Calculation of the V-belt pulley diameter. Calculation of the diameters of the belt transmission pulleys for a poly V-belt. Online calculator Calculating the number of revolutions per pulleys

". The remaining dimensions of the pulley are determined as follows.

For flat belt pulleys (see fig. 1) diameter d, rim width V and the bulge arrow y taken in accordance with GOST 17383-73, depending on the width b belt. Thickness s rims at the edge of the pulleys take:
for cast iron pulleys

For steel coiled pulleys

Rice. 1

For V-belt pulleys, the dimensions of the groove profile (Fig. 2) s, e, t, s, b and φ regulated by GOST 20898-80, depending on the profile of the belt section. The limits of the calculated diameters and the number of grooves of V-belt transmission pulleys are standardized by GOST 20889-80 .... 20897-80, depending on the profile of the belt section and the pulley design. V-belt pulley rim width (fig. 2)

where z is the number of grooves. The thickness of the rim is taken depending on the design.

Rice. 2

Outside diameter d ′ and hub length l c(see fig. 1):

title = "(! LANG: l_c = B / 3 + d_b> = 1,5d_b">!}
where d- shaft diameter.

Number of spokes

where d- pulley diameter, mm. If k c ≤3, then the pulley is performed with a disk, if k c> 3, then the pulley is made with spokes, and their number is recommended to be taken even.

Spokes are designed to bend from circumferential force F t conventionally considering them in the form of cantilever beams with a length d / 2 embedded in the hub along its diametrical section. Given the uneven distribution of the load between the spokes and the conventionality of this calculation of the spokes, we can assume that the circumferential force F t perceived ⅓ all spokes. Thus, the required moment of resistance of the conditional cross section spokes passing through the axis of the pulley,

or

The permissible bending stress is taken:

for cast iron [σ i] = 30 ... 45 MPa
for steel [σ i] = 60 ... 100 MPa.

Rice. 3

In cast iron pulleys, the thickness of the spokes is taken in the design section (see Fig. 3)
where h- the width of the spoke in the design section. Since for an ellipse

then it follows from the formulas that

where

The dimensions of various composite pulleys made from shaped parts are taken according to design and technological parameters.

The overhaul of the electric motor is nearing completion. We start calculating the pulleys belt transmission machine tool. A bit of belt drive terminology.

We will have three values as the main initial data. The first value is the rotational speed of the rotor (shaft) of the electric motor 2790 revolutions per second. The second and third are the speeds that need to be obtained on the output shaft. We are interested in two denominations of 1800 and 3500 rpm. Therefore, we will make a two-stage pulley.

The note! To start three-phase electric motor we will use a frequency converter therefore, the calculated rotational speeds will be reliable. If the engine is started using capacitors, then the values of the rotor speed will differ from the nominal in the lower direction. And at this stage it is possible to reduce the error to a minimum by making corrections. But for this you have to start the engine, use a tachometer and measure the current speed of rotation of the shaft.

Our goals have been determined, we move on to the choice of the type of belt and to the basic calculation. For each of the produced belts, regardless of the type (V-belt, poly-V-belt or other), there are a number of key characteristics. Which determine the rationality of the application in a particular design. Ideal option most projects will use a poly V-belt. The poly-wedge-shaped one got its name due to its configuration, it is a type of long closed furrows located along its entire length. The name of the belt comes from the Greek word poly, which means many. These furrows are also called by another - ribs or streams. Their number can be from three to twenty.

A poly-V-belt in front of a V-belt has a lot of advantages, such as:

due to its good flexibility, it is possible to work on small pulleys. Depending on the belt, the minimum diameter can start from ten to twelve millimeters;
high traction capacity of the belt, therefore, the operating speed can reach up to 60 meters per second, versus 20, maximum 35 meters per second for a V-belt;
the adhesion force of a poly V-belt with a flat pulley at a wrap angle of more than 133 ° is approximately equal to the adhesion force with a grooved pulley, and with an increase in the wrap angle, the adhesion force becomes higher. Therefore, for drives with a gear ratio of more than three and a wrap angle of a small pulley from 120 ° to 150 °, a flat (without grooves) larger pulley can be used;
due to the light weight of the belt, vibration levels are much lower.

