Calculation and selection (Russian methodology) - worm gearbox. Determining the efficiency of a multi-stage gearbox Determining the efficiency of a gearbox

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.
• IN 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 the series 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) Worm (one)	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) Planetary (one or more)	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 the technical characteristics of a particular type of gearbox.

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. This technical parameter manufacturers indicate 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.

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

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. 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 motor housing is pivotally fixed 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 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 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 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 for torque and braking torques consist of flat springs 6 and 7 and dial gauges 8 and 9, which measure spring deflections 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?

Laboratory work 9

Worm gear is one of the classes of mechanical gearboxes. Gearboxes are classified according to the type of mechanical transmission. The screw that underlies the worm gear looks like a worm, hence the name.

Gearmotor- this is a unit consisting of a gearbox and an electric motor, which are in one unit. Worm gear motorcreated in order to work as an electromechanical motor in various general purpose machines. It is noteworthy that this species equipment works perfectly both under constant and variable loads.

In a worm gearbox, the increase in torque and decrease in the angular velocity of the output shaft occurs due to the conversion of energy contained in the high angular velocity and low torque on the input shaft.

Errors in the calculation and selection of the gearbox can lead to its premature failure and, as a result, in the best case to financial loss.

Therefore, the work on the calculation and selection of the gearbox must be entrusted to experienced design specialists who will take into account all factors from the location of the gearbox in space and operating conditions to its heating temperature during operation. Having confirmed this with appropriate calculations, the specialist will ensure the selection of the optimal gearbox for your specific drive.

Practice shows that a properly selected gearbox provides a service life of at least 7 years for worm gearboxes and 10-15 years for cylindrical gearboxes.

The choice of any gearbox is carried out in three stages:

1. Gearbox type selection

2. Selection of the overall size (size) of the reducer and its characteristics.

3. Checking calculations

1. Gearbox type selection

1.1 Initial data:

Kinematic diagram of the drive indicating all the mechanisms connected to the gearbox, their spatial arrangement relative to each other, indicating the attachment points and mounting methods of the gearbox.

1.2 Determining the location of the axes of the gearbox shafts in space.

Helical gearboxes:

The axis of the input and output shafts of the gearbox are parallel to each other and lie in only one horizontal plane - a horizontal spur gearbox.

The axis of the input and output shaft of the gearbox are parallel to each other and lie only in one vertical plane- vertical spur gearbox.

The axis of the input and output shaft of the gearbox can be in any spatial position, while these axes lie on the same straight line (coincide) - a coaxial cylindrical or planetary gearbox.

Bevel-helical gearboxes:

The axis of the input and output shaft of the gearbox are perpendicular to each other and lie only in one horizontal plane.

Worm gears:

The axis of the input and output shaft of the gearbox can be in any spatial position, while they cross at an angle of 90 degrees to each other and do not lie in the same plane - a single-stage worm gearbox.

The axis of the input and output shaft of the gearbox can be in any spatial position, while they are parallel to each other and do not lie in the same plane, or they cross at an angle of 90 degrees to each other and do not lie in the same plane - a two-stage gearbox.

1.3 Determination of the mounting method, mounting position and gearbox assembly option.

The method of fastening the gearbox and the mounting position (mounting on the foundation or on the driven shaft of the drive mechanism) are determined according to the technical characteristics given in the catalog for each gearbox individually.

The assembly option is determined according to the schemes given in the catalog. Schemes of "Assembly options" are given in the "Designation of gearboxes" section.

1.4 In addition, the following factors can be taken into account when choosing a gearbox type

1) Noise level

• the lowest - for worm gears
• the highest - for cylindrical and bevel gears

2) Efficiency

• the highest - for planetary and single-stage spur gearboxes
• the lowest - in worm, especially two-stage

Worm gears are preferably used in intermittent operation

3) Material consumption for the same values ​​of torque on a low-speed shaft

• the lowest - for planetary single-stage

4) Dimensions with the same gear ratios and torques:

• the largest axial - in coaxial and planetary
• the largest in the direction perpendicular to the axes - for cylindrical
• the smallest radial - to planetary.

