Often it is necessary to reduce the speed of rotation of the engine that performs certain tasks in the mechanism. Reducing the number of revolutions of the electric motor can be achieved with the help of standard-manufactured control circuits.
Electric motors alternating current often used in human activities, on metalworking machines, transport, crane mechanisms and other equipment. The motors convert the energy of the alternating current supply into the rotation of the shaft and units. Mainly AC asynchronous motors are used.
The rotor, as well as the stator of the motor, consist of coils of wire laid in a core made of special steel. The classification of electric motors follows from the method of laying the winding.
A winding of brass and copper rods is inserted into the core, rings are installed along the edges. Such a coil of wire is called a squirrel-cage (CS) rotor. Small power motors have rods as well as disks that have been cast together. For electric motors with powerful moment parts are cast separately, then welded. The stator winding can be connected in two ways: delta, star.
The phase rotor consists of a 3-phase rotor winding connected slip rings and brushes for food. The winding is connected by a "star".
Calculation of the number of revolutions of an induction motor
A common engine on machine tools and lifting devices is a squirrel-cage motor, so the calculation example should be taken for it. Mains voltage is supplied to stator winding. The windings are offset from each other by 120 degrees. The emerging field of electromagnetic induction excites an electric current in the winding. The rotor begins to work under the influence of EMC.
The main characteristic of the engine is the number of revolutions per minute. Let's calculate this value:
n = 60 f/p, rpm;
where f is the network frequency, hertz, p is the number of stator poles (in pairs).
There is a rating plate on the motor housing. If it is not there, then you can calculate the number of revolutions of the equipment shaft yourself using other available data. The calculation is made in three ways.
- The calculation of the number of coils, which is compared with the norms for different voltages, follows from the table:
- Calculation of the speed of work by the step of the winding diameter according to the formula:
2 p \u003d Z 1 / y, where 2p is the number of poles, Z 1 is the number of slots in the stator, y is the winding pitch.
We select the appropriate engine speed from the table:
- We calculate the number of poles according to the parameters of the core using the formula:
2p = 0.35 Z 1 b / h or 2 p = 0.5 D i / h,
where 2p is the number of poles, Z 1 is the number of grooves, b is the size of the tooth, cm, h is the height of the back, cm, D i is the diameter of the teeth, cm.
According to the results of calculation and induction, the number of turns of the winding follows, and is compared with the values of the motor according to the passport.
How to change the engine speed?
You can change the speed of the torque of the equipment mechanism different ways, for example, mechanical gearboxes with gear shifting, clutches and other devices. But this is not always possible. In practice, 7 methods are used to correct the speed of variable speed drives. All methods are divided into two main areas.
- Correction magnetic field by influencing the frequency of the current, reducing or increasing the number of pole pairs, voltage correction. The direction is characteristic of motors with a squirrel-cage (KR) rotor.
- The slip is corrected by the supply voltage, by adding another resistor to the rotor circuit, by setting up a dual supply, by using a cascade of valves. This direction is used for rotors with phases.
- Chastotniki come with two types of control: scalar, vector. With scalar control, the device operates at certain values of the output potential difference and frequency, they work in primitive home appliances, such as fans. With vector control, the current strength is set quite accurately.
- When choosing a device, power parameters play a decisive role. The amount of power expands the scope of use, simplifies maintenance.
- When choosing a device, the operating voltage interval of the network is taken into account, which reduces the risk of its failure due to sudden changes potential differences. If the voltage is too high, the network capacitors may explode.
- Frequency is an important factor. Its value is determined by the requirements of production. The lowest value indicates the possibility of using the speed in optimal mode work. To obtain a larger frequency interval, frequency converters with vector control are used. In reality, inverters with a frequency interval of 10 to 10 Hz are often used.
- A frequency converter that has many different outputs and inputs is convenient to use, but its cost is higher, and the setting is more difficult. There are three types of chastotnik connectors: analog, discrete, digital. Communication of the reverse type of input commands is made through analog connectors. Digital terminals input signals from digital type sensors.
- When choosing a model of a frequency converter, it is necessary to evaluate control bus. Its characteristic is selected for the inverter circuit, which determines the number of pads. best choice the chastotnik works with a reserve of the number of connectors for further modernization of the device.
- Frequency converters that can withstand large overloads (15% higher than the motor power) have preferences when choosing. In order not to make a mistake when buying a frequency converter, read the instructions. It contains the main operating parameters of the equipment. If you need a device for maximum loads, then it is necessary to choose a frequency converter that keeps the current at the peak of operation higher than 10% of the nominal value.
