Determination of the mechanical efficiency of a gearbox with spur gears. Calculation and selection (Russian methodology) - worm gearbox What are the losses in the gearbox made up of?
Laboratory work
Ratio Research useful action gear reducer
1. Purpose of the work
Analytical determination of the coefficient of performance (efficiency) of a gear reducer.
Experimental determination of the efficiency of a gear reducer.
Comparison and analysis of the results obtained.
2. Theoretical provisions
Energy supplied to a mechanism in the form of workdriving forces and moments per steady state cycle, is spent on performing useful workthose. work of forces and moments of useful resistance, as well as to perform workassociated with overcoming friction forces in kinematic pairs and environmental resistance forces:. Meanings and are substituted into this and subsequent equations according to absolute value. The mechanical efficiency is the ratio
Thus, efficiency shows what proportion of the mechanical energy supplied to the machine is usefully spent on performing the work for which the machine was created, i.e. is important characteristic machine mechanisms. Since friction losses are inevitable, it is always. In equation (1) instead of works And performed per cycle, you can substitute the average values of the corresponding powers per cycle:
A gearbox is a gear (including worm) mechanism designed to reduce the angular speed of the output shaft relative to the input.
Input angular velocity ratio to the angular velocity at the exit called the gear ratio :
For the gearbox, equation (2) takes the form
Here T 2 And T 1 – average values of torque on the output (moment of resistance forces) and input (moment of driving forces) shafts of the gearbox.
The experimental determination of efficiency is based on measuring the values T 2 And T 1 and calculating η using formula (4).
When studying the efficiency of a gearbox by factors, i.e. system parameters that influence the measured value and can be purposefully changed during the experiment, are the moment of resistance T 2 on the output shaft and the rotation speed of the gearbox input shaftn 1 .
Main way increasing efficiency gearboxes is to reduce power losses, such as: the use of more modern lubrication systems that eliminate losses due to mixing and splashing of oil; installation of hydrodynamic bearings; design of gearboxes with the most optimal transmission parameters.
The efficiency of the entire installation is determined from the expression
Where – gear reducer efficiency;
– efficiency of electric motor supports,;
– coupling efficiency, ;
– efficiency of brake supports,.
The overall efficiency of a multi-stage gear reducer is determined by the formula:
Where – Gear efficiency with average manufacturing quality and periodic lubrication,;
– The efficiency of a pair of bearings depends on their design, assembly quality, loading method and is taken approximately(for a pair of rolling bearings) and(for a pair of plain bearings);
– Efficiency taking into account losses due to splashing and mixing of oil is approximately accepted= 0,96;
k– number of pairs of bearings;
n– number of pairs of gears.
3. Description of the research object, instruments and instruments
This laboratory work is carried out on a DP-3A installation, which makes it possible to experimentally determine the efficiency of a gear reducer. The DP-3A installation (Figure 1) is mounted on a cast metal base 2 and consists of an electric motor assembly3 (a source of mechanical energy) with a tachometer5, a load device11 (energy consumer), a gearbox under test8 and elastic couplings9.
Fig.1. Schematic diagram of the DP-3A installation
Loading device 11 is a magnetic powder brake that simulates the working load of the gearbox. The stator of the load device is an electromagnet, in the magnetic gap of which a hollow cylinder with a roller (rotor of the load device) is placed. The internal cavity of the loading device is filled with a mass consisting of a mixture of carbonyl powder and mineral oil.
Two regulators: potentiometers 15 and 18 allow you to adjust the speed of the electric motor shaft and the amount of braking torque of the load device, respectively. The rotation speed is controlled using a tachometer5.
The magnitude of the torque on the shafts of the electric motor and brake is determined using devices that include a flat spring6 and dial indicators7,12. Supports 1 and 10 on rolling bearings provide the ability to rotate the stator and rotor (both the engine and the brake) relative to the base.
Thus, when submitting electric current(turn on the toggle switch 14, the signal lamp 16 lights up) in the stator winding of the electric motor 3, the rotor receives a torque, and the stator receives a reactive torque equal to the torque and directed in the opposite direction. In this case, the stator under the action of the reactive torque deviates (balanced motor) from its original position depending on the magnitude of the braking torque on the driven shaft of the gearboxT 2 . These angular movements of the stator housing of the electric motor are measured by the number of divisions P 1 , to which the indicator arrow deviates7.
Accordingly, when electric current is supplied (turn on toggle switch 17) to the electromagnet winding, the magnetic mixture resists the rotation of the rotor, i.e. creates a braking torque on the output shaft of the gearbox, recorded by a similar device (indicator 12), showing the amount of deformation (number of divisions P 2) .
The springs of the measuring instruments are pre-tared. Their deformations are proportional to the magnitude of the torques on the electric motor shaft T 1 and gearbox output shaftT 2 , i.e. the magnitudes of the moment of driving forces and the moment of resistance (braking) forces.
The gearbox8 consists of six identical pairs of gears mounted on ball bearings in the housing.
The kinematic diagram of the DP 3A installation is shown in Figure 2, A The main installation parameters are given in Table 1.
Table 1. Technical characteristics of the installation
|
Parameter name |
Letter designation quantities |
Meaning |
|
Number of pairs of spur gears in the gearbox |
n |
|
|
Gear ratio |
u |
|
|
transmission module, mm |
m |
|
|
Rated torque on the motor shaft, Nmm |
T 1 |
|
|
Braking torque on the brake shaft, Nmm |
T 2 |
up to 3000 |
|
Number of revolutions of the electric motor shaft, rpm |
n 1 |
1000 |
Rice. 2. Kinematic diagram of the DP-3A installation
1 - electric motor; 2 – coupling; 3 – gearbox; 4 – brake.
