In electromechanics, there are many drives that operate with constant loads without changing the speed of rotation. They are used in industrial and household equipment such as fans, compressors and others. If the nominal characteristics are unknown, then the motor power formula is used for calculations. Parameter calculations are especially relevant for new and little known drives. The calculation is performed using special coefficients, as well as on the basis of accumulated experience with similar mechanisms. The data is essential for the correct operation of electrical installations.
What is an electric motor?
An electric motor is a device that converts electrical energy into mechanical energy. The operation of most units depends on the interaction of the magneticfields with the rotor winding, which is expressed in its rotation. They operate from DC or AC power sources. The power supply can be a battery, an inverter, or a power outlet. In some cases, the engine works in reverse, that is, it converts mechanical energy into electrical energy. Such installations are widely used in power plants powered by air or water flow.
Electric motors are classified according to the type of power source, internal design, application and power. Also, AC drives may have special brushes. They operate on single-phase, two-phase or three-phase voltage, are air or liquid cooled. AC motor power formula
P=U x I, where P is power, U is voltage, I is current.
General purpose drives with their size and characteristics are used in industry. The largest engines with a capacity of more than 100 megawatts are used in the power plants of ships, compressor and pumping stations. Smaller sizes are used in household appliances like a vacuum cleaner or fan.
Electric motor design
Drive includes:
- Rotor.
- Stator.
- Bearings.
- Air gap.
- Winding.
- Switch.
Rotor is the only moving part of the drive that rotates around its own axis. Current passing through conductorsforms an inductive disturbance in the winding. The generated magnetic field interacts with the permanent magnets of the stator, which sets the shaft in motion. They are calculated according to the formula for the power of the electric motor by current, for which the efficiency and power factor are taken, including all the dynamic characteristics of the shaft.
Bearings are located on the rotor shaft and contribute to its rotation around its axis. The outer part they are attached to the engine housing. The shaft passes through them and out. Since the load goes beyond the working area of the bearings, it is called overhanging.
The stator is a fixed element of the electromagnetic circuit of the engine. May include winding or permanent magnets. The stator core is made of thin metal plates, which are called the armature package. It is designed to reduce energy loss, which often happens with solid rods.
Air gap is the distance between the rotor and the stator. A small gap is effective, as it affects the low coefficient of operation of the electric motor. The magnetizing current increases with the gap size. Therefore, they always try to make it minimal, but to reasonable limits. Too small a distance causes friction and loosening of the locking elements.
The winding consists of copper wire assembled into one coil. Usually laid around a soft magnetized core, consisting of several layers of metal. The perturbation of the induction field occurs at the momentcurrent passing through the winding wires. At this point, the unit enters explicit and implicit pole configuration mode. In the first case, the magnetic field of the installation creates a winding around the pole piece. In the second case, the slots of the rotor pole piece are dispersed in the distributed field. The shielded pole motor has a winding that suppresses magnetic disturbance.
The switch is used to switch the input voltage. It consists of contact rings located on the shaft and isolated from each other. The armature current is applied to the contact brushes of the rotary commutator, which leads to a change in polarity and causes the rotor to rotate from pole to pole. If there is no voltage, the motor stops spinning. Modern machines are equipped with additional electronics that control the rotation process.
Operation principle
According to the law of Archimedes, the current in the conductor creates a magnetic field in which the force F1 acts. If a metal frame is made from this conductor and placed in the field at an angle of 90°, then the edges will experience forces directed in the opposite direction relative to each other. They create a torque about the axis, which begins to rotate it. Armature coils provide constant torsion. The field is created by electric or permanent magnets. The first option is made in the form of a coil winding on a steel core. Thus, the loop current generates an induction field in the electromagnet winding, which generates an electromotiveforce.
Let's consider in more detail the operation of asynchronous motors using the example of installations with a phase rotor. Such machines operate on alternating current with an armature speed that is not equal to the pulsation of the magnetic field. Therefore, they are also called inductive. The rotor is driven by the interaction of the electric current in the coils with the magnetic field.
When there is no voltage in the auxiliary winding, the device is at rest. As soon as an electric current appears on the stator contacts, a magnetic field constant in space is formed with a ripple of + F and -F. It can be represented as the following formula:
pr=nrev=f1 × 60 ÷ p=n1
where:
pr - the number of revolutions that the magnetic field makes in the forward direction, rpm;
rev - number of turns of the field in the opposite direction, rpm;
f1 - electric current ripple frequency, Hz;
p - number of poles;
1 - total RPM.
Experiencing magnetic field pulsations, the rotor receives initial motion. Due to the non-uniform impact of the flow, it will develop a torque. According to the law of induction, an electromotive force is formed in a short-circuited winding, which generates a current. Its frequency is proportional to the slip of the rotor. Due to the interaction of electric current with a magnetic field, a shaft torque is created.
There are three formulas for performance calculationspower of an asynchronous electric motor. By phase shift use
S=P ÷ cos (alpha), where:
S is the apparent power measured in Volt-Amps.
