What is gearbox efficiency. Determination of the mechanical efficiency of a gearbox with spur gears
1. PURPOSE OF THE WORK
Deepening the knowledge of theoretical material, obtaining practical skills for independent experimental determination of gearboxes.
2. MAIN 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 the driving forces N d on the gearbox input shaft:
The power of driving forces and resistance forces can be determined, respectively, by the formulas
(2)
(3)
where M d and M s are the moments of the 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 obtain
(4)
where is the gear ratio.
Any complex machine consists of a series simple mechanisms. The efficiency of a machine can be easily determined if the efficiency of all the simple mechanisms included in it is known. For most mechanisms, analytical methods have been developed for determining the efficiency, however, deviations in the cleanliness of the processing of rubbing surfaces of parts, the accuracy of their manufacture, changes in the load on the elements of kinematic pairs, lubrication conditions, relative motion speed, 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 efficiency of the gearbox ( M d, M s and L p) can be determined using DP-3K instruments.
3. DEVICE OF THE DEVICE DP-3K
The device (figure) is mounted on a cast metal base 1 and consists of an electric motor unit 2 with a tachometer 3, a load device 4 and a gearbox 5 under study.
3 6 8 2 5 4 9 7 1
 |
11 12 13 14 15 10
Rice. Kinematic diagram of the device DP-3K
The body of the electric motor is pivotally fixed in two supports so that the axis of rotation of the motor shaft coincides with the axis of rotation of the body. The motor housing is fixed from circular rotation by a flat spring 6. When torque is transmitted from the gear motor shaft, the spring creates a reactive moment applied to the motor housing. The motor shaft is connected to the gearbox input shaft through a coupling. Its opposite end is articulated with the tachometer shaft.
The gearbox in the DK-3K device consists of six identical pairs gear wheels 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 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 body of the load device is mounted balanced relative to the base of the device on two bearings. The restriction from the circular rotation of the body is carried out by a flat spring 7, which creates a reactive moment that balances the moment of the resistance forces (braking moment) created by the load device.
Measuring devices torque and braking torques consist of flat springs 6 and 7 and dial gauges 8 and 9, which measure the deflections of the springs, proportional to the magnitude of the moments. The springs are additionally glued with strain gauges, the signal from which can also be recorded on an oscilloscope through a strain gauge amplifier.
On the front part of the base of the device there is a control panel 10, on which are installed:
Toggle switch 11 on and off the electric motor;
Handle 12 for regulating the speed of the motor shaft;
Signal lamp 13 for turning on the device;
Toggle switch 14 on and off the circuit of the excitation winding of the load device;
Handle 15 for adjusting the excitation of the load device.
When performing this lab, you should:
Determine the gear ratio of the gearbox;
calibrate measuring devices;
Determine the efficiency of the gearbox depending on the resistance forces and on the number of revolutions of the electric motor.
4. ORDER OF PERFORMANCE OF WORK
4.1. Determination of the gear ratio of the gearbox
The gear ratio of the gearbox of the DP-3K device is determined by the formula
(5)
where z 2 , z 1 - the number of teeth, respectively, of the larger and smaller wheels of one stage; to=6 - the number of gear stages with the same gear ratio.
For the gearbox of the DP-3K device, the gear ratio of one stage
Found gear ratio values i p check experimentally.
4.2. Calibration of measuring devices
Calibration of measuring devices is carried out when disconnected from the source electric current device using calibration devices, consisting of levers and weights.
To calibrate the motor torque measuring device, you must:
Install the 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 setting the load on the lever for subsequent divisions, fix the indicator readings and the corresponding division on the lever;
Determine the mean m cf the price of division of the indicator according to the formula
(6)
where To- the number of measurements (equal to the number of divisions on the lever); G- cargo weight, H; N i- indicator readings, - distance between divisions on the lever ( m).
Determination of the average value m c .av the division price of the load device indicator is made by installing the calibration device DP3A sb on the body of the load device. 25 in a similar manner.
Note. Weight of cargoes in DP3K calibration devices sb. 24 and DP3K Sat. 25 is 1 and 10 respectively H.
