Electric micromotors. Encyclopedia of radio electronics and electrical engineering

Encyclopedia of radio electronics and electrical engineering / Electric motors

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Typically, electric motors are divided into three groups: large, medium and small power. For low power motors (we will call them micromotors), the upper power limit is not set, usually it is several hundred watts. Micromotors are widely used in appliances and household appliances (now each family has several micromotors - in refrigerators, vacuum cleaners, tape recorders, players, etc.), measuring technology, automatic control systems, aviation and space technology and other areas of human activity.

The first DC motors appeared in the 30s of the XIX century. A big step in the development of electric motors was made as a result of the invention in 1856 by the German engineer Siemens of a two-arm converter and the discovery by him in 1866 of the dynamoelectric principle. In 1883 Tesla and in 1885 Ferrari independently invented the AC induction motor. In 1884, Siemens created an alternating current collector motor with a series excitation winding. In 1887, Khazelwander and Dolivo-Dobrovolsky proposed a rotor design with a squirrel-cage type squirrel-cage winding, which greatly simplified the engine design. In 1890, Chitin and Leblanc first used a phase-shifting capacitor.

In household electrical appliances, electric motors began to be used from 1887 - in fans, from 1889 - in sewing machines, from 1895 - in drills, from 1901 - in vacuum cleaners. However, to date, the need for micromotors has turned out to be so great (up to six micromotors are used in a modern video camera) that specialized firms and enterprises have arisen to develop and manufacture them. A large number of types of micromotors have been developed, each of which is the subject of an article from this series.

Asynchronous micromotors

Single-phase asynchronous micromotors are the most common type, they meet the requirements of most electric drives of instruments and apparatus, featuring low cost and noise level, high reliability, maintenance-free and do not contain moving contacts.

Включение. Asynchronous micromotor can be with one, two or three windings. In a single-winding motor, there is no initial starting torque, and to start it, you need to use, for example, a starting motor. In a two-winding motor, one of the windings, called the main winding, is directly connected to the mains (Fig. 1).

To create a starting torque in the other, auxiliary, winding, a current must flow that is phase-shifted relative to the current in the main winding. To do this, an additional resistor is connected in series with the auxiliary winding, which can be active, inductive or capacitive in nature.

Most often, a capacitor is included in the power supply circuit of the auxiliary winding, while obtaining the optimal phase shift angle of the currents in the windings, equal to 90 ° (Fig. 1, b). A capacitor that is constantly connected to the power supply circuit of the auxiliary winding is called a working one. If, when starting the engine, it is necessary to provide an increased starting torque, then in parallel with the working capacitor Sv, the starting capacitor Ca is turned on for the start time (Fig. 1, c). After the engine has accelerated to speed, the starting capacitor is switched off using a relay or a centrifugal switch. In practice, the variant of Fig. 1b is more often used.

The phase shift effect can be obtained by artificially increasing the active resistance of the auxiliary winding. This is achieved either by including an additional resistor, or by making an auxiliary winding from a high-resistance wire. Due to the increased heating of the auxiliary winding, the latter is turned off after starting the engine. Such motors are cheaper and more reliable than capacitor ones, although they do not allow for a phase shift of winding currents of 90 °.

To reverse the direction of rotation of the motor shaft, an inductor or choke should be connected to the power supply circuit of the auxiliary winding, as a result of which the current in the main winding will lead the current in the auxiliary winding in phase. In practice, this method is rarely used, since the phase shift is negligible due to the inductive nature of the resistance of the auxiliary winding.

The most commonly used method is a phase shift between the main and auxiliary windings, which consists in closing the auxiliary winding. The main winding has a magnetic connection with the auxiliary one, due to which, when the main winding is connected to the supply network, an EMF is induced in the auxiliary winding and a current arises that lags in phase with the current of the main winding. The motor rotor begins to rotate in the direction from the main to the auxiliary winding.

A three-winding three-phase asynchronous motor can be used in single-phase power supply mode. Figure 2 shows the inclusion of a three-winding motor according to the "star" and "triangle" schemes in a single-phase operation mode (Steinmetz schemes). Two of the three windings are directly connected to the supply network, and the third is connected to the supply voltage through a starting capacitor. To create the necessary starting torque, a resistor must be connected in series with the capacitor, the resistance of which depends on the parameters of the motor windings.

Windings. Unlike three-winding asynchronous motors, which are characterized by a symmetrical spatial arrangement and the same parameters of the windings on the stator, in motors with a single-phase supply, the main and auxiliary windings have different parameters. For symmetrical windings, the number of slots per pole and phase can be determined from the expression:

q = N / 2pm,

where N is the number of stator slots; m - number of windings (phases); p is the number of poles.

In quasi-symmetrical windings, the number of slots and the width of the windings differ slightly, while the active and inductive resistances of the main and auxiliary windings have different values.

In asymmetric windings, the number of slots occupied by each winding varies significantly. Therefore, the main and auxiliary windings have a different number of turns. A typical example is the 2/3-1/3 winding (Fig. 3), in which 2/3 of the stator slots is occupied by the main winding, and 1/3 by the auxiliary winding.

Design. Figure 4 shows a section of a motor with two concentrated or coil windings located on the stator poles.

Each winding (main 1 and auxiliary 2) is formed by two coils located at opposite poles. The coils are put on the poles and inserted into the yoke of the machine, which in this case has a square shape. From the side of the working air gap, the coils are held by special protrusions that act as pole shoes 3. Thanks to them, the distribution curve of the magnetic field in the working air gap approaches a sinusoid. Without these protrusions, the shape of this curve is close to rectangular. As a phase-shifting element for such an engine, both a capacitor and a resistor can be used. It is also possible to short-circuit the auxiliary winding. In this case, the motor is converted into a split-pole asynchronous machine.

Shaded pole motors are the most commonly used due to their simple design, high reliability and low cost. Such a motor also has two windings on the stator (Fig. 5).

The main winding 3 is made in the form of a coil and is connected directly to the supply network. Auxiliary winding 1 is short-circuited with one to three turns per pole. It covers part of the pole, which explains the name of the engine. The auxiliary winding is made of round or flat copper wire with a cross section of a few square millimeters, which is bent into coils of the appropriate shape. Then the ends of the winding are connected by welding. The motor rotor is made short-circuited, and cooling fins are attached to its ends, which improve heat removal from the stator windings.

Structural options for shaded pole motors are shown in Figures 6 and 7.

In principle, the main winding can be arranged symmetrically or asymmetrically with respect to the rotor. Figure 6 shows the design of a motor with an asymmetric main winding 5 (1 - mounting hole; 2 - magnetic shunt; 3 - short-circuited winding; 4 - mounting and adjustment holes; 6 - winding frame; 7 - yoke). Such an engine has significant magnetic flux leakage in the external magnetic circuit, so its efficiency does not exceed 10-15%, and it is manufactured for a power of not more than 5-10 watts.

From the point of view of manufacturability, a motor with a symmetrically located main winding is more complex. In engines with a power of 10-50 W, a composite stator is used (Fig. 7, where: 1 - yoke ring; 2 - short-circuited ring; 3 - pole; 4 - rotor with "squirrel cage" winding; 5 - magnetic shunt). Due to the fact that the motor poles are covered by a yoke and the windings are located inside the magnetic system, the leakage magnetic fluxes here are much less than in the design in Fig.6. Engine efficiency 15-25%.

To change the speed of a shaded-pole motor, a cross-pole circuit is used (Fig. 8). It quite simply implements the switching of the number of pairs of poles of the stator winding, to change which it is enough to turn on the windings turned on in opposite directions. Shaded pole motors also use the principle of speed control, which consists in switching the winding coils from series connection to parallel.

Synchronous micromotors

Single-phase synchronous motors are used in clocks, counters, time relays, regulation and control systems, measuring instruments, sound recording equipment, etc. In a synchronous motor, a rotating magnetic field is created, the rotational speed of which is constant and does not depend on changes in the load. Like a single-phase induction motor, a synchronous motor generates an elliptical rotating magnetic field. When overloaded, synchronous micromotors fall out of synchronism. After applying the supply voltage to them, it is necessary to create conditions under which the engine will accelerate and be drawn into synchronism. There are reactive, hysteresis synchronous motors, as well as motors with excitation from permanent magnets.