4. Research methodology and results processing
4.1 The experimental value of the gearbox efficiency is determined by the formula:
Where T 2 – moment of resistance forces (torque on the brake shaft), Nmm;
T 1 – moment of driving forces (torque on the electric motor shaft), Nmm;
u– gear ratio of the gear reducer;
– efficiency of the elastic coupling;= 0,99;
– efficiency of bearings on which the electric motor and brake are installed;= 0,99.
4.2. Experimental tests involve measuring the torque on the motor shaft at a given rotation speed. In this case, certain braking torques are sequentially created on the output shaft of the gearbox according to the corresponding indicator readings12.
When turning on the electric motor with toggle switch 14 (Figure 1), the motor stator support with your hand to prevent hitting the spring.
Turn on the brake with toggle switch 17, after which the indicator arrows are set to zero.
Using potentiometer 15, set the required number of engine shaft revolutions on the tachometer, for example, 200 (Table 2).
Potentiometer 18 creates braking torques on the output shaft of the gearbox T 2 corresponding to indicator readings 12.
Record the indicator readings7 to determine the torque on the motor shaft T 1 .
After each series of measurements at one speed, potentiometers 15 and 18 are moved to their extreme counterclockwise position.
|
Rotation frequencyn 1 shaft electric motor, rpm |
Indicator readings 12, P 2 |
|
200, 350, 550, 700 |
120, 135, 150, 165, 180, 195 |
|
850, 1000 |
100, 105, 120, 135, 150, 160 |
4.3. By changing the load on the brake with potentiometer 18 and on the engine with potentiometer 15 (see Figure 1), with a constant engine rotation speed, record five indicator readings 7 and 12 ( P 1 and P 2) in table 3.
Table 3. Test results
|
Number of revolutions of the electric motor shaft,n 1 , rpm |
Indicator readings 7 P 1 |
Torque on the motor shaft, Nmm |
Indicator readings 12 P 2 |
Torque on the brake shaft, Nmm |
Experimental efficiency, |
Veselova E. V., Narykova N. I.
Research of instrument gearboxes
Guidelines for laboratory work No. 4, 5, 6 for the course “Fundamentals of instrument design”
Original: 1999
Digitized: 2005
The digital layout based on the original was compiled by: Alexander A. Efremov, gr. IU1-51
Purpose of work
Familiarization with the designs of installations to determine the efficiency of gearboxes.
Experimental and analytical determination of the efficiency of a given type of gearbox depending on the load on the output shaft.
Devices called drives are widely used in various types of devices. They consist of an energy source (motor), gearbox and control equipment.
A gearbox is a mechanism consisting of a system of gear, worm or planetary gears that reduce the speed of rotation of the driven link compared to the speed of rotation of the driving link.
A similar device that serves to increase the rotation speed of the driven link compared to the rotation speed of the driving link is called a multiplier.
In these laboratory works, the following types of gearboxes are studied: helical multi-stage gearbox, planetary gearbox and single-stage worm gearbox.
The concept of efficiency
When the mechanism is in steady motion, the power of the driving forces is expended entirely on overcoming useful and harmful resistances:
Here P g- power of driving forces; P c- power expended to overcome friction resistance; P n- power expended to overcome useful resistances.
The efficiency is the ratio of the power of the useful resistance forces to the power of the driving forces:
(2)
Index 1-2 indicates that the movement is transmitted from link 1, to which the driving force is applied, to link 2, to which the useful resistance force is applied.
Magnitude 
called transmission loss factor. Obviously:
(3)
In the case of lightly loaded gears (they are typical in instrument making), the efficiency depends significantly on its own friction losses and on the degree of force loading of the mechanism. In this case, formula (3) takes the form:
(4)
Where c- coefficient taking into account the influence of own losses on friction and load F,
Components a And b depend on the type of transmission.
At 
coefficient 
reflects the influence of own losses on friction in lightly loaded gears. With increasing F coefficient c(F) decreases, approaching the value 
at a large value F.
For serial connection m mechanisms with efficiency 
Efficiency of the entire connection of mechanisms:
(5)
Where P g- power supplied to the first mechanism; P n- power removed from the last mechanism.
A gearbox can be considered as a device with a series connection of gears and supports. Then the efficiency is determined by the expression:
(6)
Where 
- efficiency i-
oh pairs of engagement; 
- efficiency of one pair of supports; 
- number of pairs of supports.
Support efficiency
The efficiency of the support is determined by the formula
(7)
since the ratio of the powers at the output and input of the support is equal to the ratio of the corresponding moments due to the constancy of the rotation speed. Here M- torque on the shaft; M tr- friction moment in the support.
The frictional moment in a rolling bearing can be determined by the formula:
(8)
Where M 1 - friction moment, depending on the load on the support; M 0 - friction torque, depending on the bearing design, rotation speed and lubricant viscosity.
In instrument gearboxes the component M 1 is much less than the component M 0 . Thus, we can assume that the friction moment of the supports is practically independent of the load. Consequently, the efficiency of the support does not depend on the load. When calculating the efficiency of a gearbox, the efficiency of one pair of bearings can be taken as 0.99.
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.
Top part gearbox 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:
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 measuring devices torque and braking torque?
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?
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 during 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 (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 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 coefficient);
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.
During 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:
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 the same 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 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– 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 coefficient);
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.
During 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:
