Shafts, axles and supports. Structural elements of shafts and axes Supports of shafts and axes bearings

SHAFT AND AXLES

The gear wheels are mounted on special oblong parts with a circular cross-section. Among such parts there are axles and shafts.

Axis- a part that serves to hold the wheels and center their rotation. Shaft– axis transmitting torque.

The concepts of “wheel axis”, this is a part, and “rotation axis”, this is a geometric line of centers of rotation, should not be confused.

The shapes of shafts and axles are very diverse, from the simplest cylinders to complex cranked structures. There are known designs of flexible shafts, which were proposed by the Swedish engineer Karl de Laval back in 1889.

The shape of the shaft is determined by the distribution of bending and torque moments along its length. A properly designed shaft is a beam of equal resistance.

Shafts and axles rotate and therefore experience alternating loads, stresses and deformations. Therefore, failures of shafts and axles are of a fatigue nature.

The causes of shaft and axle failures can be traced at all stages of their “life”.

1. At the design stage - incorrect choice of shape, incorrect assessment of stress concentrators.

2. At the manufacturing stage there are cuts, nicks, dents from careless handling.

3. At the operating stage - incorrect adjustment of bearing units.

For the shaft or axle to function, it is necessary to ensure:

è volumetric strength (ability to resist M izg And M cool );

è surface strength (especially at joints with other parts);

è bending rigidity;

è torsional rigidity (especially for long shafts).

All shafts must be calculated for volumetric strength.

Loading patterns for shafts and axles depend on the number and location of rotating parts installed on them and the direction of the forces. For complex loading, choose two orthogonal planes (for example, frontal and horizontal) and consider the circuit in each plane. Of course, not real structures are calculated, but simplified calculation models, which are beams on hinged supports, beams with embedding, and even statically indeterminate problems.

When drawing up a design diagram, the shafts are considered as straight bars lying on hinged supports. When choosing the type of support, it is assumed that the deformations of the shafts are small and, if the bearing allows at least a slight tilt or movement of the axle, it is considered a hinged-fixed or hinged-movable support. Sliding or rolling bearings that simultaneously perceive radial and axial forces are considered as articulated-fixed supports, and bearings that perceive only radial forces are considered as articulated-movable.

Such problems are well known to students from courses in theoretical mechanics (statics) and strength of materials.

The calculation of the shaft for volumetric strength is carried out in three stages.

I. Preliminary calculation of shafts

It is carried out at the stage of development of the Technical Specifications, when only the torques on all shafts of the machine are known. In this case, it is assumed that the shaft experiences only shear torsional stresses

t cr= M vr / W p £ [ t ] cr ,

Where Wp - polar moment of resistance of the section.

For round section: Wp = pd 3/16 , [ t ] cr = 15 ¸ 20 N/mm 2 .

The strength condition for torsional stresses is conveniently solved relative to the shaft diameter

This is the minimum shaft diameter. In all other sections of the shaft it can only be greater. The calculated minimum shaft diameter is rounded to the nearest larger normal range. This diameter is the starting point for further design.

II. Refined calculation of shafts

At this stage, it takes into account not only torque, but also bending moments. It is carried out at the stage of the preliminary layout, when the bearings are pre-selected, the length of all sections of the shaft is known, the position of all the wheels on the shaft is known, and the forces acting on the shaft are calculated.

Design diagrams of the shaft are drawn in two planes. By known forces in gears and distances to supports, diagrams of bending moments in the horizontal and frontal planes are constructed. Then the total bending moment is calculated

Where α =0,75 or 1 depending on the adopted energy theory of strength, accepted by most authors to be equal 1 .

The equivalent stress from the combined action of bending and torsion is calculated s eq = M eq / W p .

The equation is also solved with respect to the minimum shaft diameter

Or the same for comparison with permissible normal stresses:

The minimum shaft diameter obtained in the updated calculation is finally accepted for further design.

III. Shaft endurance calculation

It is carried out as a test at the detailed design stage, when the working drawing of the shaft is almost ready, i.e. its exact shape, dimensions and all stress concentrators are known: keyways, annular grooves, through and blind holes, interference fits, fillets (smooth, rounded diameter transitions).

When calculating, it is assumed that bending stresses change according to a symmetrical cycle, and tangential torsional stresses change according to a non-zero pulsating cycle.

The test calculation of a shaft for endurance essentially comes down to determining the actual safety factor n , which is compared with the permissible

Here ns And n t - safety factors for normal and tangential stresses

Where s -1 And τ -1 – endurance limits of the shaft material during bending and torsion with a symmetrical cycle; k σ And k τ – effective stress concentration coefficients during bending and torsion, taking into account fillets, keyways, press fits and threads; ε α And ε τ – scale factors of the shaft diameter; s a And τ a – amplitude voltage values; s m And τ m – average cycle voltages ( s m = 0 , τ m =τ a ); ψ σ And ψ τ – the coefficients of influence of average cycle stress on fatigue strength depend on the type of steel.

