Starter

Starter as a DC motor

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Description

The Starter block implements a starter assembly as a separately excited DC motor, permanent magnet DC motor, or series connection DC motor. The motor operates as a torque source to an internal combustion engine.

Use the Starter block:

  • In an engine model with a front-end accessory drive (FEAD)

  • To model engine start and stop scenarios

The Starter block supports only an angular speed input to the DC motor. A load torque input requires engine dynamics.

Separately Excited DC Motor

In a separately excited DC motor, the field winding is connected to a separate source of DC power.

The relationship between the field winding voltage, field resistance, and field inductance is given by:

Vf=Lfdifdt+Rfif

The counter-electromotive force is a product of the field resistance, mutual inductance, and motor shaft angular speed:

EMF=LaifLafω

The armature voltage is given by:

Va=Ladiadt+Raia+ EMF

The starter motor current load is the sum of the field winding current and armature winding current:

iload= if+ ia

The starter motor shaft torque is the product of the armature current, field current, and mutual inductance:

Tmech= iaifLaf

Permanent Magnet DC Motor

In a permanent magnet DC motor, the magnets establish the excitation flux, so there is no field current.

The counter-electromotive force is proportional to the motor shaft angular speed:

EMF= Ktω

The armature voltage is given by:

Va=Ladiadt+Raia+ EMF

The starter motor current load is equal to the armature winding current:

iload= ia

The starter motor shaft torque is proportional to the armature winding current:

Tmech= Ktia

Series Excited DC Motor

A series excited DC motor connects the armature and field windings in series with a common DC power source.

The counter-electromotive force is a product of the field and armature initial series current, field, and armature mutual inductance and motor shaft angular speed:

EMF=iafLafω

The field and armature winding voltage is given by:

Vaf=Lserdiafdt+Rseriaf+ EMF

The starter motor current load is equal to the field and armature series current:

iload= iaf

The starter motor shaft torque is the product of the squared field and armature series current and the field and armature mutual inductance:

Tmech= iaf2Laf

For motor stability, the motor shaft angular speed must be greater than the ratio of the series connected field and armature resistance to the mutual inductance:

ω>RserLaf

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionVariableEquations

PwrInfo

PwrTrnsfrd — Power transferred between blocks

  • Positive signals indicate flow into block

  • Negative signals indicate flow out of block

PwrMtr

Mechanical power

Pmot

Pmot= ωTmech

PwrBus

Electrical power

Pbus

Separately excited DC motor

Pbus= vaia+vfif

PM excited DC motor

Pbus= vaia

Series excited DC motor

Pbus= vafiaf

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

  • Positive signals indicate an input

  • Negative signals indicate a loss

PwrLoss

Motor losses

Ploss

Ploss= (Pmot+PbusPind)

PwrStored — Stored energy rate of change

  • Positive signals indicate an increase

  • Negative signals indicate a decrease

PwrInd

Electrical inductance

Pind

Separately excited DC motor

Pind= Lfifdifdt+Laiadiadt

PM excited DC motor

Pind= Laiadiadt

Series excited DC motor

Pind=Lseriafdiafdt

The equations use these variables.

Ra

Armature winding resistance

La

Armature winding inductance

EMF

Counter-electromotive force

Rf

Field winding resistance

Lf

Field winding inductance

Laf

Field and armature mutual inductance

ia

Armature winding current

if

Field winding current

Kt

Motor torque constant

ω

Motor shaft angular speed

Va

Armature winding voltage

Vf

Field winding voltage

Vaf

Field and armature winding voltage

iaf

Field and armature series current

Rser

Series connected field and armature resistance

Lser

Series connected field and armature inductance

iload

Starter motor current load

Tmech

Starter motor shaft torque

Ports

Inputs

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Motor shaft angular speed, in rad/s.

  • Armature winding voltage Va and field winding voltage Vf, in V.

  • In series excited DC motor, armature and field winding voltage Vaf.

Output

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Bus signal containing these block calculations.

SignalDescriptionUnits

ArmCurr

Armature winding current

A

FldCurr

Field winding current

A

PwrInfo

PwrTrnsfrd

PwrMtr

Mechanical power

W

PwrBus

Electrical power

W

PwrNotTrnsfrd

PwrLoss

Motor power loss

W

PwrStored

PwrInd

Electrical inductance

W

Starter motor load current, in A.

Starter motor shaft torque, in N·m.

Parameters

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Configuration

Select one of the three motor types.

Dependencies

The table summarizes the motor parameter dependencies.

Motor TypeEnables Motor Parameter
Separately Excited DC MotorArmature winding resistance, Ra
Armature winding inductance, La
Field winding resistance Rf
Field winding inductance, Lf
Mutual inductance, Laf
Initial armature and field current, Iaf
Permanent Magnet Excited DC MotorArmature winding resistance, Rapm
Armature winding inductance, Lapm
Torque constant, Kt
Initial armature current, Ia
Series Connection DC MotorTotal resistance, Rser
Total inductance, Lser
Initial current, Iafser
Mutual inductance, Lafser

Separately Excited DC Motor

Armature winding resistance, in ohm.

Dependencies

To enable this parameter, select Separately Excited DC Motor for the Motor Type parameter.

Armature winding inductance, in H.

Dependencies

To enable this parameter, select Separately Excited DC Motor for the Motor Type parameter.

Field winding resistance, in ohm.

Dependencies

To enable this parameter, select Separately Excited DC Motor for the Motor Type parameter.

Field winding inductance, in H.

Dependencies

To enable this parameter, select Separately Excited DC Motor for the Motor Type parameter.

Mutual inductance, in H.

Dependencies

To enable this parameter, select Separately Excited DC Motor for the Motor Type parameter.

Initial armature and field current, in A.

Dependencies

To enable this parameter, select Separately Excited DC Motor for the Motor Type parameter.

Permanent Magnet Excited DC Motor

Armature winding resistance, in ohm.

Dependencies

To enable this parameter, select Permanent Magnet Excited DC Motor for the Motor Type parameter.

Armature winding inductance, in H.

Dependencies

To enable this parameter, select Permanent Magnet Excited DC Motor for the Motor Type parameter.

Motor torque constant, in N·m/A.

Dependencies

To enable this parameter, select Permanent Magnet Excited DC Motor for the Motor Type parameter.

Initial armature current, in A.

Dependencies

To enable this parameter, select Permanent Magnet Excited DC Motor for the Motor Type parameter.

Series Excited DC Motor

Series connected field and armature resistance, in ohm.

Dependencies

To enable this parameter, select Series Excited DC Motor for the Motor Type parameter.

Series connected field and armature inductance, in H.

Dependencies

To enable this parameter, select Series Excited DC Motor for the Motor Type parameter.

Initial series current, in A.

Dependencies

To enable this parameter, select Series Excited DC Motor for the Motor Type parameter.

Field and armature mutual inductance, in H.

Dependencies

To enable this parameter, select Series Excited DC Motor for the Motor Type parameter.

References

[1] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1994.

Extended Capabilities

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