Calculation of V-belt transmission. Belt drive calculation How to calculate the speed on the pulleys

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

For flat belt pulleys (see fig. 1) diameter d, rim width AT and arrow bulge y accept according to GOST 17383-73 depending on the width b belt. Thickness s rims at the edge of the pulleys accept:
for cast iron pulleys

For steel coiled pulleys

For V-belt pulleys, groove profile dimensions (fig. 2) c, e, t, s, b and φ are regulated by GOST 20898-80 depending on the profile of the belt section. The limits of the design diameters and the number of grooves of the V-belt 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- number of grooves. The thickness of the rim is taken depending on the design.

Outside diameter d' and hub length lc(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 a k c ≤3, then the pulley is made with a disk if k c >3, then the pulley is made with spokes, and it is recommended to take their number even.

Spokes count on bending from the action of 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. Taking into account the uneven distribution of the load between the spokes and the conditionality 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 of the spoke passing through the pulley axis is

or

Allowable bending stress is taken:

• for cast iron [σi]=30...45 MPa
• for steel [σi]=60...100 MPa.

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

then it follows from the formulas that

where

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

Works on the bulkhead of the electric motor are nearing completion. We proceed to the calculation of the belt drive pulleys of the machine. A little bit of belt drive terminology.

We will have three main input data. The first value is the speed of rotation 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 secondary shaft. We are interested in two denominations of 1800 and 3500 rpm. Therefore, we will make a two-stage pulley.

The note! To start a three-phase electric motor, we will use a frequency converter therefore, 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 one in a smaller direction. And at this stage, it is possible to minimize the error by making adjustments. But for this you have to start the engine, use the tachometer and measure the current speed of rotation of the shaft.

Our goals are defined, we proceed to the choice of the type of belt and to the main calculation. For each of the produced belts, regardless of the type (V-belt, multi-V-belt or other), there are a number of key characteristics. Which determine the rationality of the application in a particular design. The ideal option most projects will use a ribbed belt. The polywedge-shaped got its name due to its configuration, it is a type of long closed furrows located along the entire length. The name of the belt comes from the Greek word "poly", which means many. These furrows are also called differently - ribs or streams. Their number can be from three to twenty.

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

• due to good flexibility, work on small pulleys is possible. Depending on the belt, the minimum diameter can start from ten to twelve millimeters;
• high traction ability of the belt, therefore, the operating speed can reach up to 60 meters per second, against 20, a maximum of 35 meters per second for the V-belt;
• The grip force of a V-ribbed belt with a flat pulley at a wrap angle over 133° is approximately equal to the grip force with a grooved pulley, and as the wrap angle increases, the grip becomes higher. Therefore, for drives with a gear ratio greater than three and a small pulley wrap angle 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 poly V-belts, we will use this type in our designs. Below is a table of the five main sections of the most common V-ribbed belts (PH, PJ, PK, PL, PM).

Drawing of a schematic designation of the elements of a poly-V-belt in a section.

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

The minimum pulley radius is set for a reason, this parameter regulates the life of the belt. It would be best if you deviate slightly from the minimum diameter to the larger side. For specific task we have chosen the most common belt of the "RK" type. Minimum radius for of this type belts is 45 millimeters. Given this, we will also start from the diameters of the available blanks. In our case, there are blanks with a diameter of 100 and 80 millimeters. Under them, we will adjust the diameters of the pulleys.

We start the calculation. Let’s revisit our initial data and set goals. The speed of rotation of the 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 pulley diameters, taking into account the required speeds. The first speed of the secondary 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. First of all, we will find the gear ratio of each of the pairs.

The formula for determining the gear ratio:

, where n1 and n2 are shaft rotation speeds, D1 and D2 are pulley diameters.

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

, where h0 is the neutral layer of the belt, 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.

Instruction how to use 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 "PK" column. We enter the value h0 equal to 1.5 millimeters. In the next field, set the rotation speed of the motor shaft to 2790 rpm. In the electric motor pulley diameter field, enter the minimum value regulated for a particular 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 click the "Calculate" button. We will get the corresponding diameter of the counter pulley in the field, and it is 71.4 millimeters.

Note: If it is necessary to perform an estimated calculation for a flat belt or a V-belt, then the value of the neutral layer of the belt can be neglected by setting the “ho” field 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 the drive belt or increase the coefficient of adhesion of the belt-pulley pair. Also, large pulleys are sometimes made intentionally 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 dimensions pulleys. After several iterations of values, we settled on the following diameters D1 - 60 millimeters and D2 - 94.5 millimeters for the first pair.