4.3. Determination of the efficiency of the gearbox
Determination of the efficiency of the gearbox depending on the 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 adjustment knob 12 to set the rotational speed n set by the teacher;
Set the handle 15 for adjusting the excitation current of the load device to the zero position, turn on the 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 in the direction of the indicator M s resistance;
Using the speed adjustment knob 12, 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);
Maintaining the rotational speed unchanged, fix the readings of the indicators;
Determine the values of the moments of the driving forces M d and resistance forces M s for all measurements by formulas
(7)
(8)
Determine for all measurements the efficiency of the reducer according to the formula (4);
Record indicator readings h 1 and h 2 , moment values M d and M s and the found values of the efficiency of the reducer for all measurements in the table;
Build a dependency graph.
4.4. Determination of the efficiency of the gearbox depending on the number of revolutions of the electric motor
To determine the graphical dependency, you must:
Turn on the toggle switch 14 of the power and excitation circuit and use the handle 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 adjustment knob 12 successively a series of values (from minimum to maximum) of the rotational speed of the motor shaft and maintaining a constant value of the moment M s load, fix the indicator readings h 1 ;
Give a qualitative assessment of the influence of rotational speed n on the efficiency of the gearbox.
5. PREPARATION OF THE REPORT
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. CONTROL QUESTIONS
1. What is called mechanical efficiency? Its dimension.
2. What determines the mechanical efficiency?
3. Why is mechanical efficiency determined empirically?
4. What is a sensor in torque and brake torque measuring devices?
5. Describe the load 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 forces increases (decreases) by 1.5 times?
Lab 9
This article contains detailed information on the selection and calculation of a gearmotor. We hope that the information provided will be useful to you.
When choosing a specific model of a gearmotor, the following technical characteristics are taken into account:
- gearbox type;
- power;
- output speed;
- gear ratio of the gearbox;
- design of the input and output shafts;
- installation type;
- additional functions.
Reducer type
The presence of a kinematic drive scheme will simplify the choice of the type of gearbox. Structurally, gearboxes are divided into the following types:
- Worm gear single stage with crossed input/output shaft arrangement (90 degree angle).
- Worm two-stage with a perpendicular or parallel arrangement of the axes of the input / output shaft. Accordingly, the axes can be located in different horizontal and vertical planes.
- Cylindrical horizontal with parallel input/output shafts. The axes are in the same horizontal plane.
- Cylindrical coaxial at any angle. The axes of the shafts are located in the same plane.
- AT conical-cylindrical In the gearbox, the axes of the input/output shafts intersect at an angle of 90 degrees.
Important! The location of the output shaft in space is of decisive importance 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 more often possible in a horizontal plane. With the same weight and size 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 the number of stages and type of transmission
| Reducer type | Number of steps | Transmission type | Axle arrangement |
|---|---|---|---|
| Cylindrical | One or more cylindrical | Parallel |
|
| Parallel/Coaxial |
|||
| Parallel |
|||
| Conical | conical | intersecting |
|
| Conical-cylindrical | conical | Crossed/Crossed |
|
| Worm | Worm (one or two) | Crossbreeding |
|
| Parallel |
|||
| Cylindrical-worm or worm-cylindrical | Cylindrical (one or two) | Crossbreeding |
|
| Planetary | Two central gears and satellites (for each step) | ||
| Cylindrical-planetary | Cylindrical (one or more) | Parallel/Coaxial |
|
| conical planetary | Conical (one) Planetary (one or more) | intersecting |
|
| Worm planetary | Worm (one) | Crossbreeding |
|
| Wave | Wave (one) |
Gear ratio [I]
The gear ratio of the gearbox is calculated by the formula:
I = N1/N2
where
N1 - shaft rotation speed (number of rpm) at the input;
N2 - shaft rotation speed (number of rpm) at the output.
The value obtained during the calculations is rounded up to the value specified in technical specifications particular type of gearboxes.
Table 2. Range of gear ratios for different types gearboxes
Important! The speed of rotation of the motor shaft and, accordingly, the input shaft of the gearbox cannot exceed 1500 rpm. The rule is valid for any type of gearboxes, except for cylindrical coaxial ones with a rotation speed of up to 3000 rpm. Manufacturers indicate this technical parameter in the summary characteristics of electric motors.
Reducer torque
Torque on the output shaft is the torque on the output shaft. The rated power is taken into account, the safety factor [S], the estimated duration of operation (10 thousand hours), the efficiency of the gearbox.
Rated torque- maximum torque for safe transmission. Its value is calculated taking into account the safety factor - 1 and the duration of operation - 10 thousand hours.
