# Shunt Motor

Shunt motor with electrical and torque characteristics

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• Simscape / Electrical / Electromechanical / Brushed Motors

## Description

The Shunt Motor block represents the electrical and torque characteristics of a shunt motor using the following equivalent circuit model.

When you set the Model parameterization parameter to `By equivalent circuit parameters`, you specify the equivalent circuit parameters for this model:

• RaArmature resistance

• LaArmature inductance

• RfField winding resistance

• LfField winding inductance

The Shunt Motor block computes the motor torque as follows:

1. The magnetic field in the motor induces the following back emf vb in the armature:

`${v}_{b}={L}_{af}{i}_{f}\omega$`

where Laf is a constant of proportionality and ω is the angular velocity.

2. The mechanical power is equal to the power reacted by the back emf:

`$P={v}_{b}{i}_{a}={L}_{af}{i}_{f}{i}_{a}\omega$`

3. The motor torque is:

`$T=P/\omega ={L}_{af}{i}_{f}{i}_{a}$`

The torque-speed characteristic for the Shunt Motor block model is related to the parameters in the preceding figure. When you set the Model parameterization parameter to ```By rated power, rated speed & no-load speed```, the block solves for the equivalent circuit parameters as follows:

1. For the steady-state torque-speed relationship, L has no effect.

2. Sum the voltages around the loop:

`$\begin{array}{l}V={i}_{a}{R}_{a}+{L}_{af}{i}_{f}\omega \\ V={i}_{f}{R}_{f}\end{array}$`

3. Solve the preceding equations for ia and if:

`$\begin{array}{l}{i}_{f}=\frac{V}{{R}_{f}}\\ {i}_{a}=\frac{V}{{R}_{a}}\left(1-\frac{{L}_{af}w}{{R}_{f}}\right)\end{array}$`

4. Substitute these values of ia and if into the equation for torque:

`$T=\frac{{L}_{af}}{{R}_{a}{R}_{f}}\left(1-\frac{{L}_{af}\omega }{{R}_{f}}\right){V}^{2}$`

The block uses the rated speed and power to calculate the rated torque. The block uses the rated torque and no-load speed values to get one equation that relates Ra and Laf/Rf. It uses the no-load speed at zero torque to get a second equation that relates these two quantities. Then, it solves for Ra and Laf/Rf.

The block models motor inertia J and damping B for all values of the Model parameterization parameter. The output torque is:

`${T}_{load}=\frac{{L}_{af}}{{R}_{a}{R}_{f}}\left(1-\frac{{L}_{af}\omega }{{R}_{f}}\right){V}^{2}-J\stackrel{˙}{\omega }-B\omega$`

The block produces a positive torque acting from the mechanical C to R ports.

### Thermal Ports

The block has two optional thermal ports, one per winding, hidden by default. To expose the thermal ports, right-click the block in your model, and then from the context menu select Simscape > Block choices > Show thermal port. This action displays the thermal ports on the block icon, and exposes the Temperature Dependence and Thermal Port parameters. These parameters are described further on this reference page.

Use the thermal ports to simulate the effects of copper resistance losses that convert electrical power to heat. For more information on using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

## Ports

### Conserving

expand all

Electrical conserving port associated with the shunt motor positive terminal.

Electrical conserving port associated with the shunt motor negative terminal.

Mechanical rotational conserving port associated with the shunt motor case.

Mechanical rotational conserving port associated with the shunt motor rotor.

## Parameters

expand all

### Electrical Torque

Select one of the following methods for block parameterization:

• ```By equivalent circuit parameters``` — Provide electrical parameters for an equivalent circuit model of the motor.

• ```By rated power, rated speed & no-load speed``` — Provide power and speed parameters that the block converts to an equivalent circuit model of the motor.

Resistance of the armature.

#### Dependencies

This parameter is visible only when you set the Model parameterization parameter to ```By equivalent circuit parameters```.

Resistance of the field winding.

#### Dependencies

This parameter is visible only when you set the Model parameterization parameter to ```By equivalent circuit parameters```.

The ratio of the voltage generated by the motor to the motor speed.

Inductance of the armature. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. The value can be zero.

Inductance of the field winding. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. The value can be zero.

Speed of the motor when no load is applied.

#### Dependencies

This parameter is visible only when you set the Model parameterization parameter to ```By rated power, rated speed & no-load speed```.

Motor speed at the rated load.

#### Dependencies

This parameter is visible only when you set the Model parameterization parameter to ```By rated power, rated speed & no-load speed```.

The mechanical load for which the motor is rated to operate.

#### Dependencies

This parameter is visible only when you set the Model parameterization parameter to ```By rated power, rated speed & no-load speed```.

The voltage at which the motor is rated to operate.

#### Dependencies

This parameter is visible only when you set the Model parameterization parameter to ```By rated power, rated speed & no-load speed```.

The initial current when starting the motor with the rated DC supply voltage.

#### Dependencies

This parameter is visible only when you set the Model parameterization parameter to ```By rated power, rated speed & no-load speed```.

### Mechanical

Resistance of the rotor to change in motor motion. The value can be zero.

Energy dissipated by the rotor. The value can be zero.

Speed of the rotor at the start of the simulation.

### Temperature Dependence

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

A 1 by 2 row vector that defines the coefficient α in the equation relating resistance to temperature, as described in Thermal Model for Actuator Blocks. The first element corresponds to the field winding, and the second to the armature. The default value is for copper.

The temperature for which motor parameters are defined.

### Thermal Port

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

A 1 by 2 row vector that defines the thermal mass for the field and armature windings. The thermal mass is the energy required to raise the temperature by one degree.

A 1 by 2 row vector that defines the temperature of the field and armature thermal ports at the start of simulation.

## References

[1] Bolton, W. Mechatronics: Electronic Control Systems in Mechanical and Electrical Engineering, 3rd edition Pearson Education, 2004..