Starter

Starter as a DC motor

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Powertrain Blockset / Energy Storage and Auxiliary Drive / Starter

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:

$V_{f} = L_{f} \frac{d i_{f}}{d t} + R_{f} i_{f}$

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

$E M F = L_{a} i_{f} L_{a f} ω$

The armature voltage is given by:

$V_{a} = L_{a} \frac{d i_{a}}{d t} + R_{a} i_{a} + E M F$

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

$i_{l o a d} = i_{f} + i_{a}$

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

$T_{m e c h} = i_{a} i_{f} L_{a f}$

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:

$E M F = K_{t} ω$

The armature voltage is given by:

$V_{a} = L_{a} \frac{d i_{a}}{d t} + R_{a} i_{a} + E M F$

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

$i_{l o a d} = i_{a}$

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

$T_{m e c h} = K_{t} i_{a}$

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:

$E M F = i_{a f} L_{a f} ω$

The field and armature winding voltage is given by:

$V_{a f} = L_{s e r} \frac{d i_{a f}}{d t} + R_{s e r} i_{a f} + E M F$

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

$i_{l o a d} = i_{a f}$

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

$T_{m e c h} = i_{a f}^{2} L_{a f}$

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:

$ω > - \frac{R_{s e r}}{L_{a f}}$

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Variable	Equations
`PwrInfo`	`PwrTrnsfrd` — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	`PwrMtr`	Mechanical power	P_mot	$P_{m o t} = - ω T_{m e c h}$
		`PwrBus`	Electrical power	P_bus	Separately excited DC motor $P_{b u s} = v_{a} i_{a} + v_{f} i_{f}$
					PM excited DC motor $P_{b u s} = v_{a} i_{a}$
					Series excited DC motor $P_{b u s} = v_{a f} i_{a f}$
	`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrLoss`	Motor losses	P_loss	$P_{l o s s} = - (P_{m o t} + P_{b u s} - P_{i n d})$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrInd`	Electrical inductance	P_ind	Separately excited DC motor $P_{i n d} = L_{f} i_{f} \frac{d i_{f}}{d t} + L_{a} i_{a} \frac{d i_{a}}{d t}$
					PM excited DC motor $P_{i n d} = L_{a} i_{a} \frac{d i_{a}}{d t}$
					Series excited DC motor $P_{i n d} = L_{s e r} i_{a f} \frac{d i_{a f}}{d t}$

The equations use these variables.

R_a	Armature winding resistance
L_a	Armature winding inductance
EMF	Counter-electromotive force
R_f	Field winding resistance
L_f	Field winding inductance
L_af	Field and armature mutual inductance
i_a	Armature winding current
i_f	Field winding current
K_t	Motor torque constant
ω	Motor shaft angular speed
V_a	Armature winding voltage
V_f	Field winding voltage
V_af	Field and armature winding voltage
i_af	Field and armature series current
R_ser	Series connected field and armature resistance
L_ser	Series connected field and armature inductance
i_load	Starter motor current load
T_mech	Starter motor shaft torque

Examples

Build Conventional Vehicle Model

Build a vehicle with an internal combustion engine using the conventional vehicle reference application.

Ports

Inputs

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MtrSpd — Angular speed
`scalar`

Motor shaft angular speed, in rad/s.

StartVolt — Armature and field voltage
`scalar`

Armature winding voltage V_a and field winding voltage V_f, in V.
In series excited DC motor, armature and field winding voltage V_af.

Output

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Info — Bus signal
bus

Bus signal containing these block calculations.

Signal			Description	Units
`ArmCurr`			Armature winding current	A
`FldCurr`			Field winding current	A
`PwrInfo`	`PwrTrnsfrd`	`PwrMtr`	Mechanical power	W
	`PwrTrnsfrd`	`PwrBus`	Electrical power	W
	`PwrNotTrnsfrd`	`PwrLoss`	Motor power loss	W
	`PwrStored`	`PwrInd`	Electrical inductance	W

LdCurr — Starter motor load current
`scalar`

Starter motor load current, in A.

MtrTrq — Starter motor shaft torque
`scalar`

Starter motor shaft torque, in N·m.

Parameters

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Configuration

Motor Type — Select motor type
`Separately Excited DC Motor` (default) | `Permanent Magnet Excited DC Motor` | `Series Connection DC Motor`

Select one of the three motor types.

Dependencies

The table summarizes the motor parameter dependencies.

Motor Type	Enables Motor Parameter
`Separately Excited DC Motor`	Armature 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 Motor`	Armature winding resistance, Rapm
	Armature winding inductance, Lapm
	Torque constant, Kt
	Initial armature current, Ia
`Series Connection DC Motor`	Total resistance, Rser
	Total inductance, Lser
	Initial current, Iafser
	Mutual inductance, Lafser

Separately Excited DC Motor