5) Relative cost rub/(Nm) for the same center distances:

• the highest - in conical
• the lowest - in planetary

2. Selection of the overall size (size) of the reducer and its characteristics

2.1. Initial data

Drive kinematic diagram containing the following data:

• type of drive machine (engine);
• the required torque on the output shaft T required, Nxm, or the power of the propulsion system P required, kW;
• frequency of rotation of the input shaft of the gearbox n in, rpm;
• frequency of rotation of the output shaft of the gearbox n out, rpm;
• the nature of the load (uniform or uneven, reversible or irreversible, the presence and magnitude of overloads, the presence of shocks, shocks, vibrations);
• the required duration of operation of the gearbox in hours;
• average daily work in hours;
• the number of starts per hour;
• duration of inclusions with load, PV%;
• environmental conditions (temperature, heat removal conditions);
• duration of inclusions under load;
• radial cantilever load applied in the middle of the landing part of the ends of the output shaft F out and the input shaft F in;

2.2. When choosing the size of the gearbox, the following parameters are calculated:

1) Gear ratio

U= n in / n out (1)

The most economical is the operation of the gearbox at an input speed of less than 1500 rpm, and for the purpose of longer trouble-free operation of the gearbox, it is recommended to use an input shaft speed of less than 900 rpm.

The gear ratio is rounded up to the nearest number according to table 1.

The table selects the types of gearboxes that satisfy the given gear ratio.

2) Calculated torque on the gearbox output shaft

T calc \u003d T required x K dir, (2)

T required - the required torque on the output shaft, Nxm (initial data, or formula 3)

K dir - operating mode coefficient

With a known power of the propulsion system:

T required \u003d (P required x U x 9550 x efficiency) / n in, (3)

P required - power of the propulsion system, kW

n in - the frequency of rotation of the input shaft of the gearbox (provided that the shaft of the propulsion system directly transmits rotation to the input shaft of the gearbox without additional gear), rpm

U - gear ratio of the gearbox, formula 1

Efficiency - efficiency of the gearbox

The operating mode coefficient is defined as the product of the coefficients:

For gear reducers:

K dir \u003d K 1 x K 2 x K 3 x K PV x K roar (4)

For worm gears:

K dir \u003d K 1 x K 2 x K 3 x K PV x K rev x K h (5)

K 1 - coefficient of the type and characteristics of the propulsion system, table 2

K 2 - coefficient of duration of work table 3

K 3 - coefficient of the number of starts table 4

K PV - coefficient of duration of inclusions table 5

K rev - coefficient of reversibility, with non-reversible operation K rev = 1.0 with reverse operation K rev = 0.75

K h - coefficient taking into account the location of the worm pair in space. When the worm is located under the wheel, K h \u003d 1.0, when located above the wheel, K h \u003d 1.2. When the worm is located on the side of the wheel, K h \u003d 1.1.

3) Calculated radial cantilever load on the gearbox output shaft

F out. calculated = F out x K dir, (6)

F out - radial cantilever load applied in the middle of the landing part of the ends of the output shaft (initial data), N

K dir - operating mode coefficient (formula 4.5)

3. The parameters of the selected gearbox must meet the following conditions:

1) T nom > T calc, (7)

T nom - rated torque on the output shaft of the gearbox, given in this catalog in the technical specifications for each gearbox, Nxm

T calc - estimated torque on the output shaft of the gearbox (formula 2), Nxm

2) F nom > F out calc (8)

F nom - rated cantilever load in the middle of the landing part of the ends of the gearbox output shaft, given in the technical specifications for each gearbox, N.

F out.calc - calculated radial cantilever load on the output shaft of the gearbox (formula 6), N.

3) R inlet calc< Р терм х К т, (9)

R in.calc - the estimated power of the electric motor (formula 10), kW

P term - thermal power, the value of which is given in the technical characteristics of the gearbox, kW

K t - temperature coefficient, the values ​​\u200b\u200bof which are given in table 6

The rated power of the electric motor is determined by:

R in.calc \u003d (T out x n out) / (9550 x efficiency), (10)

T out - estimated torque on the output shaft of the gearbox (formula 2), Nxm

n out - the speed of the output shaft of the gearbox, rpm

Efficiency - the efficiency of the gearbox,

A) For spur gearboxes:

• single-stage - 0.99
• two-stage - 0.98
• three-stage - 0.97
• four-stage - 0.95

B) For bevel gears:

• single-stage - 0.98
• two-stage - 0.97

C) For bevel-helical gearboxes - as the product of the values ​​​​of the bevel and cylindrical parts of the gearbox.

D) For worm gearboxes, the efficiency is given in the technical specifications for each gearbox for each gear ratio.

The managers of our company will help you to buy a worm gearbox, find out the cost of the gearbox, choose the right components and help you with questions that arise during operation.

