Shafts are designed to attach parts to them (gears, worms, sprockets, pulleys, coupling halves, etc.) and transmit torque. Axes serve only to support rotating parts of mechanisms and, unlike shafts, do not transmit torque. The axes can be rotating or stationary.

According to the type of geometric axis, shafts are divided into straight, cranked and flexible. Straight shafts are most widely used (Fig. 4.68, A – V). Crankshafts (Fig. 4.68, d) are used only in piston machines to convert rotational motion into linear motion and vice versa (internal combustion engines, pumps, compressors). Flexible shafts with an arbitrary shape of the geometric axis are used to transmit rotation in mechanisms whose components change their position during operation, for example, remote control devices, dental drills, etc. Crankshafts and flexible shafts are classified as special-purpose parts and are not covered in the “Machine Parts” course are being considered.

Straight shafts are divided into smooth according to the shape of the outer surface (see Fig. 4.68, A) and stepped or shaped (see Fig. 4.68, b, O). The smooth shafts along the entire length have the same memorial size, and the corresponding landings various parts are provided by maximum deviations. In power mechanisms, smooth shafts have limited use. They are mainly used in transmissions to transmit torque only. Greater use

Rice. 4.68

I received omi in unloaded small-sized kinematic mechanisms.

Stepped shafts are less technologically advanced to manufacture, but more convenient to assemble, especially complex multi-stage mechanisms. Each part passes freely into its place, and on one side its axial fixation is ensured. In addition, the stepped shaft has less mass, since its shape is close to that of a beam of equal bending resistance. Hollow shafts (see Fig. 4.68, V) more expensive to manufacture than solid ones, and they are used with strict requirements for the mass of the structure (for example, mechanisms of aviation and space technology). When the ratio of the inner diameter of the shaft to the outer d/D= 0.6÷0.7 its mass is reduced by 40–50%, and the bending moment of the section W – only by 15–25%, which does not cause sharp decline strength. Usually taken d/D < 0,75, что связано с необходимостью выполнения шпоночных пазов, шлицев, резьбы. Применяют полые валы также тогда, когда через вал пропускают другую деталь, подводят смазочный материал и пр.

The design of the stepped shaft is determined by the number and design of the parts that are placed on it, the location of the supports, and the assembly conditions. Individual elements can be distinguished on the shaft: end sections; transition areas between adjacent steps of different diameters; seating locations for bearings, seals and torque-transmitting parts.

The input and output shafts of the transmission mechanisms must have cantilever sections for installing pulleys, sprockets, gears, and coupling halves. The end sections are made cylindrical, less often conical, the shape and dimensions of which are determined by the standards. Cylindrical ones are easier to manufacture, while conical ones (with a taper of 1:10) provide high accuracy of basing and centering of mating parts, ease of assembly and disassembly.

In places where the shaft diameter changes, a smooth transition is made - a fillet of constant radius (Fig. 4.69, A). To reduce stress concentration, the difference between the diameters of the shaft steps should be minimal, and the fillet radius should be maximum. Attitude r/d take at least 0.1. In order to ensure that the part mated to the shaft rests along the plane of the shoulder, the radius of the fillet must be less than the leg of the part chamfer /, and the height of the shoulder t> 2/. When transmitting large axial forces, the height of the ledge is selected from the condition of the crushing strength of the end surface, and the thickness of the shoulder is selected from the condition of ensuring shear strength. The height of the shoulder (or shoulder) for supporting the inner ring of the bearing must allow the bearing to be removed during dismantling. If at the end section of the shaft the key has a tight connection with the shaft, the height of the shoulder t must be greater than the height of the key protruding from the shaft so that the bearing can be installed in its place without removing the key. Tolerances for runout of the thrust collars of the shafts are assigned in the range of 0.01–0.06 mm.

One of the ways to increase the fatigue strength of the shaft is to overlap the fillet (Fig. 4.69, b), which is used when installing parts that have a small radius of curvature or chamfer at the entrance. Axial fixation of the part is carried out using an intermediate ring 1, which allows you to increase the fillet radius r. Sometimes, to increase the radius, a fillet with an undercut is used (Fig. 4.69, c), while the length of the cylindrical part of the shaft decreases.

If it is necessary to grind the seats on the shaft adjacent to the shoulder, provide grooves for the exit of the grinding wheel (Fig. 4.69, G). For small-diameter shafts, such grooves reduce resistance to bending and torsion, so grinding the seating surfaces of such shafts is only possible with high values safety margins P> 2.0÷2.5.

Rice. 4.69

The seating surfaces of axles and shafts are mainly cylindrical. The design of these sections of the bores depends on the type of part being mounted and the method of transmitting torque. The length of the sections is taken to be mm less than the length of the hub to ensure axial fixation of the part. Surface roughness () is assigned depending on the nature of the mating, quality, type of mounted part, etc.

Lead-in chamfers are made at the ends of the shafts or intermediate sections to facilitate assembly and prevent chipping of the edges and cutting the assembler's hands. The chamfer dimensions c are assigned depending on the shaft diameter mm at mm; mm at mm and mm at mm.

The supporting surfaces of the shaft under the bearings when receiving a radial load are called trunnions or necks for intermediate supports. These sections are cylindrical for rolling bearings, but may have conical or spherical journals for plain bearings. The landing diameters for rolling bearings are selected from the standard range of diameters for the holes of rolling bearings. When perceiving axial loads, these sections of the shafts are called heels. The roughness of the supporting surfaces for bearings is determined depending on the nature of the interface between the bearing and the shaft, the diameter of the journal and the accuracy class of the bearing. For bearings of zero accuracy class, the roughness of the seats is microns, the ends of the shoulders are microns; for bearings of higher accuracy classes Ra equal to 0.63 and 1.25 µm, respectively. Deviations from the roundness and cylindricity of the landing sites should not exceed 0.5 tolerances per diameter, and for bearings of accuracy classes 5.4 and 2 - no more than 0.003–0.018 mm.

The material of the shafts and axles are carbon and alloy steels, which have high strength, the ability to be surface and volumetrically hardened (to increase fatigue strength and wear resistance) and good machinability. The shaft material is selected taking into account the operating conditions of the mechanism. In lightly loaded mechanisms, shafts that are not subjected to heat treatment are made of carbon steels 20, 45A, 50, etc. For medium and heavily loaded shafts, alloy steels 40X, 40X11, 40X112MA, 30KhGSA, etc. are used. Shafts made of alloy steels are subjected to improvement, hardening with high vacation; To increase wear resistance, individual sections of the shafts are subjected to high-frequency surface hardening. The journals of the axles and axles for the sliding bearings of mechanisms with a long service life are cemented to increase wear resistance. The choice of the type of heat treatment is carried out in accordance with the grade of steel (cemented or allowing nitriding). To increase wear resistance, chromium-nickel steels are used or shaft journals are chrome-plated, and the service life increases by 3–5 times.

The seats of highly loaded shafts and axles are ground after turning. Under alternating loading, surface irregularities act as stress microconcentrators. Grinding and polishing reduce the amount of unevenness and increase the longevity of the shaft. High-stress shafts are ground over the entire surface.

The calculation of shafts is carried out in three stages.

In the absence of data on the linear dimensions of the shaft and, accordingly, on bending moments, at the first stage, the approximate value of the shaft diameter in the most loaded section is determined. From the condition of the torsional strength of the shaft we have

Where T - torque transmitted by the shaft, N mm; [τ] – permissible torsional stress, MPa (for steel shafts take [τ] = 12÷20 MPa).

At the second stage, in accordance with the obtained diameter, the shaft is given a structural shape that meets the kinematic diagram and reflects the requirements for manufacturability and assembly. As a result, all shaft dimensions are established.

At the third stage, a verification calculation of the shaft is performed. The main criterion for rotating shafts and axles is cyclic strength, since forces that are constant in value and direction cause alternating stresses in them. Fixed axes and some shafts are calculated for static strength under the action of large starting torques. Insufficient rigidity of shafts negatively affects the operation of associated joints, bearings, gears and other parts; increases wear; reduces the fatigue resistance of parts and connections; reduces the accuracy of mechanisms, etc. Calculation of shaft stiffness is performed in cases where these influences are significant and require mandatory consideration.

Fatigue resistance calculation. In the calculation of the shaft, the following stages can be distinguished: drawing up a design diagram; determination of design loads and construction of diagrams of normal forces, bending and torsional moments; calculation of stresses and safety margins in dangerous sections of the shaft.

For calculations, rotating shafts and axles are represented in the form of a beam on hinged supports. The location of the supports depends on the type of bearing. When installing a shaft in radial ball or roller bearings, the support points are considered to be the middle of the width of each bearing (Fig. 4.70, a, b). When installing the shaft in angular contact bearings, the supports are located offset from the end by the amount A depending on the contact angle. For ball bearings (Fig. 4.70, V), and for conical roller (Fig. 4.70, G), where is the axial load coefficient, depending on the contact angle (Table 4.16). When installing two bearings in a support, the conditional support is placed at a distance of one third from the middle of the inner bearing (Fig. 4.70, ∂). U shafts rotating in plain bearings, conventional

Rice. 4.70

the hinge support is located at a distance of (0.254-0.3)/ from the end of the bearing (Fig. 4.70, e).

Loads acting on the shaft are transmitted from associated parts, such as gears and worm wheels,

Table 4.16

bearing	contact, α°		Single row bearings				Double row bearings
Ball radial
Angular contact balls
Roller conical

pulleys, sprockets, etc. They are determined by the corresponding dependencies of gear calculations or experimentally. In shaft calculations, these loads, distributed over the contact surface, are replaced by concentrated equivalent forces and applied in the middle of the part hub. The found loads are transferred to the shaft axis, and the corresponding diagrams are constructed.

When calculating fatigue, the sections with stress concentrators are considered: fillet transitions, splines, keyways, transverse holes, threads, in which high bending and torque moments act. In shafts of complex design, it is sometimes difficult to single out one dangerous section and then the calculation is carried out for several sections. For each of the design sections, safety factors are determined and compared with the permissible value. To ensure reliable operation there must be. Strength is estimated using the formula

where and are safety margins for normal and tangential stresses:

where and are the endurance limits of the standard sample under a symmetrical cycle of stress changes; and are the amplitude stresses of normal and tangential stress cycles; and are the average stresses of the cycles; coefficients for reducing the fatigue limits of a part; and – coefficients of sensitivity of the material to the asymmetry of the stress cycle.

For carbon articles for alloy steels. Reduction factor for the fatigue limit of the part:

When calculating bending

When calculating torsion

where and are the effective stress concentration coefficients (depending on the type of stress concentrator); and – coefficients of influence of part dimensions; – coefficient taking into account the increase in the endurance limit during surface hardening; and – roughness influence coefficients.

Effective coefficients and stress concentrations for steel during bending and torsion of shafts at the location of the annular groove are found from Table. 4.17; in a stepped transition with a fillet - according to table. 4.18; when bending and torsion of shafts with splines, keyways, threads and transverse holes - but table. 4.19.

Coefficients – and are given in table. 4.20; coefficient – ​​in table. 4.21.

Values ​​depending on roughness parameters Ra And Rz are shown in Fig. 4.71. The value is determined from the relation

Table 4.17

Effective concentration factors

Rice. 4.71

Table 4.18

Effective coffee concentrations

Gears, pulleys, sprockets and other rotating machine parts are mounted on shafts or axles.

Shaft designed to transmit torque along its axis, to support the parts located on it and to perceive the forces acting on them. During operation, the shaft experiences bend And torsion, and in some cases - additional stretching or compression.

Axis only supports the parts installed on it and perceives the forces acting on them. Unlike a shaft, an axle does not transmit torque and, therefore, does not experience torsion. Axles can be motionlessmi or can rotate together with the parts mounted on them.

According to the shape of the geometric axis shafts are divided into straight(Fig.2) And indirect- cranked and eccentric. Indirect shafts are classified as special parts.

axles, usually, outcastsell straight(see Fig. 1). In design, straight shafts and axles differ little from each other.

Rice. 1. Trolley axle

Straight shafts and axles can be smooth or stufoamy(see Fig. 2).

R is. 2. Straight stepped shaft:

1 - thorn; 2 - neck; 3 - bearing; 4 - a ring with a transverse groove to accommodate the bearing puller rods

The stepped shape promotes equal tension in individual sections and simplifies the manufacture and installation of parts on the shaft.

According to cross-sectional shape shafts and axles are solid and hollow(with axial hole). Hollow shafts are used to reduce weight or to be placed inside another part.

According to the external outline of the cross section shafts are divided into splined and keyed, having a spline profile or a profile with a keyway along a certain length.

2. Structural elements. Shaft and axle materials

Trunnions- supporting sections of the shaft or axle. They are divided into spikes, necks and heels.

Sh Ipom called a journal located at the end of a shaft or axis and transmitting predominantly radial force (see Fig. 2). Neck called a journal in the middle part of a shaft or axle. The supports for the tenons and necks of the shafts areunderthorns. Spikes and necks can be shaped cylindersical, conical or spherical. In most cases it is used cylindrical pins.

Fig.3. Heels

Fifth called a trunnion that transmits axial force (Fig. 3). They serve as supports for the heelsthrust bearings. Heels there are different shapes solidmi (Fig. 3,A), ringyou (Fig. 3,b) And greebenched(Fig. 3, V). Comb heels are now rarely used.

Landing surfaces shafts and axles under the hubs mounted parts are performed cylindrical and conicalkimi(see Fig. 2). When making interference fits, the diameter of these surfaces is larger than the diameter of adjacent areas for ease of pressing and reducing stress concentration (see Fig. 2). The diameters of the seating surfaces and the diameters for sliding bearings are selected from a number of normal linear dimensions; the diameters for rolling bearings are selected according to bearing standards.

The conical ends of the shafts (see Fig. 2) are made withtaper 1:10. They are used to facilitate installation parts installed on the shaft.

Transitional areas shafts and axles between two stages of different diameters:

A)with groove with rounded to exit the grinding wheel (Fig. 4, A);

b)with a fillet of constant radius, rice. 4, b(fillet is the surface of a smooth transition from a section of a smaller section to a larger one);

V ) with fillet of variable radius(rice. 4, V).

Rice. 4. Transition sections of the shaft

Transition sections are voltage concentratorsGrooms. An effective way to reduce stress concentration in transition areas is promotion

pliability by making relief grooves (Fig. 5, A), increasing fillet radii, making holes in steps of larger diameter (Fig. 5, b). Strain hardening (atriveting) fillets increases the load-bearing capacityproperty of shafts and axles.

Rice. 5.Methods of increasing the nominal strength of shafts

Shaft and axle materialsmust be goodsho to be processed, to be durable andhave a high elastic modulus.This The requirements are most fully met by carbon and alloy steels, from which shafts and axles are mainly made. For shafts and axles without hardening heat treatment, steels St5, St6 are used; for shafts with heat treatment - steel 45, 40Х. High-speed shafts operating in plain bearings are made of steel 20, 20Х, 12ХНЗА.The journals of these shafts are cementedto increase wear resistance.

Shafts and axles are processed on lathes, followed by grinding journals and seating surfaces.

Shafts are often used. Let's figure out what a shaft is called, how it differs from an axle, what the shaft part consists of, its classification and the materials used in the production of shafts.

Definition, design features

Val - a mechanism part made of, having a cross-section of a certain shape and transmitting torque to other elements, causing them to rotate.

The axis differs from the shaft in that it serves only for their support. If axes are divided into moving and static, then the shafts are always rotating. The geometric shape of the axis can only be straight.

The shaft consists of the following sections:

1. Support.
2. Intermediate.
3. Terminal.

The annular thickening is called a collar. The intermediate part between different diameters for fixing the parts to be worn is called the shoulder.

The area where the shaft diameter changes is called the fillet. In order to increase strength, the curvature of the fillet changes smoothly. There are 2 types of curvature: constant and variable. Increasing the fillet curvature and making special holes increases the reliability of the shaft by one tenth.

Depending on the distribution of loads, reflected in special graphs (diagrams), the length and shape of the shaft are determined. This parameter also depends on the assembly conditions and manufacturing method.

The dimensions of the seats for rotating elements located at the ends of the shafts are strictly standardized according to GOST standards.

Materials

Depending on the external forces to which the shaft part is subjected during operation is carried out for its manufacture.

For this purpose, they are used with a high carbon content, as they have improved mechanical characteristics and wear resistance. These parts are obtained by rolling.

The bulk of the shafts are made from alloy steel grade 45X, with an average carbon content. For shafts subjected to high stresses, steels 40ХН, 40ХНГМА, 30ХГТ and others are used, which are subjected to a hardening process with high tempering.

In addition, for heavy crankshafts, the material used is high-strength cast iron, formed by interspersing spherical carbon inclusions into a metal lattice and containing Mg, Ca, Se, Y.

Shaft classification

By purpose:

1. Gear shafts on which parts of the gear mechanism are located (gears, couplings, pulleys).
2. The indigenous ones who carry the other parts.

According to the shape of the axis:

1. Direct.
2. Crank.
3. Flexible.

Direct lines are divided into:

1. Smooth.
2. Stepped.
3. Worm type.
4. Flanged.
5. Cardan shafts.

According to the sectional shape:

1. Smooth.
2. Hollow.
3. Splined.

Production

There are several manufacturing stages:

1. Carrying out design and engineering work and calculations using special software.
2. Selection and purchase of the necessary material that meets the required characteristics. Equipping with additional production equipment, if necessary.
3. Molding.
4. Welding and grinding.
5. Dynamic balancing.
6. Application of a protective coating.

The first stage is usually carried out in the design office. Upon completion of the work it is issued project documentation, containing calculations and processed data, in strict accordance with which the production of this type of part will be carried out.

At the second stage, the selection of workpiece material that meets the required performance characteristics is made and the production is re-equipped with technological equipment.

The third stage is performed using turning equipment, where the workpiece is machined and acquires its geometry and size. In this case, all surfaces of the workpiece are subject to change.

At the fourth stage, fastening is carried out individual elements workpieces by welding them and making the necessary holes and grooves. Then, using modern methods measurements, grinding and finishing to their final dimensions.

At the next stage, the balancing of the parts is checked by subjecting them to dynamic tests, since the completeness of the transfer of rotational energy to other elements of the mechanism depends on this. Improper balancing can lead to malfunction of the equipment on which the shaft will be installed.

The last - sixth stage is characterized by applying a special layer to its surface. The choice of method and type of coating depends on operating conditions.

A thin layer of rubber on the surface of the shafts protects against the action of reaction media. Corrosion resistance is ensured by electric arc metal spraying of these parts.

The chrome plating method is used to increase wear resistance and reduce friction of this type of part.

The shaft part is widely used in many areas of industry: automotive, machine tool, railway, textile, woodworking industries.

Having examined in detail the questions posed above, we can conclude:

1. The shaft differs from the axis in its functionality and geometry.
2. The shaft consists of 3 sections (trunnion, neck, tenon).
3. There are different types of shaft classification according to purpose and shape.
4. The material for the part is alloy steel of various grades, less often with spherical inclusions of carbon.
5. The manufacture of a shaft includes several stages and requires special knowledge and significant expenditure of energy resources.
6. To increase the operating time of the shafts at the production stage, their surface is coated with special materials.
7. The shaft is widely used in many mechanisms in various fields of human activity.

APPLIED MECHANICS AND

DESIGN BASICS

Lecture 8

SHAFT AND AXLES

A.M. SINOTIN

Department of Technology and Production Automation

Shafts and axles General information

Gears, pulleys, sprockets and other rotating machine parts are mounted on shafts or axles.

Shaft designed to support parts sitting on it and to transmit torque. During operation, the shaft experiences bending and torsion, and in some cases additional tension and compression.

Axis- a part intended only to support the parts sitting on it. Unlike a shaft, an axle does not transmit torque and therefore does not experience torsion. The axes can be stationary or rotate together with the parts mounted on them.

Variety of shafts and axles

According to their geometric shape, shafts are divided into straight (Figure 1), cranked and flexible.

1 – spike; 2 – neck; 3 – bearing

Figure 1 – Straight stepped shaft

Crankshafts and flexible shafts are special parts and are not covered in this course. Axles are usually made straight. In design, straight shafts and axles differ little from each other.

The length of straight shafts and axles can be smooth or stepped. The formation of steps is associated with different tensions of individual sections, as well as manufacturing conditions and ease of assembly.

According to the type of section, shafts and axles can be solid or hollow. The hollow section is used to reduce weight or to be placed inside another part.

Structural elements of shafts and axles

1 Trunnions. The sections of the shaft or axis lying in the supports are called axles. They are divided into spines, necks and heels.

Thorn called a journal, located at the end of a shaft or axis and transmitting predominantly radial load (Fig. 1).

Figure 2 – Heels

Neck called a journal located in the middle part of the shaft or axis. Bearings serve as supports for the necks.

Spikes and necks can be cylindrical, conical or spherical in shape. In most cases, cylindrical pins are used (Fig. 1).

Fifth called a journal that transmits axial load (Figure 2). Thrust bearings serve as supports for the heels. The shape of the heels can be solid (Figure 2, a), ring (Figure 2, b) and comb (Figure 2, c). Comb heels are rarely used.

2 Landing surfaces. The seating surfaces of shafts and axles for the hubs of mounted parts are cylindrical (Figure 1) and less often conical. When pressing fits, the diameter of these surfaces is taken to be approximately 5% larger than the diameter of adjacent areas for ease of pressing (Figure 1). The diameters of the seating surfaces are selected in accordance with GOST 6336-69, and the diameters for rolling bearings are selected in accordance with GOST standards for bearings.

3 Transitional areas. The transition sections between two stages of shafts or axles perform:

With a rounded groove for the exit of the grinding wheel in accordance with GOST 8820-69 (Figure 3, a). These grooves increase stress concentration and are therefore recommended at end sections where bending moments are small;

Figure 3 – Transition sections of the shaft

with a fillet * of constant radius according to GOST 10948-64 (Figure 3, b);

With a fillet of variable radius (Figure 3, c), which helps reduce stress concentration and is therefore used on heavily loaded areas of shafts and axles.

Effective means for reducing stress concentration in transition areas are turning relief grooves (Figure 4, a), increasing the fillet radii, and drilling in large diameter steps (Figure 4, b).

Figure 4 – Methods for increasing the fatigue strength of shafts

PURPOSE AND CLASSIFICATION OF SHAFT.SHAFT AND AXLES

Rotating machine parts (gears, pulleys, sprockets, etc.) are placed on shafts and axles. The shafts are designed to transmit torque along their axis. The forces that arise during the transmission of torque cause torsional and bending stresses, and sometimes tensile or compressive stresses.

The axles do not transmit torque; The forces acting in them cause only bending stresses (minor torques from friction forces are not taken into account). The shafts rotate in bearings. The axes can be rotating or fixed.

According to their purpose, they distinguish between gear shafts and main shafts, which carry the load not only from gear parts, but also from the working parts of machines (disks, cutters, drums, etc.).

According to their design, shafts can be divided into straight, cranked and flexible (Fig. 4.1). Straight shafts of stepped design are widely used. This shape of the shaft is convenient during installation, as it allows you to install the part with interference without damaging adjacent areas and ensure its axial fixation. Shaft shoulders can absorb significant axial loads. However, at the junctions of sections of different diameters, stress concentration occurs, which reduces the strength of the shaft.

To reduce the weight of the shaft and ensure the supply of oil, coolant or air, hollow shafts are used.

A special group includes flexible shafts used to transmit torque between shafts whose axes of rotation are displaced in space.

Agricultural, lifting and transporting and other machines often use transmission shafts, the length of which reaches several meters. They are made composite, connecting using flanges or couplings.

Shaft performance criteria.

The design, dimensions and material of the shaft significantly depend on the criteria that determine its performance. The performance of shafts is characterized mainly by their strength and rigidity, and in some cases, vibration resistance and wear resistance.

Most gear shafts fail due to low fatigue strength. Shaft failures in the stress concentration zone occur due to the action of alternating stresses. For low-speed shafts operating under overloads, the main criterion for performance is static strength. The rigidity of shafts during bending and torsion is determined by the values ​​of deflections, angles of rotation of the elastic line and angles of twist. Elastic movements of shafts negatively affect the operation of gear and worm gears, bearings, couplings and other drive elements, reducing the accuracy of mechanisms, increasing the concentration of loads and wear of parts.

For high-speed shafts, the occurrence of resonance is dangerous - a phenomenon when the frequency of natural oscillations coincides with or is a multiple of the frequency of the disturbing forces. To prevent resonance, vibration resistance calculations are performed. When installing shafts on sliding bearings, the dimensions of the shaft journals are determined from the condition of the wear resistance of the sliding support.

Rice. 4.1 Types of shafts and axles:

a - straight axis; b - stepped solid shaft; in - steppedhollow shaft; g - crankshaft; d - flexible shaft

The shaft construction is carried out in stages.

At the first stage determine the design loads, develop a design diagram of the shaft, and draw moment diagrams. This stage is preceded by a sketch layout of the mechanism, during which the main dimensions of the shaft and the relative position of the parts involved in the transfer of loads are preliminarily determined.

The current loads that are transferred to the shaft from the part (pulley, sprocket, gear, etc.) or from the shaft to the part include:

Forces in the engagement of gear and worm gears;

Loads on the shafts of belt and chain drives;

Loads arising during installation of couplings as a result of inaccurate installation and other errors.

The determination of forces in engagement and loads on the shafts of belt and chain drives is discussed above.

When installed at the ends of the input; output shafts of connecting couplings take into account the radial cantilever load, which causes bending of the shaft. It is recommended to determine this load according to GOST 16162-85.