The calculation of safety factors based on stress was described in detail in the course "Strength of Materials", in the section "Cyclic Stress State".

If the safety factor turns out to be less than the required one, then fatigue resistance can be significantly increased by using surface hardening: nitriding, surface hardening with high-frequency currents, shot peening, roller rolling, etc. In this case, you can get an increase in the endurance limit of up to 50% or more.

CONTROL QUESTIONS

s What is the difference between shafts and axles?

s What is the dynamic nature of bending stresses in shafts and axles?

s What are the causes of shaft and axle failures?

s In what order are the stages of strength calculation of shafts performed?

s What diameter is determined in the design calculation of the shafts?

SUPPORTS OF SHAFT AND AXLES - BEARINGS

Shafts and axles are supported by special parts that act as supports. The name "bearing" comes from the word "spike" ( English shaft, German zappen, hol. shiffen – shaft). This is what they used to call shaft shanks and journals, where, in fact, bearings are installed.

The purpose of a bearing is that it must provide a reliable and precise connection between a rotating (shaft, axis) part and a stationary housing. Hence, main feature bearing operation - friction of mating parts.

Based on the nature of friction, bearings are divided into two large groups:

è plain bearings (sliding friction);

è rolling bearings (rolling friction).

shaft, in which the turns of the outer layer of the shaft will twist and compact the inner layers of the wire.

Keyways, threads for mounting nuts, transverse through holes for pins or holes for set screws, grooves, as well as sudden changes in shaft cross-sections cause stress concentrations that reduce its fatigue strength. Therefore, whenever possible, the use of elements that cause stress concentrations should be avoided.

5.2. Shaft materials

Most shafts and axles are made from carbon steels

(20, 30, 40, 45, 50 stamps) and alloy steels(grades 20Х, 40ХН, 30ХГСА, 40ХН2МА, 18Х2Н4МА), etc.

The choice of material is determined by the design of the shaft or axis, the requirements for it and operating conditions, required period guarantees of trouble-free operation. For example, the use of alloy steels makes it possible, if necessary, to limit the weight and overall dimensions of the shaft and increase the durability of spline joints. The choice of gear shaft (or worm) material is determined by the requirements for surface hardness and bending endurance of the gear shaft teeth (worm turns).

For improvement mechanical characteristics Various types of heat treatment are used on shafts and axles, for example, their journals are hardened by heating with high frequency current or carburized to increase their wear resistance.

5.3. Performance criteria for shafts and axles

Shafts are among the most critical machine parts. Excessive disruption of the shape of the shaft due to high radial compliance or vibrations, and in extreme cases, destruction of the shaft, entails failure of the entire structure.

Fixed axles, low-speed shafts,

working in conditions large overloads, count on statistical

ical strength.

Shafts of high-speed machines are often exposed fatigue failure and they must be counted on fatigue resistance

ness . Characteristics fatigue strength is a safety factor.

Under the influence of applied forces, the shafts develop bending and torsion deformations. Excessive bending of the shafts disrupts the normal operation of bearing units, gears, and friction mechanisms. Therefore, the magnitude of deformations of shafts and axes is limited, and

their rigidity, characterized permissible deflection in places where parts fit, as well as permissible tilt angles And twisting of sections, is one of the main performance criteria.

5.4. Strength calculations and shaft design

5.4.1. General information

The purpose of strength calculations is to determine the main dimensions of axles and shafts at which their static pro-

strength and endurance (fatigue strength).

The established practice of calculating and designing shafts divides this procedure into three stages:

- approximate calculation;

- shaft design;

- updated (verification) calculation.

Approximate calculation of the shaft is performed in order to pre-

to determine the value of its minimum permissible diameter. At the stage design develop the shaft design, ensuring

considering the conditions of manufacturability and assembly. At this stage, the diameters and axial dimensions of the output end, seats for bearings, gears and other parts mounted on the shaft are determined.

The purpose of the refined (checking) calculation of the shaft is to determine

stress and safety factor (when calculating for static strength) or safety factor (when calculating for high-

tolerance) and comparing the obtained values ​​with the acceptable ones.