Table 1

table 2

Leading machine	Generators, elevators, centrifugal compressors, evenly loaded conveyors, mixers of liquid substances, centrifugal pumps, gear, screw, boom mechanisms, blowers, fans, filtering devices.	Water treatment plants, unevenly loaded conveyors, winches, cable drums, running, rotary, lifting mechanisms cranes, concrete mixers, furnaces, transmission shafts, cutters, crushers, mills, oil industry equipment.	Punch presses, vibrators, sawmills, screens, single cylinder compressors.	Equipment for the production of rubber products and plastics, mixing machines and equipment for shaped steel.
electric motor, steam turbine
4, 6 cylinder internal combustion engines, hydraulic and pneumatic engines
1, 2, 3 cylinder internal combustion engines

Table 3

Table 4

Table 5

Table 6

cooling	Ambient temperature, C o	Duration of inclusion, PV%.
Reducer without outsider cooling.
Reducer with water cooling spiral.

Laboratory work

The study of the efficiency of the gear reducer

1. The purpose of the work

Analytical determination of the efficiency factor (COP) of a gear reducer.

Experimental determination of the efficiency of a gear reducer.

Comparison and analysis of the obtained results.

2. Theoretical provisions

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

Thus, the efficiency shows what proportion of the mechanical energy supplied to the machine is usefully spent on doing the work for which the machine was created, i.e. is an important characteristic of the mechanism of machines. Since friction losses are inevitable, it is always. In equation (1) instead of works And performed per cycle, we can substitute the average values ​​of the corresponding powers per cycle:

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

The ratio of the angular velocity at the input to the output angular velocity called gear ratio :

For the reducer, equation (2) takes the form

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

The experimental determination of the efficiency is based on the measurement of the values T 2 And T 1 and calculation of η by formula (4).

In the study of the efficiency of the gearbox by factors, i.e. system parameters that affect the measured value and can purposefully change 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 eliminate losses due to mixing and splashing of oil; installation of hydrodynamic bearings; designing gearboxes with the most optimal transmission parameters.

The efficiency of the entire installation is determined from the expression

Where - efficiency of the gear reducer;

– efficiency of motor supports,;

– coupling efficiency, ;

– Efficiency of brake mounts,.

The overall efficiency of a gear multi-stage gearbox is determined by the formula:

Where – Efficiency of gearing with 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 plain bearings);

– Efficiency taking into account losses due to splashing and mixing of oil is approximately taken= 0,96;

k– number of pairs of bearings;

n- the number of pairs of gears.

3. Description of the object of study, devices and instruments

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

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

The load device 11 is a magnetic powder brake that simulates the working load of the gearbox. The load device stator is an electromagnet, in the magnetic gap of which a hollow cylinder with a roller (load device rotor) is placed. The internal 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 speed is controlled by a tachometer5.

The torque values ​​on the motor and brake shafts are determined by means of devices that include a flat spring6 and dial gauges7,12. Supports 1 and 10 on rolling bearings provide the ability to rotate the stator and rotor (for both the motor and 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) in the stator winding of the electric motor 3, the rotor receives a torque, and the stator receives a reactive torque equal to the torque and directed in the opposite direction. In this case, the stator under the action of the reactive torque deviates (balancing motor) from the initial position depending on the magnitude of the braking torque on the driven shaft of the gearboxT 2 . These angular movements of the stator housing of the electric motor are measured by the number of divisions P 1 , to which the indicator needle deviates7.

Accordingly, when an electric current is supplied (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 P 2) .

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

The reducer8 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 given in Table 1.

Table 1. Technical specifications installations

Parameter name	Letter designation quantities	Meaning
The number of pairs of spur gears in the gearbox	n
Gear ratio	u
transmission module, mm	m
Nominal 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 motor shaft, 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 - the moment of driving forces (torque on the motor shaft), Nmm;

u- gear ratio of the gear reducer;

– Efficiency of the elastic coupling;= 0,99;

– 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 rotation speed. At the same time, certain braking torques are sequentially created on the output shaft of the gearbox according to the corresponding indications of the indicator12.

When the electric motor is turned on with 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 toggle switch 17, after which the indicator arrows are set to zero.

Using potentiometer 15, set the required number of revolutions of the motor shaft on the tachometer, for example - 200 (table 2).

Potentiometer 18 on the output shaft of the gearbox creates braking torques T 2 corresponding to the indications of the indicator12.

Record indicator 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 12, P 2
200, 350, 550, 700	120, 135, 150, 165, 180, 195
850, 1000	100, 105, 120, 135, 150, 160

4.3. By changing the load on the brake with potentiometer 18 and on the engine with potentiometer 15 (see Figure 1), at a constant engine speed, record five indicator readings 7 and 12 ( P 1 and P 2) in table 3.

Table 3. Test results

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

Indicator 7 readings P 1

Torque on the motor shaft Nmm

Indicator 12 P 2

Torque on the brake shaft Nmm

Efficiency experimental,

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

Control 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

Goal 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 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; 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. main part 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 the teeth of the wheel, 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 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