Calculation and selection (Russian method) - worm gearbox. Moscow State Technical University. N.E.Bauman Determination of the efficiency of a reducer

Purpose of work: 1. Determination of geometrical parameters of gear wheels and calculation of gear ratios.

3. construction of graphs of dependence at and at.

The work was carried out by: Full name

group

The work was accepted by:

Results of measurements and calculation of parameters of wheels and gearbox

Number of teeth

Tooth tip diameter d a, mm

Module m according to the formula (7.3), mm

Center distance a w according to the formula (7.4), mm

Ratio u by formula (7.2)

The total gear ratio according to the formula (7.1)

Gearbox kinematic diagram

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

Control questions

1. What are the losses in the gear train and what are the most effective measures to reduce transmission losses?

2. The 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 gear wheels and gears?

Laboratory work No. 8

DETERMINING THE EFFICIENCY OF THE WORM REDUCER

purpose of work

1. Determination of the geometric parameters of the worm and worm wheel.

2. An image of the kinematic diagram of the gearbox.

3. Construction of graphs of dependence at and at.

Basic safety rules

1. Turn on the installation with the permission of the teacher.

2. The instrument must be connected to the rectifier and the rectifier to the mains.

3. After finishing the work, disconnect the unit from the network.

Installation Description

Cast base 7 (Fig. 8.1) the investigated gearbox is mounted 4 , electric motor 2 with tachometer 1 showing the speed, and the loading device 5 (magnetic powder brake). Measuring devices are mounted on the brackets, consisting of flat springs and indicators 3 and 6 , the rods of which abut against the springs.

The control panel contains a toggle switch 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 loading device and handle 8 potentiometer for adjusting the braking torque T 2.

The stator of the electric motor is mounted on two ball bearings installed in a bracket and can rotate freely around an axis that coincides with the axis of the rotor. The reactive torque generated 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 balancing motor.

Rice. 8.1. Installation DP - 4K:

1 - tachometer; 2 - electric motor; 3 , 6 - indicators; 4 - worm gear;
5 - powder brake; 7 - base; 8 - handle for adjusting the load;
9 - toggle switch for switching on the loading 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 magnitude of the moment developed by the motor, a lever is attached to the stator, which presses on the flat spring of the measuring device. Spring deformation is transmitted to the indicator stem. By the deviation of the indicator arrow, one can judge the magnitude of this deformation. If the spring is calibrated, i.e. establish the dependence of the moment T 1, turning the stator, and the number of indicator divisions, then when the experiment is performed, it is possible to judge the magnitude of the moment by the indicator readings 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

The calibration coefficient of the braking device is determined in a similar way:

General information

Kinematic research.

Worm gear ratio

where z 2 - the number of teeth of the worm wheel;

z 1 - the number of entries (turns) of the worm.

The worm of the gearbox of the DP-4K unit has a module m= 1.5 mm, which corresponds to GOST 2144–93.

Worm pitch diameter d 1 and the coefficient of the diameter of the worm q are determined by solving the equations

; (8.2)

According to GOST 19036–94 (the original worm and the original producing worm), the coefficient of the coil head height is taken.

Estimated step of the worm

Coil stroke

Pitch angle

Sliding speed, m / s:

, (8.7)

where n 1 - frequency of rotation of the electric motor, min –1.

Determination of gearbox efficiency

The power loss in the worm gear is the sum of the losses due to friction in the gearing, friction in the bearings, and hydraulic losses due to stirring and splashing of the oil. The main part of the losses is made up of losses in engagement, depending on the accuracy of manufacture and assembly, the rigidity of the entire system (especially the rigidity of the worm shaft), the method of lubrication, the materials of the worm and the teeth of the wheel, the roughness of the contact surfaces, sliding speed, the geometry of the worm and other factors.

Overall efficiency of 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 bearing pairs;

η p = 0.99 - efficiency, taking into account hydraulic losses;

η 3 - efficiency, taking into account the losses in the 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 gearbox efficiency based on simultaneous and independent measurement of torques T 1 at the entrance 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.