Gear classification. Depending on the shape of the cross-section of the transmission belt, there are: flat-belt, V-belt, round-belt, poly-V-belt (Fig. 69). Flat-belt transmissions by location are cross and semi-cross (angular), fig. 70. In modern mechanical engineering, V-belts and V-ribbed belts are most widely used. Round belt transmission has limited application ( sewing machines, desktop machines, devices).

The type of belt drive is toothed belt, which transfers the load by engaging the belt with pulleys.

Rice. 70. Types of flat-belt gears: a - cross, B - semi-cross (angular)

Appointment. Belt transmissions are mechanical friction transmissions with a flexible connection and are used if it is necessary to transfer the load between shafts that are located at considerable distances and in the absence of strict requirements for the gear ratio. The belt drive consists of driving and driven pulleys located at some distance from each other and connected by a belt (belts) put on tensioned pulleys. The rotation of the driving pulley is converted into rotation of the driven pulley due to the friction developed between the belt and the pulleys. According to the cross-sectional shape flat , Wedge , Polyclinic and Round drive belts. There are flat belt transmissions - open , which carry out transmission between parallel shafts rotating in one direction; cross, which carry out the transmission between parallel shafts when the pulleys rotate in opposite directions; in Corner (semi-cross) In flat belt drives, pulleys are located on intersecting (usually at right angles) shafts. To ensure friction between the pulley and the belt, the belts are tensioned by preliminary elastic deformation, by moving one of the transmission pulleys or using a tension roller (pulley).

Advantages. Due to the elasticity of the belts, the transmissions operate smoothly, without shock and silently. They protect the mechanisms from overload due to possible slippage of the belts. Flat-belt transmissions are used at large center distances and operating at high belt speeds (up to 100 m/s). With small center distances, large gear ratios and transmission of rotation from one drive pulley to several driven pulleys, V-belt drives are preferable. Low transmission cost. Ease of installation and maintenance.

Disadvantages. Large gears. Gear ratio change due to belt slippage. Increased loads on shaft bearings with pulleys. The need for belt tensioners. Poor belt durability.

Application areas. Flat belt transmission is simpler, but V-belt transmission has increased traction and fits into smaller dimensions.

V-ribbed belts - flat belts with longitudinal wedge-shaped projections-ribs on the working surface, which are included in the V-grooves of the pulleys. These belts combine the advantages of flat belts - flexibility and V-belts - increased adhesion to pulleys.

Round belt drives are used in small machines, such as sewing machines and Food Industry, desktop machines, as well as various devices.

In terms of power, belt drives are used in various machines and units at 50 HF T, (in some transmissions up to 5000 kW), at peripheral speed - 40 m/s, (in some programs up to 100 m/s), according to gear ratios 15, gear efficiency: flat belt 0.93 ... 0.98, and V-belt - 0.87 ... 0.96.

Rice. 71 Belt drive scheme.

Force calculation . Circumferential force on the drive pulley

. (12.1)

The calculation of belt drives is performed according to the calculated circumferential force, taking into account the dynamic load factor AND the transmission mode:

Where is the dynamic load factor, which is taken = 1 at a calm load, = 1.1 - moderate load fluctuations, = 1.25 - significant load fluctuations, = 1.5 - shock loads.

Belt initial tension F O (pre-tension) is taken so that the belt can maintain this tension sufficiently long time, without being exposed to a large hood and without losing the required durability. Accordingly, the initial tension in the belt for flat standard belts without automatic tensioners = 1.8 MPa; with automatic tensioners = 2MPa; for wedge standard belts =1.2...1.5 MPa; for polyamide belts = 3...4 MPa.

Initial belt tension

Where BUT - The cross-sectional area of ​​a flat-belt drive belt, or the cross-sectional area of ​​all V-belt drive belts.

Tension forces driving and driven S 2 Belt branches in a loaded transmission can be determined from the pulley balance condition (Fig. 72).

Rice. 72. Scheme for the power calculation of the transmission.

From the equilibrium condition of the drive pulley

(12.4)

Taking into account (12.2), the circumferential force on the drive pulley

Lead Strand Tension

, (12.6)

Driven branch tension

. (12.7)

Drive shaft pressure

. (12.8)

The relationship between the tension forces of the driving and driven branches is approximately determined by the Euler formula, according to which the tensions of the ends of a flexible, weightless, inextensible thread enclosing the drum are related by the dependence

Where is the coefficient of friction between the belt and the pulley, is the angle of the pulley.

The average value of the coefficient of friction for cast iron and steel pulleys can be taken: for rubber belts = 0.35, for leather belts = 0.22 and for cotton and wool belts = 0.3.

