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Shunt motor with electrical and torque characteristics

**Library:**Simscape / Electrical / Electromechanical / Brushed Motors

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.

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.

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