How to connect a frequency converter
If the cable for connecting to 220 V is with the 1st phase, the "triangle" scheme is used. Do not connect a frequency converter if the output current is higher than 50% of the nominal value.
If the power cable is three-phase 380 V, then a “star” circuit is made. To make it easier to connect the power, contacts and terminals with letter designations are provided.
- Contacts R, S, T are designed to connect the power supply in phases.
- Terminals U , V , W serve as the motor connection. To reverse, it is enough to change the connection of two wires to each other.
The device must have a block with a terminal for connecting to ground. More details on how to connect.
How to maintain frequency converters?
For long-term operation of the inverter, it is necessary to monitor its condition and comply with the requirements:
- Clean from dust internal elements. You can use a compressor to remove dust compressed air. The vacuum cleaner is not suitable for this purpose.
- Periodically check the condition of the nodes, replace them. The service life of electrolytic capacitors is five years, fuse links ten years. Cooling fans run for 3 years before replacement. Loops of wires are used for six years.
- Bus voltage monitoring direct current and the temperature of the mechanisms is necessary action. At elevated temperature The thermal paste dries out and destroys the capacitors. Every 3 years, a layer of conductive paste is applied to the power terminals.
- The conditions and mode of operation must be observed in strict accordance. Temperature environment should not exceed 40 degrees. Dust and humidity adversely affect the condition of the working elements of the device.
Payback of the frequency converter
Electricity is constantly becoming more expensive, heads of organizations are forced to save different ways. In industrial production, most of the energy is consumed by mechanisms that have electric motors.
Manufacturers of devices for electrical machines and units offer special devices and devices for controlling electric motors. Such devices save energy electric current. They are called inverters or frequency converters.
The financial costs of buying a chastotnik do not always justify the savings, since their cost is comparable to the cost. Not always the mechanism drive can be quickly equipped with an inverter. What difficulties arise in this case? Let's look at ways to start induction motors to understand the advantages of inverters.
Engine starting methods
It is possible to define 4 methods for starting motors.
- Direct switching, for motors up to 10 kW. The method is ineffective for acceleration, increasing torque, overloads. Currents are 7 times higher than the nominal value.
- Switching on with a choice of "triangle" and "star" schemes.
- Integration of a soft starter.
- Inverter application. The method is especially effective for motor protection, acceleration, torque, energy saving.
Economic justification for the effect of the inverter
The payback time of an inverter is calculated by the ratio of purchase costs to energy savings. Savings are typically between 20% and 40% of the rated motor power.
Costs reduce factors that increase the performance of frequency converters:
- Reduced maintenance costs.
- Increasing engine life.
Savings calculated:
where E - saving money in rubles;
Ppch - inverter power;
H - hours of operation per day;
D is the number of days;
K is the coefficient of the expected percentage of savings;
T is the energy tariff in rubles.
The payback time is equal to the ratio of the cost of buying an inverter to saving money. Calculations show that the payback period is from 3 months to 3 years. It depends on the power of the motor.
Since the linear speed uniformly changes direction, then the movement along the circle cannot be called uniform, it is uniformly accelerated.
Angular velocity
Pick a point on the circle 1 . Let's build a radius. For a unit of time, the point will move to the point 2 . In this case, the radius describes the angle. The angular velocity is numerically equal to the angle of rotation of the radius per unit time.
Period and frequency
Rotation period T is the time it takes the body to make one revolution.
RPM is the number of revolutions per second.
The frequency and period are related by the relationship
Relationship with angular velocity
Line speed
Each point on the circle moves at some speed. This speed is called linear. The direction of the linear velocity vector always coincides with the tangent to the circle. For example, sparks from under a grinder move, repeating the direction of instantaneous speed.
Consider a point on a circle that makes one revolution, the time that is spent - this is the period T. The path traveled by a point is the circumference of a circle.
centripetal acceleration
When moving along a circle, the acceleration vector is always perpendicular to the velocity vector, directed to the center of the circle.
Using the previous formulas, we can derive the following relations
Points lying on the same straight line emanating from the center of the circle (for example, these can be points that lie on the wheel spoke) will have the same angular velocities, period and frequency. That is, they will rotate in the same way, but with different linear speeds. The farther the point is from the center, the faster it will move.
The law of addition of velocities is also valid for rotational motion. If the motion of a body or frame of reference is not uniform, then the law applies to instantaneous velocities. For example, the speed of a person walking along the edge of a rotating carousel is equal to the vector sum of the linear speed of rotation of the edge of the carousel and the speed of the person.
