Shafts and axles

Plan 1. Purpose. 2. Classification. 3. Structural elements of shafts and axles. 4. Materials and heat treatment. 5. Calculations of shafts and axes.

Purpose

Shafts - parts designed to transmit torque along their axis and to support rotating machine parts. The shaft receives the forces acting on the parts and transmits them to the supports. During operation, the shaft experiences bending and torsion.

Axles designed to support rotating parts, they do not transmit useful torque. The axes do not experience torsion. The axes can be fixed or rotating.

Shaft classification

By purpose:

a) gear shafts, load-bearing parts of gears - couplings, gears, pulleys, sprockets;

b) main shafts of machines;

c) other special shafts that carry the working parts of machines or tools - turbine wheels or disks, cranks, tools, etc.

By design and shape:

a) straight;

b) cranked;

c) flexible.

Straight shafts are divided into:

a) smooth cylindrical;

b) stepped;

c) shafts - gears, shafts - worms;

d) flanged;

d) cardan shafts.

According to cross-sectional shape:

a) smooth, solid section;

b) hollow (to accommodate a coaxial shaft, control parts, oil supply, cooling);

c) splined.

The axes are divided into rotating ones, providing better job bearings, and stationary, requiring the integration of bearings into rotating parts,

Structural elements of shafts and axles

The supporting part of the shaft or axle is called pin. The end pin is called thorn, and the intermediate one – neck.

The annular thickening of the shaft, which forms one whole with it, is called shoulder. The transitional surface from one section to another, which serves to support parts mounted on the shaft, is called shoulder.

To reduce concentration and increase strength, transitions in places where the diameter of the shaft or axis changes are made smooth. curved surface smooth transition from smaller section to larger section is called fillet. Fillets come in constant and variable curvature. The variable radius of curvature of the fillet increases the load-bearing capacity of the shaft by 10%. Fillets with undercuts increase the base length of the hubs.

Increasing the strength of shafts in transition sections is also achieved by removing low-stress material: making relief grooves and drilling holes in large-diameter steps. These measures ensure a more uniform distribution of stresses and reduce stress concentrations

The shape of the shaft along its length is determined by the distribution of loads, i.e. diagrams of bending and torque moments, assembly conditions and manufacturing technology. Transitional sections of shafts between steps of different diameters are often made with a semicircular groove for the exit of the grinding wheel.

The landing ends of shafts intended for installing parts that transmit torque in machines, mechanisms and devices are standardized. GOST establishes the nominal dimensions of cylindrical shafts of two designs (long and short) with diameters from 0.8 to 630 mm, as well as the recommended dimensions of threaded shaft ends. GOST establishes the main dimensions of the conical ends of shafts with a taper of 1:10, also in two designs (long and short) and two types (with external and internal threads) with diameters from 3 to 630 mm.

“To facilitate fitting of parts and to avoid crushing and damage to workers’ hands, the shafts are beveled with chamfers.

Materials and heat treatment

Material selection and heat treatment of shafts and axles is determined by the criteria for their performance.

The main materials for shafts and axles are carbon and alloy steels due to their high mechanical characteristics, the ability to harden and the ease of obtaining cylindrical blanks by rolling.

For most shafts, medium-carbon and alloy steels 45, 40X are used. For high-stress shafts of critical machines, alloy steels 40ХН, 40ХНГМА, 30ХГТ, 30ХГСА, etc. are used. Shafts made of these steels are usually subjected to improvement, hardening with high tempering or surface hardening with high-frequency heating and low tempering.

For the manufacture of shaped shafts - crankshafts, with large flanges and holes - and heavy shafts, along with steel, high-strength cast irons (nodular graphite) and modified cast irons are used.

Calculation of shafts and axes

Shafts experience bending and torsion stresses, axles - only bending.

During operation, the shafts experience significant loads, therefore, to determine the optimal geometric dimensions, it is necessary to perform a set of calculations, including the determination of:

Static strength;

Fatigue strength;

Bending and torsional rigidity.

At high speeds rotation, it is necessary to determine the natural frequencies of the shaft in order to prevent it from entering resonant zones. Long shafts are checked for stability.

The calculation of shafts is carried out in several stages.

To perform the calculation of a shaft, it is necessary to know its design (places of load application, location of supports, etc.) At the same time, developing a shaft design is impossible without at least an approximate estimate of its diameter. In practice, the following procedure for calculating the shaft is usually used:

1. Preliminarily estimate the average diameter based on torsion only at reduced permissible stresses (the bending moment is not yet known, since the location of the supports and the places where the loads are applied are unknown).

