What is the power of an electric motor and how to determine it: formulas and examples

An electric motor is an electromechanical device based on electromagnetism, which allows you to convert electrical energy, for example, into work or mechanical energy. This process is reversible and can be used to generate electricity. However, all of these electrical machines are reversible and can be a "motor" or "generator" in the four quadrants of the torque plane.

Early developments

In 1821, after the discovery of the phenomenon of the connection between electricity and magnetism, by the Danish chemist Oersted, Ampere's theorem and Biot-Savard's law, the English physicist Michael Faraday built two devices, which he called "electromagnetic rotation": the continuous circular motion of the magnetic force around the wire is an actual demonstration of the first electric motor.

In 1822, Peter Barlow built what could be considered the first electric motor in history: the Barlow Wheel. This device is a simple metal disc, cut into a star, and the ends of which are dipped into a cup containing mercury to provide a flowing stream. However, he creates only a force capable of turning it, preventing its practical use.

The first experimentally used switch was invented in 1832 by William Sturgeon. The first DC motor manufactured for commercial purposes was invented by Thomas Davenport in 1834 and patented in 1837. These motors did not experience any industrial development due to the high cost of batteries at the time.

DC motor

A switched DC apparatus has a set of rotating windings wound on an armature mounted on a rotating shaft. The shaft also has a commutator, a permanent rotary electrical switch that periodically changes the current flow in the rotor windings as the shaft rotates. Thus, each DC bridge motor has an alternating current flowing through the rotating windings. The current flows through one or more pairs of brushes carried on the switch; the brushes connect the external power source to the rotating armature.

A rotating armature consists of one or more coils of wire wound around a laminated ferromagnetic core. The current from the brush flows through the commutator and one armature winding, making it a temporary magnet (electromagnet). The magnetic field generated by the armature interacts with the stationary magnetic field generated by either the PM or another winding (field coil) as part of the motor frame.

The force between the two magnetic fields tends to rotate the motor shaft. The switch switches power to the coils as the rotor turns, keeping the magnetic poles from ever completely aligning with magnetic poles of the stator field, so that the rotor never stops (like a compass needle), but rather rotates while it is nutrition.

While most switches are cylindrical, some are flat discs with multiple segments (usually at least three) mounted on an insulator.

Larger brushes are desirable for a larger brush contact area to maximize motor power, but smaller brushes desirable for low masses in order to maximize the speed at which the engine can operate without excessive rebound and sparking brushes. Stiffer brush springs can also be used to generate brushes of a given mass at a higher speed, but at the expense of higher frictional losses and wear on the accelerated brush and commutator. Therefore, the design of the DC motor involves a trade-off between power output, speed and efficiency / wear.

Design of DC motors:

• The armature circuit is a winding, it carries the load current, which can be a stationary or rotating part of the engine or generator.
• A field circuit is a set of windings that create a magnetic field so that electromagnetic induction can exist in electrical machines.
• Commutation. A mechanical technique in which rectification can be achieved, or where a direct current can be obtained.

There are four main types of DC motors:

1. Shunt-wound electric motor.
2. DC motor.
3. Combined engine.
4. PM engine.

Basic calculation indicators

How to find out the power of an electric motor in the article will be shown later, using an example with initial data.

A good science project doesn't stop at designing a power apparatus. It is very important to calculate the power of the electric motor and the various electrical and mechanical parameters. your device and calculate the formula for the power of the electric motor using unknown values ​​and useful formulas.

We will use the International System of Units (SI) to calculate the motor. This is the modern metric system, officially adopted in electrical engineering.

One of the most important laws of physics is Ohm's fundamental law. He states that the current through a conductor is directly proportional to the applied voltage and is expressed as:

I = V / R

where I is the current, in amperes (A);

V is the applied voltage, in volts (V);

R is the resistance, in ohms (Ω).

