Design of a mass-productionlow-cost claw-pole motor for an

automotive applicationR. Felicetti and I. Ramesohl

Robert Bosch GmbH, Division: Body Electronics,Technical Centre for Electronic Commutated Motors, Buhl, Germany

Keywords Rotors, Motors, Electrical machines, Mechatronics

Abstract This paper describes a thermal and electrical model, used at Robert Bosch GmbH for thedesign of an innovative motor for a water-pump. In addition, it offers an example of a highlyintegrated mechatronic system. A bonded-ferrite inner rotor has been developed with an integratedfront centrifugal impeller which is driven by the magnetic interaction of a rotating field created byclaw-poles. The two phase unipolar coil arrangement is fed by an internal circuit using twoMOSFETS controlled by the commutation signal from a bipolar Hall-IC. This is the firstmass-production example of an electrical machine for an automotive application where the clawpole topology is used to realise the armature of the motor (i.e. the rotating field) and not theexcitation field.

1. IntroductionThis paper shows several design and calculation tools for a special claw-polemotor.

First, the construction of the motor, with some peculiarities, is presented.The cost-aspects and ambient conditions as an automobile application have tobe taken into consideration. The most important ambient condition is thetemperature of the fluid in which the rotor (Figure 1) runs which is about 1208Cand the temperature of the surrounding air is more than 1008C.

A 3D magnetic field calculation of the claw-pole arrangement is shown inFigure 2 to provide informations about saturation effects in the claws, themagnetic flux density distribution and armature reaction effect.

In Section 2, the electrical principle of the motor is described and in Section 3a novel method of characterising electrical machines in terms of their thermalbehaviour is presented. The methods described are transferable to any type ofelectrical machine and gives the electrical machine designer a fast andcomfortable way to optimise the winding and active magnetic componentsthrough the definition of the electrical loading and current density. The methodpresented, in this paper, has the advantage of providing a good overview of thethermal behaviour of a machine with varying electric load, current density andmain geometrical dimensions. The use of this method is very efficient in thedevelopment stage because it is fast and reliable. For fine optimization, thecoefficients of the model can be adapted through the use of FE-tools or withmeasurement adapted R-C-meshes.

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Design of a motor

937

COMPEL: The International Journalfor Computation and Mathematics inElectrical and Electronic Engineering

Vol. 22 No. 4, 2003pp. 937-952

q MCB UP Limited0332-1649

DOI 10.1108/03321640310482913

Figure 1.Auxiliary water-pumpmotor. (a) Magneticactive components(prototype), (b) explodedview of all components ofthe pump

Figure 2.No-load flux densitydistribution of half of themagnet and claw polestructure

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Section 4 presents an analytically based electromagnetic model of the motorwith a detailed description on how to calculate all relevant components of theequivalent electric circuit.

Thermal and electrical results are compared with measurements andpresented in Section 5. A further section explains the parameter-calculation.

2. The claw-pole motor and driveThe usual application of the claw-pole topology is the production of anexcitation field in synchronous motors and alternators.

The claw-pole arrangement considered here is used to generate the armaturereaction field of the motor (Figure 2). A bonded-ferrite inner rotor magnetisedwith eight poles provides the excitation field. In order to avoid corrosion, nointernal rotor iron yoke was allowed. Therefore, a lateral magnetisation was thebest practical solution. At standstill, the rotor is positioned with its q-axisaligned with the symmetry axis of the eight armature claw-poles. This is thenatural tendency of the rotor to rest in the position of minimum magneticreluctance. The cogging torque of this machine is a helpful functionalphenomenon because it aids the starting torque. The armature field is providedby two bobbin coils, which are positioned in the internal toroidal space of theiron core. This produces good magnetic mutual coupling. The coils areswitched to the battery voltage, depending on the position of the rotor, by twoMOSFETS. The circuit is shown in Figure 3(a). The Hall-IC senses the rotorposition and switches the phases.

The current flows from the battery through the switched phase for a rotorangle of 180 electrical degrees. This generates the electromagnetic torque.To complete one electrical revolution, the first phase is then switched-off andthe other switched-on.

This switching strategy is favoured due to the good magnetic couplingbetween the two phases. The rapid decrease of the current observed in thefirst phase of this topology (Figure 3(b)) is not accomplished by thedissipation of the leakage field energy through the FETs, but through itstransfer from one phase to the other by a good magnetic coupling. Due to this,no significant transient time exists in the commutation. Poor couplingbetween the two coils ðM ! LÞ would lead to high avalanche losses in theFETs. The mechanical design and the quality of the winding processdetermines the coupling factor.