Max Torque- the limiting torque that the gearbox can withstand under constant or varying 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 that meets the customer's criteria. Its value is less than or equal to the rated torque.
Estimated torque- the value needed to select the reducer. The calculated value is calculated using the following formula:
Mc2 = Mr2 x Sf<= Mn2
where
Mr2 is the required torque;
Sf - service factor (operational factor);
Mn2 - rated torque.
Service Factor (Service Factor)
The service factor (Sf) is calculated experimentally. The type of load, the daily duration of operation, the number of starts / stops per hour of operation of the gearmotor are taken into account. You can determine the service factor 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 |
|||
|---|---|---|---|---|---|
| Soft start, static operation, moderate mass acceleration | |||||
| Moderate starting load, variable duty, medium mass acceleration | |||||
| Heavy duty operation, variable duty, high mass acceleration | |||||
Drive power
Properly calculated drive power helps to overcome the mechanical frictional resistance that occurs during rectilinear and rotary movements.
The elementary formula for calculating power [P] is the calculation of the ratio of force to speed.
In rotational movements, power is calculated as the ratio of torque to the number of revolutions per minute:
P = (MxN)/9550
where
M - torque;
N - the number of revolutions / min.
The output power is calculated by the formula:
P2 = PxSf
where
P - power;
Sf - service factor (operational factor).
Important! The value of the input power must always be higher than the value of the output power, which is justified by the losses during engagement: P1 > P2
It is not possible to make calculations using an approximate value of the input power, since the efficiency can vary significantly.
Efficiency factor (COP)
Consider the calculation of efficiency using the example of a worm gear. It will be equal to the ratio of mechanical output power and input power:
η [%] = (P2/P1) x 100
where
P2 - output power;
P1 - input power.
Important! In worm gears P2< 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.
Efficiency is affected by the duration of operation and quality 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. Efficiency of the wave reducer
Table 6. Efficiency of gear reducers
Regarding the calculation and purchase of motor gearboxes various types contact our specialists. The catalog of worm, spur, planetary and wave gear motors offered by Techprivod can be found on the website.
Romanov Sergey Anatolievich,
head of the department of mechanics
Techprivod company
1. The purpose of the work
The study of the efficiency of the gearbox at various modes loading.
2. Installation description
To study the operation of the gearbox, a device of the DP3M brand is used. It consists of the following main units (Fig. 1): the gearbox under test 5, the electric motor 3 with an electronic tachometer 1, the load device 6, the device for measuring moments 8, 9. All units are mounted on the same base 7.
The body of the electric motor is hinged in two supports 2 so that the axis of rotation of the motor shaft coincides with the axis of rotation of the body. The fixation of the motor housing from circular rotation is carried out by a flat spring 4.
The gearbox consists of six identical spur gears with a gear ratio of 1.71 (Fig. 2). The block of gears 19 is mounted on a fixed axle 20 on a ball bearing. The design of blocks 16, 17, 18 is similar to block 19. The transmission of torque from the wheel 22 to the shaft 21 is carried out through the key.
The load device is a magnetic powder brake, the 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 was used as a magnetizable medium.
Measuring devices for torque and braking torques consist of flat springs that create reactive torques for the electric motor and load device, respectively. Strain gauges connected to the amplifier are glued on flat springs.
On the front part of the base of the device there is a control panel: power button of the device "Network" 11; button for powering on the excitation circuit of the load device "Load" 13; button for turning on the electric motor "Engine" 10; knob for regulating the frequency of rotation of the electric motor "Speed control" 12; handle for regulating the excitation current of the load device 14; three ammeters 8, 9, 15 to measure respectively the frequency n, moment M 1 moment M 2 .
Rice. 1. Installation diagram
Rice. 2. Gearbox under test
Technical characteristics of the device DP3M:
3. Calculated dependencies
The determination of the efficiency of the gearbox is based on the simultaneous measurement of the moments on the input and output shafts of the gearbox at a steady value of the speed. In this case, the calculation of the efficiency of the gearbox is carried out according to the formula:
= , (1)
where M 2 is the moment created by the load device, N × m; M 1 - the moment developed by the electric motor, N × m; u is the gear ratio of the gearbox.
4. Order of work
At the first stage, at a given constant speed of the electric motor, the efficiency of the gearbox is studied depending on the moment created by the load device.
