Calculation and selection (Russian methodology) - worm gearbox. Actual output shaft speed Determination of the desired drive ratio

1 Torque on the output shaft of the gearbox M2 [Nm]
The torque on the output shaft of the gearbox is the torque supplied to the output shaft of the gearmotor, with the installed rated power Pn, the safety factor S, and the estimated service life of 10,000 hours, taking into account the efficiency of the gearbox.
2 Rated torque of the gearbox Mn2 [Nm]
The rated torque of a gearbox is the maximum torque that the gearbox is designed to safely transmit, based on the following values:
. safety factor S=1
. service life 10,000 hours.
Mn2 values ​​are calculated in accordance with the following standards:
ISO DP 6336 for gears;
ISO 281 for bearings.

3 Maximum torque M2max [Nm]
The maximum torque is the maximum torque that the gearbox can withstand under conditions of static or heterogeneous load with frequent starts and stops (this value is understood as the instantaneous peak load when the gearbox is operating or the starting torque under load).
4 Required torque Mr2 [Nm]
Torque value that meets the necessary consumer requirements. This value must always be less than or equal to the rated output torque Mn2 of the selected gearbox.
5 Rated torque M c2 [Nm]
The torque value that must be used to guide the selection of a gearbox, taking into account the required torque Mr2 and the service factor fs, is calculated by the formula:

The dynamic efficiency values ​​of gearboxes are shown in table (A2)

Ultimate thermal power Pt [kW]

This value is equal to the limiting value of the mechanical power transmitted by the gearbox under conditions of continuous operation at temperature environment 20°C without damage to gear units and parts. At ambient temperatures other than 20°C and intermittent operation, the Pt value is adjusted taking into account the thermal coefficients ft and speed coefficients given in table (A1). The following condition must be met:

Efficiency factor (efficiency)

1 Dynamic efficiency [ηd]
Dynamic efficiency is the ratio of the power received at the output shaft P2 to the power applied to the input shaft P1.

Gear ratio [i]

The characteristic inherent in each gearbox is equal to the ratio of the rotation speed at input n1 to the rotation speed at output n2:

Rotational speed

1 Input speed n1 [min -1]
Rotation speed applied to the gearbox input shaft. In case of direct connection to the electric motor given value equal to the output speed of the electric motor; in the case of connection through other drive elements, to obtain the input speed of the gearbox, the motor speed should be divided by the gear ratio of the input drive. In these cases, it is recommended to set the gearbox to a rotation speed below 1400 rpm. The input speed of the gearboxes specified in the table must not be exceeded.

2 Output speed n2 [min-1]
The output speed n2 depends on the input speed n1 and the gear ratio i; calculated by the formula:

Safety factor [S]

The value of the coefficient is equal to the ratio of the rated power of the gearbox to the real power of the electric motor connected to the gearbox:

Classification of gearboxes depending on the location of the axes of the input and output shafts in space.

Classification of gearboxes depending on the mounting method.

Design versions according to installation method.

Conventional images and digital designations of design versions of gearboxes and geared motors for general machine-building applications: (products) according to the installation method are established by GOST 30164-94.
Depending on the design, gearboxes and gearmotors are divided into the following groups:

a) coaxial;
b) with parallel axes;
c) with intersecting axes;
d) with crossing axes.

Group a) also includes products with parallel axes, in which the ends of the input and output shafts are directed in opposite directions, and their interaxle distance is no more than 80 mm.
Groups b) and c) also include variators and variator drives. Conventional images and digital designations of designs according to the installation method characterize the design of the housings, as well as the location in space of the mounting surfaces of the shafts or shaft axes.

The first is the design of the body (1 - on feet, 2 - with a flange);
The second is the location of the mounting surface (1 - floor, 2 - ceiling, 3 - wall);
The third is the location of the end of the output shaft (1 - horizontal to the left, 2 - horizontal to the right, 3 - vertical down, 4 - vertical top).

The symbol for products of group a) consists of three numbers:
the first is the design of the body (1 - on feet; 2 - with a flange); the second is the location of the mounting surface (1 - floor; 2 - ceiling; 3 - wall); the third is the location of the end of the output shaft (1 - horizontal to the left; 2 - horizontal to the right; 3 - vertical down; 4 - vertical up).