For input and output shafts of single-stage helical bevel gearboxes and for high-speed shafts of gearboxes of any type, the cantilever load can be approximately calculated using the formula

; (4.1)

for low-speed shafts of two- and three-stage gearboxes, as well as worm gears

; (4.2.)

where T is the torque on the shaft, N.m.

The forces and moments transmitted by the hub to the part are simply assumed to be concentrated and applied in the middle of its length.

When performing the design scheme, the shaft is considered as a hinged beam. The position of the shaft fulcrum depends on the type of bearing (Fig. 4.2).

Rice. 4.2. Shaft support points:

A - on a radial bearing; b — on an angular contact bearing;

V - on two bearings in one support; G - on a plain bearing.

Forces acting in two mutually perpendicular planes (vertical and horizontal) are transferred to points on the shaft axis. Construct diagrams of bending and torque moments in two planes (Fig. 4.3).

The moment from the circumferential force is depicted on the diagram of torques, from the axial force in the vertical plane - in the form of a jump M′ z on the diagram of bending moments. Diagrams are constructed according to the methodology outlined in the course on strength of materials.

Using the diagrams, the total bending moments in any section are determined. So in section 1-1 the greatest total moment

where M z 1 — bending moment in a dangerous section in the ZY plane ; M x1 - bending moment in a dangerous section in the XY plane; M k1 is the bending moment in the plane of action of the cantilever load. By comparing the obtained values, the most dangerous shaft sections are identified.

At the second stage develop the shaft design. The diameter of the outlet section is preliminarily determined by the conditional permissible torsional stress [τ], taking it equal to 15-25 MPa.

Shaft diameter, mm,

If a stepped shaft design is chosen, determine the diameters and lengths of its sections using a calculation diagram or sketch layout (see above)

Rice. 4.3. Shaft loading diagrams. Diagrams of bending and torque moments It is recommended to specify the accepted dimensions according to GOST 6636-69*.

The stepped shape of the shaft is preferable, as it simplifies the assembly of tension joints, prevents damage to areas with surfaces of increased surface finish, and the shape of the shaft approaches an equal-strength beam. However, where sections of different diameters meet, stress concentrations occur, which reduces the strength of the shaft, and when using a rod or forging as a workpiece, the manufacturing technology becomes more complicated and metal consumption increases. To reduce the stress concentration and, consequently, increase the fatigue strength of the shaft, transition sections are most often made with fillets (Fig. 4.4). The fillet radius r and the height of the shoulder (ledge) are selected depending on the shaft diameter d, axial force, dimensions R, c 1 and the shape of the installed part (Table 4.1).

Rice. 4.4. Transitional sections of the shaft in the form of fillets

Table 4.1 Dimensions of fillets, mm. (see Fig. 4.4.)

If the ledge serves for axial fixation of the bearing, then the height h. (Table 4.2) should be less than the thickness of the inner ring of the bearing by an amount t sufficient to accommodate the puller legs during dismantling.

Grooves for the exit of the grinding wheel (Fig. 4.5) cause a higher stress concentration than fillets. Transitions with such grooves are performed with a significant safety margin of the shaft. The dimensions of the grooves are given in Table 4.3.

To eliminate axial clearances, the length of the shaft landing section should be slightly less than the length of the hub of the mounted part. For ease of installation, the section of the shaft for the interference fit must have bevels and chamfers (Fig. 4.6, a, b, Table 4.4).

Rice. 4.5. Grinding wheel outlet grooves:

a, b - for grinding the cylindrical surface of the shaft;

c - for grinding a cylindrical surface and the end of a shoulder

If the shaft section does not have thrust collars, then its diameter is recommended to be 5% less than the landing diameter (Fig. 4.6, c).

The shape of the output section of the shaft (Fig. 4.7) can be cylindrical (GOST 12080-66*) or conical (GOST 12081-72*). The tapered end of the shaft is more difficult to make. However, conical joints have a high load capacity and are easier to assemble and disassemble. Axial force is created by tightening the nut. To do this, a fastening thread is provided at the end of the shank.

Rice. 4.6. Chamfers (a), bevels (b) and transition areas (c)

Rice. 4.7. Output shaft sections: a - cylindrical, b - conical

The shape and dimensions of the keyways on the shaft depend on the type of key and cutting tool. Slots for parallel keys made with a disk cutter cause less stress concentration. However, the fixation of the key here is less reliable, and the groove is longer due to the areas for the cutter to exit (Fig. 4.8). If there are grooves for parallel keys, it is necessary to provide such dimensions for the sections of stepped shafts so that the disassembly of parts occurs without removing the keys, since the keys are installed in the grooves using a press fit and their removal is undesirable.