The Earth participates in two main rotational movements: daily (around its axis) and orbital (around the Sun). The period of rotation of the Earth around the Sun is 1 year or 365 days. The Earth rotates around its axis from west to east, the period of this rotation is 1 day or 24 hours. Latitude is the angle between the plane of the equator and the direction from the center of the Earth to a point on its surface.
According to Newton's second law, the cause of any acceleration is a force. If a moving body experiences centripetal acceleration, then the nature of the forces that cause this acceleration may be different. For example, if a body moves in a circle on a rope tied to it, then active force is the elastic force.
If a body lying on a disk rotates along with the disk around its axis, then such a force is the force of friction. If the force ceases to act, then the body will continue to move in a straight line
Consider the movement of a point on a circle from A to B. The linear velocity is equal to v A And v B respectively. Acceleration is the change in speed per unit of time. Let's find the difference of vectors.
When buying an electric motor from your hands, you can’t count on the availability of technical documentation for it. Then the question arises of how to find out the number of revolutions of the purchased device. You can trust the words of the seller, but conscientiousness is not always their hallmark.
Then there is a problem with determining the number of revolutions. You can solve it by knowing some of the subtleties of the motor device. This will be discussed further.
Determine the turnover
There are several ways to measure motor speed. The most reliable is to use a tachometer - a device designed specifically for this purpose. However, not every person has such a device, especially if he does not professionally deal with electric motors. Therefore, there are several other options that allow you to cope with the task "by eye".
The first involves removing one of the engine covers in order to locate the winding coil. There may be several of the latter. The one that is more accessible and located in the visibility zone is selected. The main thing is to prevent violation of the integrity of the device during operation.
When the coil opened up, you need to carefully examine it and try to compare the size with the stator ring. The latter is a fixed element of the electric motor, and the rotor, being inside it, rotates.
When the ring is half closed by the coil, the number of revolutions per minute reaches 3000. If the third part of the ring is closed, the number of revolutions is approximately 1500. At a quarter, the number of revolutions is 1000.
The second way is connected with the windings inside the stator. The number of slots occupied by one section of any coil is considered. The grooves are located on the core, their number indicates the number of pairs of poles. 3000 rpm will be in the presence of two pairs of poles, with four - 1500 revolutions, with six - 1000.
The answer to the question of what the number of revolutions of the electric motor depends on will be the statement: on the number of pairs of poles, and this is an inversely proportional relationship.
On the body of any factory engine there is a metal tag on which all the characteristics are indicated. In practice, such a tag may be missing or erased, which slightly complicates the task of determining the number of revolutions.
We adjust the speed
Working with a variety of electrical tools and equipment at home or at work will certainly raise the question of how to regulate the speed of the electric motor. For example, it becomes necessary to change the speed of movement of parts in the machine or along the conveyor, adjust the performance of pumps, reduce or increase the air flow in ventilation systems.
It is almost pointless to carry out these procedures by lowering the voltage, the revolutions will drop sharply, and the power of the device will significantly decrease. Therefore, special devices are used to adjust the engine speed. Let's consider them in more detail.
Frequency converters act as reliable devices that can radically change the frequency of the current and the shape of the signal. They are based on semiconductor triodes (transistors) high power and a pulse modulator.
The microcontroller controls the entire process of the converter. Thanks to this approach, it becomes possible to achieve a smooth increase in engine speed, which is extremely important in mechanisms with a large load. Slow acceleration reduces loads, positively affecting the service life of industrial and household equipment.
All converters are equipped with protection having several degrees. Some models operate at the expense of a single-phase voltage of 220 V. The question arises whether it is possible to make three-phase motor rotated due to one phase? The answer will be positive if one condition is met.
When a single-phase voltage is applied to the winding, it is required to “push” the rotor, since it itself will not budge. This requires a start capacitor. After the engine starts rotating, the remaining windings will provide the missing voltage.
A significant disadvantage of such a scheme is a strong phase imbalance. However, it is easily compensated by the inclusion of an autotransformer in the circuit. All in all, it's pretty complex scheme. The advantage of the frequency converter is the ability to connect asynchronous type motors without the use of complex circuits.
What does the converter give?
The need to use an electric motor speed controller in the case of asynchronous models is as follows:
Significant energy savings are achieved. Since not all equipment requires high speeds rotation motor shaft, it makes sense to reduce it by a quarter.
Provided reliable protection all mechanisms. The frequency converter allows you to control not only the temperature, but also the pressure and other parameters of the system. This fact is especially important if a pump is driven by a motor.
The pressure sensor is installed in the tank, sends a signal when the proper level is reached, due to which the motor stops.