5.4.2. Approximate shaft calculation

At this design stage, the geometric parameters of the shaft are not determined, so the calculation is carried out only on the shear stresses arising during torsion. Because of at approximately

This calculation does not take into account the influence of the bending moment, the presence of weakening factors of keyways, rings, transitions etc.), then at this stage the value of the permissible shear stress to p

is assumed to be underestimated compared to the permissible tangential stresses to p for structural materials given in

reference books. Values ​​kp at approximate calculations for shafts made of medium-carbon steels are taken in the range of 20 N / mm2

up to 30 N/mm2 depending on the shaft material and type of load.

Minimum allowed the diameter of a round solid shaft d min without taking into account the presence of key or spline grooves is determined based on the condition of torsional strength according to the formula (see section

where T is the maximum torque on the shaft;

to p – permissible tangential stress at approximately

nom calculation.

For cantilever sections of input or output shafts (Fig. 5.1.4)

the resulting value d min should be rounded to the nearest larger standard value of the output shaft section.

5.4.3. Shaft design

5.4.3.1. Determination of diameters in different sections of the shaft

Based on the value d min, the diameters of the intermediate non-mating sections of the shaft are assigned, and the nominal diameters of the connections are selected.

Drop consecutive steps of diameters d i, and d i 1 of the shafts, necessary for the free transportation of parts to the places of their interference fits, should be assigned to the minimum - (5-10)%, but the absolute value of the difference is not recommended to be assigned more than 10 mm.

The assigned diameters of individual sections are rounded to the nearest value from a range of standard sizes.

The diameter of the rolling bearing journal is approx.

are adjusted to the nearest larger bearing inner diameter.

5.4.3.2. Determination of axial dimensions of shaft sections

The axial dimensions of the shafts and axles are determined during the preliminary design of the gearbox in accordance with the recommendations for determining the position of the bearings and the width of the gear rims, determined when calculating the transmission. For example, the distance between the supports of the worm wheel is taken equal to L 0.50 0.75 d 2 (where d 2 is the pitch diameter of the worm wheel), and the distance between the supports of the cantilever gear is L 3 4 B (where B is the width of the rolling bearings).

The length of the cantilever section of the shaft must be consistent with the length of the half-coupling hub, pulley or sprocket.

The lengths of the cantilever sections dk of the input or output shafts must be taken depending on their diameters from the corresponding range of standard sizes for cylindrical or conical shaft ends.

5.4.4. Refined (verification) calculation

5.4.4.1. Calculation of shafts for strength and fatigue resistance

5.4.4.1.1. General provisions

To perform calculations of shafts and axles according to the main performance criteria, it is necessary first of all to establish the magnitude, nature and location of application of the forces acting on them. Therefore, based on the structural dimensions of the shaft obtained as a result of the approximate design, a design diagram is drawn up, simplifying the consideration of the shaft as beam on hinged supports, whose role is played by bearings.

Bearings that simultaneously support axial and radial loads replace hingedly motionless supports, and bearings that perceive only radial forces - articulatedly movable supports (Fig. 5.4.2).

The position of the support is determined taking into account the contact angle of the rolling bearing. When the contact angle is zero (for radial bearings), the support position is taken in the middle of the bearing width

(Fig. 5.4.2).

Loads transmitted to the shaft from the parts mounted on it in the form of distributed forces acting along the width of the parts lead to the center of the connection in the form of a concentrated torque T, axial R z radial R x, R y forces and moments M x, M y, action -

located in two mutually perpendicular planes (Fig. 5.4.3).

If the loads acting on the shaft and reduced to the shaft axis are located in different planes, then they should be decomposed into components lying in two mutually perpendicular planes and the support reactions and internal forces should be determined in each of these planes.

When drawing up a design diagram, the weight of the shaft and parts located on them, as well as the friction forces in the supports, are not taken into account.

Also when calculating the strength of the shaft neglect the voltage

yami arising from the action of tensile or compressive and cutting forces.

5.4.4.1.2. Determination of loads acting on the shaft

To calculate the strength of a shaft, it is necessary to determine the magnitude of bending and torque moments in various sections of the shaft, while finding the most dangerous sections using construction techniques

y max M

F x 2 (a +b )-R Ax b =R Bx c

Fx 2 a

T 2 ðï T 1 ÷ï

The design diagram represents the shaft axis, depicted as a straight line with a length equal to length shaft, to which all forces acting on the shaft (both external and reactive) are applied at the same distances from each other and from the ends of the axis as on the shaft, and at the same distances from the axis as from the axis of the shaft. It should be borne in mind that transverse forces (forces normal to the shaft axis) can, like sliding vectors, be brought to the shaft axis.

The method for determining reactions in supports is described in the course on strength of materials.

When constructing diagrams, you should pay attention to the following: 1. The moment equations required when constructing the diagram are

are set relative to the section under consideration based on the system

fishing factors acting on one side of this section.