The symbol for products from groups b) and c) consists of four numbers:
the first is the design of the body (1 - on feet; 2 - with a flange; 3 - mounted; 4 - mounted); the second is the relative position of the mounting surface and the shaft axes for group b): 1 - parallel to the shaft axes; 2 - perpendicular to the axes of the shafts; for group c): 1 - parallel to the axes of the shafts; 2 - perpendicular to the axis of the output shaft; 3 - perpendicular to the axis of the input shaft); third - location of the mounting surface in space (1 - floor; 2 - ceiling; 3 - left wall, front, rear; 4 - right wall, front, rear);

fourth - location of shafts in space for group b): 0 - horizontal shafts in a horizontal plane; 1 - horizontal shafts in a vertical plane; 2 - vertical shafts; for group c): 0 - horizontal shafts; 1 - vertical output shaft; 2 - vertical input shaft).
The symbol for products of group d) consists of four numbers:
the first is the design of the body (1 - on feet; 2 - with a flange; 3 - mounted; 4 - mounted);
the second is the relative position of the mounting surface and the shaft axes (1 - parallel to the shaft axes, from the worm side; 2 - parallel to the shaft axes, from the wheel side; 3, 4 - perpendicular to the wheel axis; 5, 6 - perpendicular to the worm axis);
third - the location of the shafts in space (1 - horizontal shafts; 2 - vertical output shaft: 3 - vertical input shaft);
fourth - the relative position of the worm pair in space (0 - worm under the wheel; 1 - worm above the wheel: 2 - worm to the right of the wheel; 3 - worm to the left of the wheel).
Mounted products are installed with a hollow output shaft, and the housing is fixed at one point from turning by a reactive torque. Mounted products are installed with a hollow output shaft, and the body is fixedly fixed at several points.
In geared motors, the image of the design according to the installation method must contain an additional simplified image of the motor circuit in accordance with GOST 20373.
Examples symbols and images:
121 - coaxial gearbox, body design on feet, ceiling mounting, horizontal shafts, output shaft on the left (Fig. 1, a);
2231 - gearbox with parallel axes, housing design with a flange, the mounting surface is perpendicular to the axes of the shafts, fastening to the left wall, the shafts are horizontal in the vertical plane (Fig. 1, b);
3120 - gearbox with intersecting axes, mounted housing, mounting surface parallel to the axes of the shafts, ceiling mounting, horizontal shafts (Fig. 1, c);
4323 - gearbox with crossing axes, the housing is mounted, the mounting surface is perpendicular to the wheel axis, the output shaft is vertical, the worm is to the left of the wheel (Fig. 1, d). The symbol LLLL indicates the point of fixation of the product from rotation by the reactive torque and the fastening of the hollow output shaft to the shaft working machine.

Ministry of Education and Science Russian Federation.

Federal Agency for Education.

State educational institution higher vocational education.

Samara State Technical University.

Department: “Applied mechanics”

Course project in mechanics

Student 2 – HT – 2

Head: Ph.D., Associate Professor

Technical assignment No. 65.

Bevel gear.

Motor shaft rotation speed:

Torque on the output shaft of the gearbox:

Output shaft speed:

Gearbox service life in years:

Gearbox load factor throughout the year:

Gearbox load factor during the day:

1. Introduction_______________________________________________________________4

2. Kinematic and power calculation of the drive__________________________4

2.1 Determination of speed of rotation of gearbox shafts______________________________4

2.2. Calculation of numbers of wheel teeth_____________________________________________4

2.3. Determination of actual gear ratio_______________5

2.4. Determination of gearbox efficiency_____________________________________________5

2.5. Determination of rated load moments on each shaft, mechanism diagram__________________________________________________________5

2.6. Calculation of required power and choice of electric motor, its dimensions___5

3. Selection of materials and calculation of permissible stresses_________________7

3.1. Determination of the hardness of materials, selection of material for a gear ____________________________________________________________7

3.2. Calculation of permissible stresses _________________________________7

3.3. Permissible stresses for contact endurance______________7

3.4. Allowable stresses for bending endurance________________8

4. Design and verification calculation of transmission__________________________8

4.1. Calculation of the preliminary pitch diameter of the gear______8

4.2. Calculation of the preliminary transmission module and its clarification according to GOST___________________________________________________________8

