Multi-strand springs. Springs and elastic elements springs and elastic elements Elastic spring elements

They are formed by protrusions on the shaft that fit into mating grooves in the wheel hub. Both in appearance and in terms of dynamic operating conditions, splines can be considered multi-key connections. Some authors call them gear joints.

Straight-sided splines (a) are mainly used; involute (b) GOST 6033-57 and triangular (c) spline profiles are less common.

Straight-sided splines can center the wheel on the side surfaces (a), on the outer surfaces (b), on the inner surfaces (c).

In comparison with keys, splines:

They have a large load-bearing capacity;

Better centering of the wheel on the shaft;

They strengthen the shaft cross-section due to the greater moment of inertia of the ribbed section compared to the round one;

` require special equipment to make holes.

The main criteria for the performance of splines are:

è resistance of the side surfaces to crushing (calculation is similar to dowels);

è wear resistance during fretting corrosion (small mutual vibration movements).

Collapse and wear are associated with one parameter - contact stress (pressure) s cm . This allows splines to be calculated using a generalized criterion for both crushing and contact wear. Allowable stresses [ s]cm are prescribed based on experience in operating similar structures.

For the calculation, the uneven distribution of load across the teeth is taken into account,

Where Z – number of splines, h – working height of the splines, l – working length of splines, d avg – average diameter of the spline connection. For involute splines, the working height is assumed to be equal to the profile module, as d avg take the pitch diameter.

The symbols for a straight-sided spline connection are made up of the symbol for the centering surface D , d or b , number of teeth Z , nominal sizes d x D (as well as designations of tolerance fields along the centering diameter and on the lateral sides of the teeth). For example, D 8 x 36H7/g6 x 40 means an eight-spline connection centered along the outer diameter with dimensions d = 36 And D =40 mm and fit along the centering diameter H7/g6 .

CONTROL QUESTIONS

s What is the difference between detachable and permanent connections?

s Where and when are welded joints used?

s What are the advantages and disadvantages of welded joints?

s What are the main groups of welded joints?

s How are the main types of welds different?

s What are the advantages and disadvantages of riveted joints?

s Where and when are riveted joints used?

s What are the criteria for strength design of rivets?

s What is the design principle of threaded connections?

s What are the applications of the main types of threads?

s What are the advantages and disadvantages of threaded connections?

s Why is it necessary to lock threaded connections?

s What designs are used to lock threaded connections?

s How is the compliance of parts taken into account when calculating a threaded connection?

s What thread diameter is found from the strength calculation?

s What is the thread diameter used to indicate the thread?

s What is the design and main purpose of pin connections?

s What are the types of loading and design criteria for pins?

s What is the design and main purpose of keyed joints?

s What are the types of loading and the design criteria for keys?

s What is the design and main purpose of spline joints?

What are the types of loading and the criteria for calculating splines?

SPRINGS. ELASTIC ELEMENTS IN MACHINES

Each car has specific parts that are fundamentally different from all the others. They are called elastic elements. Elastic elements have various, very different designs from each other. Therefore, a general definition can be given.

Elastic elements are parts whose rigidity is much less than that of others, and whose deformations are higher.

Thanks to this property, elastic elements are the first to perceive shocks, vibrations, and deformations.

Most often, elastic elements are easy to detect when inspecting a car, such as rubber wheel tires, springs and springs, soft seats for drivers and drivers.

Sometimes the elastic element is hidden under the guise of another part, for example, a thin torsion shaft, a stud with a long thin neck, a thin-walled rod, a gasket, a shell, etc. However, even here, an experienced designer will be able to recognize and use such a “camouflaged” elastic element precisely by its relatively low rigidity.

On the railway, due to the severity of transport, the deformations of the track parts are quite large. Here, the elastic elements, along with the springs of the rolling stock, actually become rails, sleepers (especially wooden, not concrete) and the soil of the track embankment.

Elastic elements find the widest application:

è for shock absorption (reduction of accelerations and inertial forces during shock and vibration due to a significantly longer deformation time of the elastic element compared to rigid parts);

è to create constant forces (for example, elastic and split washers under the nut create a constant friction force in the threads, which prevents self-unscrewing);

è for force closure of mechanisms (to eliminate unwanted gaps);

è for the accumulation (accumulation) of mechanical energy (clock springs, the spring of a weapon striker, the arc of a bow, the rubber of a slingshot, a ruler bent near a student’s forehead, etc.);

è for measuring forces (spring scales are based on the relationship between the weight and deformation of a measuring spring according to Hooke’s law).

Typically, elastic elements are made in the form of springs of various designs.

Elastic compression and extension springs are most common in cars. The coils in these springs are subject to torsion. The cylindrical shape of the springs is convenient for placing them in machines.

The main characteristic of a spring, like any elastic element, is rigidity or its inverse compliance. Rigidity K determined by the elastic force dependence F from deformation x . If this dependence can be considered linear, as in Hooke’s law, then stiffness is found by dividing the force by the deformation K =F/x .

If the dependence is nonlinear, as is the case in real structures, the stiffness is found as the derivative of the force with respect to deformation K =∂ F/ ∂ x.

Obviously, here you need to know the type of function F =f (x ) .

For heavy loads, when it is necessary to dissipate vibration and shock energy, packages of elastic elements (springs) are used.

The idea is that when composite or layered springs (springs) are deformed, energy is dissipated due to mutual friction of the elements.

A package of disc springs is used to absorb shock and vibration in the inter-bogie elastic coupling of electric locomotives ChS4 and ChS4 T.

In development of this idea, on the initiative of the staff of our academy on Kuibyshevskaya Road, disc springs (washers) are used in bolted connections of rail joint linings. Springs are placed under the nuts before tightening and provide high constant frictional forces in the connection, also unloading the bolts.

Materials for elastic elements must have high elastic properties, and most importantly, not lose them over time.

The main materials for springs are high-carbon steels 65.70, manganese steels 65G, silicon steels 60S2A, chrome vanadium steel 50HFA, etc. All these materials have higher mechanical properties compared to conventional structural steels.

In 1967, a material called metal rubber "MR" was invented and patented at the Samara Aerospace University. The material is made from crumpled, tangled metal wire, which is then pressed into the required shapes.

The enormous advantage of metal rubber is that it perfectly combines the strength of metal with the elasticity of rubber and, in addition, due to significant interwire friction, it dissipates (dampers) vibration energy, being a highly effective means of vibration protection.

The density of the tangled wire and the pressing force can be adjusted, obtaining specified values ​​of rigidity and damping of the metal rubber in a very wide range.

Metal rubber undoubtedly has a promising future as a material for the manufacture of elastic elements.

Elastic elements require very precise calculations. In particular, they must be designed for rigidity, since this is the main characteristic.

However, the designs of elastic elements are so diverse, and the calculation methods are so complex, that it is impossible to present them in any generalized formula. Especially within the framework of our course, which is completed here.

CONTROL QUESTIONS

1. By what criteria can elastic elements be found in the design of a machine?

2. For what tasks are elastic elements used?

3. What characteristic of the elastic element is considered the main one?

4. What materials should elastic elements be made of?

5. How are Belleville spring washers used on the Kuibyshevskaya Road?

INTRODUCTION…………………………………………………………………………………
1. GENERAL ISSUES OF CALCULATION OF MACHINE PARTS……………………………………………………...
1.1. Rows of preferred numbers………………………………………………………………...
1.2. Basic criteria for the performance of machine parts…………………… 1.3. Calculation of fatigue resistance under variable stresses………..
1.3.1. Variable voltages……………………………………………………….. 1.3.2. Endurance limits…………………………………………….. 1.4. Safety factors…………………………………………………………….
2. MECHANICAL TRANSMISSIONS………………………………………………………………………………... 2.1. General information…………………………………………………………….. 2.2. Characteristics of drive gears……………………………………………..
3. GEARS ………………………………………………………………………………….. 4.1. Operating conditions for teeth………………………………………………………. 4.2. Gear materials…………………………………………........... 4.3. Characteristic types of tooth destruction……………………………………… 4.4. Design load……………………………………………………………. 4.4.1. Design load factors……………………………………. 4.4.2. Accuracy of gears…………………………………….. 4.5. Spur gears………………………………………
4.5.1. Forces in engagement……………………………………………………. 4.5.2. Calculation of resistance to contact fatigue……………………. 4.5.3. Calculation of flexural fatigue resistance……………………… 4.6. Bevel gears…………………………………………… 4.6.1. Main parameters…………………………………………………. 4.6.2. Forces in engagement……………………………………………………. 4.6.3. Calculation of resistance to contact fatigue…………………… 4.6.4. Calculation of fatigue resistance in bending…………………….
5. WORM GEARS…………………………………………………………………………………. 5.1. General information…………………………………………………………….. 5.2. Forces in engagement………………………………………………………. 5.3. Worm gear materials…………………………………………… 5.4. Strength calculation………………………………………………………..
5.5. Thermal calculation…………………………………………………………………………………. 6. SHAFT AND AXLES………………………………………………………………………………. 6.1. General information…………………………………………………………….. 6.2. Design load and performance criterion………………………… 6.3. Design calculation of shafts……………………………………………. 6.4. Design diagram and procedure for calculating the shaft…………………………………….. 6.5. Calculation of static strength……………………………………………. 6.6. Fatigue resistance calculations…………………………………………………….. 6.7. Calculation of shafts for rigidity and vibration resistance……………………………
7. ROLLING BEARINGS……………………………………………………………… 7.1. Classification of rolling bearings…………………………………… 7.2. Designation of bearings according to GOST 3189-89……………………………… 7.3. Features of angular contact bearings…………………………… 7.4. Schemes for installing bearings on shafts…………………………………… 7.5. Design load on angular contact bearings………………….. 7.6. Reasons for failure and calculation criteria………………………........... 7.7. Materials of bearing parts……..……………………………………. 7.8. Selection of bearings based on static load capacity (GOST 18854-94)………………………………………………………………
7.9. Selection of bearings based on dynamic load capacity (GOST 18855-94)……………………………………………………………… 7.9.1. Initial data……………………………………………………. 7.9.2. Basis for selection…………………………………………………………….. 7.9.3. Features of bearing selection………………………………..
8. SLIDING BEARINGS……………………………………………………….
8.1. General information……………………………………………………..
8.2. Operating conditions and friction modes………………………………………………………………
7. COUPLINGS
7.1. Rigid couplings
7.2. Compensating couplings
7.3. Movable couplings
7.4. Flexible couplings
7.5. Friction clutches
8. CONNECTIONS OF MACHINE PARTS
8.1. Permanent connections
8.1.1. Welded joints
Calculation of strength of welded seams
8.1.2. Rivet connections
8.2. Detachable connections
8.2.1. THREADED CONNECTIONS
Calculation of the strength of threaded connections
8.2.2. Pin connections
8.2.3. Keyed connections
8.2.4. Spline connections
9. Springs……………………………………

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Metallic and non-metallic elements are used as elastic devices in the suspensions of modern cars. The most common metal devices are springs, leaf springs and torsion bars.

