This article contains detailed information about 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 | One or more cylindrical | Parallel |
|
| Parallel/coaxial |
|||
| Parallel |
|||
| Conical | Conical | Intersecting |
|
| Conical-cylindrical | Conical | Intersecting/crossing |
|
| 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 stage) | ||
| Cylindrical-planetary | Cylindrical (one or more) | Parallel/coaxial |
|
| Cone-planetary | Conical (single) Planetary (one or more) | Intersecting |
|
| Worm-planetary | Worm (one) | Crossbreeding |
|
| Wave | Wave (one) |
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 of 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 summary characteristics 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 duration of operation - 10 thousand hours.
Maximum torque- maximum torque maintained by the gearbox 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 that meets customer 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 |
|||
|---|---|---|---|---|---|
| Soft start, static operation, medium mass acceleration | |||||
| Moderate starting load, variable mode, medium mass acceleration | |||||
| Operation under heavy loads, alternating mode, large mass acceleration | |||||
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 calculating 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:
η [%] = (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
For questions regarding calculation and purchase of gear motors various types contact our specialists. The catalog of worm, cylindrical, planetary and wave gear motors offered by the Tehprivod company can be found on the website.
Romanov Sergey Anatolievich,
head of mechanical department
Tekhprivod company
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 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:
Purpose of the work: 1. Determination of the geometric parameters of gears and calculation of gear ratios.
3. plotting dependences at and at .
Work completed: Full name
group
Accepted the job:
Results of measurements and calculations of wheel and gearbox parameters
Number of teeth
Tooth tip diameter d a, mm
Module m according to formula (7.3), mm
Center distance a w according to formula (7.4), mm
Gear ratio u according to formula (7.2)
Total gear ratio according to formula (7.1)
Kinematic diagram of the gearbox
Table 7.1
Dependency graph
η
T 2 , N∙mm
Table 7.2
Experimental data and calculation results
Dependency graph
η
n, min –1
Security questions
1. What are the losses in gear transmission and what are the most effective measures to reduce transmission losses?
2. The essence of relative, constant and load losses.
3. How does transmission efficiency change depending on the transmitted power?
4. Why does the efficiency of gears and gears increase with increasing precision?
Laboratory work No. 8
DETERMINING THE EFFICIENCY OF A WORM REDUCER
Purpose of the work
1. Determination of the geometric parameters of the worm and worm wheel.
2. Image of the kinematic diagram of the gearbox.
3. Plotting graphs of dependence 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 network.
3. After finishing work, disconnect the installation from the network.
Description of installation
On a cast base 7 (Fig. 8.1) the gearbox under study is mounted 4 , electric motor 2 with tachometer 1 , showing the rotation speed, and the load device 5 (magnetic powder brake). Measuring devices consisting of flat springs and indicators are mounted on the brackets 3 And 6 , the rods of which rest against the springs.
There is a toggle switch on the control panel 11 , turning the electric motor on and off; pen 10 a potentiometer that allows you to continuously adjust the speed of the electric motor; toggle switch 9 including a loading device and a handle 8 potentiometer to adjust the braking torque T 2.
The electric motor stator is mounted on two ball bearings installed in a bracket and can freely rotate around an axis coinciding with the rotor axis. The reactive torque generated during 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 balanced motor.
Rice. 8.1. Installation of DP – 4K:
1
– tachometer; 2
– electric motor; 3
, 6
– indicators; 4
– worm gearbox;
5
– powder brake; 7
– base; 8
– load control knob;
9
– toggle switch for turning on the load device; 10
– knob for regulating the speed of rotation of the electric motor; 11
– toggle switch for turning on the electric motor
To measure the amount of torque developed by the engine, a lever is attached to the stator, which presses on the flat spring of the measuring device. The spring deformation is transferred to the indicator rod. By the deviation of the indicator needle, one can judge the magnitude of this deformation. If the spring is calibrated, i.e. establish torque dependence T 1 turning the stator, and the number of divisions of the indicator, then when performing the experiment, you can judge the magnitude of the torque based on the indicator readings T 1, developed by an electric motor.