Torsional stress

Where Wp is the moment of resistance of the section, mm.

You can also preliminary estimate the diameter of the shaft based on the diameter of the shaft with which it is connected (the shafts transmit the same torque T). For example, if a shaft is connected to the shaft of an electric motor (or other machine), then the diameter of its input end can be taken equal to or close to the diameter of the output end of the electric motor shaft.

2.Basic calculation of the shaft.

After assessing the diameter of the shaft, its design is developed. We take the length of the shaft sections, and, consequently, the arm of application of force from the layout. Let's say we need to calculate the diameter of the shaft on which the helical gear sits. Let's draw a diagram of the shaft loads. For this shaft, taking into account the inclination of the gear teeth and the direction of the moment T, we replace the left support with a hinged-fixed one, and the right one with a hinged-movable one. Design loads are usually considered as concentrated, although actual loads are not concentrated, they are distributed along the length of the hub and the width of the bearing. In our example, the shaft is loaded with forces Ft, Fa. Fr acting in the engagement pole and torque T. The axial force Fa gives a moment in the vertical plane

The main calculation of shafts and axes consists of constructing diagrams of bending moments in the horizontal and vertical planes, constructing diagrams of resulting moments, diagrams of torques, diagrams of equivalent moments, and determining dangerous sections.

Stage 3 calculation- verification calculation consists of determining the safety factor in dangerous sections

- safety factors for normal and tangential stresses

endurance limits of materials.

- effective stress concentration coefficients.

- scale factor (depending on the shaft diameter).

- hardening coefficient. - sensitivity coefficients of the material depend on mechanical characteristics.

- variable voltage components.

- constant components of stress.

Stiffness calculation

Deflection of axles and shafts negatively affects the operation of bearings and gear engagement. Stiffness is characterized by the maximum angle of rotation of the axis or shaft

and deflection The required stiffness is ensured if the actual values and do not exceed permissible limits. At large angles of rotation in sliding bearings, the shaft is pinched (especially with a large length of the bearing and axle), and in rolling bearings the cage may collapse. Large deflections worsen the operating conditions of gears (especially with an asymmetrical gear arrangement).

Allowable values ​​of rotation angles under the gear [

SHAFTS and AXLES PURPOSE Shafts and axles are designed to guide and support rotating parts in space (gears, pulleys, blocks, sprockets, etc.). They differ from each other in terms of working conditions. The AXLE does not transmit torque and only works on bending. It can be rotating or stationary. The SHAFT always rotates and always transmits torque, works mainly on bending and torsion. Some shafts do not support rotating parts and only work in torsion. For example, car drive shafts, flexible shafts in power tool drives, etc.

AXIS Design of a unit with a rotating axis: Design of a unit with a fixed axis: 1 – running wheel; 2 – key; 3 – axis; 4 – tapered roller bearings 1 – rope block; 2 – axis; 3 – locking strips; 4 – block holder

DESIGNS OF WALKING WHEELS OF CRANES b a a – on a fixed axis: 1 – wheel; 2 – axis; 3 – gear b – on a rotating axis

SHAFT The mechanism of movement of the crane with a low-speed transmission shaft: 1 – electric motor; 2 – coupling; 3 – gearbox; 4 – transmission shaft; 5 – brake. Cardan shaft Gearbox shaft

CLASSIFICATION OF SHAFTS According to the shape of the cross sections of the shafts a – cylindrical solid b – cylindrical hollow c – with a keyway d – with splined grooves d – profile

By purpose Ø Gear shafts – bearing gears, pulleys, sprockets and other parts. Ø Main shafts - in addition to gear parts, also carry working parts of machines or tools (turbine disks, chucks of lathes and boring machines, etc.) According to the shape of the geometric axis Ø Straight Ø Crankshafts - used not only for transmitting rotating torque, but also for converting reciprocating motion in rotational Ø Flexible, with a variable shape of the geometric axis. They are used in drives, instruments, dental drills, etc.

SUPPORTING AREAS OF SHAFT Shaft 1 has a large number of supports called bearings 2. The part of the shaft covered by the support is called a journal. The end journals are called tenons 3, and the intermediate journals 4.

