Calculation and selection (Russian methodology) - worm gearbox. Selecting a geared motor Classification of gearboxes depending on the mounting method
This article contains detailed information on the selection and calculation of a gearmotor. We hope the information provided will be useful to you.
When choosing a specific gearmotor model, the following technical characteristics are taken into account:
- gearbox type;
- power;
- output speed;
- gear ratio;
- design of input and output shafts;
- type of installation;
- additional functions.
Gearbox type
The presence of a kinematic drive diagram will simplify the choice of gearbox type. Structurally, gearboxes are divided into the following types:
Worm single stage with a crossed input/output shaft arrangement (angle 90 degrees).
Worm two-stage with perpendicular or parallel arrangement of the input/output shaft axes. Accordingly, the axes can be located in different horizontal and vertical planes.
Cylindrical horizontal with parallel arrangement of input/output shafts. The axes are in one horizontal plane.
Cylindrical coaxial at any angle. The shaft axes are located in the same plane.
IN conical-cylindrical In the gearbox, the axes of the input/output shafts intersect at an angle of 90 degrees.
IMPORTANT!
The spatial location of the output shaft is critical for a number of industrial applications.
- The design of worm gearboxes allows them to be used in any position of the output shaft.
- The use of cylindrical and conical models is often possible in the horizontal plane. With the same weight and dimensional characteristics as worm gearboxes, the operation of cylindrical units is more economically feasible due to an increase in the transmitted load by 1.5-2 times and high efficiency.
Table 1. Classification of gearboxes by number of stages and type of transmission
| Gearbox type | Number of steps | Transmission type | Axes location |
|---|---|---|---|
| Cylindrical | 1 | One or more cylindrical | Parallel |
| 2 | Parallel/coaxial | ||
| 3 | |||
| 4 | Parallel | ||
| Conical | 1 | Conical | Intersecting |
| Conical-cylindrical | 2 | Conical Cylindrical (one or more) | Intersecting/crossing |
| 3 | |||
| 4 | |||
| Worm | 1 | Worm (one or two) | Crossbreeding |
| 1 | Parallel | ||
| Cylindrical-worm or worm-cylindrical | 2 | Cylindrical (one or two) Worm (one) | Crossbreeding |
| 3 | |||
| Planetary | 1 | Two central gears and satellites (for each stage) | Coaxial |
| 2 | |||
| 3 | |||
| Cylindrical-planetary | 2 | Cylindrical (one or more) | Parallel/coaxial |
| 3 | |||
| 4 | |||
| Cone-planetary | 2 | Conical (single) Planetary (one or more) | Intersecting |
| 3 | |||
| 4 | |||
| Worm-planetary | 2 | Worm (one) Planetary (one or more) | Crossbreeding |
| 3 | |||
| 4 | |||
| Wave | 1 | Wave (one) | Coaxial |
Gear ratio [I]
The gear ratio is calculated using the formula:
I = N1/N2
Where
N1 – shaft rotation speed (rpm) at the input;
N2 – shaft rotation speed (rpm) at the output.
The value obtained in the calculations is rounded to the value specified in technical specifications specific type of gearbox.
Table 2. Range gear ratios For different types gearboxes
IMPORTANT!
The rotation speed of the electric motor shaft and, accordingly, the input shaft of the gearbox cannot exceed 1500 rpm. The rule applies to all types of gearboxes, except cylindrical coaxial gearboxes with rotation speeds up to 3000 rpm. This technical parameter Manufacturers indicate in the summary characteristics of electric motors.
Gearbox torque
Output torque– torque on the output shaft. The rated power, safety factor [S], estimated service life (10 thousand hours), and gearbox efficiency are taken into account.
Rated torque– maximum torque ensuring safe transmission. Its value is calculated taking into account the safety factor - 1 and the service life - 10 thousand hours.
Maximum torque– the maximum torque that the gearbox can withstand under constant or changing loads, operation with frequent starts/stops. This value can be interpreted as an instantaneous peak load in the operating mode of the equipment.
Required torque– torque, satisfying the customer’s criteria. Its value is less than or equal to the rated torque.
Design torque– value required to select a gearbox. The estimated value is calculated using the following formula:
Mc2 = Mr2 x Sf ≤ Mn2
Where
Mr2 – required torque;
Sf – service factor (operational factor);
Mn2 – rated torque.
Operational coefficient (service factor)
Service factor (Sf) is calculated experimentally. The type of load, daily operating duration, and the number of starts/stops per hour of operation of the gearmotor are taken into account. The operating coefficient can be determined using the data in Table 3.