Jet engines

With a power of up to 100 W, a synchronous motor is made with two windings - main and auxiliary, and a phase-shifting capacitor is switched on in series with the latter. The stator of a synchronous reluctance motor is not structurally different from the stator of an induction motor. On the rotor of the synchronous motor there is a short-circuited winding ("squirrel cage"), which provides a reliable start of the synchronous micromotor. Up to a speed close to synchronous, the motor accelerates as an asynchronous one, and then independently retracts into synchronism, and the rotor continues to rotate at a synchronous speed. The design of the rotor of a synchronous motor is shown in Figure 9.

Grooves are located along its circumference with a uniform step (Fig. 9, a), and the depth of the grooves is 10-20 times greater than the length of the working air gap. Aluminum is poured into these slots, and the rotor winding rods thus formed are short-circuited with aluminum rings welded on both sides to the ends of the rods. With the same value of reactive power consumed from the network, the useful moment on the shaft of a synchronous motor is two times less than the moment on the shaft of an asynchronous motor. The efficiency and cosf of a synchronous motor is also worse than that of an asynchronous motor. This is due to the fact that the working air gap of a synchronous motor is larger than that of an asynchronous motor.

By changing the conductivity of individual sections of the magnetic circuit of the motor, it is possible to direct the magnetic flux in the desired direction. This can be achieved by using special cavities in a soft magnetic material filled with aluminum alloy. Figure 9b shows a two-pole rotor made in a similar way. In this case, the length of the working air gap, as in the case of an asynchronous motor, remains unchanged over the entire circumference of the stator. The power of such a synchronous motor is close to the power of a single-phase asynchronous motor.

Hysteresis motors

In terms of design, the stator of a hysteresis motor does not differ from the stators of the previously considered motors (asynchronous, synchronous reluctance). At a low rotational speed of the hysteresis motor, its stator is made with claw-shaped poles (Fig. 10).

It contains a yoke 1 with a winding, and its coils alternate along the circumference of the stator, thus forming a sequence of electromagnets with alternating polarity (NSNS...); 2 - claw-shaped poles; 3 - sleeve made of synthetic material; 4 - leakage flux, 5 - useful magnetic flux; 6 - rotor; 7 - annular winding; 8 - winding frame. Plates for closing the magnetic flux are installed on the sides of the coils. When the stator winding is connected to the supply network, a multi-pole magnetic field is created in the working air gap.

Figure 11 shows four poles arranged one after another (1 - main north; 2 - auxiliary north; 3 - short-circuited ring; 4 - ring excitation winding; 5 - main south pole; 6 - auxiliary south pole). Short-circuited rings (or windings) located concentrically with respect to the stator winding coil have different coupling coefficients with the main and auxiliary poles. Thus, a phase shift of the magnetic fluxes of the indicated poles is provided, the consequence of which is the appearance of an elliptical rotating magnetic field.

A ring made of ferromagnetic material with a wide hysteresis loop is mounted on the rotor. The coercive force of this material should be less than that of hard magnetic materials used to make permanent magnets. Otherwise, a powerful magnetic field is required to remagnetize the ring. There are windows on the rotor ring, the number of which corresponds to the number of stator poles, which ensures synchronous rotation of the rotor due to the reactive torque.

Motors with permanent magnet excitation

A synchronous motor containing a permanent magnet rotor is structurally similar to a claw pole motor (see Figure 10). The main advantage of a permanent magnet motor over hysteresis motors is that the torque it develops with the same dimensions is 20-30 times greater than the hysteresis motor torque. In addition, permanent magnet motors are more reliable. To start the engine, you need to set its rotor in motion, so the load should not be attached to the shaft using a rigid connection. Motors of small power contain a rotor with a ferrite permanent magnet ring, which, with a small number of poles, is magnetized in the radial direction.

With a large number of poles, the rotor is magnetized in the axial direction and has claw-shaped poles (Fig. 12), where 1 ring is made of a permanent magnet; 2 - bushing. The stator design used in high power motors is practically the same as the stator design of an induction motor with a distributed winding. Rotor designs are very diverse.

Figure 13 shows three design options for four-pole synchronous motors with permanent magnet excitation. In Fig. 13, a, barium ferrite is used for engines, in Fig. 13, b - an alloy based on a combination of rare earth elements and cobalt, in Fig. 13, c - an alnico alloy (1 - squirrel cage winding; 2 - permanent magnets; 3 - magnetic shunts).

To ensure asynchronous starting, all rotors have a short-circuited rod winding, as in an asynchronous motor.

Universal motors

Collector motors with series excitation are called universal, since they can operate both from a DC network and from an AC network. They form the most important group of micromachines. The motor speed does not depend on the frequency of the supply voltage, as a result of which, unlike asynchronous motors, these motors can have a speed of more than 3000 rpm. The advantage of universal motors is the ease of speed control by switching taps of the series excitation winding or by phase control using triacs. As a disadvantage, one can note the higher cost of a universal motor compared to an asynchronous one, due to the presence of a winding on the rotor and a brush-collector assembly (which also creates additional noise and wears out quickly).

Design. Universal motors have a two-pole design. To reduce losses from eddy currents, the stator and rotor magnetic circuits are laminated.

Figure 14 shows several options for the design of the motor stator: Figure 14, a - stator with machine-made winding; fig.14,b - stator with excitation winding, made and laid by hand; Fig. 14, c - stator with two external excitation windings; fig.14,d - stator with one remote excitation winding. The stator (excitation) winding of a universal motor usually consists of two sections or coils, between which there is an armature, the winding of which is connected in series with the excitation winding. You can wind the armature windings with a double wire. With a rectangular shape of the grooves of the rotor, the coils are placed parallel to each other. The armature winding consists of two parallel branches, which distribute the motor current passing through the brushes.

Particular attention in the universal motor should be given to the brush-collector assembly.

The most commonly used designs of brush holders are shown in Fig. 15, a, b, the designs of Fig. 15, c, d are cheaper and are used in less powerful engines, Fig. 15, e shows a brush with fuses (1 - cover; 2 output ; 3 - holder; 4 - brush; 5 collector; 6 - filter throttle; 7 axis of rotation; 8 - ring; 9 - hook; 10 - copper lamella; 11 - groove; 12 - insulator; 13 - output; 14 - spring ; 15 dielectric nipple). The body of the brush has a cylindrical cavity. The design of the brush (Fig. 15, e) is such that when the brush is actuated to the end of the cavity, the nipple abuts against the surface of the collector. Since the nipple is made of insulating material, the contact of the brush with the commutator is broken, and further operation of the engine becomes impossible.

Features of work on direct current. When the motor is running from a DC network, the voltage drop on the armature and excitation windings depends only on their active resistance, therefore, all other things being equal, the voltage, current, magnetic flux, EMF in the armature winding are more important than when powered by AC. This results in a change in engine speed. If, when powered by direct current and alternating current, it is necessary that the motor operates at the same speed, then in the motor for direct current mode it is necessary to have a greater number of turns in the field winding.

Speed ​​control. If additional conclusions are made in the excitation winding, then by switching them you can change the rotation frequency (Fig. 16, a). With a decrease in the number of turns, the rotational speed increases. The second way is to install a variable resistor in series with the motor windings (Fig. 16, b). As the resistance of the resistor increases, the engine speed decreases. The third way is to use a regulating transformer (Fig. 16, c). An increase in the supply voltage leads to an increase in the engine speed. The fourth method is shunting the armature winding with a variable resistor (Fig. 16, d). When the resistance of the resistor decreases, the number of revolutions also decreases. This method is good because when the load is dropped, the engine does not run wild.

Precise speed control can be obtained in an electronic triac circuit (Fig. 17). The triac performs "cut-off" of a part of the half-cycle of the alternating voltage. To reverse the motor, it is necessary to change the polarity of the connection of the armature winding or the excitation winding.

Speed ​​stabilization. Universal motors have a very soft mechanical characteristic, i.e. strong dependence of rotational speed on load torque. To stabilize the rotational speed under variable load, in particular, mechanical regulators are used. For example, you can use a centrifugal switch, the contact of which is connected in parallel with the additional resistor. This method provides speed stability within 1%, but only for the speed value for which the centrifugal switch is designed. Therefore, electronic regulators are increasingly being used.