4.3. Calculation of transmission geometric parameters_______________________8

4.4. Transmission verification calculation_____________________________________________9

4.5. Engagement forces_________________________________________________9

5. Design calculation of the shaft and selection of bearings ______________________________12

6. Sketch layout and calculation of structural elements_______________12

6.1. Gear calculation_____________________________________________12

6.2. Calculation of hull elements_______________________________________________13

6.3. Calculation of oil-retaining rings______________________________13

6.4. Calculation of bearing caps________________________________________________13

6.5. Execution of layout drawing__________________________13

7. Selection and verification calculation of key connections _______________14

8. Test calculation of the shaft for fatigue endurance______________15

9. Test calculation of output shaft bearings for durability___18

10. Selection and calculation of the coupling___________________________19

11. Gearbox lubrication________________________________________________19

12. Assembling and adjusting the main components of the gearbox___________________20

13. List of used literature________________________________22

14. Applications_________________________________________________23

Introduction.

A gearbox is a mechanism consisting of gear or worm gears, made in the form of a separate unit and used to transmit rotation from the engine shaft to the shaft of the working machine.

The purpose of the gearbox is to reduce the angular velocity and, accordingly, increase the torque of the driven shaft compared to the drive shaft.

The gearbox consists of a housing (cast iron or welded steel), in which transmission elements are placed - gears, shafts, bearings, etc. In some cases, devices for lubrication of gears and bearings or devices for cooling are also placed in the gearbox housing.

Gearboxes are classified according to the following main characteristics: transmission type (gear, worm or gear-worm); number of stages (single-stage, two-stage, etc.); type of gears (cylindrical, bevel, bevel-cylindrical, etc.); relative location of the gearbox shafts in space (horizontal, vertical); features of the kinematic scheme (unfolded, coaxial, with a bifurcated stage, etc.).

Bevel gearboxes are used to transmit motion between shafts, the axes of which usually intersect at an angle of 90. Gears with angles other than 90 are rare.

The most common type of bevel gearbox is a gearbox with a vertically located low-speed shaft. It is possible to design the gearbox with a vertically located high-speed shaft; in this case the drive is carried out from a flange electric motor

The gear ratio u of single-stage bevel gearboxes with spur wheels, as a rule, is not higher than 3; in rare cases, u = 4. For oblique or curved teeth, u = 5 (as an exception, u = 6.3).

For gearboxes with bevel spur wheels, the permissible peripheral speed (along the pitch circle of the average diameter) is v ≤ 5 m/s. At higher speeds, it is recommended to use bevel wheels with circular teeth, which provide smoother engagement and greater load-bearing capacity.

2 Kinematic and power calculation of the drive.

2.1 Determination of speed of rotation of gearbox shafts:

Rotation speed of the first (input) shaft:

Rotation speed of the second (output) shaft:

2.2 Calculation of numbers of gear teeth.

Estimated number of gear teeth

Meaning

Estimated number of wheel teeth

Meaning

2.3 Determination of actual gear ratio:

2.4 Determination of gearbox efficiency.

For bevel gear

Torque (load) torque on the output shaft of the gearbox:

On the input shaft:

2.5 Determination of rated load moments on each shaft, mechanism diagram.

Power at the output shaft of the gearbox, kW:

Estimated power of the electric motor.

A worm gearbox is one of the classes of mechanical gearboxes. Gearboxes are classified according to the type of mechanical transmission. The screw that forms the basis of the worm gear is similar in appearance to a worm, hence the name.

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

In a worm gearbox, the increase in torque and decrease in the angular speed of the output shaft occurs by converting the energy contained in the high angular speed 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 losses.

Therefore, the work of calculating and selecting a 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 spur gearboxes.

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

1. Selecting the type of gearbox

2. Selecting the size (standard size) of the gearbox and its characteristics.

3. Verification calculations

1. Selecting the type of gearbox

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 mounting locations and methods of mounting the gearbox.

1.2 Determination of 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 shafts of the gearbox are parallel to each other and lie in only one vertical plane - a 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 shafts of the gearbox are perpendicular to each other and lie in only one horizontal plane.