3. Pre-sizing and thermal designTo calculate the size of the motor, depending on the required torque, thefollowing relationship can be applied:

Tem ¼ KBavAR2int

L ð1Þ

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939

where

Tem¼ electromagnetic torque (N m)

K ¼ motor constant (-)

Bav¼ average air gap induction (T)

A ¼ electric loading (A/m)

Rint¼ air gap radius (m)

L ¼ stator length (m)

The maximum allowed electric loading A leads to the smallest possible motorsize and is limited thermally by the winding insulation and permanentmagnets. If the specific machine iron-losses cFe (W/kg) and the permitted

Figure 3.Motor model andsimulated current.

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copper over-temperature are fixed in advance, it is possible to predict the valueof A from the following equation:

AðSÞ ¼a*

air ·DTair þ a*water ·DTwater

Rint

Rext

� �KCu

KRKfS

rKbKCuS 2 þ cFegFeKFeð2Þ

where

S¼ current density (A/m2)

r¼ specific electric copper resistance (Vm)

a*air; a

*water ¼ convection/radiation factors (W/m2K)

Kb¼ duty factor (per cent)

KCu¼ copper fill factor (per cent)

KFe¼ iron-copper volume ratio (per cent)

cFe¼ specific iron losses (W/kg)

gFe¼ specific iron mass (kg/m3)

KR¼ radial factor (-)

Kf¼ current form factor (-)

With reference to Figures 4 and 5, it is possible to explain the meaning of eachparameter.

The electric loading and the current density are so defined:

A ¼pWI average

pRintð3Þ

Figure 4.The stator radial

structure

Design of a motor

941

S ¼W I rms

LH KCuð4Þ

where

p¼ pole pairs (-)

W ¼ number of turns/phase (-)

Iaverage ¼ mean current value over a period (A)

Irms¼ effective phase current (A)

L ¼ stator axial length (m)

H ¼ stator radial height (m)

The copper fill and the iron factors are calculated using the followingequations:

KCu ¼2Wp

f2Cu

4

LHð5Þ

KFe ¼AFe

LH¼

ðL þ H 2 2tsÞ

LHð6Þ

where fCu is the copper wire diameter (m), AFe is the iron cross-sectional area(m2), and ts is the steel lamination thickness (m).

It is also possible to describe the heat sources in the motor (copper and ironlosses) by the following equations:

PCu ¼ LHKCu2pRmrS 2KB ð7Þ

Figure 5.The stator cross-section

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PFe ¼ cFegFeKFeLH2pRm ð8Þ

where Rm is the average radius of the winding

Rm ¼Rint þ Rout

2ð9Þ

The ratio between A and S is the dimensional length (Vogt, 1996):

A

S¼

KCu

Kf

LH

t, to a length ðmÞ ð10Þ

where t is the tooth pitch (m) and

Kf ¼I rms

I averageð11Þ

It is assumed that the heat-rate flows from the stator to the ambient and waterin the radial direction only.

Depending on the enclosed construction of the motor, the lateral surfaces ofthe stator can be assumed adiabatic. With this assumption, it is possible toexpress the heat transfer coefficients a*

airðW=8C m2Þ and a*waterðW=8C m2Þ

(depending on the stator geometry and thermal properties of the materials andneglecting the temperature drop on the metal parts) as:

a*air ¼

1

aairþ

dout

lairþ

dout

lplastic

� �21

ð12Þ

a*water ¼

1

awaterþ

dint

lairþ

dint

lplastic

� �21

ð13Þ

where

aair¼ convection + radiation air coefficient (W/8C m2)

awater ¼ convection + radiation water coefficient (W/8C m2)

lair¼ thermal air conductivity (W/8C m)

lplastic ¼ thermal plastic conductivity (W/8C m)

At steady state, the power losses are equal to the total heat flow through thestator:

PCu þ PFe ¼ a*air2pRoutL · DTair þ a*

water2pRintL · DTwater ð14Þ

where DTair is the copper over-temperature referred to ambient (8C), andDTwater is the copper over-temperature referred to water (8C)

Design of a motor

943

By substituting equations (7) and (8) in equation (14), taking intoconsideration the relationships (3), (4) and (10), it is possible to deriveequation (2).

It produces the A(S ) curve shown in Figure 6. From this curve, themaximum value of the electric loading Amax and the related current density Scan be determined, which relates to the permitted copper over-temperature.This curve has several properties. The most important is the ratio between Aand S (the slope of a straight through the origin) which is proportional to theslot depth of the motor H (m).

It is possible to express H as a function of S which is represented by h(S ).This curve is also shown in Figure 6 and it can be calculated using thefollowing equation:

hðSÞ ¼AðSÞ

S

Kf

KCuð15Þ

This curve has a maximum value of hth which is named the thermal slot depthof the machine under the specified thermal conditions.

hth ¼ hðSÞjS¼0 ¼a*

air ·DTair þ a*water ·DTwater · Rint

Rout

� �cFegFeKFeKR

ð16Þ

This is the maximum permitted radial height of the stator, which is compatiblewith the assumed copper over-temperatures.