Table 3. Parameters for calculating the service factor
| Load type | Number of starts/stops, hour | Average duration of operation, days | |||
|---|---|---|---|---|---|
| <2 | 2-8 | 9-16h | 17-24 | ||
| Soft start, static operation, medium mass acceleration | <10 | 0,75 | 1 | 1,25 | 1,5 |
| 10-50 | 1 | 1,25 | 1,5 | 1,75 | |
| 80-100 | 1,25 | 1,5 | 1,75 | 2 | |
| 100-200 | 1,5 | 1,75 | 2 | 2,2 | |
| Moderate starting load, variable mode, medium mass acceleration | <10 | 1 | 1,25 | 1,5 | 1,75 |
| 10-50 | 1,25 | 1,5 | 1,75 | 2 | |
| 80-100 | 1,5 | 1,75 | 2 | 2,2 | |
| 100-200 | 1,75 | 2 | 2,2 | 2,5 | |
| Operation under heavy loads, alternating mode, large mass acceleration | <10 | 1,25 | 1,5 | 1,75 | 2 |
| 10-50 | 1,5 | 1,75 | 2 | 2,2 | |
| 80-100 | 1,75 | 2 | 2,2 | 2,5 | |
| 100-200 | 2 | 2,2 | 2,5 | 3 | |
Drive power
Correctly calculated drive power helps to overcome mechanical friction resistance that occurs during linear and rotational movements.
The elementary formula for calculating power [P] is the calculation of the ratio of force to speed.
For rotational movements, power is calculated as the ratio of torque to revolutions per minute:
P = (MxN)/9550
Where
M – torque;
N – number of revolutions/min.
Output power is calculated using the formula:
P2 = P x Sf
Where
P – power;
Sf – service factor (operational factor).
IMPORTANT!
The input power value must always be higher than the output power value, which is justified by the meshing losses:
P1 > P2
Calculations cannot be made using approximate input power, as efficiencies may vary significantly.
Efficiency factor (efficiency)
Let's consider the calculation of efficiency using the example of a worm gearbox. It will be equal to the ratio of mechanical output power and input power:
ñ [%] = (P2/P1) x 100
Where
P2 – output power;
P1 – input power.
IMPORTANT!
In P2 worm gearboxes< P1 всегда, так как в результате трения между червячным колесом и червяком, в уплотнениях и подшипниках часть передаваемой мощности расходуется.
The higher the gear ratio, the lower the efficiency.
The efficiency is affected by the duration of operation and the quality of lubricants used for preventive maintenance of the gearmotor.
Table 4. Efficiency of a single-stage worm gearbox
| Gear ratio | Efficiency at a w, mm | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 40 | 50 | 63 | 80 | 100 | 125 | 160 | 200 | 250 | |
| 8,0 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 | 0,94 | 0,95 | 0,96 |
| 10,0 | 0,87 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 | 0,94 | 0,95 |
| 12,5 | 0,86 | 0,87 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 | 0,94 |
| 16,0 | 0,82 | 0,84 | 0,86 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 |
| 20,0 | 0,78 | 0,81 | 0,84 | 0,86 | 0,87 | 0,88 | 0,89 | 0,90 | 0,91 |
| 25,0 | 0,74 | 0,77 | 0,80 | 0,83 | 0,84 | 0,85 | 0,86 | 0,87 | 0,89 |
| 31,5 | 0,70 | 0,73 | 0,76 | 0,78 | 0,81 | 0,82 | 0,83 | 0,84 | 0,86 |
| 40,0 | 0,65 | 0,69 | 0,73 | 0,75 | 0,77 | 0,78 | 0,80 | 0,81 | 0,83 |
| 50,0 | 0,60 | 0,65 | 0,69 | 0,72 | 0,74 | 0,75 | 0,76 | 0,78 | 0,80 |
Table 5. Wave gear efficiency
Table 6. Efficiency of gear reducers
Explosion-proof versions of gearmotors
Geared motors of this group are classified according to the type of explosion-proof design:
- “E” – units with an increased degree of protection. Can be used in any operating mode, including emergency situations. Enhanced protection prevents the possibility of ignition of industrial mixtures and gases.
- “D” – explosion-proof enclosure. The housing of the units is protected from deformation in the event of an explosion of the gear motor itself. This is achieved due to its design features and increased tightness. Equipment with explosion protection class “D” can be used at extremely high temperatures and with any group of explosive mixtures.
- “I” – intrinsically safe circuit. This type of explosion protection ensures the maintenance of explosion-proof current in the electrical network, taking into account the specific conditions of industrial application.
Reliability indicators
The reliability indicators of geared motors are given in Table 7. All values are given for long-term operation at a constant rated load. The geared motor must provide 90% of the resource indicated in the table even in short-term overload mode. They occur when the equipment is started and the rated torque is exceeded at least twice.
Table 7. Service life of shafts, bearings and gearboxes
For questions regarding the calculation and purchase of gear motors of various types, please contact our specialists. You can familiarize yourself with the catalog of worm, cylindrical, planetary and wave gear motors offered by the Tekhprivod company.
Romanov Sergey Anatolievich,
head of mechanical department
Tekhprivod company.