2. If there are concentrated moments on the shaft (for example, under the action of axial forces in the engagement applied at a certain distance from the longitudinal axis of the shaft), an instantaneous change in the magnitude of the moment by the magnitude of the concentrated moment appears, the so-called jump . This jump can be either positive or negative, depending on the sign of the concentrated moment.

3. Diagrams of bending moments are constructed in two mutually perpendicular planes. When determining the value of the total bending moment in any section, their components are determined and summed up using the Pythagorean theorem.

It should be borne in mind that in cases where in the section under consideration the diagram is located on both sides of zero line, then the calculation takes into account a large value of the moment, counted from the cul-

howl line (Fig. 5.4.4, 5.4.5).

4. For a dangerous section (Fig. 5.4.5), the calculated value of the bending moment is equal (using the third theory of strength):

The value of M, determined by formula (5.2.2), is taken positive.

5. In order for the values ​​of M x and M y to be conveniently summed,

5.4.4.1.3. Check calculation of the shaft for static strength

Calculation of a shaft for static strength comes down to determining

voltages and to the determination of the safety factor and comparison

comparison of the obtained values ​​with the permissible ones.

Equivalent voltages in the most dangerous section shafts that appear under the combined action of bending and torsion are most often determined according to the third theory of strength.

With the combined action of bending and torsion on a shaft of a round solid cross-section, the strength condition according to the third theory of strength (see sections 2.7.2.3 and 2.7.3.2) takes the form:

The value of the axial moment of inertia W for a circular solid section included in the formula is equal.

Shaft and axle supports. Bearing classification

Bearings are: 1) plain bearings; 2) rolling bearings.

Plain bearings

The plain bearing is a rotation pair, it is composed of shaft support section(trunnion) 1 and, accordingly, bearing 2 in which the axle slides (Fig. 5.1).

Rolling bearings.

General characteristics.

Basic designs

Rolling bearings are the main type of support for rotating (swinging) parts. The bearing consists of outer 1 and inner 2 elbows, between which the rolling elements 3 are located. To protect the rolling elements from contact with each other, they are separated from each other by a separator 4, which significantly reduces friction losses (Fig. 5.2).

Rolling bearings are standardized and manufactured in highly specialized mass production by bearing factories. Therefore, it is extremely rare for an engineer to design rolling bearings. Much more often it is necessary to select a bearing for a support unit, design a support housing, ensuring manufacturability, controllability and maintainability of the unit, as well as assess the residual life of the bearing during modernization or

forcing the operating mode of the equipment.

Classification. Rolling bearings are classified according to the characteristics listed below.

I. According to the shape of the rolling elements, they are divided into:

ball;

roller: with short cylindrical, conical, barrel-shaped, needle and twisted rollers.

Rice. 5.2. Ball bearings

Rice. 5.3. Roller bearings

II. Based on the direction of the forces perceived relative to the shaft axis, they are divided into types:

radial (Fig. 5.2 a, 5.3 a), receiving predominantly radial loads acting perpendicular to the axis of rotation of the bearing;

angular contact(Fig. 5.2 b, 5.3 b), perceiving simultaneously acting radial and axial loads;

thrust-radial, taking axial loads with the simultaneous action of a slight radial load;

persistent, perceiving only axial forces.

Sh. According to the ability of self-installation, they are divided into non-self-aligning and self-aligning, allowing rotation of the axis of the inner ring relative to the axis of the outer ring.

IV. By the number of rows of rolling elements located in width, they divide

not homogeneous (rie.5.2; 5.3). two-row, four-row and multi-row.

The main consumer (external) characteristics of bearings are load capacity, speed, weight, dimensions, energy loss.

Bearings of the same bore diameter are divided according to outer diameter and width into series: ultra-light, extra-light, light, light wide, medium, medium wide and heavy.

For particularly high rotation speeds and light loads, it is advisable to use bearings of the ultra-light and extra-light series. To carry increased and heavy loads at high rotation speeds, light series bearings are used, and if their load capacity is insufficient, two bearings are placed in one support.

In addition to standard bearings, they are manufactured for special reasons special bearings.

Advantages and disadvantages of bearings. Rolling bearings have a number of advantages compared to plain bearings: smaller (2-3 times) axial dimensions; less friction and resistance to starting under load and rotation at low and medium speeds, constant rotation resistance; ease of maintenance and lubricant supply; low cost and interchangeability.

The disadvantages of rolling bearings compared to plain bearings are the following: large radial dimensions; low radial rigidity and, as a consequence, a tendency for the shaft to vibrate due to rhythmic rolling through the loaded support area; more complex installation; greater rotational resistance (due to friction between rolling elements, rings, cage and hydraulic losses) at high speeds and, as a result, low durability (due to overheating).