REQUIREMENTS FOR MATERIALS FOR MANUFACTURING SHAFT ü High strength characteristics. ü Low sensitivity to stress concentration ü Ability to be subjected to thermal and chemical-thermal treatment ü Good machinability

MATERIALS AND HEAT TREATMENT OF SHAFTS Purpose of the shaft Steel grade Type of heat treatment Lightly loaded shafts and axles, the diameters of which are mainly determined by rigidity Carbon steels: St. 3, Art. 4, Art. 5 Without heat treatment Shafts and axles with increased requirements for the load-bearing capacity of splines and axles Medium carbon and alloy steels: 35, 40, 45, 40 X, 40 N, etc. Improvement to hardness H = 250... 320 HB Shafts and axes with the requirement of high wear resistance : - sliding supports; - gear shaft Low-carbon structural steels: - quality 15, 20; - alloyed 15 Х, 20 Х, 18 ХГТ, 12 ХНЗА, etc. Cementation and hardening to hardness Н=58... 63 НRc Heavily loaded shafts Alloy steels: 40 ХНМА, 18 ХГТ, 38 Х 2 МУА, etc.

TYPES OF DAMAGE TO SHAFTS Breakage of shafts in the zone of stress concentrations. They arise due to a decrease in fatigue strength due to the action of alternating stresses. Reasons: incorrect choice of structural shape of parts (fillet), violation of manufacturing technology (cuts, processing marks, etc.), violation of technical operation standards (incorrect adjustment of bearings, reduction of required clearances). Most often, breakdowns occur in the area where stress concentrators are located (keyways, fillets, holes, press fittings, etc.). Compression of working surfaces (grooves, keys, splines, wear of splines in moving joints and other types of surface damage). Frictional corrosion and pressure concentration in areas located near the ends of the hub (preconditions arise for the occurrence of sources of fatigue failure. Insufficient rigidity of shafts and axles for bending and torsion. Destruction due to transverse or torsional vibrations.

SHAFT PERFORMANCE CRITERIA Strength Rigidity Vibration resistance Wear resistance The main criterion for the performance of low-speed shafts is static strength

SUPPORT POINTS OF THE SHAFT a – on a radial bearing; b – on an angular contact bearing; c – on two bearings in one support; g – on a plain bearing

SHAFT LOADING DIAGRAMS. DIAGRAMS OF BENDING AND TORQUE MOMENTS According to GOST 16162-85 for input and output shafts of single-stage spur and bevel gearboxes and for high-speed shafts of gearboxes of any type For low-speed shafts of two- and three-stage gearboxes, as well as worm gears where T is the torque on the shaft.

PROCEDURE FOR CALCULATING SHAFTS FOR STATIC STRENGTH Draw up a calculation diagram Determine the reactions of supports in the horizontal and vertical planes Build bending moment diagrams and torque diagrams Geometrically sum up the moments For dangerous sections (where the largest total moments are), calculate the diameters and finally develop the shaft design. Since the shafts operate under conditions of bending and torsion, and the stresses from axial forces are small, the equivalent stress at the point of the outer fiber, according to the energy theory of strength, is determined by the formula where; - design stresses for bending and torsion - axial and polar moments of the shaft section

CALCULATION OF SHAFT FOR FATIGUE STRENGTH Performed as a test in the form of determining safety factors where S, S are safety factors, respectively, for bending and torsion stresses; [s] = 2… 2.5 - permissible safety factor. where σ-1, -1 are the endurance limits of the material during bending and torsion; K D, K D - stress concentration coefficients, taking into account the influence of all factors on fatigue resistance; σa, a - stress amplitudes; , - coefficients characterizing the sensitivity of the material to the asymmetry of the stress cycle; σm, m are the constant components of the stress change cycle.

NATURE OF STRESS CHANGES IN SHAFT Symmetrical stress cycle Zero stress cycle Loads that are constant in magnitude and direction cause alternating bending stresses in rotating shafts, varying in a symmetrical cycle with amplitude σа and average stress σm Changes in torsional stresses in calculations are taken according to the zero cycle

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

Classification of shafts and axles construction machine. What types of shafts are used in machines? The difference between the processing of shafts and axles, mechanisms in the form of paired shafts.

Types of machine shafts and axles

Types of shafts

Axles- support rotating machine parts. They can be rotating or stationary.

Shafts- not only support, but also transmit rotation.
There are: straight, crank and cranked.
Shafts are designed for the simultaneous action of torque and bending moments.
The axles are designed only for bending.

1. shaft with straight axis;
2. crankshaft;
3. flexible shaft;
4. cardan shaft

Types of axes

1. motionless;
2. movable.