This formula can be used in many situations. You can calculate the resistance of your motor by measuring the current draw and the applied voltage. For any given resistance (in motors this is basically the coil resistance), this formula explains that the current can be controlled by the applied voltage.

The consumed electric power of the engine is determined by the following formula:

Pin = I * V

where Pin is the input power, measured in watts (W);

I is the current measured in amperes (A);

V is the applied voltage, measured in volts (V).

How to find out the output power

The motors are supposed to do some work, and there are two important values ​​that determine how powerful it is. This is the speed and force of rotation of the engine. The mechanical output of the motor can be calculated using the following formula:

Pout = τ * ω

where Pout is the output power, measured in watts (W);

τ is the moment of force, measured in Newton meters (N • m);

ω is the angular velocity, measured in radians per second (rad / s).

It is easy to calculate the angular velocity if you know the engine speed in rpm:

ω = rpm * 2 * P / 60

where ω is the angular velocity (rad / s);

rpm - rotation speed in revolutions per minute;

П - mathematical constant (3.14);

60 is the number of seconds in a minute.

If the motor is 100% efficient, all electrical energy is converted to mechanical energy. However, such engines do not exist. Even precision small industrial motors have a maximum efficiency of 50-60%.

Measuring the torque of a motor is challenging. This requires special expensive equipment. But it is possible to do it yourself with special information and formulas.

Mechanical efficiency indicators

Motor efficiency is calculated as mechanical output divided by electrical input:

E = Pout / Pin

hence,

Pout = Pin * E

after substitution we get:

T * ω = I * V * E

T * rpm * 2 * P / 60 = I * V * E

and the formula for calculating the moment of force will be:

T = (I * V * E * 60) / (rpm * 2 * P)

To determine the power of the motor, it is necessary to connect it to the load to generate a torque. Measure current, voltage and rpm. Now you can calculate the moment of force for this load at this speed, assuming you know the efficiency of the motor.

The estimated 15 percent efficiency represents the maximum engine efficiency that occurs only at a specific speed. The efficiency can be anything between zero and maximum; in our example below 1000 rpm there may be a suboptimal speed, so for calculations you can use 10% efficiency (E = 0.1).

Example: speed 1000 rpm, voltage 6 V, and current 220 mA (0.22 A):

T = (0.22 * 6 * 0.1 * 60) / (1000 * 2 * 3.14) = 0.00126 N • m

As a result, it is usually expressed in millinewtons times meters (mN • m). 1000 mN • m to 1 N • m, so the calculated torque is 1.26 mN • m. It could be further converted to (g-cm) by multiplying the result by 10.2, and. e. The torque is 12.86 g-cm.

In our example, the motor input power is 0.22 A x 6 V = 1.32 W, the mechanical output power is 1000 rpm x 2 x 3.14 x 0.00126 N • m / 60 = 0.132 W.

The torque of the motor changes with speed. No load maximum speed and zero torque. The load adds mechanical resistance. The motor starts to draw more current to overcome this resistance and the speed decreases. When this happens, the moment of force is at its maximum.

How accurate the calculation of the torque is is determined as follows. While voltage, current, and speed can be measured accurately, the efficiency of the motor may not be correct. It depends on the accuracy of your assembly, sensor position, friction, alignment of motors and generator axles, etc.

Speed, torque, power and efficiency are not constant values. Usually the manufacturer provides the following data in special tables.

Linear motors

A linear motor is essentially an induction motor, the rotor of which "unrolls" so that instead of creating rotational force by a rotating electromagnetic field, it creates a linear force along its length by setting an electromagnetic offset fields.

Acoustic noise

Acoustic noise and vibration Electric motors usually arise from three sources:

• mechanical sources (for example, from bearings);
• aerodynamic sources (for example, thanks to the fans mounted on the shaft);
• magnetic sources (for example, due to magnetic forces such as Maxwell forces and magnetostriction acting on the stator and rotor structures).

The last source that can be responsible for motor noise is called electrically excited acoustic noise.