Worm gearboxes:

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 method of fastening, mounting position and assembly option of the gearbox.

The method of fastening the gearbox and the mounting position (mounting to the foundation or to 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 diagrams given in the catalog. Schemes of “Assembly options” are given in the “Designation of gearboxes” section.

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

1) Noise level

• the lowest - for worm gearboxes
• the highest - for helical and bevel gearboxes

2) Efficiency

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

Worm gearboxes are preferably used in repeated and short-term operating modes

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

• the lowest is for planetary single-stage

4) Dimensions with the same gear ratios and torques:

• the largest axial ones are for coaxial and planetary
• 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 is for conical ones
• the lowest is for planetary ones

2. Selecting the size (standard size) of the gearbox and its characteristics

2.1. Initial data

Kinematic diagram of the drive containing the following data:

• view drive machine(engine);
• required torque on the output shaft T required, Nm, or power of the propulsion system P required, kW;
• rotation speed of the gearbox input shaft nin, rpm;
• speed of rotation of the output shaft of the gearbox n out, rpm;
• the nature of the load (uniform or uneven, reversible or non-reversible, the presence and magnitude of overloads, the presence of shocks, impacts, vibrations);
• required duration of operation of the gearbox in hours;
• average daily work in hours;
• number of starts per hour;
• duration of switching on with load, duty cycle %;
• environmental conditions (temperature, heat removal conditions);
• Duration of switching on under load;
• radial cantilever load applied in the middle of the landing part of the ends of the output shaft F out and input shaft F in;

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

1) Gear ratio

U= n in / n out (1)

The most economical is to operate the gearbox at an input speed of less than 1500 rpm, and for 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 in the required direction to the nearest number according to Table 1.

Using the table, types of gearboxes that satisfy a given gear ratio are selected.

2) Estimated torque on the output shaft of the gearbox

T calc =T required x K rez, (2)

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

K mode - operating mode coefficient

With a known power of the propulsion system:

T required = (P required x U x 9550 x efficiency)/ n input, (3)

P required - power of the propulsion system, kW

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

U - gear ratio, formula 1

Efficiency - gearbox efficiency

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

For gear reducers:

K dir = K 1 x K 2 x K 3 x K PV x K rev (4)

For worm gearboxes:

K dir = 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 - operating duration coefficient table 3

K 3 - coefficient of number of starts table 4

K PV - switching duration coefficient table 5

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

Kh is a coefficient that takes into account the location of the worm pair in space. When the worm is located under the wheel, K h = 1.0, when located above the wheel, K h = 1.2. When the worm is located on the side of the wheel, K h = 1.1.

3) Estimated radial cantilever load on the gearbox output shaft

F out.calc = F out x K mode, (6)

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

K mode - operating mode coefficient (formula 4.5)

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

1) T nom > T calc, (7)

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

T calc - calculated torque on the output shaft of the gearbox (formula 2), Nm

2) Fnom > Fout.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) P input calculation< Р терм х К т, (9)

P input calculation - calculated power of the electric motor (formula 10), kW

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

Kt - temperature coefficient, the values ​​of which are given in Table 6

The design power of the electric motor is determined by:

P input calculation = (T out x n out)/(9550 x efficiency), (10)

Tout - calculated torque on the output shaft of the gearbox (formula 2), Nm

n out - speed of the gearbox output shaft, rpm

Efficiency is the efficiency of the gearbox,

A) For helical gearboxes:

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

B) For bevel gearboxes:

• 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.

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

Table 1

table 2

Table 3

Table 4

Table 5

Table 6

Example 1

Determine the gear ratio (Fig. 19), the number of revolutions of the driven shaft and the overall efficiency (efficiency) if the number of wheel teeth is equal: z 1 =30, z 2 =20, z 3 =45, z 4 =30, z 5 =20, z 6 =120, z 7 =25, z 8 =15 ; drive shaft speed n 1 =1600 rpm.

Solution

The mechanism consists of four stages: two cylindrical z 1 - z 2 , z 3 - z 4 external gear, cylindrical z 5 - z 6 with internal gearing and conical z 7 - z 8 .

The total gear ratio of a multi-stage transmission is equal to the product of the gear ratios of each stage forming this gear mechanism. For this case

.