Industry produces rolling bearings five accuracy classes: 0, 6; 5; 4 and 2. Designations are given in order of increasing accuracy, determined by the tolerances for the manufacture of elements, as well as the standards for smooth rotation (stroke).

The main bearing dimensions are established by GOST 3478-79 (ST SEV 402-76). They include: internal d and external diameters D, width B (height N) and radius r ring chamfers.

Materials of bearing parts. Rings and rolling elements of bearings are made mainly from ball-bearing high-carbon chromium steels ШХ15 and ШХ15СГ, ШХ20СГ, as well as case-hardened alloy steels 18ХГТ, 20Х2Н4А, etc. At operating temperatures up to 100 °C, rolling bodies and rings usually have a hardness of 60-64 HRC, balls – 62-65 HRC.

Rings and rolling elements of bearings operating at elevated temperatures (up to 500 °C) in aggressive environments are made of heat-resistant and corrosion-resistant steels.

Bearing cages are subject to intense wear due to sliding friction with rolling elements and rings, so cages are made of antifriction materials. Mass bearing cages are made by stamping from soft carbon steel, which has good anti-friction properties. High-speed bearing cages are made of massive PCB, fluoroplastic, duralumin, brass and bronze (materials are listed in order of increasing speed of the bearing).

The main types of bearings and their characteristics are given in reference books.

ROLLING SUPPORTS Supports of shafts and axes in which sliding friction is replaced by rolling friction are called rolling bearings Design of rolling bearings Installation of the bearing in the housing 1, 2 - outer and inner rings; 3 – rolling bodies; 4 – separator Bearings from d = 0.6 mm are produced; D = 2 mm; B = 0.8 mm; m = 0.015 g to d = 12 m; D = 14 m; B = 0.45 m; m = 130 g.

ADVANTAGES OF ROLLING BEARINGS Ø most standardized internationally; Ø are centrally manufactured in mass production; Ø compared to plain bearings, they have lower friction moments during startup; Ø smaller dimensions in width; Ø low consumption lubricants and ease of maintenance; Ø no need for non-ferrous metals; Ø lower heat treatment requirements for materials and

DISADVANTAGES OF ROLLING BEARINGS Ø large radial dimensions; Ø significant contact stresses that limit the service life; Ø lower damping capacity; Ø limited speed; Ø increased noise due to cyclic rolling of rolling elements through the loaded area; Ø high production; cost for small-scale production Ø non-separable in the radial direction

MATERIALS OF BEARING PARTS Bearing parts operate under conditions of high contact stresses. They must have increased strength, structural homogeneity and hardness. Rings and rolling elements are made of bearing steel grades ШХ 15, ШХ 15 -Ш, ШХ 15 -В, ШХ 15 SG-Ш, etc. The hardness of rings and rollers is 58... 66 HRCE - of balls 63... 67 HRCE. Separators are made of mild carbon steel. Massive separators made of bronze, brass, aluminum alloys, cermets, textolite, polyamides and other plastics.

CLASSIFICATION OF ROLLING BEARINGS By the shape of the rolling elements By the direction of the load received By the number of rows of rolling elements By the method of self-installation By ratio overall dimensions According to accuracy class According to vibration level According to special requirements

CLASSIFICATION OF BEARINGS ACCORDING TO THE NUMBER OF ROWS OF ROLLING BODIES ü there are single-row, double-row and multi-row bearings BY SELF-ALIGNMENT METHOD ü self-aligning (spherical), allowing misalignment of the rings up to 40 ü non-self-aligning (permissible mutual misalignment of the rings from 1 to 8 min.)

CLASSIFICATION OF ROLLING BEARINGS ACCORDING TO THE RELATIONSHIP OF OVERALL DIMENSIONS (outer diameter D, inner diameter d and width B) There are series: extra light, extra light, light wide, medium wide and heavy. In ascending order of outer diameter, there are series of diameters designated by numbers 0, 8, 9, 1, 7, 2, 3, 4 and 5. Similarly, the series of widths (heights for thrust bearings) are designated 7, 8, 9, 0, 1, 2, 3, 4 and 5. Bearings various series They differ from each other mainly in the maximum rotation speed and load capacity.

CLASSIFICATION OF ROLLING BEARINGS BY ACCURACY CLASS The standard establishes the following accuracy classes of bearings (in increasing order): 8, 7, 0, 6 X, 6, 5, 4, 2, T. The accuracy class determines the accuracy of the dimensions and shape of bearing parts. Depending on the accuracy class and additional requirements, three categories of bearings are distinguished: A, B, C. The most common are bearings of normal accuracy class 0. With an increase in the accuracy class, the cost of manufacturing a bearing increases significantly. For example: accuracy class 2 is approximately 10 times more expensive than a bearing of accuracy class 0.