First, the electric drive is turned on and the set speed is set with the speed control knob. The excitation current adjustment knob of the load device is set to the zero position. The excitation power supply is switched 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 set speed. Using microammeters 8, 9 (Fig. 1), the moments on the motor shaft and load device are recorded. By further adjusting the excitation current, the load torque is increased to the next predetermined value. Keeping the speed unchanged, determine the following values of M 1 and M 2 .
The results of the experiment are entered in Table 1, and a graph of the dependence = f(M 2) is plotted at n = const (Fig. 4).
At the second stage, at a given constant load torque M 2, the efficiency of the gearbox is studied depending on the speed of the electric motor.
The excitation power supply circuit is switched on and the set value of the torque on the output shaft of the gearbox is set by the excitation current adjustment knob. The speed control knob sets a range of speeds (from minimum to maximum). For each speed mode, a constant load torque M 2 is maintained, the moment on the motor shaft M 1 is fixed using a microammeter 8 (Fig. 1).
The results of the experiment are entered in Table 2, and a graph of the dependence = f(n) is plotted at M 2 = const (Fig. 4).
5. Conclusion
It explains what the power losses in the gear train are made up of and how the efficiency of a multi-stage gearbox is determined.
The conditions that allow to increase the efficiency of the gearbox are listed. The theoretical substantiation of the obtained graphs = f(M 2) is given; = f(n).
6. Reporting
– Prepare a title page (see sample on page 4).
- Draw the kinematic diagram of the gearbox.
Prepare and complete the table. one.
Table 1
from the moment created by the load device
– Build a dependency graph
| |
Rice. 4. Dependence graph \u003d f (M 2) at n \u003d const
Prepare and complete the table. 2.
table 2
The results of the study of the efficiency of the gearbox depending on
from the frequency of rotation of the electric motor
– Build a dependency graph.
| |
|
Rice. 5. Dependence plot = f(n) at M 2 = const
Give a conclusion (see paragraph 5).
test questions
1. Describe the design of the DPZM device, what main components does it consist of?
2. What power losses take place in the gear and what is its efficiency?
3. How do such gear transmission characteristics as power, torque, rotational speed change from the driving to the driven shaft?
4. How is the gear ratio and efficiency of a multi-stage gearbox determined?
5. List the conditions to improve the efficiency of the gearbox.
6. The procedure for performing work in the study of the efficiency of the gearbox, depending on the moment supplied by the load device.
7. The procedure for performing work in the study of the efficiency of the gearbox, depending on the engine speed.
8. Give a theoretical explanation of the obtained graphs = f(M 2); = f(n).
Bibliographic list
1. Reshetov, D. N. Machine parts: - a textbook for students of 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.
LAB #8
The presence of a kinematic drive scheme will simplify the choice of the type of gearbox. Structurally, gearboxes are divided into the following types:
Gear ratio [I]
The gear ratio of the gearbox is calculated by the formula:
I = N1/N2
where
N1 - shaft rotation speed (number of rpm) at the input;
N2 - shaft rotation speed (number of rpm) at the output.
The value obtained during the calculations is rounded up 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 speed of rotation of the motor shaft and, accordingly, the input shaft of the gearbox cannot exceed 1500 rpm. The rule is valid for any type of gearboxes, except for cylindrical coaxial ones with a rotation speed of up to 3000 rpm. Manufacturers indicate this technical parameter in the summary characteristics of electric motors.
Reducer torque
Torque on the output shaft is the torque on the output shaft. The rated power is taken into account, the safety factor [S], the estimated duration of operation (10 thousand hours), the efficiency of the gearbox.
Rated torque– maximum torque for safe transmission. Its value is calculated taking into account the safety factor - 1 and the duration of operation - 10 thousand hours.
Maximum torque (M2max]- the maximum torque that the gearbox can withstand under constant or varying 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 that meets the customer's criteria. Its value is less than or equal to the rated torque.
Estimated torque- the value required to select the gearbox. The calculated value is calculated using the following formula:
Mc2 = Mr2 x Sf ≤ Mn2
where
Mr2 is the required torque;
Sf - service factor (operational factor);
Mn2 is the rated torque.