Other useful materials:
1. Purpose of the work
Study of gearbox efficiency under various loading conditions.
2. Installation description
To study the operation of the gearbox, a DP3M device is used. It consists of the following main components (Fig. 1): gearbox under test 5, electric motor 3 with electronic tachometer 1, load device 6, torque measuring device 8, 9. All components are mounted on one base 7.
The electric motor housing is hinged in two supports 2 so that the axis of rotation of the electric motor shaft coincides with the axis of rotation of the housing. The motor housing is secured against circular rotation by a flat spring 4.
The gearbox consists of six identical spur gears with a gear ratio of 1.71 (Fig. 2). The gear block 19 is mounted on a fixed axis 20 on a ball bearing support. The design of blocks 16, 17, 18 is similar to block 19. Torque is transmitted from wheel 22 to shaft 21 through a key.
The load device is a magnetic powder brake, the operating principle of which is based on the property of a magnetized medium to resist the movement of ferromagnetic bodies in it. A liquid mixture of mineral oil and steel powder is used as a magnetizable medium.
Torque and braking torque measuring devices consist of flat springs that create reactive torques for the electric motor and the load device, respectively. Strain gauges connected to the amplifier are glued to the flat springs.
On the front part of the device base there is a control panel: power button for the device “Network” 11; power button for the excitation circuit of the load device “Load” 13; electric motor switch button “Engine” 10; electric motor speed control knob “Speed regulation” 12; knob for regulating the excitation current of the load device 14; three ammeters 8, 9, 15 for measuring frequency n, moment M 1, moment M 2, respectively.
Rice. 1. Installation diagram
Rice. 2. Gearbox under test
Technical characteristics of the DP3M device:
3. Calculation dependencies
Determination of gearbox efficiency is based on simultaneous measurement of torques on the gearbox input and output shafts at a steady-state speed. In this case, the gearbox efficiency is calculated using the formula:
= , (1)
where M 2 is the moment created by the load device, N×m; M 1 – torque developed by the electric motor, N×m; u – gear ratio of the gearbox.
4. Work order
At the first stage, at a given constant speed of rotation of the electric motor, the efficiency of the gearbox is studied depending on the torque created by the load device.
First, the electric drive is turned on and the speed control knob is used to set the desired rotation speed. The load device excitation current adjustment knob is set to the zero position. The excitation power circuit is turned on. By smoothly turning the excitation adjustment knob, the first of the specified values of the load torque on the gearbox shaft is set. The speed control knob maintains the specified rotation speed. Microammeters 8, 9 (Fig. 1) record the moments on the motor shaft and the load device. By further adjusting the excitation current, the load torque is increased to the next specified value. Keeping the rotation speed constant, determine the following values of M 1 and M 2.
The results of the experiment are entered into Table 1, and a graph of the dependence = f(M 2) at n = const is plotted (Fig. 4).
At the second stage, for a given constant load torque M 2, the efficiency of the gearbox is studied depending on the rotational speed of the electric motor.
The excitation power circuit is turned on and the excitation current adjustment knob is used to set the specified torque value on the output shaft of the gearbox. The speed control knob sets a range of rotation speeds (from minimum to maximum). For each speed mode, a constant load torque M 2 is maintained, and the torque on the motor shaft M 1 is recorded using microammeter 8 (Fig. 1).
The results of the experiment are entered into Table 2, and a graph of the dependence = f(n) at M 2 = const is plotted (Fig. 4).
5. Conclusion
It is explained what power losses in a gear drive consist of and how the efficiency of a multi-stage gearbox is determined.
The conditions that allow increasing the efficiency of the gearbox are listed. A theoretical justification for the obtained graphs is given = f(M 2); = f(n).
6. Report preparation
– Prepare a title page (see example on page 4).
– Draw the kinematic diagram of the gearbox.
Prepare and fill out the table. 1.
Table 1
from the moment created by the load device
– Build a dependence graph
| |
Rice. 4. Graph of dependence = f(M 2) at n = const
Prepare and fill out the table. 2.
table 2
Results of a study of gearbox efficiency depending on
from the electric motor speed
– Construct a dependence graph.
| |
|
Rice. 5. Graph of dependence = f(n) at M 2 = const
Give a conclusion (see paragraph 5).
Control questions
1. Describe the design of the DPZM device, what main components does it consist of?
2. What power losses occur in the gear transmission and what is its efficiency?
3. How do gear characteristics such as power, torque, and rotation speed change from the drive to the driven shaft?
4. How is the gear ratio and efficiency of a multi-stage gearbox determined?
5. List the conditions that make it possible to increase the efficiency of the gearbox.
6. The order of work when studying the efficiency of the gearbox depending on the torque supplied by the load device.
7. The order of work when studying the efficiency of the gearbox depending on the engine speed.
8. Give a theoretical explanation of the resulting graphs = f(M 2); = f(n).
Bibliography
1. Reshetov, D. N. Machine parts: - a textbook for students of mechanical engineering and mechanical specialties of universities / D. N. Reshetov. – M.: Mashinostroenie, 1989. – 496 p.