In electronic controllers (Fig. 17), for example, the EMF of the armature winding is used as a feedback signal proportional to the actual value of the rotational speed. With an increase in the specified value, the triac control angle is increased, which leads to a decrease in the engine speed. The stabilization accuracy with this method is 10%. There are more complex (but also more expensive) ways.

DC motors with permanent magnet excitation

Currently, such motors are produced mainly with a supply voltage of 12 V and are used in car drives, typewriters, medical and household equipment.

Designs permanent magnet motors are very diverse. This is due to the different performance and cost requirements of the engines.

Figure 18a shows the structural elements of simple and cheap motors with ring magnets made of ferrite compounds (1 - magnet segments; 2 - rotor; 3 - stator package; 4 - pole; 5 - ring magnet; 6 - radial magnetization; 7 - diametral magnetization; 8 - rectangular magnet). These magnets are magnetized in the radial or axial direction. The engine housing is made of laminated magnetically soft material either in the form of a cylinder or in the form of an elongated pot. The housing serves to close the magnetic flux of permanent magnets. The rotor package is assembled from sheets of electrical steel without silicon additives (1 mm thick). The rotor is located in self-centering bearings, it contains a small number of grooves, which reduces the cost of armature winding.

Figure 18b shows elements of more expensive designs of permanent magnet motors (where 9 are poles; 10 are pole shoes). They use hard magnetic materials alnico (Al, Ni, Co) and magnets made of rare earth metals. These motors have a massive body, and the rotor is made of high quality electrical steel. The efficiency of such engines exceeds 80%. Turning on the engine. If a DC motor is powered by a battery, then if it is necessary to regulate its speed, pulse regulators are used (Fig. 19, a, where U is the supply voltage; Um is the pulse voltage; Ra, La and Ui are, respectively, active resistance, inductance and EMF armature windings; Fr - magnetic flux of the pole).

Figure 19b shows the form of voltage Um and current i(t) in the motor. The number of revolutions of the engine is directly proportional to the duty cycle of the voltage pulses switched on using a thyristor or a powerful transistor.

The DC motor is powered from the AC mains through a rectifier connected in a single-phase bridge circuit (Fig. 20). In this case, the rotational speed can be controlled in the manner described above.

Another option for speed control is the use of brushes with adjustable position relative to the armature. The supply voltage can be applied to the brushes located on the geometric neutral (a-a) or to one of these brushes and an additional brush a' (Fig. 21), located at an angle β relative to the second brush. In these two cases, the ratio of engine speeds has the form

n₀/n = 2/(1 + cosβ).

DC motors with non-magnetic rotor. Servomotors and automation motors often place high demands on the values ​​of electromagnetic or electromechanical time constants, which should be as small as possible. To solve this problem, two types of engine designs have been developed: 1) with a hollow or bell-shaped; 2) with disc rotor. The first ones are produced for a power of 1 - 20 W, the second - for a power of over 20 W.

In motors with a hollow rotor, the latter is made in the form of a glass of synthetic electrical insulating material, on the surface of which a winding is fixed (Fig. 22, where 1 is a collector; 2 is a brush; 3 is a housing; 4 is the upper winding layer; 5 is the lower winding layer) . The rotor rotates in the magnetic field of permanent magnets mounted on the stator and forming a two- or four-pole excitation system.

In motors with a disc rotor, the latter has the shape of a disc, on which ring or segment magnets are located, creating a magnetic flux in the axial direction (Fig. 23, where 1 is a brush; 2 is a cylindrical and ring magnet; 3 is a disc rotor).

Magnets can be located on both sides of the rotor disc. In low power motors, the rotor disk is made of electrically insulating material with a printed or stamped winding. The torque on the motor shaft practically does not change, since the winding is evenly spaced around the circumference of the rotor. Therefore, such motors are best suited for electric drives that need to maintain a stable speed. These motors do not need a commutator, which is used in conventional DC motors, since the brushes slide over the ends of the printed winding conductors. In engines of higher power, a rotor with a winding is used, which is filled with a special composition for its attachment to the rotor. Such motors have a conventional manifold design.

Valve motors

In modern microdrives, motors are subject to increasingly stringent requirements. On the one hand, they must have high reliability and simplicity of design of asynchronous motors, on the other hand, they must be simple and have a large range of speed control for DC motors. Motors with electronic control circuits, or brushless motors, fully comply with these requirements. At the same time, they do not have the disadvantages of asynchronous (reactive power consumption, rotor losses) and synchronous motors (speed ripple, loss of synchronism).

BLDC motors are non-contact DC machines with permanent magnet excitation with a single or multi-winding stator. The switching of the stator windings is carried out depending on the position of the rotor. The electronic control circuit includes special rotor position sensors. Valve motors are used in high-quality instruments and apparatus, for example, in electric drives of tape recorders and video recorders, in measuring technology, as well as in those electric drives in which it is required to provide high-precision positioning of the rotor and the associated working element. In this capacity, they successfully compete with stepper motors.

In collector DC motors, the excitation magnetic flux has the same direction and is stationary in space. The magnetizing force of the armature winding Θ2 is located at an angle of 90 ° relative to the magnetic flux of excitation Ф₁ (fig.24). Thanks to the collector, the 90° angle maintains its value even when the rotor rotates.

At the valve motor, permanent magnets are located on the rotor, creating a magnetic excitation flux, and the armature winding is located on the stator (Fig. 25, a - in the initial position; b - when rotated through an angle α). The stator winding is powered in such a way that between its magnetizing force Θ1 and the excitation flux Ф₂ the 90° angle is maintained. With a rotating rotor, this position can be maintained when switching the stator windings. In this case, the stator windings must be switched at certain moments and with a given sequence.

The position of the rotor is determined, for example, using a Hall sensor. The position sensor controls the operation of electronic keys (transistors). Thus, without an electronic circuit, the operation of a brushless motor is impossible. With an increase in the number of stator windings, the complexity of the electronic control circuit increases. Therefore, in such motors, usually no more than four windings are used. Cheap motor designs contain a single winding.

The diagram of a single-winding motor is shown in Fig. 26, a. There is one winding 1 on the stator, which is connected to the supply voltage using the transistor VT1 (Fig. 26, b). The motor rotor is made of a permanent magnet and has one pair of poles. The control signal to the base of the transistor is supplied by the Hall sensor HG. If this sensor enters a magnetic field, for example, an additional magnet, then a voltage Un appears at its output, which turns on the transistor. The transistor can only be open or only closed.

Fig. 27a shows the location of the Hall sensor and an additional magnet (section along the axis), and Fig. 27b - across the axis. The Hall sensor reacts to the north pole of the additional magnet (N).

Figure 28, a shows a structural diagram of a two-winding motor.

There are two windings 1 and 2 on the stator, through which either currents of opposite signs flow, or the windings have opposite winding directions. The windings are switched using transistors VT1 and VT2 (Fig. 28, b) in turn. To do this, the Hall sensor must have two outputs, on one the pulse appears when passing the north pole of the additional magnet, on the other - when passing the south pole. The specified mode can also be implemented in a single-winding motor, but for this you need to have two power supplies and two transistors. In this case, one speaks of a single-winding motor with bipolar power supply.

Figure 29, a shows a diagram of a three-winding motor. On its stator there are three windings (1, 2, 3) located along its circumference at an angle of 120° with respect to each other. Each of the windings is connected to a power source through a separate transistor switch. Three Hall sensors are used to control transistors. Current flows through each of the windings for one third of the period. This pulsed current has a constant component, which does not create a torque, but increases the heating losses of the windings. A three-winding motor can be turned on according to a full-wave circuit, which contains six transistors (Fig. 29, b).

A motor with four windings on the stator is relatively inexpensive, since with four transistors it uses only two Hall sensors, which simplifies the control circuit. Windings 1-4 (Fig. 30, a, b) are located on the stator at an angle of 90 °. Hall sensors are excited by the permanent magnets of the motor rotor. There are two ways to control the motor: 90-degree and 180-degree commutation. In a 90-degree commutation, at any given time, current flows through only one of the four windings.

The motor control circuit is shown in Fig. 31, and the location of the control magnets and Hall sensors is shown in Fig. 32. With this arrangement, the transistors turn on in the following order: VT1, VT3, VT2, VT4.

