower torque.

3.6.2 Air pockets

As in the case with the tangential design, air pockets can be used to direct the flux.

By adding air along the edges exposed to high saturation in the steel, less flux will take the path through the magnet due to the increased reluctance from the air. A smart design of the pockets slots can also increase the torque by forcing more flux to cross the air gap.

The first attempt to improve the critical areas of the magnet is shown in figure 3.16. The lowest flux density went from less than 0.3 T to approximately 0.46

Figure 3.16: The V-design with air slots.

T. This was a significant improvement. Additionally, the torque increased from 3.08 Nm to 3.43 Nm. Apparently the flux leakage was reduced due to the higher saturated steel areas along the air slots. Unfortunately, 0.46 T still is within the risk of demagnetisation. By varying the shape and size of the air slot additional attempts to improve the design were made.

The results from the second attempt is shown in figure 3.17 The lowest flux density was approximately 0.55 T, a significant improvement. With 0.55 T there is an acceptable margin for demagnetisation according to figure 2.4, as long as the temperature doesn’t exceed 80-90^◦C. The torque was increased to 3.53 T.

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Figure 3.17: The V-design with air slots rev. 2.

3.6.3 Field weakening capabilities of the V-shaped design

The magnet volume and the torque density for the V-shaped design was 18.2 cm³ and 0.194 Nm/cm³ respectively. The different operation points can be seen in table 3.18.

Figure 3.19 reveals a high torque density and a large constant power speed range.

The maximum speed is below 4000 rpm. This could be due to increased flux linkage obtained with the concentration of flux in this design. If higher maximum speed is desired the possibility of reducing the magnet volume exists, although with lower nominal torque as a result.

The core losses were simulated for the V-shaped design and were approximately 5.29 W at 1950 rpm.

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2500 2750 3000 3250 3500 3750

0 3 6 9 12 15 18 21

nrot [rpm]

Absolute value currents [A]

Iq

Id

Figure 3.18: Currents with corresponding maximum speed for the V-shaped design.

0 500 1000 1500 2000 2500 3000 3500 4000

0 1 2 3 4

T [Nm]

nrot [rpm]

0 500 1000 1500 2000 2500 3000 3500 40000

250 500 750 1000

P [W]

Figure 3.19: Torque and power in the field weakening region for the V-design.

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3.7. Influence of tolerances

3.7 Influence of tolerances

With internal magnets the rotor slots must be designed with tolerances since deviations occurs during production. These tolerances must be kept to a minimum since added air can have an effect on the torque output. This was simulated in figure 3.20a and 3.20b.

(a) No air slot above magnet. (b) 0.2 mm air slot above magnet.

Figure 3.20: Different tolerances for the air slots.

The obtained torque for the rotors were compared and showed a significant decrease in torque from 2.91 to 2.68 Nm, due to the added air from the large tolerances.

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Chapter 4

Assembling and implementation

In this chapter the assembling of the two rotors and implementation of field weak- ening will be discussed.

4.1 The manufacturing process

In this project the laminations was cut with a laser. The laser ray itself has a certain thickness that will consume material if not compensated for. During cutting it tries to compensate for the effect by offsetting the laser ray to a slightly greater or smaller radius to preserve the material.

The method that has been deemed fit in this project was to determine the tolerances by trial and error, i.e. by cutting different versions of the rotor laminates and selecting the best version. The laser loads a two dimensional CAD drawing of the rotor and cuts it accordingly, an example of a CAD drawing for one design can be seen in figure 4.1.

The resulting fit was nonfunctional. When the laminates were pressed on the shaft a malformation could be seen on the stack, see figure 4.2a and 4.2b. This was due to the shaft radius in the CAD drawing being to small and not fully compensated for the effect of the laser ray.

The radius had to be increased by 0.05 mm to obtain an acceptable fit. Another problem was that the magnets would not fit in the air holes once the laminates were pressed onto the shaft. This problem could have been due to the shaft’s greater radius not aligning the laminate. By keeping the rounded parts of the shaft as is, and the flat parts of the shaft reduced to original radius, i.e. a decrease with 0.05 mm the forced alignment was improved and magnets could be inserted into the air slot.