P - active power in Watts.
alpha - phase shift.
Full power refers to the real indicator, and active power is the calculated one.
Types of electric motors
According to the power source, drives are divided into those operating from:
- DC.
- AC.
According to the principle of operation, they, in turn, are divided into:
- Collector.
- Valve.
- Asynchronous.
- Synchronous.
Vent motors do not belong to a separate class, since their device is a variation of the collector drive. Their design includes an electronic converter and a rotor position sensor. Usually they are integrated together with the control board. At their expense, coordinated switching of the armature occurs.
Synchronous and asynchronous motors run exclusively on alternating current. The rotation is controlled by sophisticated electronics. Asynchronous are divided into:
- Three-phase.
- Two-phase.
- Single-phase.
Theoretical formula for the power of a three-phase electric motor when connected to a star or a delta
P=3Uf If cos(alpha).
However, for linear voltage and current it looks like this
P=1, 73 × Uf × If × cos(alpha).
This will be a real indicator of how much powerthe engine picks up from the network.
Synchronous subdivided into:
- Step.
- Hybrid.
- Inductor.
- Hysteresis.
- Reactive.
Stepper motors have permanent magnets in their design, so they are not classified as a separate category. The operation of the mechanisms is controlled using frequency converters. There are also universal motors that operate on AC and DC.
General characteristics of engines
All motors have common parameters that are used in the formula for determining the power of an electric motor. Based on them, you can calculate the properties of the machine. In different literature, they may be called differently, but they mean the same thing. The list of such parameters includes:
- Torque.
- Engine power.
- Efficiency.
- Rated number of revolutions.
- Moment of inertia of the rotor.
- Rated voltage.
- Electrical time constant.
The above parameters are necessary, first of all, to determine the efficiency of electrical installations powered by the mechanical force of motors. Calculated values give only an approximate idea of the actual characteristics of the product. However, these indicators are often used in the formula for the power of the electric motor. It is she who determines the effectiveness of machines.
Torque
This term has several synonyms: moment of force, engine moment, Torque, torque. All of them are used to denote one indicator, although from the point of view of physics, these concepts are not always identical.
In order to unify terminology, standards have been developed that bring everything to a single system. Therefore, in technical documentation, the phrase "torque" is always used. It is a vector physical quantity, which is equal to the product of the vector values of force and radius. The radius vector is drawn from the axis of rotation to the point of applied force. From a physics point of view, the difference between torque and rotational moment lies in the point of application of the force. In the first case, this is an internal effort, in the second - an external one. The value is measured in newton meters. However, the motor power formula uses torque as the base value.
It is calculated as
M=F × r where:
M - torque, Nm;
F - applied force, H;
r - radius, m.
To calculate the rated torque of the actuator, use the formula
Mnom=30Rnom ÷ pi × nnom, where:
Rnom - rated power of the electric motor, W;
nnom - nominal speed, min-1.
Accordingly, the formula for the rated power of the electric motor should look like this:
Pnom=Mnom pinnom / 30.
Usually, all characteristics are indicated in the specification. But it happens that you have to work with completely new installations,information about which is very difficult to find. To calculate the technical parameters of such devices, the data of their analogues are taken. Also, only the nominal characteristics are always known, which are given in the specification. Real data must be calculated by yourself.
Engine power
In a general sense, this parameter is a scalar physical quantity, which is expressed in the rate of consumption or transformation of the energy of the system. It shows how much work the mechanism will perform in a certain unit of time. In electrical engineering, the characteristic displays the useful mechanical power on the central shaft. To indicate the indicator, the letter P or W is used. The main unit of measurement is Watt. The general formula for calculating the power of an electric motor can be represented as:
P=dA ÷ dt where:
A - mechanical (useful) work (energy), J;
t - elapsed time, sec.
Mechanical work is also a scalar physical quantity, expressed by the action of a force on an object, and depending on the direction and displacement of this object. It is the product of the force vector and the path:
dA=F × ds where:
s - distance traveled, m.
It expresses the distance that a point of applied force will overcome. For rotational movements, it is expressed as:
ds=r × d(teta), where:
teta - rotation angle, rad.
This way you can calculate the angular frequency of rotation of the rotor:
omega=d(teta) ÷ dt.
From it follows the formula for the power of the electric motor on the shaft: P \u003d M ×omega.
Efficiency of electric motor
Efficiency is a characteristic that reflects the efficiency of the system when converting energy into mechanical energy. It is expressed as the ratio of useful energy to spent energy. According to the unified system of units of measurement, it is designated as "eta" and is a dimensionless value, calculated as a percentage. The formula for the efficiency of an electric motor in terms of power:
eta=P2 ÷ P1 where:
P1 - electrical (supply) power, W;
P2 - useful (mechanical) power, W;
It can also be expressed as:
eta=A ÷ Q × 100%, where:
A - useful work, J;
Q - energy expended, J.