As a result of calibration of the electric motor measuring device, the value of the calibration coefficient was established
The calibration coefficient of the braking device is determined in a similar way:
General information
Kinematic study.
Worm gear ratio
Where z 2 – number of teeth of the worm wheel;
z 1 – number of starts (turns) of the worm.
The worm gearbox of the DP-4K installation has a module m= 1.5 mm, which corresponds to GOST 2144–93.
Worm pitch diameter d 1 and worm diameter coefficient q are determined by solving the equations
; (8.2)
According to GOST 19036–94 (initial worm and initial producing worm), the helix head height coefficient is adopted.
Estimated worm pitch
Stroke of revolution
Pitch angle
Sliding speed, m/s:
, (8.7)
Where n 1 – electric motor rotation speed, min –1.
Determination of gearbox efficiency
Power losses in a worm gear consist of losses due to friction in the gearing, friction in the bearings and hydraulic losses due to stirring and splashing of oil. The main part of the losses is losses in engagement, which depend on the accuracy of manufacturing and assembly, the rigidity of the entire system (especially the rigidity of the worm shaft), lubrication method, materials of the worm and wheel teeth, the roughness of the contact surfaces, sliding speed, worm geometry and other factors.
Overall worm gear efficiency
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 = 0.99 – efficiency factor taking into account hydraulic losses;
η 3 – efficiency, taking into account losses in engagement and determined by the equation
where φ is the friction angle, depending on the material of the worm and wheel teeth, the roughness of the working surfaces, the quality of the lubrication and the sliding speed.
Experimental determination of gearbox efficiency is based on simultaneous and independent measurement of torques T 1 at the input and T 2 on the output shafts of the gearbox. The gearbox efficiency can be determined by the equation
Where T 1 – torque on the electric motor shaft;
T 2 – torque on the output shaft of the gearbox.
Experimental torque values are determined from the dependencies
Where μ 1 and μ 2 – calibration coefficients;
k 1 and k 2 – indicator readings of engine and brake measuring devices, respectively.
Work order
2. According to table. 8.1 of the report, construct 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 electric motor and turn the handle 10 potentiometer (see Fig. 8.1) set the speed of the electric motor shaft n 1 = 1200 min -1.
4. Set the indicator arrows to the zero position.
5. Turn the handle 8 potentiometer to load the gearbox with different torques T 2 .
The readings of the electric motor measuring device indicator must be taken at the selected motor speed.
6. Write in the table. 8.2 Report indicator readings.
7. Using formulas (8.8) and (8.9), calculate the values T 1 and T 2. Enter the calculation results into the same table.
8. According to table. 8.2 of the report, construct a graph at .
9. Conduct experiments in a similar way at variable speed. Enter the experimental data and calculation results in the table. 8.3 reports.
10. Construct a graph of the dependence at .
Sample report format
Most mechanisms with an electric motor have a spur gearbox. It reduces the number of revolutions and increases the power of the unit. The gear mechanism for transmitting torque through cylindrical wheels has the highest efficiency compared to other methods. Various types of helical gearboxes are widely used in metallurgical and mechanical engineering equipment, electric tools and automobiles.
Design features
The basis of any gearbox is a shaft that transmits torque and changes the number of revolutions of the shaft. Cylindrical gears are characterized by the ability to rotate in both directions. If necessary, the driven shaft with the wheel is connected to the engine and becomes the drive shaft. In this design they are located parallel, horizontally and vertically. The design of helical gearboxes can be very different, but it necessarily includes in its design:
- leading;
- driven shaft;
- gear;
- wheel;
- bearings;
- frame;
- covers;
- lubrication system.