The assembling was done without professional equipment. The tools used were custom manufactured positioning and pressing cylinders to get the right position axially for the first laminate, as well as applying a distributed pressure during pressing. A smaller hydraulic press was used for the actual pressing. These can be seen in figure 4.3a and 4.3b. The press was neither accurate nor robust; therefore a

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Chapter 4. Assembling and implementation

Figure 4.1: CAD drawing of the T2 design.

(a) From above (b) From the side

Figure 4.2: Malformation of the first laminates for the T2 design.

lot of care was taken to align the laminates. The correct alignment is important to be able to insert the magnets into the slots.

The rotors to be assembled were the T2 and V-design. The difficulty was to align all 120 laminates required in the rotor stack. Since multiple magnets were used in the axial direction alignment was critical. From the cutting all the laminates had a little edge, therefore the alignment was done with those as a reference. This created a ”notch” on the rotor. Different techniques were tried. The first method was

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(a) Pressing cylinders. (b) Hydraulic press.

Figure 4.3

to force a partial stack of laminates with magnets inserted to maximum clockwise rotation during pressing. Once the laminates were pressed onto the ridges, they were in a fixed position. This was repeated for all partial stacks. The main idea was that all partial stacks then would be aligned. The procedure gave unsatisfactory results. A different technique was developed which will be described in the next section.

4.2 The tangential design

One stack (approximately 30 laminates) was aligned and magnets inserted into it.

Great care was taken to obtain the correct direction of magnetisation for each pole.

This stack was then pressed onto the shaft with the specially manufactured steel cylinders. This can be seen in figure 4.4a and 4.4b. The stack was not pressed all the way since this would have made alignment harder.

The next problem was that the magnets repelled each other in the axial direction when inserted correctly. This was overcome by mounting the magnets with the opposite magnetisation direction, thereby attracting the magnets from the previous stack. Then half a stack of laminates was applied, which allowed the magnets to be reversed to the correct polarity and still stay in place. This procedure can be seen in figure 4.5. Finally the other half of the stack was mounted and pressed onto the shaft. This technique ensured precise alignment due to the magnetic forces.

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(a) (b)

Figure 4.4: The first stack.

Figure 4.5: Reversing of the magnets.

Despite taking great care with the direction of magnetisation a mistake occurred.

One magnet was inserted in the wrong direction. This can be seen in figure 4.6a, and was corrected as seen in figure 4.6b. The technique was repeated for the remaining partial stacks. In figure 4.7a another partial stack was pressed onto the shaft, and figure 4.7b shows the complete rotor.

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(a) (b)

Figure 4.6: Polarity check.

(a) More laminates pressed onto the shaft. (b) The complete rotor.

Figure 4.7

4.2.1 Roundness of the tangential design

An interesting measurement is roundness. This can be a rough estimate of the balance in the rotor. Roundness is measured with a special gauge with the shaft mounted in a cradle. Note that the roundness was measured at several different positions along the rotor. This setup can be seen in figure 4.8. The maximum deviation with the notch excluded (which was to be sanded down) is visible from figure 4.9a and 4.9b and was 0.05 mm.

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Figure 4.8: Roundness setup.

(a) Minimum radius. (b) Maximum radius.

Figure 4.9: Roundness of tangential design rotor.

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4.3 The V-shaped design

The magnets used in the V-shaped design were much smaller and more susceptible to breakage, 10x1.9x5 mm (WxHxL) instead of the tangential design’s 15x2.5x15 mm (WxHxL). Therefore another assembling method was used.

The magnets’ length is equal to the thickness of 10 laminates. On the shaft, above the ridges approximately 10 laminates could fit on top of each other. Without being forced in a position by the ridges it was possible to align the laminates to allow insertion of the magnets into the rotor slots before being pressed onto the shaft.