Experimental values ​​of the torques are determined by the dependencies

where μ 1 and μ 2 – calibration coefficients;

k 1 and k 2 - respectively indications of indicators of measuring devices of the motor and brake.

Work order

2. According to the table. 8.1 of the report, build a kinematic diagram of a worm gear, for which use the conventions shown in Fig. 8.2 (GOST 2.770–68).

Rice. 8.2. Symbol worm gear
with cylindrical worm

3. Switch on the electric motor and turn the knob 10 potentiometer (see Fig. 8.1) set the speed of the motor shaft n 1 = 1200 min -1.

4. Set the indicator arrows to zero position.

5. By turning the handle 8 potentiometer load the reducer with different moments T 2 .

The readings of the indicator of the measuring device of the electric motor should be carried out at the selected speed of rotation of the electric motor.

6. Write down in table. 8.2 report indicator readings.

7. By formulas (8.8) and (8.9) calculate the values T 1 and T 2. Enter the calculation results in the same table.

8. According to the table. 8.2 reports build a graph at.

9. In a similar way, carry out experiments at and variable frequency of rotation. Experimental data and calculation results should be entered in table. 8.3 report.

10. Build a graph of 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 in comparison with other methods. Different kinds spur gearboxes are widely used in metallurgical and machine-building equipment, electric tool and cars.

Design features

The basis of any gearbox is the transmitting torque and changing the number of shaft revolutions. Cylindrical gearing is 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 driving one. In this design, they are located parallel, horizontally and vertically. The device of spur 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 4-10 mm thick, depending on the dimensions and power of the unit. Small gearboxes are welded. The rest have a sturdy die-cast body.

Characteristics of helical gearboxes

The number of gearing, type of tooth and mutual arrangement of shafts for all types of equipment are described by GOST cylindrical gearboxes. It indicates the standard sizes of all parts that can be used in helical gearboxes with various numbers of stages. The maximum of one pair is 6.5. The total of multi-stage gearbox can be up to 70.

The gear ratio of the worm gear can be more than that of a spur gearbox, it can reach 80. At the same time, they are compact, but are rarely used due to their low efficiency. Single-stage spur gearboxes have 99 - 98% efficiency, the highest of all types of gears. Worm and spur gearboxes are distinguished by the arrangement of the shafts. If in cylindrical they are parallel, then the worm is located at an angle to the wheel. Consequently, the driving and driven shafts come out of the perpendicularly located side walls of the housing.

Cylindrical gearboxes are the noisiest; when the teeth touch, the surface hits one another. This eliminates strong friction and overheating.

For lubrication, it is enough to pour oil into the sump so that the lower gears are partially immersed in it. As the tines rotate, they catch the oil and spray it onto other parts.

Design and calculation procedure

The calculation of the future gearbox begins with the determination of the transmission moment and its selection from the standardized pairs. After that, 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 housing 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 with an indication of the module, number of teeth and diameter. The shaft is matched to the size of the gear. Its strength is calculated taking into account the torsional and bending moment. Determined minimum size, multiplied by the strength factor. The closest larger normalized shaft size is then selected. The key is calculated only for a cut and is selected in the same way.

Download GOST 16531-83

The bearing is selected according to the shaft diameter. Its type is determined by the direction of the tooth. With a helical gear, they put stubborn, more expensive ones. The spur gear does not load them axially, and single row ball bearings run for several thousand hours.

The assembly diagram is indicated in the drawing below and is detailed in the technological documentation, which is issued for production along with the drawings. In the main drawing with general view the table indicates the technical characteristics of the gearbox, which are then transferred to the passport:

• number of steps;
• ratio;
• the number of revolutions of the drive shaft;
• output power;
• dimensions;

Additionally, the vertical arrangement of the gearing, the direction of rotation of the shaft and the installation method: flanged or on feet can be indicated.