Car suspension spring with variable stiffness

The most widely used (especially in passenger car suspensions) coil springs, made from a steel elastic rod of circular cross-section.
When the spring is compressed along the vertical axis, its coils come closer together and twist. If the spring has a cylindrical shape, then when it is deformed, the distance between the coils remains constant and the spring has a linear characteristic. This means that the deformation of a coil spring is always directly proportional to the applied force, and the spring has a constant stiffness. If you make a twisted spring from a rod of variable cross-section or give the spring a certain shape (in the form of a barrel or cocoon), then such an elastic element will have variable stiffness. When such a spring is compressed, the less rigid coils will initially come closer together, and after they touch, the more rigid coils will begin to work. Springs of variable stiffness are widely used in suspensions of modern passenger cars.
The advantages of springs used as elastic elements of suspensions include their low mass and the ability to ensure high smoothness of the vehicle. At the same time, the spring cannot transmit forces in the transverse plane and its use requires a complex guide device in the suspension.

Rear leaf spring suspension:
1 - spring eye;
2 - rubber bushing;
3 - bracket;
4 - bushing;
5 - bolt;
6 - washers;
7 - finger;
8 - rubber bushings;
9 - spring washer;
10 - nut;
11 - bracket;
12 - rubber bushing;
13 - bushing;
14 - earring plate;
15 - bolt;
16 - stabilizer bar;
17 - root leaf;
18 - spring leaves;
19 - rubber compression stroke buffer;
20 - stepladders;
21 - overlay;
22 - rear axle beam;
23 - shock absorber;
24 - clamp;
25 - frame spar;
26 - stabilizer bracket;
27 - stabilizer earring

Leaf spring served as an elastic suspension element on horse-drawn carriages and the first cars, but it continues to be used today, although mainly on trucks. A typical leaf spring consists of a series of sheets of varying lengths fastened together, made of spring steel. A leaf spring is usually shaped like a semi-ellipse.

Methods of fastening springs:
a - with twisted ears;
b - on rubber cushions;
c - with an overhead eyelet and a sliding support

The sheets that make up the spring have different lengths and curvatures. The shorter the length of the sheet, the greater its curvature should be, which is necessary for a tighter mutual fit of the sheets in the assembled spring. With this design, the load on the longest (main) leaf of the spring is reduced. The spring leaves are fastened together with a center bolt and clamps. With the help of the main leaf, the spring is hinged at both ends to the body or frame and can transmit forces from the wheels of the car to the frame or body. The shape of the ends of the main sheet is determined by the method of attaching it to the frame (body) and the need to compensate for changes in the length of the sheet. One end of the spring must be able to pivot while the other ends rotate and move.
When a spring is deformed, its leaves bend and change their length. In this case, the sheets rub against each other, and therefore they require lubrication, and special anti-friction gaskets are installed between the sheets of the springs of passenger cars. At the same time, the presence of friction in the spring makes it possible to dampen body vibrations and, in some cases, makes it possible to do without the use of shock absorbers in the suspension. The spring suspension has a simple design, but a large mass, which determines its greatest distribution in the suspensions of trucks and some off-road passenger cars. To reduce the mass of spring suspensions and improve smoothness, they are sometimes used few-leaved And single-leaf springs with sheet of variable length section. Quite rarely, springs made of reinforced plastic are used in suspensions.

Torsion bar suspension. The rear suspension of the Peugeot 206 uses two torsion bars connected to trailing arms. The suspension guide uses tubular arms mounted at an angle to the longitudinal axis of the vehicle

Torsion- a metal elastic element that works for torsion. Typically, a torsion bar is a solid metal rod of round cross-section with thickenings at the ends on which slots are cut. There are suspensions in which torsion bars are made of a set of plates or rods (ZAZ cars). One end of the torsion bar is attached to the body (frame), and the other to the guide device. When the wheels move, the torsion bars twist, providing an elastic connection between the wheel and the body. Depending on the suspension design, torsion bars can be located either along the longitudinal axis of the car (usually under the floor) or transversely. Torsion bar suspensions are compact and lightweight and make it possible to adjust the suspension by pre-twisting the torsion bars.
Non-metallic elastic elements of suspensions are divided into rubber, pneumatic And hydropneumatic.
Rubber elastic elements are present in almost all suspension designs, but not as main ones, but as additional ones, used to limit the movement of wheels up and down. The use of additional rubber stops (buffers, bumpers) limits the deformation of the main elastic elements of the suspension, increasing its rigidity during large movements and preventing metal-to-metal impacts. Recently, rubber elements are increasingly being replaced by devices made of synthetic materials (polyurethane).