This can be seen in figure 4.10a and 4.10b. This method effectively eliminated the risk of magnets not fitting into the magnet holes after being pressed onto the shaft.

(a) From above (b) From the side

Figure 4.10: Figure of a stack before being pressed onto the shaft.

This was repeated 12 times before the rotor was complete. The final result can be seen in figure 4.11

4.3.1 Roundness of the V-design

According to section 4.2.1 the roundness was measured at several different positions along the rotor to get an estimate of the imbalance. In figure 4.12a and 4.12b the maximum deviation can be seen and was approximately 0.05 mm.

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Figure 4.11: The final rotor for the V-design.

(a) Minimum radius (b) Maximum radius

Figure 4.12: Roundness of V-design rotor.

4.4 Balancing the rotor

The rotors in this project will consist of 120 laminates and multiple permanent magnets stacked in the axial direction for each pole. Since both the laminates and the magnets had tolerances, imbalances emerged. Another factor was that during the cutting of the laminates a small part of the steel was left uncut in the outer radius to ensure that the laminates didn’t fall of the steel sheet. Since they were

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4.4. Balancing the rotor

used for alignment an imbalance was created.

Imbalance of a rotor can cause unwanted noise, less torque produced and failure of bearings. This is critical in high speed applications.

At the department of Mechatronics at KTH Royal Institute of Technology it is possible to determine imbalances in a rotor, the machine can be seen in figure 4.13.

When imbalances have been detected it is important to counteract them. A simple way to make this possible is to press brass plates onto the stack endings and drill holes in them according to the imbalance. Brass was selected since it is nonmagnetic and brittle, making it easy to manipulate.

Due to several factors such as time limitations, the measured roundness of the rotors and consultations with staff from the Mechatronics department it was decided to not balance the rotors in this project.

Figure 4.13: Machine for detecting imbalances in a rotor.

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4.5 Mounting of the testing equipment

Some practical modifications were necessary to the motor and drive before testing. Since the temperatures were measured with a FLIR thermal camera, modified flanges with spokes were used. This resulted in that the drive part of the motor couldn’t be integrated into the motor housing and had to be mounted externally.

Other important factors to implement were an emergency stop switch and a power supply. Finally the analog input was to be fed with a variable voltage between 0-10 V.

To incorporate the emergency stop switch and be able to feed the analog input, an electronic box was built. This box also included connection terminals to easily be able to connect different drives or power supplies, if needed. The analog input was fed by using the 24 V pin of the D-sub connector from the drive, voltage dividing between a resistance and a potentiometer in series to be able to feed back 0-10 V to the analog input of the same D-sub connector. The inside of the box can be seen in figure 4.14. To enable an external mounting of the motor’s drive electronics, bus

Figure 4.14: Electronics box.

cables had to be extended. Due to all different components, a decision was taken to mount all equipment except the motor to a board, making the unit mobile. The complete drive board can be seen in figure 4.15.

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4.6. Implementing field weakening algorithm

Figure 4.15: Drive board.

4.6 Implementing field weakening algorithm

In this section the implementation of the field weakening algorithm in the drive system will be briefly discussed and explained.

4.6.1 Limitations in the drive system

The drive system could only handle integers and not floating numbers. This was offset by different scaling factors to get a sufficient resolution. The current reference was 30 times higher than its real value.

4.6.2 Different controls

One way of implementing the field weakening operation is to measure or calculate both the motor’s inductances in d- and q-direction and the magnetic flux generated by the magnets in the rotor. Calculations of the currents is done in the two regions described in section 4.6.3 and 4.6.4. This has been done and proved satisfactory with similar methods by e.g. Liaw et al. [8] and Sheng et al. [9]. By Youssef et al.

[10] another method of control has been proposed, the Unity Power Factor control, which also has given satisfactory results.

In this project the most suitable implementation of field weakening was decided to be an implementation that enables a fast yet robust way of switching currents for a specific motor. Therefore the current vectors for I_d and I_q respectively have been calculated and implemented into the drive system. This way of operation conflicted with the existing speed loop and therefore it was deactivated.