2. Ivanov, M. N. Machine parts: - a textbook for students of higher technical educational institutions / M. N. Ivanov. – 5th ed., revised. – M.: Higher School, 1991. – 383 p.
LABORATORY WORK No. 8
A worm gearbox is one of the classes of mechanical gearboxes. Gearboxes are classified according to the type of mechanical transmission. The screw that forms the basis of the worm gear is similar in appearance to a worm, hence the name.
Geared motor is a unit consisting of a gearbox and an electric motor, which are contained in one unit. Worm gear motorcreated in order to work as an electromechanical motor in various general purpose machines. It is noteworthy that this type of equipment works perfectly under both constant and variable loads.
In a worm gearbox, the increase in torque and decrease in the angular speed of the output shaft occurs by converting the energy contained in the high angular speed and low torque on the input shaft.
Errors in the calculation and selection of the gearbox can lead to its premature failure and, as a result, in the best case 
to financial losses.
Therefore, the work of calculating and selecting a gearbox must be entrusted to experienced design specialists who will take into account all factors from the location of the gearbox in space and operating conditions to its heating temperature during operation. Having confirmed this with appropriate calculations, the specialist will ensure the selection of the optimal gearbox for your specific drive.
Practice shows that a properly selected gearbox provides a service life of at least 7 years - for worm gearboxes and 10-15 years for spur gearboxes.
The selection of any gearbox is carried out in three stages:
1. Selecting the type of gearbox
2. Selecting the size (standard size) of the gearbox and its characteristics.
3. Verification calculations
1. Selecting the type of gearbox
1.1 Initial data:
Kinematic diagram of the drive indicating all the mechanisms connected to the gearbox, their spatial arrangement relative to each other, indicating the mounting locations and methods of mounting the gearbox.
1.2 Determination of the location of the axes of the gearbox shafts in space.
Helical gearboxes:
The axis of the input and output shafts of the gearbox are parallel to each other and lie in only one horizontal plane - a horizontal spur gearbox.
The axis of the input and output shafts of the gearbox are parallel to each other and lie in only one vertical plane - a vertical spur gearbox.
The axis of the input and output shaft of the gearbox can be in any spatial position, while these axes lie on the same straight line (coincident) - a coaxial cylindrical or planetary gearbox.
Bevel-helical gearboxes:
The axis of the input and output shafts of the gearbox are perpendicular to each other and lie in only one horizontal plane.
Worm gearboxes:
The axis of the input and output shaft of the gearbox can be in any spatial position, while they cross at an angle of 90 degrees to each other and do not lie in the same plane - a single-stage worm gearbox.
The axis of the input and output shaft of the gearbox can be in any spatial position, while they are parallel to each other and do not lie in the same plane, or they cross at an angle of 90 degrees to each other and do not lie in the same plane - a two-stage gearbox.
1.3 Determination of the method of fastening, mounting position and assembly option of the gearbox. 
The method of fastening the gearbox and the mounting position (mounting to the foundation or to the driven shaft of the drive mechanism) are determined according to the technical characteristics given in the catalog for each gearbox individually.
The assembly option is determined according to the diagrams given in the catalog. Schemes of “Assembly options” are given in the “Designation of gearboxes” section.
1.4 Additionally, when choosing a gearbox type, the following factors can be taken into account
1) Noise level
- the lowest - for worm gearboxes
- the highest - for helical and bevel gearboxes
2) Efficiency
- the highest is for planetary and single-stage spur gearboxes
- the lowest is for worm gears, especially two-stage ones
Worm gearboxes are preferably used in repeated and short-term operating modes
3) Material consumption for the same values of torque on a low-speed shaft
- the lowest is for planetary single-stage
4) Dimensions with the same gear ratios and torques:
- the largest axial ones are for coaxial and planetary
- largest in the direction perpendicular to the axes - for cylindrical
- the smallest radial - to planetary.
5) Relative cost rub/(Nm) for the same center distances:
- the highest is for conical ones
- the lowest is for planetary ones
2. Selecting the size (standard size) of the gearbox and its characteristics
2.1. Initial data
Kinematic diagram of the drive containing the following data:
- type of drive machine (engine);
- required torque on the output shaft T required, Nm, or power of the propulsion system P required, kW;
- rotation speed of the gearbox input shaft nin, rpm;
- speed of rotation of the output shaft of the gearbox n out, rpm;
- the nature of the load (uniform or uneven, reversible or non-reversible, the presence and magnitude of overloads, the presence of shocks, impacts, vibrations);
- required duration of operation of the gearbox in hours;
- average daily work in hours;
- number of starts per hour;
- duration of switching on with load, duty cycle %;
- environmental conditions (temperature, heat removal conditions);
- Duration of switching on under load;
- radial cantilever load applied in the middle of the landing part of the ends of the output shaft F out and input shaft F in;
2.2. When choosing the gearbox size, the following parameters are calculated:
1) Gear ratio
U= n in / n out (1)
The most economical is to operate the gearbox at an input speed of less than 1500 rpm, and for longer trouble-free operation of the gearbox, it is recommended to use an input shaft speed of less than 900 rpm.