CLASSIFICATION OF ROLLING BEARINGS ACCORDING TO VIBRATION LEVEL ü bearings with normal reduced vibration are distinguished low level vibrations ACCORDING to SPECIAL REQUIREMENTS ü they produce bearings that are heat-resistant, low-noise, corrosion-resistant, non-magnetic, self-lubricating, etc.

APPLICABILITY OF ROLLING BEARINGS Ball 38.6% Tapered roller 24.7% Cylindrical roller 8.9% Spherical roller 5.7% Needle 5.7% Others (instrument, precision, etc.) 16.4% TOTAL 100%

DAMAGE TO ROLLING BEARINGS 1. Fatigue spalling of working surfaces (on the raceways of the most stressed rings, due to the action of alternating stresses, microcracks appear, which are wedged by the lubricant penetrating into them, which leads to spalling). 2. Destruction of rolling bodies. 3. Wear of rings and rolling elements. 4. Formation of dents on working surfaces (brinelling) under dynamic loads, static loads, without rotation. The risk of dent formation is significant in transport vehicles where high dynamic loads and significant non-rotating loads are possible. 5. Destruction of separators.

EXAMPLES OF DAMAGE TO BEARING RINGS a, b – splitting of the outer ring of ball and roller bearings, respectively; c – chipping of the working surface of the inner ring

DISTRIBUTION OF REJECTED ROLLING BEARINGS OF TRACTORS BY TYPE OF DAMAGE Types of damage (rejection sign) Frequency of occurrence of rejection sign, % Increase in clearances above the limit values ​​of violation of fit density 65... 76 Violation of fit density 17... 21 Microscopic damage to working surfaces of tracks and rolling elements 4... 11 Breakage of parts bearings 5… 9

CALCULATION CRITERIA FOR ROLLING BEARINGS The main reasons for failure of rolling bearings are: plastic deformation under static loading and fatigue spalling under the influence of variable loads. Depending on the operating conditions, the calculation (selection) of bearings for a given service life is carried out according to static load capacity (criterion of maximum contact stresses) and dynamic load capacity (fatigue chipping criterion). Calculations based on wear resistance criteria were not found wide application due to the complexity of insufficient data required. And

CALCULATION (SELECTION) OF ROLLING BEARINGS BY STATIC LOAD CAPACITY (at n ≤ 1 rpm) P 0 ≤ C 0, where C 0 – static load capacity; P 0 – equivalent static load The static load capacity of bearings is such a radial (axial) load that causes a total residual deformation of the rolling elements and raceway equal to 0.0001 of the diameter of the rolling element. Equivalent static load: P 0 = X 0 Fr + Y 0 Fa, but not less than P 0 = Fr where X 0, Y 0 are the coefficients of radial Fr and axial Fa static loads

SELECTION OF ROLLING BEARINGS BY DYNAMIC LOAD CAPACITY FOR THE REQUIRED RESOURCE Dynamic load capacity C is the radial (axial) load that the bearing can withstand with a 90% probability without damage for one million revolutions of the inner ring. The service life of a rolling bearing is the number of revolutions that one of the rings will make relative to the other before signs of fatigue appear in the material of the rings or rolling elements. Bearing life is expressed in millions of revolutions L or in hours Lh = 106 L / (60 n), where n is the bearing rotation speed, min-1 Fatigue curve equation Fr L 1/p = C or L = (C / Fr)p p = 3 - for ball bearings p = 3, 33 - for roller bearings Lh

DETERMINATION OF THE BASIC DESIGN LIFE The basic design life L 10 in millions of revolutions, corresponding to 90% reliability, is determined for bearings made of conventional materials using conventional technology and operating under normal conditions, according to the formula: L 10 = (C / P)p where P – equivalent dynamic load, taking into account loading conditions and bearing design For radial and angular contact bearings For radial thrust bearings where Fr and Fa are radial and axial loads, respectively; X and Y – coefficients of radial and axial dynamic load; V – ring rotation coefficient, V = 1 when the inner ring rotates, V = 1, 2 when the outer ring rotates. For spherical bearings always V = 1. CT - temperature coefficient, KB - load dynamic coefficient.

