SimElectronics™

Shunt Motor - Model electrical and torque characteristics of shunt motor

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Actuators & Drivers

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:

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:
The motor torque is:

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:
Solve the preceding equations for i_a and i_f:
Substitute these values of i_a and i_f into the equation for torque:

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:

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

Dialog Box and Parameters

Electrical Torque Tab

Model parameterization

Select one of the following methods for block parameterization:

By equivalent circuit parameters — Provide electrical parameters for an equivalent circuit model of the motor. This is the default method.
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

Resistance of the armature. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter. The default value is 110 Ω.

Field winding resistance

Resistance of the field winding. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter. The default value is 2.5e+03 Ω.

Back-emf constant

The ratio of the voltage generated by the motor to the motor speed. The default value is 5.11 s*V/rad/A.

Armature inductance

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 default value is 0.1 H. The value can be zero.

Field winding inductance

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 default value is 0.1 H. The value can be zero.

No-load speed

Speed of the motor when no load is applied. This parameter is only visible when you select By rated power, rated speed & no-load speed for the Model parameterization parameter. The default value is 4.6e+03 rpm.

Rated speed (at rated load)

Motor speed at the rated load. This parameter is only visible when you select By rated power, rated speed & no-load speed for the Model parameterization parameter. The default value is 4e+03 rpm.

Rated load (mechanical power)

The mechanical load for which the motor is rated to operate. This parameter is only visible when you select By rated power, rated speed & no-load speed for the Model parameterization parameter. The default value is 50 W.

Rated DC supply voltage

The voltage at which the motor is rated to operate. This parameter is only visible when you select By rated power, rated speed & no-load speed for the Model parameterization parameter. The default value is 220 V.

Starting current at rated DC supply voltage

The initial current when starting the motor with the rated DC supply voltage. This parameter is only visible when you select By rated power, rated speed & no-load speed for the Model parameterization parameter. The default value is 2.09 A.

Mechanical Tab

Rotor inertia: Rotor inertia. The default value is 2e-04 kg*m². The value can be zero.
Rotor damping: Rotor damping. The default value is 1e-06 N*m/(rad/s). The value can be zero.
Initial rotor speed: Speed of the rotor at the start of the simulation. The default value is 0 rpm.

Ports

The block has the following ports:

+: Positive electrical input.
-: Negative electrical input.
C: Mechanical rotational conserving port.
R: Mechanical rotational conserving port.

References

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