With 180-degree commutation, the motor design is the same, but the current flows in each of the four windings for half a cycle, which causes the currents in the windings to overlap. Hall sensors do not work from permanent magnets, but from a magnetized rotor. Therefore, the form of the output voltage of the Hall sensors is cosine, and the transistors VT1-VT4 do not operate in a pulsed, but in a linear mode. The 180-degree switching mode can also be implemented in a two-winding motor, if two transistors with two power supplies are included in the circuit of each winding.

To maintain the set value of the frequency of rotation of the brushless motor, you can use the scheme of Fig.33.

The EMF of the stator winding is used as a feedback signal, which is proportional to the rotor speed. The maximum voltage selection circuit is assembled on diodes. Of the four diodes, only one is open, which currently has the highest voltage. The result is a four-phase rectifier, its constant component of the output voltage is proportional to the rotational speed. At the input of the transistor VT6, a capacitor C6 is included, which smooths out the ripple of the rectifier. With an increase in the rotational speed, the current of the transistor VT6 increases, which leads to a decrease in the current in the transistor VT5, which means that the current from the outputs of the Hall sensors to the transistors VT1-VT4 decreases. This results in a reduction in engine speed.

Stepper motors

There are many devices and devices in which the task of fast and accurate positioning of a particular unit or working body is assigned to the electric drive. In these cases, electric motors with discrete (stepping) movement of the rotor are used. A motor that converts electrical impulses into mechanical impulses is called a stepper motor.

In addition to the stepper motor, the structure of the stepper electric drive includes an electronic control unit (Fig. 34), where 1 is the setting device; 2 - control scheme; 3 - electronic unit or microprocessor; 4 - switch; 5 - power block; 6 - supply network; 7 - engine). Stepper motors work mainly on the principle of a synchronous motor, so they have similar disadvantages - the possibility of falling out of synchronism and the tendency of the rotor to oscillate when working out the step.

Design. A stepper motor consists, as it were, of several motors, the windings of which have forward and reverse winding directions. Since the windings are evenly distributed around the circumference of the stator, the rotor follows the successively switched windings (Fig. 35). The rotor is made of magnetically hard or magnetically soft material, as well as their combination. In the last two cases, the rotor has teeth. In Fig. 35, b, each part of the rotor has four teeth. With the number of m packages and 2p poles, the rotor makes z steps z = 2pm in one revolution. The number of steps determines the step size in terms of the angle αt; = 2p/z. The structure in Fig. 35b has m = 3 and 2p = 4, which corresponds to z = 12 and α = 30°.

The mode of operation with switching of single windings is called full step mode. However, it is possible to simultaneously turn on two adjacent windings in the design of Fig. 35, a. while the rotor rotates half a step. This mode is called fractional step mode. In this case, the coefficient k should be introduced into the expression for z, taking into account the mode of operation of the engine. For the full step mode, k = 1, for the fractional step mode, k = 2. Step splitting allows you to reduce the number of windings, simplify the control circuit and reduce the cost of the drive.

In addition to increasing the number of windings, the pitch can be reduced by increasing the number of poles or rotor teeth. In this case, increased requirements are placed on the accuracy of the manufacture of the rotor. In addition, a multi-pole rotor is much more difficult to magnetize. Therefore, not only the rotor is made geared, but also the stator (Fig. 36).

The stator and rotor have some difference in the number of teeth. The "extra" teeth of the rotor are located between the stator poles. In this design, it is also possible to implement full and fractional step modes. If currents of a certain value are passed through the stator winding, then in principle any step can be obtained, but this will lead to a significant complication of the control unit. Reducers can also be used to reduce the pitch. In this case, the moment on the shaft of the driven mechanism increases and its moment of inertia decreases, and the friction in the gearbox contributes to damping the oscillations of the stepper motor rotor. But the use of a gearbox leads to an increase in the error of working out the step.

A motor with a permanent magnet rotor is called an active rotor motor (PM motor). A motor whose rotor is made of a soft magnetic material is called a reluctance motor (VR motor). This motor must have at least three windings, while in a PM motor it is enough to have two windings. In addition, there are designs that combine the features of engines with an active and reactive rotor. In these hybrid designs, the permanent magnet rotor also has teeth.

Comparison of three types of stepper motors is shown in Table 1

Table 1

Stepper motors can provide not only rotational, but also translational motion of the electric drive mechanism. Such stepper motors are called linear. They are used, for example, to position various devices on the XY plane, while moving along each coordinate is carried out using a separate winding. In addition to electromagnetic linear stepper motors, there are piezoelectric ones. Figure 37a shows a diagram of such an engine. Its design includes two electromagnets M1 and M2 (1), which can slide on a steel beam 4, and a piezoelectric cable 3.

The design of the piezoelectric cable is illustrated in Fig. 37b. If a voltage is applied to the electrodes 2, then, depending on its polarity, the elements of the cable 5 will be compressed or stretched. When voltage is applied to the windings of the electromagnets, they will be fixed on the steel beam. Figure 37c shows the sequence of voltage pulses applied to the windings of the electromagnets and to the electrodes of the piezoelectric cable, as well as the process of moving the electromagnets.

Control schemes. Figure 38 shows stepper motor control circuits in which two main control methods are implemented - unipolar and bipolar. With unipolar control (Fig. 38, a), a two-package stepper motor is used, on each package of stators A and B of which there are two windings A1, A2 and B1, B2. The windings of each package form a pair of poles and create a magnetizing force of a different sign.

Figure 39 shows a diagram of the inclusion of an engine with a hybrid rotor. The annular winding of each claw-pole stator pack contains two half-windings.

The control circuit of Fig. 38, a is simple, but the use of the motor is deteriorating, since only one of the two stator windings is in operation. With bipolar control (Fig. 38b), the use of the motor increases, although the control scheme also becomes more complicated. Therefore, this control method is used in electric motors with increased requirements for weight and size indicators.

Motor control

The equations describing the motor for each phase are:

Vm = Rm Im + Em;

Em=K₁w;

M=K₂im,

where Vm is the applied voltage; Im - consumed current; Em - self-induction voltage; Rm - winding resistance; M moment of forces on the shaft; w - angular speed of rotation of the rotor; TO₁ and K₂ - coefficients of proportionality.

Thus, for each phase of the input voltage, the motor is represented by an equivalent circuit consisting of a resistor and a voltage source connected in series. The resistor is the resistance of the windings, the voltage source is the self-induction voltage of the windings (Fig. 40).

Engines operate in one of two modes. In the first mode, the engine speed is set by the frequency of the voltage supplied to it. In the second mode, the motor itself, by switching the windings with brushes or switching the windings according to signals from the position sensors, sets the speed depending on the applied voltage and the load on the shaft. The control of DC motors is reduced to supplying the required voltage of a given polarity to it, since the voltage value sets the speed, and the polarity sets the direction of rotation. A typical output stage circuit and the operation of control commands are shown in Fig.41.

From the control circuit signals F (forward) - forward and R (reverse) - back. These signals change the polarity of the voltage applied to the motor. If these commands are simultaneously applied (F = R = 1) or removed (F = R = 0), then the motor runs either in braking mode or in stop mode. The difference between the two is that the motor is practically short-circuited during deceleration. In the stop mode, the engine runs in conditions close to idling, i.e. rotates by inertia. The motor stops most quickly when braking, since the kinetic energy stored in the rotor is dissipated by the winding resistance.

As seen in Figure 41, the voltage applied to the motor cannot be greater than the voltage at the Vc (voltage control) pin. The voltage on this pin is not linear, but monotonically related to the voltage on the motor, so it is used for speed control.

Figure 42 shows the use of the ROHM BA6219B chip to control the DC motor of the VCR drive shaft. Here, as above, the F and R commands set the direction of rotation. They are supplied from the micro-computer controlling the tape drive, the control voltage Vc is generated in the servo processor

Stepper motor control

For a stepper motor, rotation to the minimum angle (step) is performed when the phase of the supply voltage changes. For a motor with p pairs of poles, the pitch is π/(np). For the convenience of setting the number of steps in binary code, the number of windings is chosen to be equal to the power of 2 (usually 4). Traveling wave voltages, which create a rotating magnetic field, are formed from the signals received at the input of the control circuit in digital form. A feature of the operation of a stepper motor is that after turning through a given angle, the rotor must maintain its occupied position, i.e. current must flow through the windings. Therefore, the windings are powered by current, not voltage. A visual version of the output stage of the stepper motor control circuit is shown in Fig. 43.