DETERMINATION OF BEARING LIFE FOR SPECIFIC OPERATING CONDITIONS Lna = a 1 a 23 (C / P)p where a 1 is the reliability factor; a 23 = a 2 a 3 ; a 2 – coefficient taking into account the properties of the material; a 3 – coefficient taking into account lubrication and operating conditions of the bearing. Durability Lna L 10 a La L 4 a L 3 a L 2 a L 1 a Reliability, % 90 95 96 97 98 99 Durability coefficient a 1 1 0. 62 0. 53 0. 44 0. 33 0. 21 Coefficient values ​​a 23 Conditions of use Bearing type I II III Ball bearings, except spherical 0, 7… 0, 8 1, 0 1, 2 Cylindrical roller bearings and spherical ball bearings 0, 5… 0, 6 0. 8 1… 1, 2 Tapered roller bearings 0, 6 … 0, 7 0, 9 1, 1… 1, 3 Double-row spherical radial roller bearings 0, 3… 0, 4 0, 6 0. 8

CONDITIONS FOR USE OF BEARINGS I – normal conditions bearing applications; II – characterized by the presence of a hydrodynamic film of oil between the contacting surfaces and the absence of distortions in the assembly; III – rings and rolling elements are made of electroslag or vacuum melted steel, other conditions correspond to II.

LOAD DISTRIBUTION AMONG THE ROLLING BODIES b a c a – on a bearing with zero radial clearance; b – with normal radial clearance; c – on a bearing with the same clearance, but under the influence of both radial and axial forces. Under axial loading (c), the radial clearance in the bearing decreases and some equalization of the forces on the rolling elements created by the load Fr occurs. A certain axial load on a bearing has a positive effect on its life. To take into account this influence, the axial loading coefficient e is introduced - the limiting ratio At e, X = 1, Y = 0. At > e, X 1, Y > 0.

FEATURES OF CALCULATION OF ANGULAR CONTACT BEARINGS The calculations take into account axial forces arising from the radial load Fr due to the inclination of the contact pads to the axis of rotation of the bearing where e’ is the minimum axial load coefficient

DETERMINATION OF RESULTING AXIAL FORCES ON SUPPORTS Loading scheme Force ratio Resulting axial forces The resulting axial load on the fixing support is equal to the sum of the external axial forces. The resulting axial load on the other support is equal to its own component

STRUCTURES OF A SHAFT WITH TWO angular contact bearings IN A FIXING SUPPORT a b a and b – worm shaft with a fixing support on angular contact ball bearings and on angular contact roller bearings, respectively.

SHAFT STRUCTURES WITH TWO FLOATING SUPPORTS a b a – shaft mounted on radial spherical ball bearings; b – shaft mounted on radial roller bearings.

Src="http://present5.com/presentation/3/50410152_192278346.pdf-img/50410152_192278346.pdf-38.jpg" alt="Lubricating bearings with liquid oils: - by dipping; - by splashing (v>3 m/s); - oil mist (v>7"> Смазка подшипников Жидкими маслами: - окунанием; - разбрызгиванием (v>3 м/с); - масляным туманом (v>7 м/с); - капельная; - циркуляционная. Пластичные смазки. Твердые смазки!}

SEQUENCE OF SELECTION OF ROLLING BEARINGS 1. Assign the bearing type and installation diagram 2. Assign the accuracy class of the bearing 3. Select the standard size of the bearing from a number of standard ones, based on the diameter of the shaft 4. Specify the standard size of the bearing taking into account the required resource.

SLIDING SUPPORTS A plain bearing is a support in which the bearing surface of the shaft (trunnion) slides on the surface of the liner (bearing) Angular contact plain bearing Fa Radial plain bearing Thrust plain bearing

ADVANTAGES AND DISADVANTAGES OF SLIDING BEARINGS ADVANTAGES operability at very high speeds ü small dimensions in the radial direction ü maintaining operability in special conditions (in aggressive environments, water, with contaminated lubricant, in the absence of lubrication) ü noiselessness ü vibration damping well ü lighter and easier to manufacture ü capable of operating virtually without wear in liquid and gas lubrication modes DISADVANTAGES ü large friction losses for bearings operating in conditions of boundary and semi-fluid friction ü significant dimensions in the axial direction ü comparative complexity of the design and high lubrication requirements for bearings operating in liquid conditions friction ü interchangeability is not ensured, there is no standardization ü the need to use non-ferrous metals

Application examples (separators, centrifuges, gas turbines, grinding machines, water pumps, ship propellers, internal combustion engines, etc.).

REQUIREMENTS FOR BEARING MATERIALS AND TURNIONS BEARING MATERIALS MUST HAVE: Ø low coefficient of friction Ø high wear resistance and fatigue resistance Ø good thermal conductivity Ø wearability Ø oil wettability Ø corrosion resistance Ø machinability Ø low coefficient of linear expansion Ø low cost Applicable a large number of various anti-friction materials. Trunnions (usually steel) Ø must have high hardness and a ground or polished surface.