Taking into account all the advantages of multi-V-belts, we will use this type in our designs. Below is a table of the five main sections of the most common poly V-belts (PH, PJ, PK, PL, PM).

Designation	PH	PJ	PK	PL	PM
Rib step, S, mm	1.6	2.34	3.56	4.7	9.4
Belt height, H, mm	2.7	4.0	5.4	9.0	14.2
Neutral layer, h0, mm	0.8	1.2	1.5	3.0	4.0
Distance to the neutral layer, h, mm	1.0	1.1	1.5	1.5	2.0
	13	20	45	75	180
Maximum speed, Vmax, m / s	60	60	50	40	35
Length range, L, mm	1140…2404	356…2489	527…2550	991…2235	2286…16764

Sectional drawing of the elements of a poly V-belt.

For both the belt and the mating pulley, there is a corresponding table with characteristics for the manufacture of pulleys.

Cross section	PH	PJ	PK	PL	PM
Distance between grooves, e, mm	1.60 ± 0.03	2.34 ± 0.03	3.56 ± 0.05	4.70 ± 0.05	9.40 ± 0.08
Total size error e, mm	± 0.3	± 0.3	± 0.3	± 0.3	± 0.3
Distance from the edge of the pulley fmin, mm	1.3	1.8	2.5	3.3	6.4
Wedge angle α, °	40 ± 0.5 °	40 ± 0.5 °	40 ± 0.5 °	40 ± 0.5 °	40 ± 0.5 °
Radius ra, mm	0.15	0.2	0.25	0.4	0.75
Radius ri, mm	0.3	0.4	0.5	0.4	0.75
Minimum diameter pulley, db, mm	13	12	45	75	180

The minimum radius of the pulley is not set casually, this parameter controls the belt service life. It will be best if you deviate slightly from the minimum diameter in big side... For a specific task, we have chosen the most common type "RK" belt. The minimum radius for this type of belt is 45 millimeters. Taking this into account, we will also build on the diameters of the available blanks. In our case, there are blanks with a diameter of 100 and 80 millimeters. We will adjust the diameters of the pulleys under them.

We start the calculation. Let's cite our initial data again and outline the goals. The rotation speed of the electric motor shaft is 2790 rpm. Poly-V-belt type "RK". The minimum diameter of the pulley, which is regulated for it, is 45 millimeters, the height of the neutral layer is 1.5 millimeters. We need to determine the optimal diameters of the pulleys, taking into account the required speeds. The first speed of the output shaft is 1800 rpm, the second speed is 3500 rpm. Therefore, we get two pairs of pulleys: the first is 2790 at 1800 rpm, and the second is 2790 at 3500. The first step is to find the gear ratio of each of the pairs.

Gear ratio formula:

, where n1 and n2 are the speeds of rotation of the shafts, D1 and D2 are the diameters of the pulleys.

First pair 2790/1800 = 1.55
Second pair 2790/3500 = 0.797

, where h0 is the neutral layer of the belt, the parameter from the table above.

D2 = 45x1.55 + 2x1.5x (1.55 - 1) = 71.4 mm

For the convenience of calculations and selection optimal diameters pulleys can be used online calculator.

Instructions how to use the calculator... First, let's define the units of measurement. All parameters except speed are indicated in millimeters, speed is indicated in revolutions per minute. In the "Neutral belt layer" field, enter the parameter from the table above, the "PК" column. Enter the value h0 equal to 1.5 millimeters. In the next field, we set the rotational speed of the shaft of the electric motor at 2790 rpm. In the field the diameter of the electric motor pulley, enter the value that is minimum regulated for a specific type of belt, in our case it is 45 millimeters. Next, we enter the speed parameter with which we want the driven shaft to rotate. In our case, this value is 1800 rpm. Now it remains to press the "Calculate" button. The diameter of the reciprocal pulley, we get the corresponding in the field, and it is 71.4 millimeters.