Types of spur gearboxes

Spur gearboxes are various in design, size and power, they are divided into types according to several characteristics:

• type of attachment;
• the location of the shafts;
• number of steps;
• tooth cutting.

Characteristics may include bearing types and shaft connections.

Single-stage cylindrical gearboxes can be attached to the engine and the housing of the working unit with flanges. Compact design, with minimal cost They are mainly installed on a sole with projections 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 arrangement

The input and output shafts can be located horizontally, vertically, parallel to each other, but in different planes for multi-stage assemblies. If there is only one engagement, the shafts are in the same plane, strictly vertical or horizontal. They are rarely brought out in one direction, only if the compact arrangement of the engine and the working unit is possible. With a two-stage helical gearbox, the center distance is larger and the motor can be mounted on the side of the actuator.

Cylindrical gearboxes can be produced with vertical shafts. They are convenient to install on machines, but the top gear and bearings are poorly lubricated. They are not suitable for long-term operation with heavy loads.

The housing of the gearbox is cylindrical horizontal, overall, takes up a lot of space. It heats up less, withstands loads and vibration, is stable. In models from 3 or more stages, the shafts are located horizontally. Grease reaches all bearings. In multi-row structures, additional irrigation is done from above, from an oil pipe installed in the cover.

Speed ​​boxes

A type of helical gearbox with a movable intermediate shaft is a well-known gearbox. When the position of the shaft changes, some pairs are disengaged, while others begin to interact. As a result, the gear ratio and the output rotation speed change.

Gearboxes are made with a straight tooth. Helical gears are rare when there is a heavy load on the actuator.

Application of helical gearboxes

- a decrease in the engine speed and an increase in the power on the output shaft. The assembly of a helical gearbox is not difficult. In the center of the holes there is a connector for the case and cover. The bearings are mounted on shafts, installed in prepared seats and supported from the outside by covers.

Wheels and gears are attached to the shafts with dowels.

To adjust the center distance, it is necessary to bore the housing with great accuracy.

Maintenance of gearboxes is simple. It is necessary to regularly top up the oil, change it periodically. The parts inside are designed to last for at least 10 years.

Gearboxes are used in various industries. Certain types of large equipment are able to withstand all weather conditions. They are installed in quarries and in open areas, on gantry cranes.

Rolling and press-forging equipment cannot operate without gearboxes. There are many types of gearboxes in demand in this industry. Straight teeth stand on cranes. Powerful chevron arms rotate crank presses, rollers, manipulators that feed metal.

Rolling t-straightening mills work exclusively thanks to stands that transmit the rotation of the engine 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 the power tool and regulate the rotational speed of the spindle of the drill, grinder and router.

Advantages and disadvantages

The cylindrical transmission mechanism has been widely used in various fields. It has undeniable advantages in comparison with a worm gear:

• high efficiency;
• does not heat up;
• works both ways.

The advantages and disadvantages of a helical gearbox depend on the features of the gearing and other structural elements.

Advantages

The main positive point is the high efficiency. It significantly exceeds the output power with the same motors, all gears and other types of transmission.

The unit can work for a long time without interruptions, 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. Grease is sprayed by the lower wheels, lubricates the upper gears, bearings and collects down into the sump all dirt, chipped metal particles. It is enough to periodically top up the 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 practically no backlash. Its movement is precise enough to use the gear mechanism as a drive for precision devices and instruments. Axial and radial runout of the mating parts does not affect the operation of the mechanism.

The efficiency of work does not depend on voltage drops. The gear ratio is stable. If the engine speed drops, the driven wheel will slow down proportionally. The power remains unchanged.

disadvantages

A positive quality - the absence of friction and braking, in certain conditions creates problems. V lifting mechanisms when installing a helical gearbox, a strong brake must be applied to keep heavy objects in weight and prevent them from falling down on their own. In worm gears, only a worm can be the leading one and, due to high friction, a self-braking effect occurs.

The problem with all gearing is the lack of a safety mechanism.