The gear ratio is rounded in the required direction to the nearest number according to Table 1.
Using the table, types of gearboxes that satisfy a given gear ratio are selected.
2) Estimated torque on the output shaft of the gearbox
T calc =T required x K rez, (2)
T required - required torque on the output shaft, Nm (initial data, or formula 3)
K mode - operating mode coefficient
With a known power of the propulsion system:
T required = (P required x U x 9550 x efficiency)/ n input, (3)
P required - power of the propulsion system, kW
nin - rotation speed of the gearbox input shaft (provided that the propulsion system shaft directly transmits rotation to the gearbox input shaft without additional gear), rpm
U - gear ratio, formula 1
Efficiency - gearbox efficiency
The operating mode coefficient is defined as the product of the coefficients: 
For gear reducers:
K dir = K 1 x K 2 x K 3 x K PV x K rev (4)
For worm gearboxes:
K dir = K 1 x K 2 x K 3 x K PV x K rev x K h (5)
K 1 - coefficient of the type and characteristics of the propulsion system, table 2
K 2 - operating duration coefficient table 3
K 3 - coefficient of number of starts table 4
K PV - switching duration coefficient table 5
K rev - reversibility coefficient, with non-reversible operation K rev = 1.0 with reverse operation K rev = 0.75
Kh is a coefficient that takes into account the location of the worm pair in space. When the worm is located under the wheel, K h = 1.0, when located above the wheel, K h = 1.2. When the worm is located on the side of the wheel, K h = 1.1.
3) Estimated radial cantilever load on the gearbox output shaft
F out.calc = F out x K mode, (6)
Fout - radial cantilever load applied in the middle of the landing part of the ends of the output shaft (initial data), N
K mode - operating mode coefficient (formula 4.5)
3. The parameters of the selected gearbox must satisfy the following conditions:
1) T nom > T calc, (7)
Tnom - rated torque on the output shaft of the gearbox, given in this catalog in the technical specifications for each gearbox, Nm
T calc - calculated torque on the output shaft of the gearbox (formula 2), Nm
2) Fnom > Fout.calc (8)
F nom - rated cantilever load in the middle of the landing part of the ends of the gearbox output shaft, given in the technical specifications for each gearbox, N.
F out.calc - calculated radial cantilever load on the output shaft of the gearbox (formula 6), N.
3) P input calculation< Р терм х К т, (9)
P input calculation - estimated power of the electric motor (formula 10), kW
R term - thermal power, the value of which is given in the technical characteristics of the gearbox, kW
Kt - temperature coefficient, the values of which are given in Table 6
The design power of the electric motor is determined by:
P input calculation = (T out x n out)/(9550 x efficiency), (10)
Tout - calculated torque on the output shaft of the gearbox (formula 2), Nm
n out - speed of the gearbox output shaft, rpm
Efficiency - efficiency factor of the gearbox,
A) For helical gearboxes:
- single-stage - 0.99
- two-stage - 0.98
- three-stage - 0.97
- four-speed - 0.95
B) For bevel gearboxes:
- single-stage - 0.98
- two-stage - 0.97
B) For bevel-helical gearboxes - as the product of the values of the bevel and cylindrical parts of the gearbox.
D) For worm gearboxes, the efficiency is given in the technical specifications for each gearbox for each gear ratio.
Our company managers will help you buy a worm gearbox, find out the cost of the gearbox, select the right components and help you with questions that arise during operation.
Table 1
table 2
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Leading car |
Generators, elevators, centrifugal compressors, evenly loaded conveyors, mixers of liquid substances, centrifugal pumps, gear pumps, screw pumps, boom mechanisms, blowers, fans, filter devices. |
Water treatment plants, unevenly loaded conveyors, winches, cable drums, running, rotating, lifting mechanisms of cranes, concrete mixers, furnaces, transmission shafts, cutters, crushers, mills, equipment for the oil industry. |
Punching presses, vibrating devices, sawmills, screens, single-cylinder compressors. |
Equipment for the production of rubber products and plastics, mixing machines and equipment for shaped rolling. |
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Electric motor, steam turbine |
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4, 6 cylinder internal combustion engines, hydraulic and pneumatic engines |
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1, 2, 3 cylinder internal combustion engines |
Table 3
Table 4
Table 5
Table 6
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cooling |
Ambient temperature, C o |
Duration of switching on, duty cycle %. |
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Gearbox without outsider cooling. |
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Reducer with water cooling spiral. |
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The presence of a kinematic drive diagram will simplify the choice of gearbox type. Structurally, gearboxes are divided into the following types:
Gear ratio [I]
The gear ratio is calculated using the formula:
I = N1/N2
Where
N1 – shaft rotation speed (rpm) at the input;
N2 – shaft rotation speed (rpm) at the output.