Note: If it is necessary to perform an estimate calculation for a flat or V-shaped belt, then the value of the neutral layer of the belt can be neglected by setting the value in the field "ho" to "0".

Now we can (if necessary or required) increase the diameters of the pulleys. For example, this may be needed to increase the life of a drive belt or to increase the adhesion coefficient of a belt-pulley pair. Also, large pulleys are sometimes made on purpose to perform the function of a flywheel. But now we want to fit into the blanks as much as possible (we have blanks with a diameter of 100 and 80 millimeters) and, accordingly, we will select for ourselves optimal sizes pulleys. After several iterations of the values, we settled on the following diameters D1 - 60 millimeters and D2 - 94.5 millimeters for the first pair.

The belt drive transmits torque from the drive shaft to the driven shaft. Depending on it, it can increase or decrease revs. The gear ratio depends on the ratio of the diameters of the pulleys - drive wheels connected by a belt. When calculating the parameters of the drive, you must also take into account the power on the drive shaft, the speed of its rotation and the overall dimensions of the device.

Belt drive device, its characteristics

The belt drive is a pair of pulleys connected by an endless loopback belt. These drive wheels are typically in the same plane and the axes are made parallel, with the drive wheels rotating in the same direction. Flat (or round) belts allow you to change the direction of rotation due to crossing, and the relative position of the axes due to the use of additional passive rollers. In this case, part of the power is lost.

V-belt drives due to the V-shape of the cross-section of the belt allow to increase the area of its engagement with the belt pulley. A wedge-shaped groove is made on it.
Toothed belt drives have equal pitch and profile teeth on the inner side of the belt and on the surface of the rim. They do not slip, allowing more power to be transmitted.

The following basic parameters are important for calculating the drive:

the number of revolutions of the drive shaft;
the power transmitted by the drive;
required number of revolutions of the driven shaft;
belt profile, thickness and length;
calculated, external, inner diameter wheels;
groove profile (for V-belt);
transmission pitch (for toothed belt)
center distance;

Calculations are usually carried out in several stages.

Basic diameters

To calculate the parameters of the pulleys, as well as the drive as a whole, are used different meanings diameters, so, for the V-belt pulley, the following are used:

estimated D calc;
outer D bunk;
internal, or landing D int.

To calculate the gear ratio, the calculated diameter is used, and the outer one is used to calculate the dimensions of the drive when assembling the mechanism.

For a toothed belt drive D, the design differs from the D bunk by the height of the tooth.
The gear ratio is also calculated based on the value of D cal.

To calculate a flat-belt drive, especially with a large rim size relative to the profile thickness, D calc is often taken to be equal to the outer one.

Pulley diameter calculation

First, you should determine the gear ratio, based on the inherent rotational speed of the drive shaft n1 and the required rotational speed of the driven shaft n2 / It will be equal to:

If a ready-made engine with a drive wheel is already available, the calculation of the pulley diameter according to i is carried out according to the formula:

If the mechanism is designed from scratch, then theoretically, any pair of drive wheels satisfying the condition will be suitable:

In practice, the calculation of the drive wheel is carried out based on:

Dimensions and design of the drive shaft. The part must be securely attached to the shaft, correspond to it in terms of the size of the inner hole, the method of fitting, and fastening. The maximum minimum pulley diameter is usually taken from the ratio D calc ≥ 2.5 D vn
Permissible transmission dimensions. When designing mechanisms, you need to keep within dimensions... In this case, the center distance is also taken into account. the smaller it is, the more the belt bends when flowing around the rim and the more it wears out. Too much long distance leads to the excitation of longitudinal vibrations. The distance is also specified based on the length of the belt. If you do not plan to manufacture a unique part, then the length is chosen from the standard range.
The transmitted power. The material of the part must withstand angular loads. This is true for high powers and torques.

The final calculation of the diameter is finally clarified according to the result of the overall and power estimates.

The overhaul of the electric motor is nearing completion. We proceed to the calculation of the belt drive pulleys of the machine. A bit of belt drive terminology.