Axles and shafts differ from other machine parts in that they carry gears, pulleys, and other rotating parts. According to operating conditions, axles and shafts differ from each other.

An axis is a part that only supports the parts mounted on it. The axis does not experience torsion, since the load on it comes from the parts located on it. It works on bending and does not transmit torque.

As for the shaft, it not only supports the parts, but also transmits torque. Therefore, the shaft experiences both bending and torsion, and sometimes also compression and tension. Among the shafts, there are torsion shafts (or simply torsion bars), which do not support the rotation of parts and work exclusively on torsion. Examples are a car's driveshaft, a rolling mill's coupling roller, and much more.

The section in the shaft or axle support is called a journal if it receives a radial load, or a fifth if an axial load is applied to it. The end journal that receives the radial load is called the tenon, and the journal located at some distance from the end of the shaft is called the journal. Well, that part of the shaft or axis that limits the axial movement of parts is called a shoulder.

The seating surface of the axle or shaft, on which the rotating parts are actually mounted, is often made cylindrical and less often conical to facilitate the installation and removal of heavy parts when high centering accuracy is required. The surface that provides a smooth transition between steps is called fillet. The transition can be made using a groove that allows the grinding wheel to exit. Stress concentration can be reduced by reducing the depth of the grooves and increasing the rounding of the grooves and dumbbells as much as possible.

To make the installation of rotating parts on an axle or shaft easier, as well as to prevent hand injuries, the ends are chamfered, that is, slightly ground to a cone.
Types of axles and shafts

The axle can be rotating (for example, the axle of a carriage) or non-rotating (for example, the axle of a block of a machine for lifting goods).

Well, the shaft can be straight, cranked or flexible. Straight shafts are the most common. Crankshafts are used in crank transmissions of pumps and engines. They convert reciprocating movements into rotational ones, or vice versa. As for flexible shafts, they are, in fact, multi-retractable torsion springs twisted from wires. They are used to transmit torque between machine components if they change position relative to each other during operation. Both crankshafts and flexible shafts are classified as special parts and are taught in special training courses.

Most often, the axis or shaft has a circular solid cross-section, but they can also have an annular cross-section, which makes it possible to reduce the total weight of the structure. The cross-section of some sections of the shaft may have a keyway or splines, or may be profiled.

With a profile connection, the parts are fastened together using contact along a round, non-smooth surface and, in addition to torque, can also transmit an axial load. Despite the reliability of the profile connection, it cannot be called technologically advanced, so their use is limited. The spline connection is classified according to the shape of the teeth profile - it can be straight-sided, involute or triangular.

19.11.2015

Shafts And axes used in mechanical engineering for fixing different bodies rotation (these can be gears, pulleys, rotors and other elements installed in mechanisms).

There is a fundamental difference between shafts and axles: the former transmit the moment of force created by the rotation of parts, and the latter experience bending stress under the influence of external forces. In this case, the shafts are always a rotating element of the mechanism, and the axes can be either rotating or stationary.

From a metalworking point of view, shafts and axles are metal parts, most often having a circular cross-section.

Types of shafts

The shafts differ in the design of the axis. The following types of shafts are distinguished:

• straight. Structurally they do not differ from axes. In turn, there are smooth, stepped and shaped straight shafts and axles. Most often in mechanical engineering, stepped shafts are used, which are distinguished by ease of installation on mechanisms
• cranked, consisting of several knees and main journals, which rest on bearings. They form an element of the crank mechanism. The operating principle is to convert reciprocating motion into rotational motion, or vice versa.
• flexible (eccentric). They are used to transmit torque between shafts with offset axes of rotation.

The production of shafts and axles is one of the most dynamic areas in the metallurgical industry. Based on these elements, the following products are obtained:

1. torque transmission elements (parts of keyed joints, splines, interference joints, etc.);
2. support bearings (rolling or sliding);
3. shaft end seals;
4. elements regulating transmission units and supports;
5. elements for axial fixation of rotor blades;
6. transition fillets between elements of different diameters in a structure.

The output ends of the shafts have the shape of a cylinder or cone, connected using couplings, pulleys, and sprockets.

Shafts and axles can also be hollow or solid. Other parts can be mounted inside hollow shafts and can also be used to lighten total weight designs.

The function of axial clamps installed on the shaft of parts is performed by steps (collars), spacer bushings with a removable axle, rings, and spring thrust rings of bearings.

The Elektromash enterprise manufactures these products at a production site equipped with the most modern equipment. With us you can buy shafts and axles any type to order.