Universal Motor

Universal (or series) motor with electrical and torque characteristics

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• Simscape / Electrical / Electromechanical / Brushed Motors

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Description

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

Where:

• R_a is the armature resistance.

• L_a is the armature inductance.

• R_f is the field winding resistance.

• L_f is the field winding inductance.

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:

1. The magnetic field in the motor induces the following back emf v_b in the armature:

   $$v_b=L_{af}{i}_f\omega$$

   where L_af is a constant of proportionality and ω is the angular velocity.

2. The mechanical power is equal to the power reacted by the back emf:

   $$P=v_b{i}_f=L_{af}{i}_f{}^2\omega$$

3. 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:

1. For the steady-state torque-speed relationship when using a DC supply, L has no effect.

2. Sum the voltages around the loop:

   $$V=(R_f+R_a)i_f+v_b=(R_f+R_a+L_{af}\omega )i_f$$

3. Solve the preceding equation for i_f and substitute this value into the equation for torque:

   $$T=L_{af}{\left(\frac{V}{R_f+R_a+L_{af}\omega }\right)}^2$$

   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_f+R_a and 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 L_f in the model. This requires information about the RMS rated current and voltage for the total inductance.

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.

Thermal 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.

Ports

Conserving

+ — Positive terminal

electrical

Electrical conserving port associated with the universal motor positive terminal.

- — Negative terminal

electrical

Electrical conserving port associated with the universal motor negative terminal.

C — Motor case

mechanical

Mechanical rotational conserving port associated with the universal motor case.

R — Motor rotor

mechanical

Mechanical rotational conserving port associated with the universal motor rotor.

Hf — Field winding thermal port

thermal

Field winding thermal port. For more information, see Thermal Ports.

Ha — Armature winding thermal port

thermal

Armature winding thermal port. For more information, see Thermal Ports.

Parameters

Electrical Torque

Model parameterization — Block parameterization

By DC rated power, rated speed & maximum torque (default) | By equivalent circuit parameters | By DC rated power, rated speed & electrical power | By AC rated power, rated speed, current & electrical power

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 DC rated power, rated speed & maximum torque — Provide DC power and speed parameters that the block converts to an equivalent circuit model of the motor.

• By DC rated power, rated speed & electrical power — Provide AC power and speed parameters that the block converts to an equivalent circuit model of the motor.

• By AC rated power, rated speed, current & electrical power — Provide AC power and speed parameters that the block converts to an equivalent circuit model of the motor.

Total armature and field winding resistance — Total resistance of the armature and field winding

132.8 Ohm (default)

Total resistance of the armature and 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

0.1722 s*V/rad/A (default)

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

Dependencies

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

Total armature and field winding inductance — Total armature and field winding inductance

0.525 H (default)

Total inductance of the armature and field winding. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number.

Note

You can set the Total armature and field winding inductance value to zero, but this only makes sense if you are driving the motor with a DC source.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By equivalent circuit parameters, By DC rated power, rated speed & maximum torque, or By DC rated power, rated speed & electrical power.

Rated speed (at rated load) — Rated speed

6500 rpm (default)

Motor speed at the rated mechanical load.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By DC rated power, rated speed & maximum torque, By DC rated power, rated speed & electrical power, or By AC rated power, rated speed, current & electrical power.

Rated load (mechanical power) — Rated load

75 W (default)

The mechanical load for which the motor is rated to operate.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By DC rated power, rated speed & maximum torque, By DC rated power, rated speed & electrical power, or By AC rated power, rated speed, current & electrical power.

Rated DC supply voltage — Rated DC supply voltage

200 V (default)

The DC voltage at which the motor is rated to operate.

Dependencies

This parameter is visible only 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.

Maximum (starting) torque — Maximum torque

0.39 N*m (default)

Maximum torque the motor produces.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By DC rated power, rated speed & maximum torque.

Electrical power in at rated load — Electrical power at the rated mechanical power

160 W (default)

The amount of electrical power the motor uses at the rated mechanical power.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By DC rated power, rated speed & electrical power or By AC rated power, rated speed, current & electrical power.

RMS rated voltage — RMS rated voltage

240 V (default)

RMS supply voltage when the motor operates on AC power.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By AC rated power, rated speed, current & electrical power.

RMS current at rated load — RMS current at rated load

0.8 A (default)

RMS current when the motor operates on AC power at the rated load.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By AC rated power, rated speed, current & electrical power.

AC frequency — AC frequency

50 Hz (default)

Frequency of the AC supply voltage.

Dependencies

This parameter is visible only when you set the Model parameterization parameter to By AC rated power, rated speed, current & electrical power.

Mechanical

Rotor inertia — Rotor inertia

2e-4 kg*m^2 (default)

Resistance of the rotor to change in motor motion. The value can be zero.

Rotor damping — Rotor dissipated energy

1e-6 N*m/(rad/s) (default)

Energy dissipated by the rotor. The value can be zero.

Initial rotor speed — Initial rotor speed

0 rpm (default)

Speed of the rotor at the start of the simulation.

Temperature Dependence

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

Field to armature resistance ratio, Rf/Ra — Stator and rotor resistance temperature coefficients

1 (default)

The ratio of the field to the armature resistance. This parameter is required only when showing the field and armature thermal ports. It is used to determine individual resistance values for the field and armature windings so that the thermal heat generated by the two resistors can be apportioned correctly.

Resistance temperature coefficients, [alpha_f alpha_a] — Stator and rotor resistance temperature coefficients

[.00393, .00393] 1/K (default)

A 1 by 2 row vector that defines the coefficient α in the equation relating resistance to temperature, as described in Thermal Model for Actuator Blocks. The first element corresponds to the field winding, and the second to the armature. The default value is for copper.

Measurement temperature — Measurement temperature

25 C (default)

The temperature for which motor parameters are defined.

Thermal Port

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

Thermal masses, [Mf Ma] — Thermal masses

[100, 100] J/K (default)

A 1 by 2 row vector that defines the thermal mass for the field and armature windings. The thermal mass is the energy required to raise the temperature by one degree.

Initial temperatures — Initial temperatures

[25, 25] C (default)

A 1 by 2 row vector that defines the temperature of the field and armature thermal ports at the start of simulation.

Model 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, select Variant->Override using and then the desired motor. All motors have been sized for roughly the same mechanical power rating.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.