The note! To start a three-phase electric motor, we will use a frequency converter, so the calculated rotation speeds will be reliable. If the engine is started using capacitors, then the values of the rotor speed will differ from the nominal in the lower direction. And at this stage it is possible to reduce the error to a minimum by making corrections. But for this you have to start the engine, use a tachometer and measure the current speed of rotation of the shaft.

Our goals have been determined, we move on to the choice of the type of belt and to the basic calculation. For each of the produced belts, regardless of the type (V-belt, poly-V-belt or other), there are a number of key characteristics. Which determine the rationality of the application in a particular design. A poly V-belt is ideal for most projects. The poly-wedge-shaped one got its name due to its configuration, it is a type of long closed furrows located along its entire length. The name of the belt comes from the Greek word poly, which means many. These furrows are also called by another - ribs or streams. Their number can be from three to twenty.

A poly-V-belt in front of a V-belt has a lot of advantages, such as:

due to its good flexibility, it is possible to work on small pulleys. Depending on the belt, the minimum diameter can start from ten to twelve millimeters;
high traction capacity of the belt, therefore, the operating speed can reach up to 60 meters per second, versus 20, maximum 35 meters per second for a V-belt;
the adhesion force of a poly V-belt with a flat pulley at a wrap angle of more than 133 ° is approximately equal to the adhesion force with a grooved pulley, and with an increase in the wrap angle, the adhesion force becomes higher. Therefore, for drives with a gear ratio of more than three and a wrap angle of a small pulley from 120 ° to 150 °, a flat (without grooves) larger pulley can be used;
due to the light weight of the belt, vibration levels are much lower.

Taking into account all the advantages of multi-V-belts, we will use this type in our designs. Below is a table of the five main sections of the most common poly V-belts (PH, PJ, PK, PL, PM).

Designation	PH	PJ	PK	PL	PM
Rib step, S, mm	1.6	2.34	3.56	4.7	9.4
Belt height, H, mm	2.7	4.0	5.4	9.0	14.2
Neutral layer, h0, mm	0.8	1.2	1.5	3.0	4.0
Distance to the neutral layer, h, mm	1.0	1.1	1.5	1.5	2.0
	13	20	45	75	180
Maximum speed, Vmax, m / s	60	60	50	40	35
Length range, L, mm	1140…2404	356…2489	527…2550	991…2235	2286…16764

Sectional drawing of the elements of a poly V-belt.

For both the belt and the mating pulley, there is a corresponding table with characteristics for the manufacture of pulleys.

Cross section	PH	PJ	PK	PL	PM
Distance between grooves, e, mm	1.60 ± 0.03	2.34 ± 0.03	3.56 ± 0.05	4.70 ± 0.05	9.40 ± 0.08
Total size error e, mm	± 0.3	± 0.3	± 0.3	± 0.3	± 0.3
Distance from the edge of the pulley fmin, mm	1.3	1.8	2.5	3.3	6.4
Wedge angle α, °	40 ± 0.5 °	40 ± 0.5 °	40 ± 0.5 °	40 ± 0.5 °	40 ± 0.5 °
Radius ra, mm	0.15	0.2	0.25	0.4	0.75
Radius ri, mm	0.3	0.4	0.5	0.4	0.75
Minimum pulley diameter, db, mm	13	12	45	75	180

The minimum radius of the pulley is not set casually, this parameter controls the belt service life. It will be best if you deviate slightly from the minimum diameter to a larger side. For a specific task, we have chosen the most common type "RK" belt. The minimum radius for this type of belt is 45 millimeters. Taking this into account, we will also build on the diameters of the available blanks. In our case, there are blanks with a diameter of 100 and 80 millimeters. We will adjust the diameters of the pulleys under them.

Gear ratio formula:

, where n1 and n2 are the speeds of rotation of the shafts, D1 and D2 are the diameters of the pulleys.

First pair 2790/1800 = 1.55
Second pair 2790/3500 = 0.797

, where h0 is the neutral layer of the belt, the parameter from the table above.

D2 = 45x1.55 + 2x1.5x (1.55 - 1) = 71.4 mm

For the convenience of calculations and selection of the optimal pulley diameters, you can use the online calculator.