(click to enlarge)

The digital signals D0 and D1, from which the traveling wave voltages are formed, are generated by the reversible counter CT2. The number of steps NS is loaded into the counter by the write command WR. The counter counts until its content is zero. At this moment, zero appears at the transfer output P, ​​and the counting stops, since the signal P closes the valve that supplies pulses of the stepping frequency FS to the counting input of the counter. The cadence is usually generated from the clock frequency by a counter or timer. The FR signal sets the direction of counting and therefore the direction of rotation of the motor. The STOP signal is used to stop the engine.

Practical control circuits have a more branched control logic, a bridged output stage, and, as a rule, contain a pulse-width current limiter. The control logic is usually supplemented with inhibit and phase rotation signals. The bridge output stage is installed to change the direction of the current in the motor winding when powered from a unipolar source. The phase rotation command changes the direction of the current: depending on its value, the transistors of only one of the diagonals of the output stage work. The pulse-width current limiter is used to reduce the power dissipated by the output stage.

The device of a typical stepper motor control circuit is shown in Fig. 44 (only one output stage).

The polarity control input P opens the gate G1 or G2, so the digital signal from the input IN1 (phase 1 input) opens the transistors of only one of the bridge diagonals: T1, T4 at P = 1 and T2, T3 at P = 0. The voltage polarity changes accordingly, applied to the motor winding. The pulse-width limiter consists of a current-sense resistor, a comparator and a timer. The timer consists of a diode, an RC circuit and a Schmitt trigger. The limiter stabilizes the current in the winding according to the level Imax =Vref/Rs as follows. Suppose that at a given time P = 1, IN1 = 1, Q = 1 (the capacitor of the timer RC circuit is discharged), the voltage across the current-measuring resistor Rs is less than Vref: IL Rs < Vref (IL is the current through the winding inductance). In this case, transistors T1 and T4 are open, and the current IL gradually increases to Imax. After the comparator is triggered, the capacitor of the timer RC circuit will be charged through diode D. For the time Tm (capacitor discharge duration), transistors T1 and T4 will close. During this time, a voltage of reverse polarity is applied to the winding, and the current decreases by dI = VL(Tm/L). VL \u1d Vm - voltage on the winding, L - inductance of the motor winding. After the end of the timer pulse, transistors T4 and T2 will open, and the polarity of the voltage on the winding will change again. The current in the winding will start to increase again, and it will increase by the value of dI in almost the same time Tm, since during the current decrease the voltage on the winding is almost the same as during the increase. Therefore, the average current Iw in the winding Iw = Imax - dI/XNUMX.

A stepper motor can be made to run in freewheel mode, then its speed will be determined by the applied voltage and the load on the shaft. To do this, it is necessary that the pulses from which the voltages of the traveling wave are formed be generated as a function of the angle of rotation of the rotor, i.e. his position. The design and operation of the stepper motor control circuit in freewheel mode are shown in Fig.45.

For clarity, the considered motor has one pair of rotor poles and two stator windings. The windings are connected through current-limiting resistors, the voltages from the sensors are fed to the inputs of the Schmitt triggers. Figure 45, c shows all four possible combinations of current signs in the windings and the corresponding positions of the rotor. They are at a 45° angle to the vertical, exactly opposite the encoders. When the rotor is in the vicinity of the sensor, the corresponding trigger is activated, as a result, a current is supplied to the windings, attracting the rotor to the next sensor in the direction of rotation. When rotating in the negative direction (clockwise), the switch contact is raised (FR \u1d 1), the voltage V1 switches the current I1 in winding 0, V0 - the current I0 in winding 0. In the initial position, when no current flows through the windings, the rotor is attracted pole to the core of one of the coils, i.e. occupies a position at an angle of 90 or XNUMX ° to the vertical.

When power is applied, the triggers will be set to some states, the rotor will tend to take the appropriate position. At the same time, it will either reach or pass by the sensor, causing the corresponding trigger to be thrown, after which the rotor will begin to rotate uniformly. Note that the described operation and especially start-up procedure is reliable if the sensors generate voltage only by position, without influence of the rotor speed. The simplest and most reliable sensors with these properties are Hall sensors, so they have practically replaced all other types of sensors used in engines.

A cassette recorder usually has a single DC motor that does not change direction. In the vast majority of tape recorders, a three-pole rotor motor is installed, the operation and design of which are shown in Fig. 45.

The requirements for speed stability are met by a regulator circuit that operates by measuring the self-inductance voltage of the motor. This voltage is directly proportional to the speed of rotation and therefore can serve as a speed sensor. The stabilization circuit must maintain the self-induction voltage equal to the specified one.

Figure 46 shows one of the most illustrative schemes that implement this idea. In this scheme, speed stabilization is carried out by comparing the voltages on the motor and its model. The motor is represented by a resistor Rm and a voltage source Em. The model consists of a resistor R2 and a control voltage source Vc. Resistor R2 represents the resistance of the motor; Vc - set self-induction voltage. Resistors R1, Rm, R2, R3 form a bridge for measuring the voltage difference Vc and Em. With a sufficiently large gain, we can assume that V1 = V2, and the motor will rotate at a given speed w0 regardless of the load on its shaft.

Figure 47 shows a block diagram of the Toshiba TA7768F integrated circuit, in which the reference voltage is directly subtracted from the motor voltage. To use this chip, you need to know the ratio of the resistance of resistors R1 / R2.

For a fixed speed, the three-pin circuit is most popular (Fig. 48). In it, a current kIm is supplied to the resistor R1 through the current mirror, which is proportional to the current Im flowing through the motor. The current in resistor R2 and the current drawn by the control circuit also flow through resistor R1, so the motor current must be large enough to be negligible.

In tape recorders with reverse tape movement, it is required to stabilize the speed of rotation of the motor in both directions. To do this, a conventional stabilizer is supplemented with a switch for connecting the engine in a certain polarity.

When setting up the described circuits, first a resistor is selected that simulates the resistance of the motor windings, from the condition of the minimum effect of the load on the motor speed. Then a resistor is selected that sets the rotation speed. The VCR drive shaft motor is multi-phase to reduce the unevenness of its rotation, and sinusoidal voltages are applied to the windings. In the vast majority of cases, three-phase motors with Hall sensors are used. The engine device is shown in Fig. 49, a. Its operation is the same as that of a stepper motor.

The circuit in Fig. 49, a consists of three identical blocks (channels), in each of which a voltage V is formed for the winding of its phase. The block consists of a sensor, a Schmitt trigger, a shaper and an output stage. The engine is represented by a two-pole rotor, the windings are located opposite the sensors. At the moment shown in Fig. 49, a, the north pole of the rotor is located at the phase A sensor, i.e. up to this point in time, a current flowed through the winding of phase A, attracting the rotor pole to it. When the rotor approaches the phase A sensor, the voltage induced in it flips the phase A trigger. The flipping of the trigger causes current to be applied to another phase of the winding, depending on the direction of rotation: in order for the rotor to rotate counterclockwise, current must be supplied to the phase C winding, and in order to rotate in clockwise - into the winding of phase B. The timing diagram of operation is shown in Fig. 49, b.

Stabilization of the speed of rotation of the drive shaft is carried out by the switching impulse of the heads with an accuracy of phase. The head switching pulse is a symmetrical frame frequency pulse uniquely assigned to the frame fields. When recording, a pulse is used that is applied to the control head, which is read from it during playback. The block diagram of the drive shaft motor control is shown in Fig.50.

The speed sensor is a gear disk mounted on the motor rotor and a Hall sensor located on the stator. The frequency of voltage pulses at the output of the Hall sensor is directly proportional to the speed of rotation of the rotor. The signal from the speed sensor is amplified, limited and fed to frequency (FR) and phase (PD) detectors. The output signals of the detectors are summed and fed to the output stage. Braking commands and direction of rotation are also brought to it. The output stage voltage is applied to the motor.

The composition of integrated circuits for engine control includes only individual nodes of the structural diagram Fig.50. Most often, it includes an output stage and a speed sensor amplifier, since they are directly connected to the engine.

Figure 51, a shows a block diagram of the KA8329 chip (Samsung), and Fig. 51, b - HA13406W (Hitachi).