Elastic elements of air suspensions:
a - sleeve type;
b- double cylinders

IN pneumatic elastic elements The elastic properties of compressed air are used. The elastic element is a cylinder made of reinforced rubber, into which air is supplied under pressure from a special compressor. The shape of air cylinders can be different. Sleeve-type cylinders (a) and double (two-section) cylinders (b) have become widespread.
The advantages of pneumatic elastic suspension elements include the high smoothness of the vehicle's ride, low weight and the ability to maintain a constant level of the body floor, regardless of the vehicle's load. Suspensions with pneumatic elastic elements are used on buses, trucks and cars. The constant level of the floor of the cargo platform ensures the convenience of loading and unloading a truck, and for cars and buses - convenience when boarding and disembarking passengers. To obtain compressed air, buses and trucks with a pneumatic braking system use standard compressors driven by the engine, and special compressors are installed on passenger cars, usually with an electric drive (Range Rover, Mercedes, Audi).

Air suspension. On new Mercedes E-class cars, pneumatic elastic elements began to be used instead of springs

The use of pneumatic elastic elements requires the use of a complex guide element and shock absorbers in the suspension. Suspensions with pneumatic elastic elements of some modern passenger cars have complex electronic control, which ensures not only a constant level of the body, but also automatically changes the stiffness of individual air springs when cornering and when braking, to reduce body roll and dive, which generally improves driving comfort and safety. .

Hydropneumatic elastic element:
1 - compressed gas;
2 - body;
3 - liquid;
4 - to the pump;
5 - to the shock absorber strut

The hydropneumatic elastic element is a special chamber divided into two cavities by an elastic membrane or piston.
One of the chamber cavities is filled with compressed gas (usually nitrogen), and the other with liquid (special oil). Elastic properties are provided by compressed gas, since the liquid is practically incompressible. The movement of the wheel causes the movement of a piston located in a cylinder filled with liquid. As the wheel moves upward, the piston displaces liquid from the cylinder, which enters the chamber and acts on the separating membrane, which moves and compresses the gas. To maintain the required pressure in the system, a hydraulic pump and a hydraulic accumulator are used. By changing the pressure of the liquid entering under the membrane of the elastic element, you can change the gas pressure and the stiffness of the suspension. When the body oscillates, the fluid passes through the valve system and experiences resistance. Hydraulic friction provides the damping properties of the suspension. Hydropneumatic suspensions provide a highly smooth ride, the ability to adjust the position of the body and effective damping of vibrations. The main disadvantages of such a suspension include its complexity and high cost.

ELASTIC ELEMENTS. SPRINGS

Wheel pairs of cars are connected to the bogie frame and the car body through a system of elastic elements and vibration dampers, called spring suspension. Spring suspension, due to elastic elements, softens shocks and impacts transmitted by the wheels to the body, and also, due to the work of dampers, dampens vibrations that occur when the car moves. In addition (in some cases), springs and springs transmit guiding forces from the wheels to the car bogie frame.
When a wheel pair passes any unevenness on the track (joints, crosses, etc.), dynamic loads arise, including shock. The appearance of dynamic loads is also facilitated by defects in the wheelset - local defects of the rolling surfaces, eccentricity of the wheel fit on the axle, imbalance of the wheelset, etc. In the absence of spring suspension, the body would rigidly perceive all dynamic influences and experience high accelerations.
Elastic elements located between the wheel pairs and the body, under the influence of dynamic force from the wheel pair, are deformed and perform oscillatory movements together with the body, and the period of such oscillations is many times longer than the period of change of the disturbing force. As a result, accelerations and forces perceived by the body are reduced.