The value obtained in the calculations is rounded to the value specified in the technical characteristics of a particular type of gearbox.
Table 2. Range of gear ratios for different types of gearboxes
IMPORTANT!
The rotation speed of the electric motor shaft and, accordingly, the input shaft of the gearbox cannot exceed 1500 rpm. The rule applies to all types of gearboxes, except cylindrical coaxial gearboxes with rotation speeds up to 3000 rpm. Manufacturers indicate this technical parameter in the summary characteristics of electric motors.
Gearbox torque
Output torque– torque on the output shaft. The rated power, safety factor [S], estimated service life (10 thousand hours), and gearbox efficiency are taken into account.
Rated torque– maximum torque ensuring safe transmission. Its value is calculated taking into account the safety factor - 1 and the service life - 10 thousand hours.
Maximum torque (M2max]– the maximum torque that the gearbox can withstand under constant or changing loads, operation with frequent starts/stops. This value can be interpreted as the instantaneous peak load in the operating mode of the equipment.
Required torque– torque, satisfying the customer’s criteria. Its value is less than or equal to the rated torque.
Design torque– value required to select a gearbox. The estimated value is calculated using the following formula:
Mc2 = Mr2 x Sf ≤ Mn2
Where
Mr2 – required torque;
Sf – service factor (operational factor);
Mn2 – rated torque.
Operational coefficient (service factor)
Service factor (Sf) is calculated experimentally. The type of load, daily operating duration, and the number of starts/stops per hour of operation of the gearmotor are taken into account. The operating coefficient can be determined using the data in Table 3.
Table 3. Parameters for calculating the service factor
| Load type | Number of starts/stops, hour | Average duration of operation, days | |||
|---|---|---|---|---|---|
| <2 | 2-8 | 9-16h | 17-24 | ||
| Soft start, static operation, medium mass acceleration | <10 | 0,75 | 1 | 1,25 | 1,5 |
| 10-50 | 1 | 1,25 | 1,5 | 1,75 | |
| 80-100 | 1,25 | 1,5 | 1,75 | 2 | |
| 100-200 | 1,5 | 1,75 | 2 | 2,2 | |
| Moderate starting load, variable mode, medium mass acceleration | <10 | 1 | 1,25 | 1,5 | 1,75 |
| 10-50 | 1,25 | 1,5 | 1,75 | 2 | |
| 80-100 | 1,5 | 1,75 | 2 | 2,2 | |
| 100-200 | 1,75 | 2 | 2,2 | 2,5 | |
| Operation under heavy loads, alternating mode, large mass acceleration | <10 | 1,25 | 1,5 | 1,75 | 2 |
| 10-50 | 1,5 | 1,75 | 2 | 2,2 | |
| 80-100 | 1,75 | 2 | 2,2 | 2,5 | |
| 100-200 | 2 | 2,2 | 2,5 | 3 | |
Drive power
Correctly calculated drive power helps to overcome mechanical friction resistance that occurs during linear and rotational movements.
The elementary formula for calculating power [P] is the calculation of the ratio of force to speed.
For rotational movements, power is calculated as the ratio of torque to revolutions per minute:
P = (MxN)/9550
Where
M – torque;
N – number of revolutions/min.
Output power is calculated using the formula:
P2 = P x Sf
Where
P – power;
Sf – service factor (operational factor).
IMPORTANT!
The input power value must always be higher than the output power value, which is justified by the meshing losses:
P1 > P2
Calculations cannot be made using approximate input power, as efficiencies may vary significantly.
Efficiency factor (efficiency)
Let's consider the calculation of efficiency using the example of a worm gearbox. It will be equal to the ratio of mechanical output power and input power:
ñ [%] = (P2/P1) x 100
Where
P2 – output power;
P1 – input power.
IMPORTANT!
In P2 worm gearboxes< P1 всегда, так как в результате трения между червячным колесом и червяком, в уплотнениях и подшипниках часть передаваемой мощности расходуется.
The higher the gear ratio, the lower the efficiency.
The efficiency is affected by the duration of operation and the quality of lubricants used for preventive maintenance of the gearmotor.