The (–) sign indicates that the direction of rotation of the wheels in these pairs is opposite. The direction of rotation of the wheels in this case can also be determined by placing arrows on the diagram (Fig. 19).

The number of revolutions of the driven shaft is determined through the gear ratio
rpm

The overall efficiency of the gear mechanism is

where the numerical values ​​are taken according to the conditions of problem T1.

Example 2

Here
,
,
– gear ratios of the converted mechanism (carriage N stopped, but the stationary wheel rotates z 3 ). The resulting gear ratio with a “+” sign indicates the coincidence of the directions of rotation of the drive and driven shafts.

Example 3

Solution

As in example 2, this mechanism refers to a single-stage planetary gear and the gear ratio from the carrier N to the wheel z 1 determined by the relation

Example 4

Solution

A complex gear train consists of two stages: the first stage is a simple cylindrical pair with external gearing z 1 -z 2, the second stage is a planetary mechanism N-z 5 , transmitting rotational motion from the carrier N to the wheel z 5 via satellite z 4 . The direction of rotation of the output shaft is determined by the algebraic sign.

1. For a two-stage transmission, we find the total gear ratio through the gear ratios of each stage, i.e.

.

Resulting gear ratio
, which indicates an increase in the rotation speed of the output shaft, and the “+” sign shows that the directions of rotation of the shafts coincide.

2. Determine the angular velocity of the output link and its angular acceleration

rad/s,

rad/s 2 .

3. Since the rotation of the wheels is accelerated (we assume uniformly accelerated), the time during which the angular velocities will double will be determined from the dependence

,

Where And - angular velocities respectively at the beginning and end of the time period under consideration
. From here

With.

4. Determine the overall transmission efficiency

Problem T2

The output link of the mechanism shown in the diagrams (Fig. 23–32) performs a reciprocating (or reciprocating) motion and is loaded during the working stroke with a constant force F c (or moment T With) useful resistance. At idle, when the direction of movement of the output link is reversed, there is no useful resistance, but harmful ones continue to act. Taking into account the effect of friction in kinematic pairs, according to the efficiency the mechanism must be determined:

1) driving moment T d , constant in magnitude, which must be applied to the input link during steady motion with a cycle consisting of working and idling strokes;

2) the work of friction forces on the worker and idling, considering that the harmful resistance is constant at each stroke, but during the working stroke it is three times greater than at idle;

3) change in the kinetic energy of the mechanism during the working stroke and during idling;

4) power required from the drive when rotating the input link at an average speed and average (per whole revolution) powers of useful resistance and friction forces.

The solution to this problem is based on the equation of motion of the mechanism, which establishes a connection between the change in kinetic energy and the work of forces (the law of kinetic energy). The work of forces and moments is determined, respectively, by the linear or angular movements of the links on which they act. In this regard, it is necessary to determine the position of the mechanism at the extreme positions of the output link. The movements of the links, linear and angular, can be determined from a drawing made to scale or calculated analytically. The dimensions of the links, according to their designations on the mechanism diagram, and other necessary quantities are given in tables of numerical data, where – efficiency factor, and in option 9 m– rack and pinion module, z – number of wheel teeth.

Table 17

Table 18

Table 19

Table 20

Table 21

Table 22

Table 23

Table 24

Table 25

Table 26

Sequence of task execution. Firstly, it is necessary to build a mechanism in extreme positions, and in given directions of the angular velocity of the input link
and constant force F With (or moment T With) useful resistance to set working and idling speeds.

When graphically determining the linear and angular movements of links, it is necessary to remove from the drawing:

1) for the input link, its rotation angles during the working stroke and at idle X;

2) for the output link during its reciprocating motion, linear movement, i.e. move s, or during its reciprocal rotational movement the swing angle
.

In order to determine the working and idling zones for the input link, it is necessary to take into account the connection of the movement with the shown direction of action of the useful resistance, which during the working stroke should prevent the movement of the output link.

In options 5 and 8, a geometric closure of the links in the highest pair is used, preventing the links from moving away from each other: in option 8, a radius roller r rolls in the circular groove of the input link, covered by the outer and inner profiles of the groove; in option 5, the round eccentric is covered by the frame of the output link.