Is being done smooth start. The regulator eliminates the need for additional electronic devices. The frequency converter is easy to set up and get the desired effect.
Reduced costs for Maintenance, since the regulator minimizes the risk of damage to the drive and other mechanisms.
Thus, electric motors with a speed controller turn out to be reliable devices with a wide range of applications.
It is important to remember that the operation of any equipment based on an electric motor will only be correct and safe when the speed parameter is adequate to the conditions of use.
Photo of motor speed
Sometimes, in relation to cars, questions from mathematics and physics pop up. In particular, one of these issues is the angular velocity. It is related to both the operation of mechanisms and the passage of turns. Let's figure out how to determine this value, what it is measured in and what formulas should be used here.
How to determine the angular velocity: what is this value?
From a physical and mathematical point of view, this quantity can be defined as follows: these are data that show how fast a certain point rotates around the center of the circle along which it moves.
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This seemingly purely theoretical value is of considerable practical importance in the operation of the car. Here are just a few examples:
- It is necessary to correctly correlate the movements with which the wheels rotate when turning. The angular velocity of the wheel of a car moving along the inner part of the trajectory must be less than that of the outer one.
- It is required to calculate how fast the crankshaft rotates in the car.
- Finally, the car itself, passing a turn, also has a certain amount of movement parameters - and in practice, the stability of the car on the track and the likelihood of a rollover depend on them.
The formula for the time it takes for a point to rotate around a circle of a given radius
In order to calculate the angular velocity, the following formula is used:
ω = ∆φ /∆t
- ω (read "omega") - actually calculated value.
- ∆φ (pronounced “delta phi”) is the angle of rotation, the difference between the angular position of the point at the first and last moment of the measurement.
- ∆t
(read "delta te") - the time during which this very shift occurred. More precisely, since "delta" means the difference between the time values at the moment when the measurement was started and when it was finished.
The above formula for angular velocity applies only to common cases. Where we are talking about uniformly rotating objects or about the relationship between the movement of a point on the surface of a part, the radius and time of rotation, it is required to use other relationships and methods. In particular, the rotation frequency formula will already be needed here.
Angular velocity is measured in a variety of units. In theory, rad/s (radian per second) or degree per second is often used. However, this value means little in practice and can only be used in design work. In practice, it is more measured in revolutions per second (or minute, if we are talking about slow processes). In this regard, it is close to the frequency of rotation.
Angle of rotation and period of revolution
Much more common than angle of rotation is rotation frequency, which indicates how many revolutions an object makes in a given period of time. The fact is that the radian used for calculations is the angle in the circle when the length of the arc is equal to the radius. Accordingly, there are 2 π radians in the whole circle. The number π is irrational, and it cannot be reduced to either a decimal or a simple fraction. Therefore, in the event that a uniform rotation occurs, it is easier to count it in frequency. It is measured in rpm - revolutions per minute.
If the matter does not concern a long period of time, but only that during which one revolution occurs, then the concept of the period of circulation is used here. It shows how quickly one thing is done Roundabout Circulation. The unit of measurement here is the second.
The relationship between angular velocity and rotational speed or revolution period is shown by the following formulas:
ω = 2 π / T = 2 π *f,
- ω is the angular velocity in rad/s;
- T is the circulation period;
- f is the rotation frequency.
You can get any of these three values from another using the rule of proportions, while not forgetting to translate the dimensions into one format (in minutes or seconds)
What is the angular velocity in specific cases?
Let's give an example of a calculation based on the above formulas. Let's say we have a car. When driving at 100 km / h, its wheel, as practice shows, makes an average of 600 revolutions per minute (f = 600 rpm). Let's calculate the angular velocity.
Let's start by converting RPM to RPM. To do this, divide 600 by 60 (the number of seconds in a minute) and get 10 rpm. Along the way, we also received the period of revolution: this value is the inverse of the frequency and, when measured in seconds, 0.1 s.
Since it is impossible to express exactly π in decimal fractions, the result will be approximately equal to 62.83 rad / s.
Relationship between angular and linear velocities
In practice, it is often necessary to check not only the speed with which the angular position of a rotating point changes, but also the speed of it itself in relation to linear motion. In the example above, calculations were made for the wheel - but the wheel moves along the road and either rotates under the influence of the speed of the car, or itself provides this speed to it. This means that each point on the surface of the wheel, in addition to the angular velocity, will also have a linear velocity.
The easiest way to calculate it is through the radius. Since the speed depends on time (which will be the period of revolution) and the distance traveled (which is the circumference), then, given the above formulas, the angular and linear speed will be related as follows:
- V is the linear speed;
- R is the radius.