When determining the friction forces in a V-belt transmission, in the formulas, instead of the coefficient, friction, it is necessary to substitute the reduced coefficient of friction for V-belts

, (12.10)

Where is the angle of the belt wedge.

By joint consideration of the given force ratios for the belt, we obtain the circumferential force on the drive pulley

, (12.11)

Where is the thrust coefficient, which is determined by the dependence

Increasing the circumferential force on the drive pulley can be achieved by increasing the belt pretension or by increasing the traction coefficient, which increases with an increase in wrap angle and coefficient of friction.

In the tables with reference data on the characteristics of the belts, their sizes are indicated, taking into account the necessary traction coefficients.

geometric calculation . The estimated length of the belts with a known center distance and pulley diameters (Fig. 71):

Where . For final belts, the length is finally agreed with the standard lengths according to GOST. For this, a geometric calculation is performed according to the scheme shown in Fig. 73.

Fig.73. Scheme for the geometric calculation of the belt drive

According to the finally established length of a flat or V-belt open transmission, the actual center distance of the transmission, provided that

Calculation formulas without taking into account sagging and initial deformation of the belt.

The angle of the belt around the drive pulley in radians:

, (12.14)

In degrees .

The procedure for performing design calculations. For belt transmission in the design calculation according to given parameters(power, torque, angular, speed and gear ratio) determines the dimensions of the belt and drive pulley, which provide the necessary fatigue strength of the belt and the critical traction coefficient at maximum efficiency. According to the selected diameter of the drive pulley, the remaining dimensions are determined from the geometric calculation:

Design calculation of a flat belt transmission according to traction ability, they are produced according to the allowable useful voltage , Which is determined by the slip curves. As a result of the calculation, the width of the belt is determined by the formula:

, (12.15)

Where is the circumferential force in the transmission; - allowable specific circumferential force, which corresponds to the maximum traction coefficient, which is determined at a belt speed =10 m/s and a wrap angle =1800; - coefficient of gear location depending on the angle of inclination of the center line to the horizontal line: =1.0, 0.9, 0.8 for inclination angles =0…600, 60…800, 80…900; - pulley wrap angle coefficient; - speed coefficient: ; - coefficient of the operating mode, which is accepted: =1.0 quiet load; =0.9 load with small changes, =0.8 - load with large fluctuations, =0.7 - shock loads.

For calculation, the diameter of the drive pulley is preliminarily determined by empirical formulas

, (12.16)

Where is the transmitted power in kW, is the rotational speed.

The drive pulley diameter is rounded to the nearest standard.

The type of belt is accepted, according to which the allowable specific circumferential force is determined according to table 12.1.

Table 12.1

Parameters of flat drive belts

The calculated belt width is rounded up to the nearest standard width according to Table 12.2.

Table 12.2 Standard Width of Flat Drive Belts

Table 12.3 Flat belt pulley rim width.

Design calculation of V-belt transmission according to the traction ability, they are produced according to the permissible power transmitted by one belt of the selected cross section, which is also determined from the slip curves. As a result of the calculation, the number of belts of the selected section is determined by the formula:

, (12.17)

Where - the permissible power transmitted by one cross section; - pulley wrap angle coefficient: ; - belt length coefficient: ; - coefficient that takes into account the uneven loading between the belts .

For the calculation according to the formula (12.17), the type of belt cross-section is preliminarily determined by empirical dependencies (Fig. 74), and the diameter of the drive pulley is preliminarily taken from it according to the transmitted power and rotational speed, according to table 12.3.

Table 12.4

Power N 0, which is transmitted by one V-belt at α =180o, belt length ℓ 0 quiet loading and gear ratio U = 1

Translation of the designation system for sections of V-belts according to GOST 1284 to international standards: O - Z, A - A, B - B, C - C, D - D, D - E, E - E0

The center distance can be specified in the initial data, or taken in the range

,

Where is the height of the selected section of the belt.

As a result of the geometric calculation of the transmission, the parameter values ​​are specified, the calculated belt length is determined, which is rounded to the nearest standard value, according to table 12.5. Table 12.5

Standard V-Belt Length

The calculated number of V-belts is rounded up to the next higher whole number.

Durability test calculation . The durability of a belt is determined by its fatigue resistance under cyclic loading. Fatigue resistance is determined by the number of loading cycles, which increases with increasing belt speed and decreasing belt length. To ensure the durability of the belt within 1000 ... 5000 hours of operation, the number of belt runs per second is checked, which corresponds to the number of loads per second

Table 12.7

Table 12.7

Dimensions and parameters of V-belts

When designing equipment, it is necessary to know the number of revolutions of the electric motor. To calculate the speed, there are special formulas that are different for AC and DC motors.