(click to enlarge)

Calculation of electric motors

The nominal data of the engine is called power, speed and voltage. Motor power is expressed in watts. This is not the power consumed from the source, but the mechanical power on the shaft. The choice of power depends on the purpose of the engine. So, for electric toys and models, power up to 3 W is enough, for a small fan - 10-15 W, for a circular saw - hundreds of watts. Engine power is closely related to rotational speed.

For a given power, the higher the engine speed, the smaller its size and less materials will be required. DC and AC commutator motors can be designed for any rotation speed (even up to 10000 rpm). But, based on the conditions for reliable operation of the brushes on the collector, it is not recommended to build motors for a rotation speed of more than 5000 rpm.

In asynchronous motors of all types, the rotor speed depends on the frequency of the alternating current, which remains unchanged. For two-pole motors, which are most commonly used, the synchronous speed at 50 Hz is 3000 rpm (including slip, 2900 rpm). Such speeds of rotation are rarely used directly, usually a gearbox is placed between the engine and the driven mechanism.

The motor voltage is determined by the power supply. An automobile electric motor, for example, counts on battery voltage.

The calculation of DC motors begins with the determination of two main dimensions: the diameter and length of the armature. These dimensions are included in the formula

D²l = Pa 10⁹/1,1 AS B n (cm³), (one)

where D is the diameter of the anchor, cm; l - anchor length, cm; Pa - design power, W; AS - linear load of the anchor, A/cm; B - magnetic induction in the air gap, Gs; n - rated rotation speed, rpm.

The left side of formula (1) is proportional to the armature volume. As can be seen from the right side of (1), the armature volume is proportional to the engine power Pa and inversely proportional to the rotation speed n. From this we can conclude that the greater the rotational speed of the engine armature, the smaller its dimensions are, and the dimensions of the other parts of the engine depend on the size of the armature.

Estimated engine power

Pa = EI = P(1 + 2y)/3y (W), (2)

where E is the EMF induced in the armature winding when it rotates in a magnetic field; I - current consumed by the engine from the source, A; P - rated motor power, W; y - engine efficiency, the value of which can be determined from Fig. 52 (as can be seen from the curve, the efficiency value decreases sharply with a decrease in engine power). The rated power of the motor is always greater than the rated power.

Current consumed by the motor

I \u3d P / U y (A), (XNUMX)

where U is the rated voltage.

Let's define the EMF E:

E \u4d Pa / I (B). (four)

Linear armature load

AS = NI/2πD (A/cm). (5)

In formula (5) N denotes the number of armature winding conductors, the two in the denominator shows that the total armature current I branches between two winding conductors, the product πD is the armature circumference.

The linear load AS and the magnetic induction in the air gap B are called electromagnetic loads. They show how heavily loaded the motor is electrically and magnetically. These values ​​must not exceed a certain limit, otherwise the engine will overheat during operation.

Motor heating depends not only on electromagnetic loads, but also on the time of its operation. Some motors run for a long time without stopping (fan motors). Other motors work intermittently, during which they have time to cool down (motors of vacuum cleaners, refrigerators). The operation of the engine with interruptions is called intermittent operation.

You can determine the linear load and magnetic induction according to Fig. 53 and 54 (where the rated powers divided by the rated rotation speeds are plotted along the horizontal axis, for example, at a power of 15 W and a speed of 3000 rpm, you need to take the number 5 along the abscissa axis).

Let us turn to formula (1). In it, the diameter and length of the anchor are interconnected by a certain ratio. Denote the ratio l/D = k. The value of k for small motors is in the range from 0,7 to 1,2. If a motor with a shorter length but a larger diameter is required, then choose k = 0,7. Conversely, if the engine needs to be placed in a small diameter pipe, then choose k = 1,2. By introducing the relation l/D = k in (1), we get rid of one unknown l, and formula (1) takes the following form:

D = (Pa 10⁹/1,1k AS B n)^1/3 (cm). (6)

Having calculated the value of D, we find l through the coefficient k. Thus, the main dimensions of the engine are determined. Now let's calculate the armature windings. To do this, you need to determine the magnetic flux of the motor. If the magnetic induction in the air gap is multiplied by the area through which the lines of force enter the armature, then we get the motor flux

Ф = B atl, (7)

where t is the pole division, i.e. part of the armature circumference per pole. In a two-pole motor, t = πD/2. The coefficient a is usually taken equal to 0,65. The value of B is found according to the graph in Fig.54. The number of armature conductors is determined by the formula

N = E 60 10⁸/F n. (eight)

The number of conductors cannot be any integer. The armature winding conductors must be equally distributed over the armature slots. The number of slots Z is determined from the relation Z = 3D. It is recommended to take the nearest odd number. The number of conductors in the slot Nz = =N/Z must be even in order to wind the winding in two layers. This choice will be explained with an example.

The cross section of the wire for the armature winding S can be determined by dividing the current in the conductor I by the current density g: S = I / 2g. Curve 1 in Fig. 55 can be used to select the current density.

This section is preliminary. According to the reference book (for example, "Radio Components and Materials", p. 8), you need to find the cross section of a standard wire that is closest to the calculated one. In the same table, we find the diameter of the wire d.

Now let's determine the size of the groove. Its cross section W, necessary to accommodate the winding wires,

W=d² Nz/Kz (mm²). (9)

The coefficient Kz is called the filling factor of the groove. It shows how tightly the conductors fill the groove. When calculating, you can take

Kz = 0,6-0,7.

In the manufacture of the anchor, the groove section should be even larger than according to formula (9), since an insulating sleeve 2 0,2 mm thick and a wedge 3 made of cardboard 0,3 mm thick must still fit in it (Fig. 56).

The area occupied by the sleeve,

Sg = p tg (mm2), (10)

where p - groove perimeter, mm; tg - sleeve thickness, mm.

wedge area

Sc = hk bk (mm2), (11)

where hk - wedge thickness, mm; bk - wedge width, mm.

Thus, the total section of the groove is Sp \u2d W + Sg + Sk. For a round groove, the diameter can be determined from its full cross section dp = XNUMX Sp / p (mm).

Having determined the size of the groove according to Fig. 56, it is possible to calculate the thickness of the tooth. First, we find the diameter of the circle Dn, on which the centers of the grooves will lie. To do this, subtract the diameter of the groove + 1 mm from the diameter of the anchor

D_n = D - (d_n +1).

Distance between adjacent slots

t = pD_n/Z (mm),

tooth thickness

b_z = t - d_n (mm). (four)

The thickness of the tooth at the narrow point must be at least 2 mm. If this does not work, it is necessary to cut grooves of complex shape, and since this is difficult, it is possible to increase the diameter of the anchor in such a way as to obtain teeth with a thickness of at least 2 mm. The slot of the groove "a" must be 1 mm larger than the wire diameter d_of.

Cross section of carbon or graphite brush

S_щ = I/d_щ(5)

where d_щ - current density under the brush.

We turn to the calculation of the magnetic system. For a homemade engine, it is easiest to use an open-type magnetic system (Fig. 57, where 1 is impregnated paper; 2 is a flange; 3 is a coil).

First of all, we determine the air gap q between the armature and the poles. In DC machines, an increased gap is taken, which reduces the demagnetizing effect of the armature magnetic field. Air gap

q = 0,45 t AS/B (cm). (6)

The dimensions of the magnetic system are calculated from magnetic inductions. When calculating the magnetic system of poles and the frame, the value of the magnetic flux should be increased by 10%, since part of the lines of force closes between the sides of the frame, bypassing the anchor. Therefore, the magnetic flux of the poles and bed

Fst \u1,1d XNUMXF.

We accept induction in the frame Vst = 5000 Gs (0,5 T).

We will determine the length of the bed Lst according to the sketch in Fig. 58.

If the shape of the frame corresponds to Fig. 59 (where 1 is a coil; 2 is a pole; 3 is a rivet), then the flow of the frame Fst must be divided in half, since it bifurcates along two parallel paths.

In Fig. 58, the dashed line shows the path of the magnetic flux. It consists of the following sections: two air gaps, two teeth, an anchor and a bed. To find out what magnetizing force Iw the field coil should have, one must calculate Iw for each of these sections, and then add them all up.

Let's start with the air gap. Air gap magnetizing force

I_w = 1,6 qkB, (7)

where q is the air gap from the side of the anchor (cm); k - coefficient that can be taken k = 1,1; B - induction in the air gap (Gs).