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Chapter 4. Assembling and implementation 4.6.3 MTPA region

The first operation region has been described in section 2.2 and the current was defined according to (2.13). In this region 20 different I_d and I_q current pairs were to be switched between in the drive, each with a different absolute value of the stator current I_s.

4.6.4 Field weakening region

In this region the starting point will be the last operation point from section 4.6.3, i.e. the MTPA point with rated stator current. From that point the negative d- current will increase in equally large steps until I_s= −I_d. The number of steps was set to 100 in the field weakening region in order to get a sufficient resolution.

The whole operation of the motors can be seen in figure 2.3. This is the operation for the motor in figure 3.7b and due to different saliency ratios different motors will vary slightly in the first region.

4.6.5 Switching current references

To switch between different current pairs a potentiometer is connected to an analog input of the drive which has a voltage span of 0-10 V and will set the reference current.

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Chapter 5

Test results

In this chapter the results from the testing will be presented as well as comparisons to the simulated values.

5.1 Testing procedure

The existing drive unit had never been tested with the d-regulator activated, since the original SPMSM had MTPA operation with q-current only. The d- and q- current regulation was implemented according to section 4.6.2. When the original rotor was tested with this setup the regulation worked in an acceptable way both with and without load. Problems arose with regulation of the currents when the internal designs were load tested. While under load the drive lost the regulation of the d-current before the q-current was increased.

To improve operation of the drive, the speed loop was reimplemented. Instead of switching currents the analog input was used for the speed reference while the q-current was regulated according to load and the d-current a fixed value. This would allow testing of one operation point at a time. At this point other problems emerged such as instability and failure to regulate the q-current.

A possible cause of these problems is according to section 7.6.3 saturation of the regulators. One drawback with the existing drive is that the real-time output of data is limited to one parameter at a time. To accurately identify drive problems and be able to optimise the regulators, real-time output of speed, i_q, i_d and the control error would be necessary. Due to this and the fact that control strategies and optimization of regulators for field weakening is a complex area that can be very time consuming, the testing procedure was altered. According to section 2.3 and [11], the fundamental component terminal voltage fed to the phase windings by the inverter has a limit of U_DC/√

3 for space vector modulation before overmodulation.

To avoid saturation of the regulators the DC-bus voltage was increased. To not exceed the original DC-bus limitations of 48 V, the RMS value of the line to line voltage of the phase windings were measured to not exceed 48/√

2 V during testing.

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Chapter 5. Test results

5.2 Field weakening performance

In this section measurements on the field weakening performance of the different designs will be presented.

5.2.1 Original surface design

Measurements were made on the surface mounted rotor with the field weakening algorithm applied and the results can be seen in figure 5.1a and 5.1b for torque and power respectively. A comparison to the simulated values is included. As seen in the figures the field weakening capabilities of the original surface mounted design is very limited. This was expected since surface mounted designs tend to have low d-axis inductances. This also corresponds roughly to the simulated results. An explanation to the deviations observed between the simulated and tested results can be that the original rotor’s dimensions were hard to measure accurately. The air gap was also hard to estimate due to the mushroom shaped surface mounted magnets. This resulted in a worse FEM-model of the rotor.

0 500 1000 1500 2000 2500

0 1 2 3 4 5

nrot [rpm]

T [Nm]

Simulated torque Measured torque

(a) Torque measurements on the original surface design.

0 500 1000 1500 2000 2500

0 200 400 600 800 1000

nrot [rpm]

P [W]

Simulated power Measured power

(b) Power measurements on the original surface design.

Figure 5.1

5.2.2 T2 design

The field weakening performance of the T2 design is presented and compared to the simulated values in figure 5.2a and 5.2b. Since an internal design will increase the d-axis inductance, the field weakening capabilities should increase in a similar manner. This is confirmed in these figures. With a top speed of 5550 rpm and a wide CPSR, the results corresponded to the simulations.

Design and Manufacturing of IPM Synchronous Motor for Field Weakening Operation