Table 4. Efficiency of a single-stage worm gearbox
| Gear ratio | Efficiency at a w, mm | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 40 | 50 | 63 | 80 | 100 | 125 | 160 | 200 | 250 | |
| 8,0 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 | 0,94 | 0,95 | 0,96 |
| 10,0 | 0,87 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 | 0,94 | 0,95 |
| 12,5 | 0,86 | 0,87 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 | 0,94 |
| 16,0 | 0,82 | 0,84 | 0,86 | 0,88 | 0,89 | 0,90 | 0,91 | 0,92 | 0,93 |
| 20,0 | 0,78 | 0,81 | 0,84 | 0,86 | 0,87 | 0,88 | 0,89 | 0,90 | 0,91 |
| 25,0 | 0,74 | 0,77 | 0,80 | 0,83 | 0,84 | 0,85 | 0,86 | 0,87 | 0,89 |
| 31,5 | 0,70 | 0,73 | 0,76 | 0,78 | 0,81 | 0,82 | 0,83 | 0,84 | 0,86 |
| 40,0 | 0,65 | 0,69 | 0,73 | 0,75 | 0,77 | 0,78 | 0,80 | 0,81 | 0,83 |
| 50,0 | 0,60 | 0,65 | 0,69 | 0,72 | 0,74 | 0,75 | 0,76 | 0,78 | 0,80 |
Table 5. Wave gear efficiency
Table 6. Efficiency of gear reducers
Explosion-proof versions of gearmotors
Geared motors of this group are classified according to the type of explosion-proof design:
- “E” – units with an increased degree of protection. Can be used in any operating mode, including emergency situations. Enhanced protection prevents the possibility of ignition of industrial mixtures and gases.
- “D” – explosion-proof enclosure. The housing of the units is protected from deformation in the event of an explosion of the gear motor itself. This is achieved due to its design features and increased tightness. Equipment with explosion protection class “D” can be used at extremely high temperatures and with any group of explosive mixtures.
- “I” – intrinsically safe circuit. This type of explosion protection ensures the maintenance of explosion-proof current in the electrical network, taking into account the specific conditions of industrial application.
Reliability indicators
The reliability indicators of geared motors are given in Table 7. All values are given for long-term operation at a constant rated load. The geared motor must provide 90% of the resource indicated in the table even in short-term overload mode. They occur when the equipment is started and the rated torque is exceeded at least twice.
Table 7. Service life of shafts, bearings and gearboxes
For questions regarding the calculation and purchase of gear motors of various types, please contact our specialists. You can familiarize yourself with the catalog of worm, cylindrical, planetary and wave gear motors offered by the Tekhprivod company.
Romanov Sergey Anatolievich,
head of mechanical department
Tekhprivod company.
Other useful materials:
1. PURPOSE OF THE WORK
Deepening knowledge of theoretical material, obtaining practical skills for independent experimental determination of gearboxes.
2. BASIC THEORETICAL PROVISIONS
The mechanical efficiency of the gearbox is the ratio of the power usefully expended (the power of the resistance forces Nc to the power of driving forces N d on the gearbox input shaft:
The powers of the driving forces and resistance forces can be determined respectively by the formulas
(2)
(3)
Where M d And M s– moments of driving forces and resistance forces, respectively, Nm; and - angular speeds of the gearbox shafts, respectively, input and output, With -1 .
Substituting (2) and (3) into (1), we get
(4)
where is the gear ratio of the gearbox.
Any complex machine consists of a number of simple mechanisms. The efficiency of a machine can be easily determined if the efficiency of all its simple mechanisms is known. For most mechanisms, analytical methods for determining efficiency have been developed, however, deviations in the cleanliness of the processing of the rubbing surfaces of parts, the accuracy of their manufacture, changes in the load on the elements of kinematic pairs, lubrication conditions, the speed of relative motion, etc., lead to a change in the value of the friction coefficient.
Therefore, it is important to be able to experimentally determine the efficiency of the mechanism under study under specific operating conditions.
The parameters necessary to determine the gearbox efficiency ( M d, M s And L r) can be determined using DP-3K devices.
3. DEVICE DP-3K
The device (figure) is mounted on a cast metal base 1 and consists of an electric motor assembly 2 with a tachometer 3, a load device 4 and a gearbox under study 5.
3 6 8 2 5 4 9 7 1
 |
11 12 13 14 15 10
Rice. Kinematic diagram of the DP-3K device
The electric motor housing is hinged in two supports so that the axis of rotation of the motor shaft coincides with the axis of rotation of the housing. The motor housing is secured against circular rotation by a flat spring 6. When transmitting torque from the electric motor shaft to the gearbox, the spring creates a reactive torque applied to the electric motor housing. The electric motor shaft is connected to the input shaft of the gearbox through a coupling. Its opposite end is articulated with the tachometer shaft.
The gearbox in the DK-3K device consists of six identical pairs of gears mounted on ball bearings in the housing.
The upper part of the gearboxes has an easily removable cover made of organic glass, and is used for visual observation and measurement of gears when determining the gear ratio.
The load device is a magnetic powder brake, the operating principle of which is based on the property of a magnetized medium to resist the movement of ferromagnetic bodies in it. A liquid mixture of mineral oil and iron powder is used as a magnetizable medium in the design of the load device. The housing of the loading device is mounted balanced in relation to the base of the device on two bearings. The restriction from the circular rotation of the housing is carried out by a flat spring 7, which creates a reactive torque that balances the moment of resistance forces (braking torque) created by the load device.
