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_b in the armature:

$v_{b} = L_{a f} i_{f} ω$
where L_af is a constant of proportionality and ω is the angular velocity.
The mechanical power is equal to the power reacted by the back emf:

$P = v_{b} i_{a} = L_{a f} i_{f} i_{a} ω$
The motor torque is:

$T = P / ω = L_{a f} i_{f} i_{a}$

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:

$\begin{array}{l} V = i_{a} R_{a} + L_{a f} i_{f} ω \\ V = i_{f} R_{f} \end{array}$
Solve the preceding equations for i_a and i_f:

$\begin{array}{l} i_{f} = \frac{V}{R_{f}} \\ i_{a} = \frac{V}{R_{a}} (1 - \frac{L_{a f} w}{R_{f}}) \end{array}$
Substitute these values of i_a and i_f into the equation for torque:

$T = \frac{L_{a f}}{R_{a} R_{f}} (1 - \frac{L_{a f} ω}{R_{f}}) V^{2}$
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_a and L_af/R_f. It uses the no-load speed at zero torque to get a second equation that relates these two quantities. Then, it solves for R_a and 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:

$T_{l o a d} = \frac{L_{a f}}{R_{a} R_{f}} (1 - \frac{L_{a f} ω}{R_{f}}) V^{2} - J \dot{ω} - B ω$

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

Motor Torque-Speed Curves

A comparison of the torque-speed characteristics for five different motor types. To select the motor type, right-click on the Electric Motor block and select Block Parameters (Subsystem) from the context menu. In the new window, specify the desired motor using the Label mode active choice parameter. All motors have been sized for roughly the same mechanical power rating.

Open Model

Ports

Conserving

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+ — Positive terminal
electrical

Electrical conserving port associated with the shunt motor positive terminal.

- — Negative terminal
electrical

Electrical conserving port associated with the shunt motor negative terminal.

C — Motor case
mechanical

Mechanical rotational conserving port associated with the shunt motor case.

R — Motor rotor
mechanical

Mechanical rotational conserving port associated with the shunt motor rotor.

Hf — Field winding thermal port
thermal

Field winding thermal port.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Ha — Armature winding thermal port
thermal

Armature winding thermal port.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Parameters

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Modeling option — Whether to enable thermal ports
`No thermal port` (default) | `Show thermal port`

Whether to enable the thermal ports of the block and model the effects of losses that convert power to heat.

Electrical Torque

Model parameterization — Block parameterization
`By equivalent circuit parameters` (default) | `By rated power, rated speed & no-load speed`

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.

Armature resistance — Armature resistance
`110` `Ohm` (default)

Resistance of the armature.

Dependencies

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

Field winding resistance — Field winding resistance
`2500` `Ohm` (default)

Resistance of the field winding.

Dependencies

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

Back-emf constant — Back-emf constant
`5.11` `s*V/rad/A` (default)

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

Armature inductance — Armature inductance
`0.1` `H` (default)

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.

Field winding inductance — Field winding inductance
`0.1` `H` (default)

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.