When overloaded or abruptly switched on, the belt slips along the pulley. The tooth can only break and the part will have to be changed. The keys are used as additional fuses. They are calculated for a cut without a safety factor. It is much easier to replace a simple part cut by a coupling.

The cost of working parts is high. The manufacturing technology is lengthy and complex, and the tooth gradually wears out 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. You have to periodically replace gears, wheels, bearings.

The more the involute is erased, the more teeth knock against each other, and the gearbox makes noise.

This article provides detailed information on the selection and sizing of a geared motor. We hope you find this information useful.

When choosing a specific model of a geared motor, the following technical characteristics are taken into account:

• gearbox type;
• power;
• output revolutions;
• gear ratio of the reducer;
• the design of the input and output shafts;
• type of installation;
• additional functions.

Reducer type

The presence of the drive kinematic diagram will simplify the choice of the gearbox type. Gearboxes are structurally divided into the following types:

• Single-stage worm gear with crossed input / output shaft (90 degree angle).
• Worm gear two-stage with 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 arrangement of 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.
• V conical-cylindrical In the gearbox, the input / output shaft axes intersect at an angle of 90 degrees.

Important! The location of the output shaft in space 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 mass-dimensional characteristics as with worm gearboxes, the operation of cylindrical units is economically expedient due to an increase in the transmitted load by 1.5-2 times and high efficiency.

Table 1. Classification of gearboxes according to the number of stages and type of transmission

Reducer type	Number of steps	Transfer type	Axis arrangement
Cylindrical		One or more cylindrical	Parallel
			Parallel / coaxial
			Parallel
Conical		Conical	Intersecting
Conical-cylindrical		Conical	Crossing / crossing
Worm		Worm gear (one or two)	Interbreeding
			Parallel
Cylindrical-worm or worm-cylindrical		Cylindrical (one or two) Worm (one)	Interbreeding
Planetary		Two central gears and satellites (for each stage)
Cylindrical planetary		Cylindrical (one or more)	Parallel / coaxial
Bevel planetary		Conical (one) Planetary (one or more)	Intersecting
Planetary worm		Worm (one) Planetary (one or more)	Interbreeding
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 (rpm) at the inlet;
N2 - shaft rotation speed (rpm) at the output.

The calculated value is rounded up to the value specified in the technical data for a 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 gearbox input shaft cannot exceed 1500 rpm. The rule applies to all types of gearboxes, except for cylindrical coaxial gearboxes with a rotation speed of 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 operating time (10 thousand hours), 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- 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.

Calculated torque- the value required to select the gearbox. Calculated value calculated by the following formula:

Mc2 = Mr2 x Sf<= Mn2

where
Mr2 is the required torque;
Sf - service factor (operating factor);
Mn2 is the rated torque.

Service factor (service factor)

Service factor (Sf) is calculated experimentally. The calculation takes into account the type of load, the daily operating time, the number of starts / stops per hour of operation of the geared motor. The service factor 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 Start Load, Variable Mode, Medium Mass Acceleration
Heavy Duty, Variable Duty, Large Mass Acceleration

Drive power

Correctly calculated drive power helps to overcome the mechanical frictional resistance that occurs during straight and rotary movements.

The elementary formula for calculating power [P] is the calculation of the ratio of force to speed.

For rotary movements, power is calculated as the ratio of torque to rpm:

P = (MxN) / 9550

where
M - torque;
N is the number of revolutions / min.

The output power is calculated using the formula:

P2 = P x Sf

where
P - power;
Sf is the service factor (operating 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 an approximate input power as the efficiency can vary significantly.

Coefficient of performance (COP)

Let us 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 is the input power.

Important! In worm gear 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 influenced by the service life and the quality of the lubricants used for preventive maintenance of the gearmotor.

Table 4. Efficiency of a single-stage worm gearbox

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

For the calculation and purchase of geared motors of various types, please contact our specialists. The catalog of worm, spur, planetary and wave gear motors offered by Techprivod can be found on the website.