Torque and braking torque measuring devices consist of flat springs 6 and 7 and dial indicators 8 and 9, which measure spring deflections proportional to the torque values. Strain gauges are additionally glued to the springs, the signal from which can also be recorded on an oscilloscope through a strain gauge amplifier.
On the front part of the device base there is a control panel 10, on which the following are installed:
Toggle switch 11 on and off the electric motor;
Handle 12 for regulating the speed of the electric motor shaft;
Signal lamp 13 for turning on the device;
Toggle switch 14 turns on and off the excitation winding circuit of the load device;
Knob 15 for adjusting the excitation of the load device.
When performing this laboratory work you should:
Determine the gear ratio;
Calibrate measuring devices;
Determine the efficiency of the gearbox depending on the resistance forces and the number of revolutions of the electric motor.
4. PROCEDURE FOR PERFORMANCE OF THE WORK
4.1. Determination of gear ratio
The gear ratio of the DP-3K device is determined by the formula
(5)
Where z 2 , z 1 – number of teeth, respectively, of the larger and smaller wheels of one stage; To=6 – number of gear stages with the same gear ratio.
For the gearbox of the DP-3K device, the gear ratio of one stage is
Found values of gear ratio i p check experimentally.
4.2. Calibration of measuring devices
Calibration of measuring devices is carried out with the device disconnected from the source of electric current using calibration devices consisting of levers and weights.
To calibrate an electric motor torque measuring device, you must:
Install calibration device DP3A sb on the motor housing. 24;
Set the weight on the lever of the calibration device to the zero mark;
Set the indicator arrow to zero;
When placing the weight on the lever at subsequent divisions, record the indicator readings and the corresponding division on the lever;
Determine the average value m avg indicator division prices using the formula
(6)
Where TO– number of measurements (equal to the number of divisions on the lever); G- cargo weight, N; N i– indicator readings, - distance between marks on the lever ( m).
Determining the average value m c .sr The division price of the load device indicator is made by installing the DP3A sb calibration device on the body of the load device. 25 using a similar method.
Note. Weight of loads in calibration devices DP3K sb. 24 and DP3K Sat. 25 is 1 and 10 respectively N.
4.3. Determination of gearbox efficiency
Determination of gearbox efficiency depending on resistance forces, i.e. .
To determine the dependency you need to:
Turn on the toggle switch 11 of the electric motor of the device and use the speed control knob 12 to set the rotation speed n specified by the teacher;
Set knob 15 for adjusting the excitation current of the load device to the zero position, turn on toggle switch 14 in the excitation power circuit;
By smoothly turning the excitation current control knob, set the first value (10 divisions) of the torque according to the indicator arrow M s resistance;
Use speed control knob 12 to set (correct) the initial set speed n;
Record the readings h 1 and h 2 of indicators 8 and 9;
By further adjusting the excitation current, increase the moment of resistance (load) to the next specified value (20, 30, 40, 50, 60, 70, 80 divisions);
Keeping the rotation speed constant, record the indicator readings;
Determine the values of the moments of driving forces M d and resistance forces M s for all measurements using formulas
(7)
(8)
Determine the gearbox efficiency for all measurements using formula (4);
Enter indicator readings h 1 and h 2, moment values M d And M s and the found values of gearbox efficiency for all measurements in the table;
Construct a dependence graph.
4.4. Determination of gearbox efficiency depending on the speed of the electric motor
To determine a graphical dependency you need to:
Turn on toggle switch 14 of the power and excitation circuit and use knob 15 for adjusting the excitation current to set the torque value specified by the teacher M s on the output shaft of the gearbox;
Turn on the electric motor of the device (toggle switch 11);
By setting the speed control knob 12 sequentially to a series of values (from minimum to maximum) of the rotational speed of the electric motor shaft and maintaining a constant torque value M s load, record the indicator readings h 1 ;
Give a qualitative assessment of the influence of rotation speed n on the efficiency of the gearbox.
5. REPORT COMPILATION
The report on the work done must contain the name,
the purpose of the work and the tasks of determining the mechanical efficiency, the main technical data of the installation (type of gearbox, number of teeth on the wheels, type of electric motor, loading device, measuring devices and instruments), calculations, description of the calibration of measuring devices, tables of experimentally obtained data.
6. CHECK QUESTIONS
1. What is called mechanical efficiency? Its dimension.
2. What does mechanical efficiency depend on?
3. Why is mechanical efficiency determined experimentally?
4. What is the sensor in torque and braking torque measuring devices?
5. Describe the loading device and its principle of operation.
6. How will the mechanical efficiency of the gearbox change if the moment of resistance forces doubles (decreases)?
7. How will the mechanical efficiency of the gearbox change if the moment of resistance increases (decreases) by 1.5 times?
Lab 9
