# Shunt Motor

Shunt motor with electrical and torque characteristics

**Libraries:**

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:

*R*—_{a}**Armature resistance***L*—_{a}**Armature inductance***R*—_{f}**Field winding resistance***L*—_{f}**Field winding inductance**

The Shunt Motor block computes the motor torque as follows:

The magnetic field in the motor induces the following back emf

*v*in the armature:_{b}$${v}_{b}={L}_{af}{i}_{f}\omega $$

where

*L*is a constant of proportionality and_{af}*ω*is the angular velocity.The mechanical power is equal to the power reacted by the back emf:

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

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:

For the steady-state torque-speed relationship,

*L*has no effect.Sum the voltages around the loop:

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

Solve the preceding equations for

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

Substitute these values of

*i*and_{a}*i*into the equation for torque:_{f}$$T=\frac{{L}_{af}}{{R}_{a}{R}_{f}}\left(1-\frac{{L}_{af}\omega}{{R}_{f}}\right){V}^{2}$$

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

*R*and_{a}*L*. It uses the no-load speed at zero torque to get a second equation that relates these two quantities. Then, it solves for_{af}/R_{f}*R*and_{a}*L*._{af}/R_{f}

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

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

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

### Model Thermal Effects

You can expose thermal ports to model the effects of losses that convert power to heat. To
expose the thermal ports, set the **Modeling option** parameter to either:

`No thermal port`

— The block does not contain thermal ports.`Show thermal port`

— The block contains multiple thermal conserving ports.

For more information about using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

## Examples

## Ports

### Conserving

## Parameters

## References

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

## Extended Capabilities

## Version History

**Introduced in R2008a**