Romanov Sergey Anatolyevich,
head of mechanics department
Tehprivod company

1. PURPOSE OF THE WORK

Deepening the knowledge of theoretical material, obtaining practical skills for independent experimental determination of gearboxes.

2. BASIC THEORETICAL PROVISIONS

Mechanical coefficient useful action 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 input shaft of the gearbox:

The powers of the driving forces and resistance forces can be determined accordingly by the formulas

(2)

(3)

where M d and M with- moments, respectively, of driving forces and resistance forces, Nm; and - angular speeds of the gearbox shafts, respectively, of the input and output, with -1 .

Substituting (2) and (3) in (1), we obtain

(4)

where is the gear ratio of the gearbox.

Any complex machine consists of a number of simple mechanisms. Machine efficiency can be easily determined if the efficiency of all simple mechanisms included in it are known. For most mechanisms, analytical methods have been developed for determining the efficiency, however, deviations in the cleanliness of the treatment of 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 coefficient of friction.

Therefore, it is important to be able to experimentally determine the efficiency of the investigated mechanism under specific operating conditions.

The parameters required to determine the gearbox efficiency ( M d, M s and L p) can be determined using DP-3K instruments.

3. STRUCTURE OF THE DP-3K DEVICE

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 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 motor housing is hinged in two supports so that the rotation axis of the motor shaft coincides with the rotation axis of the housing. The fixation of the motor housing from circular rotation is carried out by a flat spring 6. When the torque is transmitted from the shaft of the electric motor of the reducer, the spring creates a reactive moment applied to the motor housing. The motor shaft is mated 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 of gears mounted on ball bearings in the housing.

Top part 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 loading 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 magnetized medium in the design of the loading device. The body of the loading device is mounted in a balance with respect to the base of the device on two bearings. The limitation 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 resistance forces (braking torque) created by the load device.

Measuring devices for torque and braking torques consist of flat springs 6 and 7 and dial indicators 8 and 9, which measure the deflections of the springs, proportional to the values ​​of the moments. On the springs, strain gauges are additionally glued, the signal from which through a strain gauge amplifier can also be recorded on an oscilloscope.

On the front of the base of the device there is a control panel 10, on which are installed:

Toggle switch 11 for turning on and off the electric motor;

Knob 12 for adjusting the frequency of rotation of the motor shaft;

Signal lamp 13 for turning on the device;

Toggle switch 14 for turning on and off the excitation winding circuit of the load device;

Knob 15 for adjusting the excitation of the loading device.

When performing this laboratory work, you should:

Determine the gear ratio of the gearbox;

To tare measuring devices;

Determine the efficiency of the gearbox depending on the resistance forces and the number of revolutions of the electric motor.

4. ORDER OF PERFORMANCE OF THE 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

The found values ​​of the gear ratio i p check empirically.

4.2. Calibration of measuring devices

Calibration of measuring devices is carried out with the device disconnected from the electric current source using calibration devices consisting of levers and weights.

To calibrate the measuring device of the electric motor torque, 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 hand to zero;

When setting the weight on the lever for subsequent divisions, fix the indicator readings and the corresponding division on the lever;

Determine the average m Wed indicator division prices by the formula

(6)

where TO- the number of measurements (equal to the number of divisions on the lever); G- cargo weight, N; N i- indicator readings, - distance between divisions on the lever ( m).

Determination of the mean m c. wed the division price of the indicator of the loading device is made by installing a calibration device DP3A sb on the case of the loading device. 25 in a similar manner.

Note. Weight of goods in calibration devices DP3K sb. 24 and DP3K sat. 25 is 1 and 10, respectively N.

4.3. Determination of gearbox efficiency

Determination of the gearbox efficiency depending on the resistance forces, i.e. ...