The body and cover are cast from cast iron or welded from low-carbon sheet with a thickness of 4 - 10 mm, depending on the size and power of the unit. Small gearboxes are welded. The rest have a strong cast body.
Characteristics of helical gearboxes
The number of gears, the type of tooth and the relative position of the shafts for all types of equipment are described by GOST Helical gearboxes. It indicates the standard sizes of all parts that can be used in spur gearboxes with different numbers of stages. The maximum for one pair is 6.5. The total number of multi-stage gearboxes can be up to 70.
A worm gear can have a greater gear ratio than a spur gearbox; it can reach 80. At the same time, they are compact, but are rarely used due to low efficiency. Single-stage helical gearboxes have an efficiency of 99–98%, the highest of all types of gears. Worm and helical gearboxes differ in the arrangement of their shafts. If for cylindrical ones they are parallel, then the worm is located at an angle to the wheel. Consequently, the drive and driven shafts exit from the perpendicularly located side walls of the housing.
Helical gearboxes are the noisiest; when the teeth touch, the surfaces hit each other. This eliminates strong friction and overheating.
For lubrication, it is enough to pour oil into the pan so that the lower gears are partially immersed in it. As the teeth rotate, they capture oil and spray it onto other parts.
Design and calculation procedure
The calculation of the future gearbox begins with determining the transmission torque and selecting it from standardized pairs. After this, the diameters of the parts and the center distance of the shafts are specified. A kinematic diagram is drawn up, the optimal shape of the body and cover, and bearing numbers are determined. The assembly drawing includes a kinematic diagram of a two-stage gearbox, a lubrication system and methods for its control, types of bearings and their installation locations.
GOST 16531-83 describes all possible types and sizes of gears that can be used in spur gearboxes, indicating the module, number of teeth and diameter. The shaft is selected according to the size of the gear. Its strength is calculated taking into account the torque for twisting and bending. The minimum size is determined and multiplied by the strength coefficient. The nearest larger normalized shaft size is then selected. The key is calculated only for shearing and is selected in the same way.
Download GOST 16531-83
The bearing is selected based on the diameter of the shaft. Its type is determined by the direction of the tooth. For helical gears, they use persistent, more expensive gears. The spur gear does not load them in the axial direction, and single row ball bearings last for several thousand hours.
The assembly diagram is indicated in the drawing below and is described in detail in the technological documentation, which is issued to production along with the drawings. On the main drawing with a general view, the table indicates the technical characteristics of the gearbox, which are then transferred to the passport:
- number of steps;
- gear ratio;
- number of revolutions of the drive shaft;
- output power;
- dimensions;
Additionally, the vertical location of the gearing, the direction of shaft rotation and the installation method: flanged or foot-mounted can be indicated.
Types of helical gearboxes
Helical gearboxes are varied in design, size and power; they are divided into types according to several characteristics:
- fastening type;
- shaft location;
- number of steps;
- tooth cutting.
Characteristics may include types of bearings and type of shaft connection.
Single-stage cylindrical gearboxes can be attached to the engine and the body of the working unit with flanges. The design is compact, with minimal consumption of materials. They are mainly installed on a sole with protrusions around the perimeter or on feet with holes for. Small units can be installed on a welded frame. For large units, a special foundation is made.
Shaft location
The input and output shafts can be located horizontally, vertically, parallel to each other, but in different planes for multi-stage units. If there is only one gear, the shafts are in the same plane, strictly vertical or horizontal. They are rarely displayed in one direction, only if a compact arrangement of the engine and working unit is possible. A two-stage helical gearbox has a larger interaxal distance and the motor can be mounted on the actuator side.
Helical gearboxes can be produced with vertical shafts. They are convenient to install on machines, but the upper gear and bearings are poorly lubricated. They are not suitable for long-term work with heavy loads.
The housing of the cylindrical horizontal gearbox is large and takes up a lot of space. It heats up less, withstands loads and vibration, and is stable. In models with 3 or more stages, the shafts are located horizontally. The grease reaches all bearings. In multi-row structures, additional irrigation is done from above, from an oil pipeline installed in the cover.