Figure 6.A and h characteristicsagainst S

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It is interesting to note that the slot depth of the machine at Amax is half ofthe thermal slot depth. It is possible to demonstrate that:

hAmax¼ h SjdA

dS¼0

� �¼

hth

2ð17Þ

These considerations help to formulate the first design of motor by choosingthe minimum rotor volume from equation (1) at Amax and assuming a radialheight of the stator equal to half of its thermal slot depth hth.

4. Electromagnetic modelThe model used for a machine phase winding is an easy model due to thefollowing reasons (Figure 7):

(1) the mutual inductance is involved only during phase commutation,

(2) under normal operating conditions, the iron is not saturated, and

(3) the back e.m.f. is known from the FEM calculation.

During the time period when only one phase is switched to the battery voltage,the electrical and the mechanical conditions can be described by the followingequations:

UDCðtÞ2 R iðtÞ2 LsðtÞdiðtÞdt 2 eðtÞ ¼ 0

TemðtÞ þ T loadðtÞ þ T lossesðtÞ þ TcoggingðtÞ þ I dVðtÞdt

¼ 0

8<: ð18Þ

and

Figure 7.Model for one phase of

the machine

Design of a motor

945

eðtÞ ¼PNi¼1

2 ›CiðtÞdt

¼ 2pWVðtÞPNi¼1

›FiðuðtÞÞ›uðtÞ

TemðtÞ ¼

PN

i¼1

eiðtÞiðtÞ

VðtÞ¼ 2pW

PNi¼1

›FiðuðtÞÞ›uðtÞ

iðtÞ

8>>>>>><>>>>>>:

ð19Þ

where

UDC¼ supply voltage (V)

R ¼ phase resistance (V)

Ls¼ leakage inductance (H)

I ¼ moment of inertia (kg m2)

V¼ angular speed (rad/s)

Fi¼ ith harmonic of the flux (Vs)

u ¼ electric angular rotor position (rad)

Tem¼ electromagnetic torque (N m)

Tload ¼ mechanical load (N m)

Tlosses¼ torque due to the magnetic and mechanical losses (N m)

The solution of these differential equations for the steady-state is possible byan analytical closed form calculation, if it is assumed as a nearly constantangular rotor speed V, which agrees well with the reality of the motor (motorspeed ripple ,4 per cent). In this case, equations (18) and (19) can be written inthe following way:

UDCðtÞ2 RiðtÞ2 pVLsdiðuÞdu 2 eðuÞ ¼ 0

�Tem þ �Tload þ �Tlosses ¼ 0

8<: ð20Þ

and

eðuÞ ¼ 2pWVPNi¼1

›FiðuÞ›u

�Tem ¼

1T

R T

0

PN

i¼1

eiðtÞiðtÞ dt

V¼ 2pW 1

p

Z p

0

PNi¼1

›FiðuÞ›u

iðuÞ du

8>>>>><>>>>>:

ð21Þ

where �Tx is average value over a period of the x-torque (N m).For the ith flux harmonic, the following expression is assumed:

FiðuÞ ¼ fi sinðiuþ giÞ ð22Þ

and for the ith e.m.f. harmonic:

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eiðuÞ ¼ 2pWVifi sin iuþ gi þp

2

� �ð23Þ

Assuming that the reference rotor angular position is that at the switch-on of aphase, it is possible to operate a variable substitution:

u ¼ b2 a2 g1 2p

2ð24Þ

where a is the commutation angle (phase advance switching) (rad).Under this assumption, the phase current is equal to the sum of the two

b-functions, the transient response it(b) and the steady-state response ip(b),respectively:

itðbÞ ¼ Kða;VÞe2

b

pVL

R ð25Þ

ipðbÞ ¼U

R2pWV

XN

i¼1

ifi

ziðVÞsin iðb2a2g1Þ þgi 2 ði21Þ

p

22wiðVÞ

h ið26Þ

where

ziðVÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR 2 þðipVLÞ2

qð27Þ

wiðVÞ ¼ a tan ipVL

R

� �ð28Þ

The phase current over an half period is:

iðbÞ ¼ itðbÞþ ipðbÞ ð29Þ

To find the specific solution of this general integral, it is necessary to fix theinitial condition of i(b).