Service Factor (Service Factor)
The service factor (Sf) is calculated experimentally. The type of load, the daily duration of operation, the number of starts / stops per hour of operation of the gearmotor are taken into account. You can determine the service factor 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, moderate 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 duty, 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 | |
| Heavy duty operation, variable duty, high 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
Properly calculated drive power helps to overcome the mechanical frictional resistance that occurs during rectilinear and rotary movements.
The elementary formula for calculating power [P] is the calculation of the ratio of force to speed.
In rotational movements, power is calculated as the ratio of torque to the number of revolutions per minute:
P = (MxN)/9550
where
M is torque;
N is the number of revolutions / min.
The output power is calculated by the formula:
P2 = PxSf
where
P is power;
Sf - service factor (operational factor).
IMPORTANT!
The value of the input power must always be higher than the value of the output power, which is justified by the losses during engagement:
P1 > P2
It is not possible to make calculations using an approximate value of the input power, since the efficiency can vary significantly.
Efficiency factor (COP)
Consider the calculation of efficiency using the example of a worm gear. 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 worm gears P2< 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 the 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. Efficiency of the wave reducer
Table 6. Efficiency of gear reducers
Explosion-proof versions of gearmotors
Gearmotors of this group are classified according to the type of explosion-proof design:
- "E" - units with a high degree of protection. They can be used in any mode of operation, including emergency situations. Reinforced protection prevents the possibility of ignition of industrial mixtures and gases.
- "D" - flameproof enclosure. The housing of the units is protected from deformation in the event of an explosion of the motor-reducer itself. This is achieved due to its design features and increased tightness. Equipment with explosion protection class "D" can be used in extremely high temperatures and with any group of explosive mixtures.
- "I" - intrinsically safe circuit. This type of protection ensures the maintenance of explosion-proof current in the electrical network, taking into account the specific conditions of industrial applications.
Reliability indicators
Reliability indicators of gearmotors are given in table 7. All values are given for long-term operation at a constant rated load. The motor-reducer must provide 90% of the resource indicated in the table even in the mode of short-term overloads. They occur when starting the equipment and exceeding the rated torque twice, at least.
Table 7. Resource of shafts, bearings and gearboxes
For the calculation and purchase of motor reducers of various types, please contact our specialists. you can get acquainted with the catalog of worm, cylindrical, planetary and wave gear motors offered by Techprivod.
Romanov Sergey Anatolievich,
head of the department of mechanics
Techprivod company.
Other useful resources:
The purpose of the work: 1. Determination of the geometric parameters of gears and calculation of gear ratios.
3. construction of dependence graphs at and at .
The work was completed by: F.I.O.
Group
Job accepted:
The results of measurements and calculation of the parameters of the wheels and gearbox
Number of teeth
Tooth tip diameter d a, mm
Module m according to the formula (7.3), mm
center distance aw according to the formula (7.4), mm
Gear ratio u by formula (7.2)
The total gear ratio according to the formula (7.1)
Kinematic diagram of the gearbox
Table 7.1
Dependency graph for
η
T 2 , N∙mm
Table 7.2
Experimental data and calculation results
Dependency graph for
η
n, min -1
test questions
1. What are the losses in a gear train and what are the most effective measures to reduce transmission losses?
2. Essence of relative, constant and load losses.
3. How does the transmission efficiency change depending on the transmitted power?
4. Why does the efficiency increase with an increase in the degree of accuracy of gears and gears?
Lab #8
DETERMINATION OF THE EFFICIENCY OF THE WORM GEAR
Objective
1. Determination of the geometric parameters of the worm and worm wheel.
2. Image of the kinematic diagram of the gearbox.
3. Plotting dependencies at and at .
Basic Safety Rules
1. Turn on the installation with the permission of the teacher.
2. The device must be connected to a rectifier, and the rectifier must be connected to the mains.
3. After finishing work, disconnect the unit from the network.
Installation Description
On a cast base 7 (Fig. 8.1) the researched reducer is mounted 4 , electric motor 2 with tachometer 1 , showing the rotational speed, and the load device 5 (magnetic powder brake). Mounted on brackets are measuring devices consisting of flat springs and indicators. 3 and 6 , the rods of which rest against the springs.
A toggle switch is located on the control panel 11 , turning on and off the electric motor; a pen 10 a potentiometer that allows you to steplessly adjust the speed of the electric motor; toggle switch 9 , including a load device, and a handle 8 potentiometer to adjust the braking torque T 2.