Therefore, the diameter d 2 of the adjacent landing site is determined taking into account the height hdowels:

where t 2 is the depth of the groove in the hub, mm

Rice. 4.8. Keyways:

a - made with a finger cutter; b—disc cutter.

Designations: l - working length of the key; b—width of the key;

lout - length of the section for the cutter exit; Dfr - diameter of the disk cutter

If this condition cannot be met on the output sections of the shafts, then the keyway is milled “for passage”. When installing several keys on a shaft, they should be placed in the same plane and, if possible, the same width of grooves should be provided, subject to the conditions for the strength of the key connections. This allows you to process grooves without changing the position of the shaft and with one tool.

The dimensions of the teeth of the spline sections are selected taking into account the diameters of the adjacent shaft landing sections. For the cutting tool to exit, the internal diameter d of the teeth of the splined section located between the bearings must be greater than the seat diameter of the bearing. Otherwise, for the exit of the cutter, a section of length l out (Fig. 4.9, Table 4.5).

Using the same principle, threaded sections of shafts are designed for round spline nuts. In sections, grooves are provided for the exit of the thread-cutting tool (Fig. 4.10, Table 4.6) and for the tongue of the multi-jaw lock washer.

Rice. 4.9. Splined shaft sections

Table 4.5. Diameter of cutter for straight splines (see Fig. 4.9)

Table 4.6. Groove sizes different types, mm (see Fig. 4.11.)

Note. For Type I grooves, the bevel radius is r 1= 0.5 mm.

When manufacturing a shaft as one piece with a gear (Fig. 4.11), the shaft material and heat treatment method are selected according to the conditions of the strength of the gear teeth.

For the manufacture of shafts, carbon structural steels 40, 45, 50 and alloy steel 40X hardness are used HB≤ 300. Alloy steels 40KhN, 30KhGSA, 30KhGT and other grades with subsequent hardening by high-frequency heat are used for highly loaded shafts. To increase the wear resistance of the journals, high-speed shafts rotating in plain bearings are made from case-hardening steels 20Х, 12ХНЗА, 18ХГТ or nitriding steel 38Х2МУА. If the dimensions of the shaft are determined by the rigidity conditions, then it is possible

use steel Art. 5, Art. 6. This is allowed if there are no wear surfaces on the shaft (trunnions, splines, etc.), requiring strong, heat-treated steels. Shaped shafts (for example, crankshafts) are made from high-strength and modified cast iron.

The mechanical characteristics of the shafts are indicated in Table 4.7.

At the third stage design engineers perform a test calculation of the shaft, determining the equivalent stress or safety factor in the most dangerous sections.

For shafts operating under short-term overloads, in order to prevent plastic deformations, a test calculation for static strength is performed. Equivalent stress in the dangerous section, MPa,

; (4.6)

where d is the shaft diameter, mm; M—maximum bending moment, N. m; T—maximum torque, N.m.

Permissible stress, MPa,

where σ t is the yield strength, MPa; S T - safety margin for yield strength: S T = 1.2-1.8.

The verification calculation of the axes is performed according to formula (4.6) at T = 0.

For long-term loads, a test calculation for fatigue resistance is performed. Fatigue safety factor

; (4.8)

where S σ ; Sτ - safety factors for bending and torsion stresses, respectively; [S] - permissible safety factor: [S] = 2-2.5.

Safety factor for bending stresses

; (4.9)

Rice. 4.11. The design of the shaft is gears.

Designations: da1 - gear diameter; dB—shaft diameter;

dП - landing diameter of the shaft for the bearing by torsional stress

; (4.10)

where σ -1, -1 are the endurance limits of the shaft material, respectively, during bending and torsion with a symmetrical alternating cycle, MPa (see Table 4.7); K σ D , K D - stress concentration coefficients, taking into account the influence of all factors on fatigue resistance; σ a, D—variable components of the stress (amplitude) cycle, MPa; ψ σ ψ — coefficients characterizing the sensitivity of the material to the asymmetry of the stress cycle (see Table 4.7); σm; m are the constant components of the stress change cycle, MPa.

Components of the bending stress change cycle:

; (4.11)

where M Σ is the total bending moment, N. m; W o - moment of resistance of the shaft section to bending) mm 3; F a - axial force. N; A is the cross-sectional area of ​​the shaft, mm 2: A = nd 2 /4.