Now we can (if necessary or required) increase the diameters of the pulleys. For example, this may be needed to increase the life of a drive belt or to increase the adhesion coefficient of a belt-pulley pair. Also, large pulleys are sometimes made on purpose to perform the function of a flywheel. But now we want to fit into the workpieces as much as possible (we have workpieces with a diameter of 100 and 80 millimeters) and, accordingly, we will select the optimal pulley sizes for ourselves. After several iterations of the values, we settled on the following diameters D1 - 60 millimeters and D2 - 94.5 millimeters for the first pair.

When designing equipment, it is necessary to know the number of revolutions of the electric motor. There are special formulas for calculating the speed, which are different for AC and DC motors.

Synchronous and asynchronous electrical machines

There are three types of AC motors: synchronous, angular velocity the rotor of which coincides with the angular frequency of the stator magnetic field; asynchronous - in them, the rotation of the rotor lags behind the rotation of the field; collector, the design and principle of operation of which are similar to DC motors.

Synchronous speed

Rotational speed of the electric machine alternating current depends on the angular frequency of the stator magnetic field. This speed is called synchronous. In synchronous motors, the shaft rotates at the same speed, which is the advantage of these electric machines.

To do this, there is a winding in the rotor of high-power machines, to which a constant voltage is applied, which creates a magnetic field. In devices low power inserted into the rotor permanent magnets, or there are pronounced poles.

Slip

In asynchronous machines, the shaft speed is less than the synchronous angular frequency. This difference is called "S" slip. Sliding in the rotor induces electricity and the shaft rotates. The larger S, the higher the torque and less speed... However, when the slip exceeds a certain value, the electric motor stops, begins to overheat and may fail. The rotational speed of such devices is calculated using the formula in the figure below, where:

n is the number of revolutions per minute,
f - network frequency,
p is the number of pole pairs,
s - slip.

There are two types of such devices:

WITH squirrel cage rotor... The winding in it is cast from aluminum during the manufacturing process;
With phase rotor. The windings are made of wire and are connected to additional resistances.

Speed control

In the process of work, it becomes necessary to adjust the speed electric cars... It is carried out in three ways:

Increase of additional resistance in the rotor circuit of electric motors with a wound rotor. If it is necessary to greatly reduce the speed, it is allowed to connect not three, but two resistances;
Connection of additional resistances in the stator circuit. It is used for starting high-power electric cars and for adjusting the speed of small electric motors. For example, the speed of a desktop fan can be reduced by connecting an incandescent lamp or capacitor in series with it. The same result is obtained by reducing the supply voltage;
Changing the network frequency. Suitable for synchronous and asynchronous motors.

Attention! The speed of rotation of collector electric motors powered by an alternating current network does not depend on the frequency of the network.

DC motors

In addition to AC voltage machines, there are electric motors that are connected to the network direct current... The number of revolutions of such devices is calculated using completely different formulas.

Rated speed of rotation

The number of revolutions of the DC apparatus is calculated using the formula in the figure below, where:

n is the number of revolutions per minute,
U - mains voltage,
Rя and Iя - resistance and armature current,
Ce - motor constant (depends on the type of electric machine),
Ф - stator magnetic field.

These data correspond to the nominal values of the parameters of the electric machine, the voltage on the field winding and the armature or the torque on the motor shaft. Changing them allows you to adjust the speed. It is very difficult to determine the magnetic flux in a real motor, therefore, for calculations, they use the strength of the current flowing through the excitation winding or the voltage at the armature.

The number of revolutions of AC brushed motors can be found using the same formula.

Speed regulation

Adjustment of the speed of an electric motor powered by a DC network is possible within a wide range. It is available in two ranges:

Up from par. For this, the magnetic flux is reduced using additional resistances or a voltage regulator;
Down from par. To do this, it is necessary to reduce the voltage at the armature of the electric motor or include a resistance in series with it. In addition to reducing the number of revolutions, this is done when starting the electric motor.

Knowing which formulas are used to calculate the speed of rotation of an electric motor is necessary when designing and setting up equipment.