Synchronous and asynchronous electric machines

There are three types of AC motors: synchronous, the angular speed of the rotor of which coincides with the angular frequency magnetic field stator; 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

The rotation speed of an AC electric machine 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 an advantage of these electric machines.

To do this, in the rotor of high-power machines there is a winding 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 explicit poles.

Slip

In asynchronous machines, the number of revolutions of the shaft is less than the synchronous angular frequency. This difference is called the "S" slip. Due to the slip, an electric current is induced in the rotor, and the shaft rotates. The larger S, the higher the torque and the lower the speed. However, if the slip exceeds a certain value, the electric motor stops, starts to overheat and may fail. The rotational speed of such devices is calculated according to the formula in the figure below, where:

• n is the number of revolutions per minute,
• f - network frequency,
• p is the number of pairs of poles,
• 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 number of revolutions electrical machines. It is carried out in three ways:

• Increasing the additional resistance in the rotor circuit of electric motors with a phase 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 to start high power electrical machines and to adjust the speed of small electric motors. For example, the number of revolutions of a table fan can be reduced by connecting an incandescent lamp or a capacitor in series with it. The same result gives a decrease in the supply voltage;
• Network frequency change. Suitable for synchronous and asynchronous motors.

Attention! The speed of rotation of collector electric motors operating from the AC network does not depend on the frequency of the network.

DC motors

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

Rated rotation speed

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

• n is the number of revolutions per minute,
• U - network voltage,
• Rya and Iya - armature resistance and current,
• Ce – motor constant (depends on the type of electric machine),
• F is the magnetic field of the stator.

These data correspond to the nominal values ​​of the parameters of the electric machine, the voltage on the field winding and 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, the strength of the current flowing through the excitation winding or the armature voltage is used.

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

Speed ​​control

Adjustment of the speed of an electric motor operating from a DC network is possible over a wide range. It is available in two ranges:

1. Up from nominal. To do this, the magnetic flux is reduced with the help of additional resistances or a voltage regulator;
2. Down from par. To do this, it is necessary to reduce the voltage at the armature of the electric motor or turn on a resistance in series with it. In addition to reducing the speed, this is done when starting the electric motor.

Knowing what formulas are used to calculate the speed of rotation of the electric motor is necessary when designing and commissioning equipment.

Video

The belt drive transmits torque from the drive shaft to the driven shaft. Depending on it, it can increase or decrease the speed. 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, its speed of rotation and the overall dimensions of the device.

Belt drive device, its characteristics

A belt drive is a pair of pulleys connected by an endless looped belt. These drive wheels are usually located in the same plane, and the axles are made parallel, while the drive wheels rotate in the same direction. Flat (or round) belts allow you to change the direction of rotation by crossing, and mutual arrangement axes - through the use of additional passive rollers. In this case, some of the power is lost.

V-belt drives due to the wedge-shaped cross-section of the belt allow you to increase the area of ​​its engagement with the belt pulley. A wedge-shaped groove is made on it.

Toothed belt drives have teeth of equal pitch and profile on inside belt and on the surface of the rim. They do not slip, allowing you to transfer more power.

The following basic parameters are important for the calculation of the drive:

• the number of revolutions of the drive shaft;
• power transmitted by the drive;
• the required number of revolutions of the driven shaft;
• belt profile, its thickness and length;
• settlement, 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, different diameter values ​​\u200b\u200bare used, so, for a V-belt drive pulley, the following are used:

• calculated D calc;
• outer D out;
• internal, or landing D vn.

To calculate the gear ratio, the estimated diameter is used, and the outer diameter is used to calculate the dimensions of the drive when configuring the mechanism.

For a gear-belt drive, D calc differs from D nar by the height of the tooth.
The gear ratio is also calculated based on the value of D calc.

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

Pulley Diameter Calculation

First, you should determine the gear ratio, based on the inherent speed of rotation of the drive shaft n1 and the required speed of rotation 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 for i is carried out according to the formula:

If the mechanism is designed from scratch, then theoretically any pair of drive wheels that satisfy the condition:

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 fastened to the shaft, correspond to it in size inner hole, method of landing, fastening. The maximum minimum pulley diameter is usually taken from the ratio D calc ≥ 2.5 D ext
• Permissible transmission dimensions. When designing mechanisms, it is required to meet dimensions. This also takes into account the center distance. 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 it is not planned to manufacture a unique part, then the length is selected from the standard range.
• transmitted power. The material of the part must withstand the angular loads. This is true for high powers and torques.

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