To determine the magnetizing force (n.s.) of the armature teeth, you need to know the induction in the tooth. The thickness of the tooth is determined by the formula (4). The magnetic flux enters the tooth through the portion of the armature circumference per tooth. It is called tooth division and is determined by the formula

t₁ = pD/Z. (eight)

The induction in the tooth will be as many times greater than the induction in the air gap, how many times the thickness of the tooth is less than the tooth division. In addition, it must be taken into account that part of the length of the armature is occupied by insulating layers between the sheets, which make up 10%. Therefore, the induction in the tooth

B_z =B_t/b_z 0,9. (9)

According to Table 2, this induction corresponds to the field strength Hz.

Table 2

To calculate n.s. by two tooth heights, Hz must be multiplied by twice the tooth height I_wz = H_z 2h_z. In the table, in the vertical column, the magnetic induction is plotted, expressed in thousands of gauss, and in the horizontal line - in hundreds of gauss. If, for example, the induction is 10500 gauss, then the desired value of the field strength is found at the intersection of row 10000 and column 500 (in this case 6,3). The magnetizing force can be determined by multiplying the intensity by the length of the field line.

When calculating the induction in the armature core, it should be taken into account that the magnetic flux in it branches, and therefore only half of the flux falls on one section. The cross section of the armature core (according to Fig. 58) is equal to the distance h_a from the base of the groove to the shaft, multiplied by the length of the armature h_a = D/2 - h_z - of_b/2. You also need to take into account the insulating layers between the sheets. Thus, the induction in the armature core

B_a = Ф/(2h_al 0,9).

This induction on the above table corresponds to Ha. Magnetizing force of armature core I_w = HL_a, where L_a - the length of the power line in the core according to Fig. 58:

L_a = n(D - 2h_z -h_a)/2 (cm).

As can be seen in Fig. 58, this motor does not have protruding poles that have merged with the frame. Therefore, the calculation of the fixed part of the magnetic circuit is reduced to the calculation of the frame.

The width of the frame is determined by the given induction B = 5000 Gs.

Hence

b_cm = F_cm/5000 x l x 0,9 (cm).

The field strength Hcm for an induction of 5000 Gs is found in Table 2. When determining the length of the field line in the frame, there is difficulty. After all, the length of the side of the bed depends on the thickness of the coil, but it is unknown. Therefore, we take the coil thickness equal to 30 values ​​of the air gap. Having determined the length of the field line in the frame Lst from the sketch, we calculate the magnetizing force (n.s.) for the frame

Iw_Ct =L_Ct Н_Ct.

Now we add the n.s. all sites

Iw₀ =Iw_d +Iw_z +Iw_a +Iw_Ct .

Such a n.s. should create a coil when the engine is idling, but when loaded, the demagnetizing effect of the magnetic field of the armature will appear. Therefore, we need a margin, which we calculate by the formula

Iw_p = 0,15 t AS (A-turns). (ten)

The number of turns of the coil can be calculated from the total Iw: w = Iw/I. To determine the cross section of the wire, you need to divide the current by the current density (we determine it from curve 2 in Fig. 55. According to the tables of the "Radio Components and Materials" reference book, we find the nearest standard cross section and diameter of the wire in insulation d_of. The area occupied by the turns of the coil, F = wd_of2 / k_з (k_з - fill factor). Divide the area F by the length of the coil (on the sketch l_к) and get its width b_к = F/l_к.

DC motor calculation example

Rated motor data: P = 5 W, U = 12 V, n = 4000 rpm. According to the curve in Fig. 52, we determine the engine efficiency of 30%, according to formula (2) - the estimated engine power

Pa \u5d 1 (2 + 0,3x3) / 0,3x8,9 \uXNUMXd XNUMX W.

To find the values ​​of AS and B according to the curves of Fig. 53 and 54, we calculate the ratio of the engine power, expressed in milliwatts, to the rotation speed 5000/4000 = 1,25. From Fig. 53 we find AS = 50 A/cm. Similarly, according to Fig. 54, we find the induction in the air gap B = 2200 Gs. We take the ratio l/D = 1. Substitute the numerical values ​​of the calculated values ​​into formula (6) and find the armature diameter D=(8,9x10⁹/1,1x50x2200x4000)^1/2 = 2,6 cm.

With k = 1, the length of the anchor is l = 2,61 = 2,6 cm.

Armature current according to the formula (3)

I \u5d 0,3 / 12x1,4 \uXNUMXd XNUMX A.

EMF of the armature winding according to the formula (4)

E \u3,14d 2,6 1,4 / 6,3 \uXNUMXd XNUMX V.

Pole division of the anchor t \u3,14d 2,6x2 / 4,1 \uXNUMXd XNUMX cm.

Magnetic flux according to the formula (7)

F \u0,65d 4,1x2,6x2200x15200 \uXNUMXd XNUMX.

The number of conductors of the armature winding according to the formula (8) N = = 6,3x60x10⁸/ 15200x4000 \u620d 3. The number of armature grooves z \u2,6d 7,8x7 \u620d 7. Round up to the nearest odd number z = 88. The number of conductors in the slot is Nz = =2/10= 2. This number is divisible by 1,4, so there is no need to round it. The cross section of the armature winding conductor at d = 2A / mm10 s = 0,07 / 2xXNUMX = XNUMX mmXNUMX.

According to curve 1 Fig.55 with a cross section of 0,07 mm² it is necessary to take the current density of 8 A/mm2. Adjust the wire cross section 0,07x10/8 = 0,085 mm² and wire diameter 0,33 mm. Taking into account the thickness of the insulation, the diameter of the insulated wire is 0,37 mm². The section of the groove according to the formula (9) S = diz2 88/0,7 = 17,2 mm2. The diameter of the circle occupied by the conductors of the winding d0 = (4x17,2 / 3,14) 1/2 = 4,7 mm. The perimeter of the insulating sleeve p \u3,14d \u4,7d 14,7x10 \u14,7d 0,2 mm. The area of ​​the groove occupied by the sleeve according to the formula (2,9) Sg = XNUMX XNUMX = XNUMX mm². The area of ​​the groove occupied by the wedge, according to the formula (11) Sc = 0,3 3 = 0,9 mm². Full section of the groove Sp \u17,2d 2,9 + 0,9 + 21 \uXNUMXd XNUMX mm². Groove diameter dp \u4d (21x3,14 / 1) 2/5,2 \u26d 5,2 mm. The diameter of the circle on which the centers of the grooves are located, Dp = 1 - (19,8 + 3,14) = 19,8 mm. The distance between adjacent grooves is 7 8,9/8,9 = 5,2 mm. The thickness of the tooth at the narrow point bz = 3,7 - 0,37 = 1 mm. Slot slot a \u1,37d 7 + 1,4 \u6d 0,23 mm. The number of collector plates K \uXNUMXd XNUMX. The cross section of the brush Ssh \uXNUMXd XNUMX / XNUMX \uXNUMXd XNUMX cm². You can take a square brush with sides 5 x 5 mm. The air gap between the armature and the pole according to the formula (6, RE 10/2000) is 0,45x4,1x50/2200 = 0,4 mm.

To determine n.s. coils, we will calculate the magnetic circuit according to Fig. 58. N.s. air gap according to the formula (7, RE 10/2000) Iwd = 1,6x0,04x1,1x2200 = 155 A-turns.

Tooth division according to the formula (8, RE 10/2000) t1 = 3,14x2,6/7 = 1,2 cm. Induction in the tooth according to the formula (9, RE 10/2000) Bz = 2200x1,2 / 0,37x0,9, 8000 = 10 gauss. The intensity of the tooth field according to the table (RE 2000/10, p. 4,05) Нz = 4,05. N.s. teeth Iwz \u2d 0,57x4,6x15200 \u2d 0,5 Avitkov. Induction in the armature core Ba = 2,6 / 0,9x6500x3,2x3,2 = 1,5 Gs. According to the same table for this induction, Na = 4,8. N.s. for the armature core Iw = 1,1x15200 = 16700 A-turns. We determine the n.s. for fixed parts of the magnetic circuit. The magnetic flux of the bed Fst = XNUMXxXNUMX = XNUMX.