This can be achieved through energy considerations. Depending on the goodvalue of the magnetic coupling factor ðk ø 1Þ during the commutation almostall of the energy of the leakage field is transferred from one phase to the other.It can be assumed that:

i1ðpÞ ø 2i2ð0Þ ¼ 2i1ð0Þ ð30Þ

or

iðpÞ ø 2ið0Þ ð31Þ

Applying this condition, it is possible to obtain the value of the unknownconstant K(a,V):

Design of a motor

947

Kða;VÞ ¼1

1 þ e2 p

pVLR

22U

Rþ pWV

XN

i¼1

ifi

ziðVÞ

(::

£ sin 2iðaþ g1Þ þ gi 2 ði 2 1Þp

22 wiðVÞ

h ih

þ sin iðp2 a2 g1Þh

þgi þ ði 2 1Þp

22 wiðVÞ

ii)ð32Þ

In Figure 8, the results of a link current simulation for the claw-pole motor ata speed of 3,170 rpm are shown.

5. ConclusionsThe prototype of the claw-pole motor was calculated with the describedanalytical tools. The validity of the thermal analysis tool was confirmed bymeasurements carried out on the prototype auxiliary water-pump. Themeasured copper, iron, ambient and water temperatures are shown in Figure 9.

The measured copper over-temperatures, with respect to the water andambient temperatures given in Figure 9, are very near to the predicted values(Table I):

The analytical model can also simulate with good accuracy theelectromechanical behaviour of the machine. Figure 10 shows the measuredcurrent from the claw-pole motor at a speed of 3,170 rpm. Channel 1 (Ch1) ofFigure 10 shows the shape of the link-current waveform, which agrees wellwith the simulated current waveform given in Figure 8. Channel 2 (Ch2) shows

Figure 8.Link current simulation

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Figure 9.Results from the thermal

measurements

Figure 10.Motor link current

Predicted (8C) Measured (8C)

20 2340 42 Table I.

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949

the measured current (voltage across a precision shunt). The rms values of thesimulated and measured currents agree very well: simulated 1.12 Arms;measured 1.14 Arms.

6. Analytical calculations6.1 The electrical resistance of a phaseIn the area A of Figure 5, ð2 £ W Þ turns of circular wire with diameter f andaverage length is equal to:

la ¼ 2pðRint þ ts þ tpÞ þ ðRout 2 ts 2 DÞ

2ð33Þ

The resistance of a phase is then:

RðW ;TÞ ¼ r0½1 þ a0ðT 2 T0Þ�la

pf 2

4

W

¼ r0½1 þ a0ðT 2 T0Þ�2la

KCuLHW 2

ð34Þ

6.2 The inductance of a motor phaseThe inductance of a phase consists generally of the main self inductance, Lm

and the leakage inductance, Ls. In this motor, it is impossible to find apreferable magnetic path for the main stator flux into the rotor with theabsence of a rotor yoke. It is therefore, possible to consider the stator flux, in thedirection of the rotor, as a part of the leakage flux. The inductance of a phaseconsists then only of the leakage inductances. It is possible to determine threedifferent leakage inductance components.

(1) The leakage inductance in the slot. This component is dependent on themagnetic energy in the winding volume, Lss

. Its calculation is based onthe following equation, which terms the magnetic energy in the windingslot when a phase is excited:

1

2Lss

I 2 ¼

ZV s

1

2m0H

2sðI Þ dV s ð35Þ

It is possible, using equation (33) to demonstrate (Richter, 1967) that:

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Lss¼ 2pm0

W 2

L 2 2ts

H 2c

4þ

H cðRint þ tp þ tsÞ

3

"

þD2

2þ D · ðH c þ Rint þ tp þ tsÞ

#:

¼ m0lssLW 2

ð36Þ

(2) The leakage inductance between the claws. The simplest way to calculatethis leakage inductance Lst

is by using the reluctance between the claws(Figure 11)

Ls t¼

W 2

R¼ NCm0ts

L

d

W 2

cos2ðgÞ¼ m0ls t

LW 2 ð37Þ

(3) The leakage inductance due to the tooth leakage flux. The calculationof Lsth

can be approximated by the use of the principle of magneticsymmetry and Carter’s theory for the air-gap field (Pestarini, 1943). Anadditional condition is required: adjacent claws should quasi lay on aplanar surface. Due to the high number of claws in this machine it ispossible to match this condition quite well (Figure 12).

It results that:

Lsth¼ m0lsth

LW 2 ð38Þ

where

lsthø

5

4ð39Þ

The total leakage inductance of a phase is then:

Ls ¼ Lssþ Lst

þ Lsthð40Þ

Figure 11.Top view of the claws

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951

References

Pestarini, G.M. (1943), Elettromeccanica, Edizioni Italiane, Rome, Vol. 1, pp. 55-7.

Richter, R. (1967), Elektrische Maschinen, Birkhauser Verlag, Basel-Stuttgart, Vol. 1, pp. 265-78.

Vogt, K. (1996), Berechnung Elektrischer Maschinen, VCH-Verlag, Weinheim, p. 434.

Further reading

Smolenski, I. (1980), Electrical Machines, MIR publisher, Moscow, Vol. 2, pp. 34-41.

Figure 12.The symmetry principle

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