It is clear from the formula that more radius, the higher the value of such speed. Applied to the wheel with the most high speed a point on the outer surface of the tread will move (R is maximum), but exactly in the center of the hub, the linear velocity will be zero.
Acceleration, moment and their connection with mass
In addition to the above quantities, there are several other points associated with rotation. Considering how many rotating parts of different weights are in the car, their practical significance cannot be ignored.
Uniform rotation is an important thing. But there is not a single detail that would spin evenly all the time. The number of revolutions of any rotating assembly, from the crankshaft to the wheel, always eventually rises and then falls. And the value that shows how much the revolutions have increased is called angular acceleration. Since it is a derivative of angular velocity, it is measured in radians per second squared (as linear acceleration is in meters per second squared).
Another aspect is also connected with the movement and its change in time - the angular momentum. If up to this point we could only consider purely mathematical features of the movement, then here it is already necessary to take into account the fact that each part has a mass that is distributed around the axis. It is determined by the ratio of the initial position of the point, taking into account the direction of movement - and the momentum, that is, the product of mass and speed. Knowing the moment of impulse that occurs during rotation, it is possible to determine what load will fall on each part when it interacts with another
Hinge as an example of momentum transfer
A typical example of how all of the above data applies is the hinge of equal angular velocities(SHRUS). This item is primarily used for front wheel drive vehicles, where it is important not only to ensure a different rate of rotation of the wheels when turning - but also at the same time their controllability and the transfer of an impulse to them from the operation of the engine.
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The design of this node is precisely designed to:
- equalize how fast the wheels spin;
- provide rotation at the moment of rotation;
- guarantee the independence of the rear suspension.
As a result, all the formulas given above are taken into account in the operation of the SHRUS.
The shaft rotation frequency (speed) of an induction motor (IM) is directly related to the number of winding poles. The number of poles is indicated in the series not only of domestic electric motors, but quite often in imported engines. For example, AIR112M6 or W22 160M2P, the number of poles is six or two, respectively. This is also typical for crane motors MTN112-6 - six-pole, MTN225M8 - eight-pole.
The ratio of the poles and the revolutions of the motor shaft is very simple. Each number of poles corresponds to a certain frequency of rotation of the IM shaft. If the designation of an asynchronous motor has two poles (2P), then its nominal shaft speed is three thousand revolutions per minute (3000 rpm). If the motor has four poles (4P), then the nominal speed of rotation of the output shaft is one and a half thousand revolutions per minute (1500 rpm). If an asynchronous motor has six poles (6P), then the shaft speed is one thousand revolutions per minute (1000 rpm). If the motor has eight poles (8P), then the shaft speed is seven hundred and fifty revolutions per minute (750 rpm). A twelve pole motor (12P) has a shaft speed of five hundred revolutions per minute (500 rpm).
In addition, even for multi-speed asynchronous motors, the number of poles is also in the brand and it also correlates with the shaft speed. In general, electric motors can have one, two, three or four shaft speeds.
Two-speed motors can have the following ratios of the number of poles and shaft speeds:
- four and two poles (4/2) correspond to the nominal shaft speed of one and a half and three thousand revolutions per minute (1500/3000);
- six and four poles (6/4) correspond to the speed of rotation of the shaft per thousand and one and a half thousand revolutions per minute (1000/1500);
- twelve and six poles (12/6) - shaft rotation speeds of five hundred and thousand revolutions per minute (500/1000);
- eight and four poles (8/4) - rated frequency seven hundred and fifty per one and a half thousand revolutions per minute (750/1500);
- eight and six poles (8/6) - nominally give seven hundred and fifty and a thousand revolutions per minute (750/1000).
Three-speed motors have the following ratios of the number of poles and shaft speeds:
- six, four and two poles (6/4/2) correspond to one thousand, one and a half and three thousand revolutions per minute (1000/1500/3000);
- eight, four and two poles (8/4/2) give seven hundred and fifty, one and a half thousand and three thousand revolutions per minute (750/1500/3000);
- eight, six and four poles (8/6/4) correspond to seven hundred and fifty, one thousand and one and a half thousand revolutions per minute on the output shaft (750/1000/1500).
Four-speed motors are twelve by eight by six and four poles (12/8/6/4), that is, the shaft speed is five hundred, seven hundred and fifty, one thousand and one and a half thousand revolutions per minute (500/750/1000/1500).
Knowing the binding of the shaft speed to the number of poles, even by brand, it is not difficult to determine the speed of the output shaft of the electric motor.
Moreover, for imported electric motors, the poles are indicated in exactly the same way, the designation rpm = rpm.
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