The stator of the electric motor is mounted on two ball bearings mounted in a bracket and can freely rotate around an axis coinciding with the axis of the rotor. The reactive torque that has arisen during the operation of the electric motor is completely transferred to the stator and acts in the direction opposite to the rotation of the armature. Such an electric motor is called a balancer.
Rice. 8.1. Installation of DP - 4K:
1
- tachometer; 2
– electric motor; 3
, 6
– indicators; 4
– worm gear;
5
– powder brake; 7
- base; 8
– load control knob;
9
– toggle switch for switching on the load device; 10
– the handle of regulation of speed of rotation of the electric motor; 11
- toggle switch for turning on the electric motor
To measure the magnitude of the moment developed by the engine, a lever is attached to the stator, which presses on a flat spring of the measuring device. The deformation of the spring is transferred to the indicator rod. By the deviation of the indicator arrow, one can judge the magnitude of this deformation. If the spring is calibrated, i.e. establish moment dependence T 1 , turning the stator, and the number of divisions of the indicator, then when performing the experiment, it is possible to judge the magnitude of the moment by the indications of the indicator T 1 developed by an electric motor.
As a result of the calibration of the measuring device of the electric motor, the value of the calibration coefficient is set
In a similar way, the calibration coefficient of the braking device is determined:
General information
Kinematic study.
Worm gear ratio
where z 2 - the number of teeth of the worm wheel;
z 1 - the number of visits (turns) of the worm.
The gearbox worm of the DP-4K unit has a module m= 1.5 mm, which corresponds to GOST 2144–93.
Pitch diameter of the worm d 1 and worm diameter factor q are determined by solving the equations
; (8.2)
According to GOST 19036–94 (original worm and original producing worm), the coil head height coefficient is accepted.
Estimated worm pitch
Coil stroke
Dividing angle of elevation
Sliding speed, m/s:
, (8.7)
where n 1 – electric motor speed, min –1.
Determination of the efficiency of the gearbox
The power losses in the worm gear are made up of friction losses in the gear, friction in the bearings and hydraulic losses due to stirring and splashing of the oil. The main part of the losses are losses in gearing, depending on the accuracy of manufacturing and assembly, the rigidity of the entire system (especially the rigidity of the worm shaft), the lubrication method, the materials of the worm and wheel teeth, the roughness of the contact surfaces, the sliding speed, the geometry of the worm and other factors.
Overall efficiency of the worm gear
where η p – Efficiency taking into account losses in one pair of bearings for rolling bearings η n = 0.99…0.995;
n– number of pairs of bearings;
η p \u003d 0.99 - efficiency taking into account hydraulic losses;
η 3 – Efficiency taking into account losses in gearing and determined by the equation
where φ is the angle of friction, depending on the material of the worm and the teeth of the wheel, the roughness of the working surfaces, the quality of the lubricant and the sliding speed.
Experimental determination of the efficiency of the gearbox is based on the simultaneous and independent measurement of torques T 1 at the input and T 2 on the output shafts of the gearbox. The efficiency of the gearbox can be determined by the equation
where T 1 - torque on the motor shaft;
T 2 - torque on the output shaft of the gearbox.
Experienced values of torques are determined by dependencies
where μ 1 and μ 2 – calibration coefficients;
k 1 and k 2 - readings of the indicators of the measuring devices of the engine and brake, respectively.
Work order
2. According to the table. 8.1 of the report, build a kinematic diagram of a worm gear, for which use the symbols shown in fig. 8.2 (GOST 2.770–68).
Rice. 8.2. Symbol for worm gear
with cylindrical worm
3. Turn on the motor and turn the knob 10 potentiometer (see Fig. 8.1) set the motor shaft speed n 1 = 1200 min -1.
4. Set the indicator arrows to zero position.
5. Turning the handle 8 potentiometer to load the gearbox with different torques T 2 .
Reading of the indicator of the measuring device of the electric motor must be carried out at the selected frequency of rotation of the electric motor.
6. Record in table. 8.2 Report indicator readings.
7. Using formulas (8.8) and (8.9), calculate the values T 1 and T 2. Record the results of the calculations in the same table.
8. According to the table. 8.2 reports build a graph for .
9. In a similar way, carry out experiments with and variable speed. Enter the experimental data and the results of the calculations in Table. 8.3 reports.
10. Build a dependency graph for .
Sample report format