Gearboxes
A type of helical gearbox with a movable intermediate shaft is a well-known gearbox. When the position of the shaft changes, some pairs disengage, others begin to interact. As a result, the gear ratio and the output rotation speed change.
Gearboxes are made with straight teeth. Helical teeth are rare when there are large loads on the actuator.
Application of helical gearboxes
– lowering the engine speed and increasing the power on the output shaft. Assembling a helical gearbox is not difficult. The housing and cover connector runs through the center of the holes. Bearings are mounted on shafts, installed in prepared seats and supported from the outside with covers.
Wheels and gears are attached to the shafts using keys.
To adjust the center distance, it is necessary to bore the body with great precision.
Maintenance of gearboxes is simple. It is necessary to regularly add oil and change it periodically. The parts located inside are designed for long-term use for at least 10 years.
Gearboxes are used in various industries. Certain types of large equipment can withstand any weather conditions. They are installed in quarries and open areas, on gantry cranes.
Rolling and forging equipment will not be able to operate without gearboxes. There are many types of gearboxes in demand in this industry. Straight teeth stand on cranes. Powerful chevrons rotate crank presses, rollers, and manipulators that feed metal.
Rolling straightening mills operate exclusively thanks to stands that transmit engine rotation to the rolls and working units.
A gearbox is hidden under each hood. Each machine has a gearbox or several. Small gears are installed in power tools and regulate the rotation speed of the spindle of a drill, grinder and router.
Advantages and disadvantages
The cylindrical transmission mechanism has been widely used in various fields. It has undeniable advantages compared to worm gear:
- high efficiency;
- does not heat up;
- works both ways.
The advantages and disadvantages of a spur gearbox depend on the characteristics of the gearing and other structural elements.
Advantages
The main positive point is the high efficiency. It significantly exceeds the output power for the same engines, all gears and other types of transmissions.
The unit can operate for a long time without interruption, switch an infinite number of times from one mode to another, and even change the direction of rotation.
Heat generation is minimal. There is no need to install a cooling system. The lubricant is sprayed onto the lower wheels, lubricates the upper gears, bearings and collects all the dirt and chipped metal particles down into the pan. It is enough to periodically add oil and change it every 3 to 6 months. The frequency of preventive measures depends on the operating mode.
The output shaft is mounted in rolling bearings and has virtually no play. Its movement is accurate enough to use the gear mechanism as a drive for precision devices and instruments. Axial and radial runout of mating parts does not affect the operation of the mechanism.
Operating efficiency does not depend on voltage fluctuations. The gear ratio is stable. If the engine speed drops, the rotation of the driven wheel slows down proportionally. Power remains unchanged.
Flaws
A positive quality is the absence of friction and braking, but in certain conditions it creates problems. In lifting mechanisms, when installing a spur gearbox, it is necessary to install a strong brake in order to hold heavy objects in weight and prevent them from lowering on their own. In worm gears, only the worm can be the driver, and due to high friction, a self-braking effect occurs.
The problem with all gears is the lack of a safety mechanism.
When overloaded or turned on suddenly, the belt slips along the pulley. The tooth can only break, and the part will have to be replaced. Keys are used as additional fuses. They are designed for shearing without a safety margin. Replacing a simple part cut off by a coupling is much easier.
The cost of working parts is high. The manufacturing technology is long and complex. At the same time, the tooth is gradually worn away, and the gap between the working surfaces increases. It is impossible to change the center-to-center distance, as in rack and worm gears in a gearbox. It is necessary to periodically replace gears, wheels, and bearings.
The more the involute wears out, the more the teeth knock against each other and the gearbox makes noise.
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 N c 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
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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 the DP3A sb calibration device on the electric 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 toggle switch 11 of the electric motor of the device and use 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