Let's take the induction in the bed 5000 gauss. Then the bed width bst = 16700/5000x2,6x0,9 = 1,4 cm. According to the table, the induction of 5000 Gs corresponds to the value Hst = 2,5. To determine the length of the field line in the frame, we take the thickness of the coil bk \u30d 30d \u0,04d 1,2x58 \u4,5d 2,5 cm. According to Fig. 4,5, we determine the average length of the field line Lst \u11d 0 cm. beds Iwct \u155d 4,6x4,8 \u11d 175 A-turns. Now we add the n.s. all sections IwXNUMX = XNUMX + XNUMX + XNUMX + XNUMX = XNUMX A-turns.

Demagnetizing force according to the formula (10) Iwp = 0,15x4,1x50 = 31 A-turn. Then n.s. at engine load Iw = 175 + 31 = 206 A-turns. The number of coil turns w = 206 / 1,4 = 147 turns. We take the current density in the coil equal to 5 A / mm², then the wire cross section s = 1,4/5 = 0,28 mm2. The nearest section of a standard wire s = 0,273 mm² and wire diameter 0,59 mm. The diameter of the insulated wire is 0,64 mm. The area occupied by the turns of the coil F = 147x0,642 / 0,7 = 86 mm². The length of the coil according to Fig. 58 is equal to lk = 12 mm. Hence the thickness of the coil bk=86/12=7,2 mm.

Calculation of single-phase asynchronous motors

We set the engine power P (W), voltage U (V) and rotation speed n (rpm). Estimated engine power

value η cos φ is taken from the curve in Fig.60.

Stator outside diameter

Da = (14Pa)^1/3 (cm). ( 2 )

Stator inner diameter

D = 0,55 Da (cm). ( 3 )

Stator length l = D (cm). Pole division t = 3,14 D/2 (cm). We select the magnetic induction in the air gap B according to the curve in Fig. 54. The magnetic flux, as above, is determined by the formula Ф = a B t l. For single-phase motors, the value "a" can be chosen equal to 0,72.

The number of stator slots for motors with a switchable starting winding is selected as a multiple of 6. For motors with a power of up to 10 W, 12 stator slots can be taken. Of these, 8 will be occupied by the working winding, and 4 - by the starting one. For motors of greater power, 18 stator slots are required (12 slots - working winding, 6 - starting). Number of turns of the working winding

w_p = U 10^6/2,5 F. ( 4 )

The number of conductors in the groove of the working winding

N_z = 2w_p/z_p, ( 5 )

where z_p - the number of slots occupied by the working winding. Current in the working winding

I=P_a/U(A). ( 6 )

The cross section of the conductor of the working winding S = I / d. We find the diameter of the wire in insulation as above. The dimensions of the slots are determined similarly to the calculation of DC motors. The starting winding occupies 1/3 of the stator slots. The number of turns of the starting winding depends on which element is switched on during start-up in series with the starting winding. If active resistance serves as an element, then the number of turns of the starting winding is taken 3-4 times less than the number of turns of the working winding. But it occupies 2 times less slots, therefore, in each slot there will be 1,5-2 times fewer turns than in the slot of the working winding. We wind the starting winding with the same wire as the working one. If a capacitor is used as a starting element, then the number of turns of the starting winding is equal to the number of turns of the working one.

In order for the starting winding to fit in its grooves, the wire cross section must be taken half as large. The winding scheme and the order of laying it in the grooves are shown in Fig. 61.

The number of rotor slots is selected depending on the number of stator slots. With 12 stator slots, you can take 9 rotor slots, and with 18 stator slots, 15 rotor slots. The diameter of the rotor groove is chosen so that the total cross section of the rotor rods is 1,5-2 times greater than the total cross section of the conductors of the working stator winding. Copper rods must be driven into the grooves of the rotor, which are soldered to the closing rings at the ends of the rotor. The cross section of the closing ring should be approximately three times the cross section of the rod. The starting torque of the motor depends on the resistance of the rotor winding, therefore, for a motor with a large starting torque, the rotor rods should be made of brass or bronze. The air gap between the stator and the rotor in asynchronous motors should be taken as small as possible. In factory-made engines, the gap is usually 0,25 mm. In homemade engines 0,3-0,4 mm.

The starting capacitor for low power motors is typically 3-10uF. It should be borne in mind that a voltage is generated at the terminals of the capacitor that is much higher than the mains voltage, so the capacitors must be set to a voltage equal to three times the mains voltage. With a decrease in voltage, the capacitance of the capacitor increases according to a quadratic law, therefore, for an operating voltage of 12 V, capacitors of a huge capacity (up to 1000 microfarads) would have to be taken.

An example of the calculation of a single-phase asynchronous motor

Rated data: power 3 W, voltage 220 V, rotation speed 3000 rpm, intermittent operation of the engine. According to the curve in Fig. 60 we find the product η cos φ = 0,25.

Estimated engine power according to the formula (1) P_а = 3 / 0,25 = 12 V.A. The outer diameter of the stator according to the formula (2)

D_a =(14x12)^1/3 = 5,5 cm.

To simplify, let's take the shape of the stator in the form of a square described near the outer diameter (Fig. 62).

The inner diameter of the stator according to the formula (3) D = 0,55x0,55 = 3 cm. The length of the stator l = 3 cm. Pole division t = 3,14x3/2 = 4,7 cm. Magnetic induction in the air gap along the upper curve ( see Fig. 54) is equal to 2800 Gauss, but with a square stator, it has to be increased to 4000 Gauss. Magnetic flux Ф \u0,72d 4000x4,7x3x40600 \u12d 8. The number of stator slots is 4, of which 4 for the working winding, XNUMX for the starting one. The number of turns of the working winding according to (XNUMX)

w_p = 220х10⁶/ 2,5x40600 = 2170 turns.

The number of conductors in the groove of the working winding N_z \u2d 2170x8 / 542 \u6d 12. Current strength in the working winding according to formula (220) I \u0,055d 5/XNUMX \uXNUMXd XNUMX A. At current density d \uXNUMXd XNUMX A / mm² wire cross section s = 0,055/5 = 0,011 mm². This section corresponds to the diameter of the PEL wire in insulation 0,145 mm. With a fill factor of the groove with conductors equal to 0,5, the area of ​​the groove occupied by the conductors is s = 0,1452x542 / 0,5 = 27 mm². The diameter of the circle occupied by the conductors of the winding, d₀ \u4d (27x3,14 / 1) 2/5,9 \u3,14d 5,9 mm. The perimeter of the insulating sleeve p \u18,3d XNUMXxXNUMX \uXNUMXd XNUMX mm. Groove area occupied by the sleeve, S_z = 18,3x0,2 = 3,7 mm². Groove area occupied by the wedge Sk = 0,3x3 = 0,9 mm². The total section of the groove S = 27 + 3,7 + 0,9 = 31,6 mm2. Groove diameter dn \u4d (31,6x3,14 / 1) 2/6,3 \u6,5d XNUMX mm, rounded up to XNUMX mm. The diameter of the circle on which the centers of the grooves are located, D_n = 30 + (6,5 + 1) = 37,5 mm.

The distance between adjacent grooves t \u3,14d 37,5x12 / 9,6 \u9,6d 6,5 mm. The thickness of the tooth at the narrow point bz = 3,1 - 0,145 = 1 mm. Groove cut a = 1,145 + 1,2 = XNUMX mm, rounded up to XNUMX mm.

The air gap is assumed to be 0,3 mm. Rotor diameter Dp = 30 - 2x0,3 = 29,4 mm. The number of rotor slots is 9. The total copper section in the slots of the working stator winding is 0,011x542x8 = 47 mm². The total copper section in the rotor slots is 47x1,5 = 70,5 mm2. Cross section of the rotor rod 70,5: 9 = 7,8 mm². Rotor rod diameter (4x7,8/3,14)^1/2 = 3,1 mm. The closest standard wire diameter is 3,05mm. Rotor slot diameter with allowance for driving rods 3,05 + 0,25 = 3,3 mm. The diameter of the circle on which the centers of the rotor slots are located is 29,4 - (3,3 + 1) = 25,1 mm. The distance between adjacent grooves is 3,14x25,1/9 = 8,7 mm. The thickness of the rotor tooth at the narrow point is 8,7 - 3,3 = 5,4 mm.

Author: A.D. Pryadko

See other articles Section Electric motors.

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