Starter as a DC motor
Powertrain Blockset / Energy Storage and Auxiliary Drive / Starter
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 frontend 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.
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:
${V}_{f}={L}_{f}\frac{d{i}_{f}}{dt}+{R}_{f}{i}_{f}$
The counterelectromotive force is a product of the field resistance, mutual inductance, and motor shaft angular speed:
$EMF={L}_{a}{i}_{f}{L}_{af}\omega $
The armature voltage is given by:
${V}_{a}={L}_{a}\frac{d{i}_{a}}{dt}+{R}_{a}{i}_{a}+EMF$
The starter motor current load is the sum of the field winding current and armature winding current:
${i}_{load}={i}_{f}+{i}_{a}$
The starter motor shaft torque is the product of the armature current, field current, and mutual inductance:
${T}_{mech}={i}_{a}{i}_{f}{L}_{af}$
In a permanent magnet DC motor, the magnets establish the excitation flux, so there is no field current.
The counterelectromotive force is proportional to the motor shaft angular speed:
$EMF={K}_{t}\omega $
The armature voltage is given by:
${V}_{a}={L}_{a}\frac{d{i}_{a}}{dt}+{R}_{a}{i}_{a}+EMF$
The starter motor current load is equal to the armature winding current:
${i}_{load}={i}_{a}$
The starter motor shaft torque is proportional to the armature winding current:
${T}_{mech}={K}_{t}{i}_{a}$
A series excited DC motor connects the armature and field windings in series with a common DC power source.
The counterelectromotive force is a product of the field and armature initial series current, field, and armature mutual inductance and motor shaft angular speed:
$EMF={i}_{af}{L}_{af}\omega $
The field and armature winding voltage is given by:
${V}_{af}={L}_{ser}\frac{d{i}_{af}}{dt}+{R}_{ser}{i}_{af}+EMF$
The starter motor current load is equal to the field and armature series current:
${i}_{load}={i}_{af}$
The starter motor shaft torque is the product of the squared field and armature series current and the field and armature mutual inductance:
${T}_{mech}={i}_{af}^{2}{L}_{af}$
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:
$\omega >\frac{{R}_{ser}}{{L}_{af}}$
For the power accounting, the block implements these equations.
Bus Signal  Description  Variable  Equations  



 Mechanical power  P_{mot}  ${P}_{mot}=\omega {T}_{mech}$ 
PwrBus  Electrical power  P_{bus}  Separately excited DC motor ${P}_{bus}={v}_{a}{i}_{a}+{v}_{f}{i}_{f}$  
PM excited DC motor ${P}_{bus}={v}_{a}{i}_{a}$  
Series excited DC motor ${P}_{bus}={v}_{af}{i}_{af}$  
 PwrLoss  Motor losses  P_{loss}  ${P}_{loss}=({P}_{mot}+{P}_{bus}{P}_{ind})$  
 PwrInd  Electrical inductance  P_{ind}  Separately excited DC motor ${P}_{ind}={L}_{f}{i}_{f}\frac{d{i}_{f}}{dt}+{L}_{a}{i}_{a}\frac{d{i}_{a}}{dt}$  
PM excited DC motor ${P}_{ind}={L}_{a}{i}_{a}\frac{d{i}_{a}}{dt}$  
Series excited DC motor ${P}_{ind}={L}_{ser}{i}_{af}\frac{d{i}_{af}}{dt}$ 
The equations use these variables.
R_{a}  Armature winding resistance 
L_{a}  Armature winding inductance 
EMF  Counterelectromotive 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 
[1] Krause, P. C. Analysis of Electric Machinery. New York: McGrawHill, 1994.