To determine the dependence it is necessary:

Turn on the toggle switch 11 of the electric motor of the device and use the speed control knob 12 to set the 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 field current control knob, set the first value (10 divisions) of the torque in the direction of the indicator arrow M with resistance;

Use the 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 preset value (20, 30, 40, 50, 60, 70, 80 divisions);

While maintaining the speed of rotation unchanged, fix the readings of the indicators;

Determine the values ​​of the moments of driving forces M d and resistance forces M with for all measurements by formulas

(7)

(8)

Determine for all measurements of the gearbox efficiency according to the formula (4);

Record indicator readings h 1 and h 2, moment values M d and M with and the found values ​​of the gearbox efficiency for all measurements in the table;

Build a dependency graph.

4.4. Determination of gearbox efficiency 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 supply and excitation circuit and use the handle 15 for adjusting the excitation current to set the torque value set by the teacher M with on the output shaft of the gearbox;

Switch on the electric motor of the device (toggle switch 11);

By setting the speed control knob 12 sequentially a number of values ​​(from minimum to maximum) of the speed of the motor shaft and maintaining a constant value of the torque M with load, record the indicator h 1 ;

Give a qualitative assessment of the influence of the speed n on the efficiency of the gearbox.

5. DRAFTING OF THE REPORT

The report on the work done must contain the title,

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 wheels, type of electric motor, loading device, measuring devices and instruments), calculations, description of 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 transducer 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 forces increases (decreases) by 1.5 times?

Lab 9

Laboratory work

Study of the efficiency of the gear reducer

1. Purpose of work

Analytical determination of the efficiency of the gear reducer.

Experimental determination of the efficiency of a gear reducer.

Comparison and analysis of the results obtained.

2. Theoretical provisions

Energy supplied to the mechanism in the form of workdriving forces and moments for a steady-state cycle, is spent on performing useful workthose. work of forces and moments of useful resistance, as well as for the performance of workassociated with overcoming the friction forces in kinematic pairs and the forces of resistance of the medium:... The values ​​and are substituted into this and subsequent equations in absolute value. The mechanical efficiency is the ratio

Thus, the efficiency shows what fraction of the mechanical energy supplied to the machine is usefully spent on the performance of the work for which the machine was created, i.e. is an important characteristic mechanism of machines. Since frictional losses are inevitable, it is always. In equation (1), instead of works and , performed per cycle, it is possible to substitute the values ​​of the corresponding powers averaged over the cycle:

A reducer is a gear (including a worm) mechanism designed to reduce the angular velocity of the output shaft in relation to the input.

Input Angular Velocity Ratio to the angular velocity at the exit called the gear ratio of the gearbox :

For a reducer, equation (2) takes the form

Here T 2 and T 1 - the average values ​​of the torques on the output (moment of resistance forces) and input (moment of driving forces) shafts of the gearbox.

Experimental determination of efficiency is based on measurement of values T 2 and T 1 and calculating η by formula (4).

When examining the efficiency of the gearbox by factors, i.e. system parameters that affect the measured value and can be purposefully changed during the experiment, are the moment of resistance T 2 on the output shaft and the speed of the input shaft of the gearboxn 1 .

The main way to increase the efficiency of gearboxes is to reduce power losses, such as: the use of more modern lubrication systems that exclude losses due to mixing and oil splashing; 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 - efficiency of the gear reducer;

- the efficiency of the motor supports,;

- coupling efficiency,;

- efficiency of brake supports,.

The overall efficiency of a gear multistage gearbox is determined by the formula:

where - The efficiency of the gearing with an average workmanship with periodic lubrication,;

- The efficiency of a pair of bearings depends on their design, assembly quality, loading method and is approximately taken(for a pair of rolling bearings) and(for a pair of sleeve bearings);

- The efficiency, taking into account the losses due to splashing and mixing of the oil, is approximately taken= 0,96;

k- number of bearing pairs;

n- the number of pairs of gears.

