How to calculate the gear ratio on pulleys. Calculation of V-belt transmission. Rated rotation speed

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

AC motors are three types: 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

Electric machine rotation speed 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 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 of electric 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 DC network. 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

Works on the bulkhead of the electric motor are nearing completion. Getting to the calculation of pulleys belt drive 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 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 above 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;
• thanks to light weight belt vibration levels are much less.

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.

Formula to determine 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 value “0” in the “ho” field.

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.

In drives various machines and mechanisms, belt drives are very widely used due to their simplicity and low cost in design, manufacture and operation. The transmission does not need a housing, unlike a worm or gear drive, it does not need ...

Grease. The belt drive is silent and fast. The disadvantages of a belt drive are: significant dimensions (in comparison with the same gear or worm gear) and limited transmitted torque.

The most widespread transmissions are: V-belt, with a toothed belt, CVT wide-belt, flat-belt and round-belt. In the article brought to your attention, we will consider the design calculation of the V-belt transmission, as the most common. The result of the work will be a program that implements step by step algorithm calculation in MS Excel.

For blog subscribers at the bottom of the article, as usual, a link to download the working file.

The proposed algorithm is implemented on materials GOST 1284.1-89,GOST 1284.3-96 and GOST 20889-80. These GOSTs are freely available on the Web, they must be downloaded. When performing calculations, we will use the tables and materials of the above listed GOSTs, so they should be at hand.

What exactly is being offered? A systematic approach to solving the issue of design calculation of V-belt transmission is proposed. You do not need to study the above GOSTs in detail, you just need to strictly follow the instructions below step by step - the calculation algorithm. If you are not constantly designing new belt drives, then over time the procedure is forgotten and, restoring the algorithm in memory, each time you have to spend a lot of time. Using the program below, you will be able to perform calculations faster and more efficiently.

Design calculation in Excel for V-belt transmission.

If you do not have MS Excel installed on your computer, then the calculations can be performed in the OOo Calc program from the Open Office package, which can always be freely downloaded and installed.

The calculation will be carried out for a transmission with two pulleys - driving and driven, without tension rollers. General scheme V-belt transmission is shown in the figure below this text. We launch Excel, create a new file and start working.

In cells with a light turquoise fill, we write the initial data and data selected by the user according to the GOST tables or refined (accepted) calculated data. In the cells with a light yellow fill, we read the results of the calculations. Cells with a pale green fill contain initial data that is not subject to change.

In comments to all cells of a columnDexplanations are given of how and from where all values ​​are selected or by what formulas are calculated!!!

We begin to “walk” along the algorithm - we fill in the cells with the initial data:

1. Transmission efficiency efficiency ( this is the efficiency of the belt drive and the efficiency of two pairs of rolling bearings) we write

to cell D2: 0,921

2. Preliminary gear ratio u’ write down

to cell D3: 1,48

3. small pulley shaft speed n1 in rpm we write

to cell D4: 1480

4. Drive Rated Power (Small Pulley Shaft Power) P1 we enter in kW

to cell D5: 25,000

Further, in the dialog mode of the user and the program, we perform the calculation of the belt drive:

5. We calculate the torque on the shaft of a small pulley T1 in n*m

in cell D6: =30*D5/(PI()*D4)*1000 =164,643

T1 =30* P 1 /(3,14* n 1 )

6. We open GOST1284.3-96, assign according to clause 3.2 (table 1 and table 2) the coefficient of dynamic load and mode of operation cp and write down

to cell D7: 1,0

7. Estimated drive power R in kW, according to which we will choose the section of the belt, we consider

in cell D8: =D5*D7 =25,000

P = P1 *Cp

8. In GOST1284.3-96, according to clause 3.1 (Fig. 1), we select the standard size of the belt section and enter

into the merged cell C9D9E9: C(B)

9. We open GOST20889-80, assign the calculated diameter of the small pulley according to clause 2.2 and clause 2.3 d1 in mm and write down

to cell D10: 250

It is advisable not to prescribe the calculated diameter of the small pulley is equal to the minimum possible value. How larger diameter pulleys, the longer the belt will last, but the larger the transmission will be. A reasonable compromise is needed here.

10. Belt Linear Speed v in m/s, calculated

in cell D11: =PI()*D10*D4/60000 =19,0

v = 3.14* d1 *n1 /60000

The linear speed of the belt must not exceed 30 m/s!