More often the coefficient is calculated using the formula for the power consumption of an electric motor, since these indicators are always easier to measure.
The decrease in the efficiency of the electric motor is due to:
- Electrical losses. This occurs as a result of the heating of the conductors from the passage of current through them.
- Magnetic loss. Due to excessive magnetization of the core, hysteresis and eddy currents appear, which is important to take into account in the motor power formula.
- Mechanical loss. They are related to friction and ventilation.
- Additional losses. They appear due to the harmonics of the magnetic field, since the stator and rotor are toothed. Also in the winding there are higher harmonics of the magnetomotive force.
It should be noted that efficiency is one of the most important componentsformulas for calculating the power of an electric motor, as it allows you to get numbers that are closest to reality. On average, this figure varies from 10% to 99%. It depends on the design of the mechanism.
Rated number of revolutions
Another key indicator of the electromechanical characteristics of the engine is the shaft speed. It is expressed in revolutions per minute. Often it is used in the pump motor power formula to find out its performance. But it must be remembered that the indicator is always different for idling and working under load. The indicator represents a physical value equal to the number of full revolutions for a certain period of time.
RPM calculation formula:
n=30 × omega ÷ pi where:
n - engine speed, rpm.
In order to find the power of the electric motor by the formula for the speed of the shaft, it is necessary to bring it to the calculation of the angular velocity. So P=M × omega would look like this:
P=M × (2pi × n ÷ 60)=M × (n ÷ 9, 55) where
t=60 seconds.
Moment of inertia
This indicator is a scalar physical quantity that reflects a measure of the inertia of the rotational movement around its own axis. In this case, the mass of the body is the value of its inertia during translational motion. The main characteristic of the parameter is expressed by the distribution of body masses, which is equal to the sum of the products of the square of the distance from the axis to the base point and the masses of the object. In the International System of Unitsmeasurement it is denoted as kg m2 and has is calculated by the formula:
J=∑ r2 × dm where
J - moment of inertia, kg m2;
m - mass of the object, kg.
Moments of inertia and forces are related by the relation:
M - J × epsilon, where
epsilon - angular acceleration, s-2.
The indicator is calculated as:
epsilon=d(omega) × dt.
Thus, knowing the mass and radius of the rotor, you can calculate the performance parameters of mechanisms. The motor power formula includes all of these characteristics.
Rated voltage
It is also called nominal. It represents the base voltage, represented by a standard set of voltages, which is determined by the degree of insulation of electrical equipment and the network. In reality, it may differ at different points of the equipment, but should not exceed the maximum permissible operating conditions, designed for continuous operation of the mechanisms.
For conventional installations, rated voltage is understood as the calculated values for which they are provided by the developer in normal operation. The list of standard network voltage is provided in GOST. These parameters are always described in the technical specifications of the mechanisms. To calculate the performance, use the formula for the power of the electric motor by current:
P=U × I.
Electrical time constant
Represents the time required to reach the current level up to 63% after energizing thedrive windings. The parameter is due to transient processes of electromechanical characteristics, since they are fleeting due to the large active resistance. The general formula for calculating the time constant is:
te=L ÷ R.
However, the electromechanical time constant tm is always greater than the electromagnetic time constant te. the rotor accelerates at zero speed to maximum idle speed. In this case, the equation takes the form
M=Mst + J × (d(omega) ÷ dt), where
Mst=0.
From here we get the formula:
M=J × (d(omega) ÷ dt).
In fact, the electromechanical time constant is calculated from the starting torque - Mp. A mechanism operating under ideal conditions with rectilinear characteristics will have the formula:
M=Mp × (1 - omega ÷ omega0), where
omega0 - idle speed.
Such calculations are used in the pump motor power formula when the piston stroke directly depends on the shaft speed.
Basic formulas for calculating engine power
To calculate the real characteristics of mechanisms, you always need to take into account many parameters. first of all, you need to know what current is supplied to the motor windings: direct or alternating. The principle of their work is different, therefore, the calculation method is different. If the simplified view of the drive power calculation looks like this:
Pel=U × I where
I - current strength, A;
U - voltage, V;
Pel - supplied electric power. Tue.
In the AC motor power formula, phase shift (alpha) must also be taken into account. Accordingly, the calculations for an asynchronous drive look like:
Pel=U × I × cos(alpha).
In addition to active (supply) power, there is also:
- S - reactive, VA. S=P ÷ cos(alpha).
- Q - full, VA. Q=I × U × sin(alpha).
The calculations also need to take into account thermal and inductive losses, as well as friction. Therefore, a simplified formula model for a DC motor looks like this:
Pel=Pmech + Rtep + Rind + Rtr, where
Рmeh - useful generated power, W;
Rtep - heat loss, W;
Rind - cost of charge in the induction coil, W;
RT - loss due to friction, W.
Conclusion
Electric motors are used in almost all areas of human life: in everyday life, in production. For the correct use of the drive, it is necessary to know not only its nominal characteristics, but also the real ones. This will increase its efficiency and reduce costs.
