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Universal (or series) motor with electrical and torque characteristics

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

The Universal Motor block represents the electrical and torque characteristics of a universal (or series) motor using the following equivalent circuit model.

Where:

*R*is the armature resistance._{a}*L*is the armature inductance._{a}*R*is the field winding resistance._{f}*L*is the field winding inductance._{f}

When you set the **Model parameterization** parameter to ```
By
equivalent circuit parameters
```

, you specify the equivalent circuit parameters for
this model. The Universal 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:

$$P={v}_{b}{i}_{f}={L}_{af}{i}_{f}{}^{2}\omega $$

The motor torque is:

$$T=P/\omega ={L}_{af}{i}_{f}{}^{2}$$

The torque-speed characteristic for the Universal Motor block
model is related to the parameters in the preceding figure. When you set the **Model
parameterization** parameter to ```
By DC rated power, rated speed &
maximum torque
```

or ```
By DC rated power, rated speed & electrical
power
```

, the block solves for the equivalent circuit parameters as follows:

For the steady-state torque-speed relationship when using a DC supply,

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

$$V=({R}_{f}+{R}_{a}){i}_{f}+{v}_{b}=({R}_{f}+{R}_{a}+{L}_{af}\omega ){i}_{f}$$

Solve the preceding equation for

*i*and substitute this value into the equation for torque:_{f}$$T={L}_{af}{\left(\frac{V}{{R}_{f}+{R}_{a}+{L}_{af}\omega}\right)}^{2}$$

The block uses the rated speed and power to calculate the rated torque. The block uses the rated torque and rated speed values in the preceding equation plus the corresponding electrical power to determine values for

*R*and_{f}+R_{a}*L*._{af}

When you set the **Model parameterization** parameter to ```
By AC
rated power, rated speed, current & electrical power
```

, then the block must
include the inductive terms *L _{a}* and

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

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

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..