11. Estimated diameter big pulley(tentatively) d2’ in mm calculated

in cell D12: =D10*D3 =370

d2’ = d 1 * u’

12. According to GOST20889-80, according to clause 2.2, we assign the calculated diameter of the large pulley d2 in mm and write

to cell D13: 375

13. Specifying the gear ratio u

in cell D14: =D13/D10 =1,500

u=d2/d1

14. We calculate the deviation of the gear ratio of the final from the preliminary delta in % and compare with the allowable value given in the note

in cell D15: =(D14-D3)/D3*100 =1,35

delta =(u-u’) / u'

The gear ratio deviation should preferably not exceed 3% modulo!

15. Large pulley shaft speed n2 in rpm we count

in cell D16: =D4/D14 =967

n2 =n1 /u

16. Large pulley shaft power P2 in kW we determine

in cell D17: =D5*D2 =23,032

P2 =P1 *Efficiency

17. We calculate the torque on the shaft of a large pulley T2 in n*m

in cell D18: =30*D17/(PI()*D16)*1000 =227,527

T2 =30* P 2 /(3,14* n 2 )

in cell D19: =0.7*(D10+D13) =438

amin =0,7*(d 1 + d 2 )

19. Calculate the maximum center-to-center transmission distance amax in mm

in cell D20: =2*(D10+D13) =1250

amax =2*(d 1 + d 2 )

20. From the resulting range and based on design features project, we assign a preliminary center-to-center transmission distance a’ in mm

in cell D21: 700

21. Now you can determine the preliminary estimated length of the belt lp’ in mm

in cell D22: =2*D21+(PI()/2)*(D10+D13)+(D13-D10)^2/(4*D21)=2387

Lp" =2*a" +(3,14/2)*(d1 +d2 )+((d2 -d1 )^2)/(4*a" )

22. We open GOST1284.1-89 and select, according to clause 1.1 (table 2), the estimated length of the belt lp in mm

in cell D23: 2500

23. We recalculate the center-to-center transmission distance a in mm

in cell D24: =0.25*(D23- (PI()/2)*(D10+D13)+((D23- (PI()/2)*(D10+D13))^2-8*((D13-D10 )/2)^2)^0.5)=757

a \u003d 0.25 * (Lp - (3,14 /2)*(d1 +d2 )+((Lp - (3,14 /2)*(d1 +d2 ))^2-8*((d2 ​​-d1 ) /2)^2)^0.5)

in cell D25: =2*ACOS ((D13-D10)/(2*D24))/PI()*180=171

A =2*arccos ((d2 -d1 )/(2*a ))

25. We determine according to GOST 1284.3-96 p.3.5.1 (tables 5-17) the rated power transmitted by one belt P0 in kW and write down

to cell D26: 9,990

26. We determine according to GOST 1284.3-96 p.3.5.1 (table 18) the wrap angle coefficient CA and enter

to cell D27: 0,982

27. We determine according to GOST 1284.3-96 p.3.5.1 (table 19) the belt length coefficient CL and write

to cell D28: 0,920

28. We assume that the number of belts will be 4. We determine according to GOST 1284.3-96 p.3.5.1 (table 20) the coefficient of the number of belts in the transmission CK and write down

to cell D29: 0,760

29. Determine the estimated required number of belts in the drive K’

in cell D30: =D8/D26/D27/D28/D29 =3,645

K"=P /(P0 *CA *CL *CK )

30. We finally determine the number of belts in the drive K

in cell D31: \u003d OKRUP (D30, 1) =4

K = round up to integer (K ’ )

We performed a design calculation in Excel for a V-belt transmission with two pulleys, the purpose of which was to determine the main characteristics and overall parameters based on partially specified power and kinematic parameters.

I will be glad to see your comments, dear readers!!!

To receive information about the release of new articles, you should subscribe to announcements in the window located at the end of the article or at the top of the page.

Enter your address Email, click on the "Receive article announcements" button, confirm the subscription in a letter that will immediately come to you at the specified mail .

From now on, small notifications about the appearance of new articles on my site will come to your mail about once a week. (You can unsubscribe at any time.)

REST can be downloaded just like that ... - no passwords!

". 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 spokes passing through the axis of the pulley,

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.

The belt drive transmits torque from the drive shaft to the driven one. 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 due to crossing, and the relative position of the 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;
• calculated, outer, inner diameter of the wheel;
• 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, apply various meanings diameters, so, for a V-belt 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 when big size rims with respect to the thickness of the profile, often take Dcalc equal to the outer one.

Pulley Diameter Calculation

First you need to 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 finished engine with a drive wheel is already available, the calculation of the pulley diameter using 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 large a 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.