BEARING ANTI-FRICTION MATERIALS STEEL babbitt bronzes zinc-based alloys aluminum-based alloys anti-friction cast irons METAL-NON-METAL-CERAMIC bronze-graphite iron-graphite plastics wood plastics rubber graphite materials

EXAMPLES OF SLIDING BEARINGS Sheet rolling mill bearing with a wood liner: 1 – bearing housing; 2 – liner made of pressed wood; 3 – side plates Polyamide bearing: 1 – metal bushing; 2 – polyamide tube; 3 – gap; 4 – elastic rings Rubber liner made of material based on thermosetting reinforced rubber of cold vulcanization, saturated with graphite or molybdenum dusylphide.

DESIGN DIAGRAMS OF VIBRATION-RESISTANT BEARINGS a – lemon-shaped bore of liners; b – assembly with mutual displacement of liners.

OPERATING MODES OF SLIDING BEARINGS The most important operational characteristics of sliding bearings are load-bearing capacity and friction losses. 1 – area of ​​boundary friction. Corresponds to high loads, low sliding speeds, f = 0.1... 0.2; 2 – area of ​​semi-fluid friction, the rubbing surfaces partially touch each other; 3 – area of ​​liquid friction, the rubbing surfaces do not touch each other.

HYDROSTATIC BEARING DIAGRAM 1 – throttles (metering hole); 2 – pockets in liners. The throttle approximately halves the oil pressure entering the pocket, which ensures the stability of the journal in the bearing

TYPES OF DAMAGE AND PERFORMANCE CRITERIA FOR SLIDING BEARINGS DAMAGES: Ø wear of working surfaces (the main cause of failure) Ø seizing of working surfaces Ø fatigue failure under cyclically acting loads (shock, vibration machines) Ø melting of the liner filling Ø jamming of the shaft in the bearing PERFORMANCE CRITERIA Ø wear resistance Ø resistance to fatigue of antifriction material under variable load Ø heat resistance Ø vibration resistance

CHECKING A BEARING FOR HEAT RESISTANCE CONDITIONS It is assumed that all the work of friction forces on rubbing surfaces is converted into heat. In this case, the specific work of friction forces should not exceed a certain limit. At steady motion f, heat resistance will be ensured at = const condition

CHECKING THE BEARING FOR HEAT RESISTANCE CONDITION It is believed that basic work friction forces are the same for all points of the supporting surface of the heel. This hypothesis assumes a sharply uneven distribution of pressure on the supporting surface of the heel with a significant increase in the center. The use of ring heels allows for uniform pressure distribution. provide more

For the transmission of rotational motion, the most typical typical parts and assembly units of machines are shafts, axles, axles, shaft and axle supports (bearings) and couplings (Fig. 37, a - d).

Rice. 37.
Shafts, axles and supports:
a - shaft on supports; b - one-piece sliding bearing, c, d - detachable sliding bearing; 1 - axle-spike; 2 - support (bearing), 3 - pulley, 4 - mounting journal, 5 - support (bearing), 6 - gear wheel, 7 - pin-neck, 8 - axle, 9 - block

Shafts are machine parts designed to transmit torque (power) and carry parts such as pulleys, gears, couplings, flywheels. Shafts can have different locations: horizontal, vertical, inclined. During operation, the shafts are subjected to torsion, bending, transverse and longitudinal loads. Shafts can be cylindrical, smooth, hollow, stepped, cranked, cranked and compound. When the shaft of a machine or mechanism is located in relation to the engine shaft in such a way that it is impossible to connect them with rigid gears, flexible wire shafts are used, for example, a remote control and monitoring drive.

Axles are machine parts that serve only as a support for rotating parts (they do not transmit torque). Axes can be stationary, when the rotating parts are freely mounted, or movable, when the parts are fixed and rotate together with the axle. The shape of the axes is cylindrical (straight or stepped).

Trunnions are the supporting ends of the shaft. Depending on the position on the shaft and the direction of the load, the axles are divided into tenons, necks and heels.

The tenon and neck take a radial load, the heel - an axial load. The spike is located at the end of the shaft or axle and no torque is transmitted through it. The neck is placed on areas of the shaft subject to torque.

The spines and necks have a cylindrical (less often conical or spherical) shape. The heel is the end part of the axle or shaft.

Supports in machines are the stationary parts on which the rotating shaft and axle rest. Depending on the direction of the applied load, supports are divided into bearings and thrust bearings.

Bearings take radial load, and thrust bearings take axial load. For combined loads, angular contact supports are used. Depending on the type of friction, sliding bearings and rolling bearings are distinguished.