3. Description of the research object, devices and instruments

This laboratory work is carried out on the DP-3A unit, which makes it possible to experimentally determine the efficiency of a gear reducer. The DP-3A unit (Figure 1) is mounted on a cast metal base 2 and consists of an electric motor unit 3 (a source of mechanical energy) with a tachometer 5, a load device 11 (an energy consumer), a tested gearbox 8 and elastic couplings 9.

Fig. 1. Schematic diagram of the DP-3A installation

The loading device 11 is a magnetic powder brake that simulates the working load of the gearbox. The stator of the loading device is an electromagnet, in the magnetic gap of which a hollow cylinder with a roller is placed (the rotor of the loading device). The inner cavity of the loading device is filled with a mass, which is a mixture of carbonyl powder with mineral oil.

Two regulators: potentiometers 15 and 18 allow you to adjust the speed of the motor shaft and the magnitude of the braking torque of the load device, respectively. The rotational speed is controlled with a tachometer 5.

The values ​​of the torques on the shafts of the electric motor and the brake are determined by means of devices including a flat spring6 and dial indicators7,12. Supports 1 and 10 on rolling bearings provide the ability to rotate the stator and rotor (both at the motor and at the brake) relative to the base.

Thus, when an electric current is applied (turn on the toggle switch 14, the signal lamp 16 lights up) into 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 influence of the reactive torque deviates (balancing motor) from the initial position depending on the amount of braking torque on the driven shaft of the gearboxT 2 ... These angular displacements of the stator housing of the electric motor are measured by the number of divisions NS 1 , to which the indicator pointer deviates 7.

Accordingly, when an electric current is applied (turn on the 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 NS 2) .

Springs measuring instruments pre-tare. Their deformations are proportional to the values ​​of the torque on the motor shaft T 1 and the output shaft of the gearboxT 2 , i.e. the values ​​of the moment of forces of the driving forces and the moment of the forces of resistance (braking).

The reducer 8 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 parameters of the installation are shown in Table 1.

Table 1. Technical specifications installations

Parameter name	Letter designation magnitudes	Meaning
The number of pairs of spur cylindrical wheels in the gearbox	n
Gear ratio of the reducer	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
The number of revolutions of the shaft of the electric motor, rpm	n 1	1000

Rice. 2. Kinematic diagram of the DP-3A installation

1 - electric motor; 2 - clutch; 3 - reducer; 4 - brake.

4. Research methodology and processing of results

4.1 The experimental value of the efficiency of the gear reducer 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 shaft of the electric motor), Nmm;

u- gear ratio of the gear reducer;

- the efficiency of the elastic coupling;= 0,99;

- the efficiency of the bearings of the supports 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 rotational speed. In this case, certain braking torques are consistently created on the output shaft of the gearbox according to the corresponding readings of the indicator12.

When the electric motor is turned on with the toggle switch 14 (Figure 1), the stator of the electric motor support with your hand to prevent hitting the spring.

Turn on the brake with the toggle switch 17, after that the indicator arrows are set to zero.

Using the potentiometer 15, set the required engine speed on the tachometer, for example - 200 (table 2).

Potentiometer 18 creates braking torques on the output shaft of the gearbox T 2 corresponding to the readings of the indicator 12.

Record indicator readings 7 to determine the torque on the motor shaft T 1 .

After each series of measurements at one speed, potentiometers 15 and 18 are brought to the extreme counterclockwise position.

Rotation frequencyn 1 shaft electric motor, rpm	Indicator reading 12, NS 2
200, 350, 550, 700	120, 135, 150, 165, 180, 195
850, 1000	100, 105, 120, 135, 150, 160

4.3. Changing the load on the brake with potentiometer 18 and on the motor with potentiometer 15 (see Figure 1) with constant engine speed, record five readings of indicator 7 and 12 ( NS 1 and NS 2) in table 3.

Table 3. Test results

The number of revolutions of the shaft of the electric motor,n 1 , rpm

Indicator readings 7 NS 1

Torque on the motor shaft, Nmm

Indicator readings 12 NS 2

Torque on the brake shaft, Nmm

Experimental efficiency,