SimElectronics™

DC Motor - Model electrical and torque characteristics of DC motor

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Actuators & Drivers

Description

The DC Motor block represents the electrical and torque characteristics of a DC motor using the following equivalent circuit model:

You specify the equivalent circuit parameters for this model when you set the Model parameterization parameter to By equivalent circuit parameters. The resistor R corresponds to the resistance you specify in the Armature resistance parameter. The inductor L corresponds to the inductance you specify in the Armature inductance parameter. The permanent magnets in the motor induce the following back emf v_b in the armature:

where k_v is the Back-emf constant and ω is the angular velocity. The motor produces the following torque, which is proportional to the motor current i:

where k_t is the Torque constant. The DC Motor block assumes that there are no electromagnetic losses. This means that mechanical power is equal to the electrical power dissipated by the back emf in the armature. Equating these two terms gives:

As a result, you specify either k_v or k_t in the block dialog box.

The torque-speed characteristic for the DC Motor block is related to the parameters in the preceding figure. When you set the Model parameterization parameter to By stall torque & no-load speed or 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 and rearrange for i:
Substitute this value of i into the equation for torque:

When you set the Model parameterization parameter to By stall torque & no-load speed, the block uses the preceding equation to determine values for R and k_t (and equivalently k_v).
When you set the Model parameterization parameter to By rated power, rated speed & no-load speed, the block uses the rated speed and power to calculate the rated torque. The block uses the rated torque and no-load speed values in the preceding equation to determine values for R and k_t.

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

When a positive current flows from the electrical + to - ports, a positive torque acts 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 stall torque & no-load speed — Provide torque and speed parameters that the block converts to 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

Resistance of the conducting portion of the motor. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter. The default value is 3.9 Ω.

Armature inductance

Inductance of the conducting portion of the motor. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. The default value is 1.2e-05 H.

Define back-emf or torque constant

Indicate whether you will specify the motor's back-emf constant or torque constant. When you specify them in SI units, these constants have the same value, so you only specify one or the other in the block dialog box. This parameter is only visible when you select By equivalent circuit parameters for the Model parameterization parameter. The default value is Specify back-emf constant.

Back-emf constant

The ratio of the voltage generated by the motor to the speed at which the motor is spinning. The default value is 7.2e-05 V/rpm. This parameter is only visible when you select Specify back-emf constant for the Define back-emf or torque constant parameter.

Torque constant

The ratio of the torque generated by the motor to the current delivered to it. This parameter is only visible when you select Specify torque constant for the Define back-emf or torque constant parameter. The default value is 6.876e-04 N*m/A.

Stall torque

The amount of torque generated by the motor when the speed is approximately zero. This parameter is only visible when you select By stall torque & no-load speed for the Model parameterization parameter. The default value is 2.4e-04 N*m.

No-load speed

Speed of the motor when not driving a load. This parameter is only visible when you select By stall torque & no-load speed or By rated power, rated speed & no-load speed for the Model parameterization parameter. The default value is 1.91e+04 rpm.

Rated speed (at rated load)

Motor speed at the rated mechanical power level. 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 1.5e+04 rpm.

Rated load (mechanical power)

The mechanical power the motor is designed to deliver at the rated speed. 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 0.08 W.

Rated DC supply voltage

The voltage at which the motor is rated to operate. This parameter is only visible when you select By stall torque & no-load speed or By rated power, rated speed & no-load speed for the Model parameterization parameter. The default value is 1.5 V.

Mechanical Tab

Rotor inertia: Resistance of the rotor to change in motor motion. The default value is 0.01 g*cm². The value can be zero.
Rotor damping: Energy dissipated by the rotor. The default value is 1e-08 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.

Examples

See the following demos:

References

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