Let us consider the softening effect of spring suspension when transmitting shocks to the body using the example of the movement of a car along a rail track. When a car wheel rolls along a rail track, due to the unevenness of the rail and defects in the rolling surface of the wheel, the car body, when connected without springs to the wheel pairs, will copy the trajectory of the wheel (Fig. A). The trajectory of the car body (line a1-b1-c1) coincides with the unevenness of the track (line a-b-c). If there is a spring suspension, vertical shocks (Fig. b) are transmitted to the body through elastic elements, which, softening and partially absorbing shocks, ensure a calmer and smoother ride of the car, protect the rolling stock and track from premature wear and damage. The trajectory of the body can be depicted by the line a1-b2-c2, which has a flatter appearance compared to the line a in c. As can be seen from Fig. b, the period of vibration of the body on the springs is many times greater than the period of change of the disturbing force. As a result, accelerations and forces perceived by the body are reduced.

Springs are widely used in railcar construction, in bogies of freight and passenger cars, and in shock-traction devices. There are screw and spiral springs. Helical springs are made by curling steel rods of round, square or rectangular cross-section. Coil springs are cylindrical and conical in shape.

Types of coil springs
a - cylindrical with a rectangular cross-section of the rod; b - cylindrical with a round cross-section of the rod; c - conical with a round cross-section of the rod; g - conical with a rectangular cross-section of the rod

In the spring suspension of modern cars, cylindrical springs are most common. They are easy to manufacture, reliable in operation and well absorb vertical and horizontal shocks and impacts. However, they cannot dampen vibrations of the car's sprung masses and are therefore used only in combination with vibration dampers.
Springs are manufactured in accordance with GOST 14959. The supporting surfaces of the springs are made flat and perpendicular to the axis. To do this, the ends of the spring blank are pulled back to 1/3 the length of the coil circumference. As a result, a smooth transition from round to rectangular cross-section is achieved. The height of the drawn end of the spring should be no more than 1/3 of the rod diameter d, and the width should be no less than 0.7d.
The characteristics of a cylindrical spring are: diameter of the rod d, average diameter of the spring D height of the spring in the free Нсв and compressed Нсж states, the number of working turns nр and index m. The spring index is the ratio of the average diameter of the spring to the diameter of the rod, i.e. t = D/d.

Cylindrical spring and its parameters

Material for springs and leaf springs

The material for springs and springs must have high static, dynamic, impact strength, sufficient ductility and maintain its elasticity throughout the entire service life of the spring or spring. All these properties of the material depend on its chemical composition, structure, heat treatment and the state of the surface of the elastic element. Springs for cars are made of steel 55S2, 55S2A, 60S2, 60S2A (GOST 14959–79). Chemical composition of steels in percent: C = 0.52 - 0.65; Mn = 0.6 - 0.9; Si = 1.5 - 2.0; S, P, Ni not more than 0.04 each; Cr no more than 0.03. Mechanical properties of heat-treated steels 55С2 and 60С2: tensile strength 1300 MPa with elongation of 6 and 5% and reduction in cross-sectional area of ​​30 and 25%, respectively.
During manufacturing, springs and springs are subjected to heat treatment - hardening and tempering.
The strength and wear resistance of springs and springs largely depends on the condition of the metal surface. Any damage to the surface (small cracks, stains, sunsets, dents, risks and similar defects) contribute to stress concentration under loads and sharply reduce the endurance limit of the material. For surface hardening, factories use shot blasting of spring sheets and springs.
The essence of this method is that the elastic elements are exposed to a flow of metal shot with a diameter of 0.6–1 mm, ejected at a high speed of 60–80 m/s onto the surface of the spring leaf or spring. The flight speed of the shot is selected such that a stress is created at the point of impact above the elastic limit, and this causes plastic deformation (hardening) in the surface layer of the metal, which ultimately strengthens the surface layer of the elastic element.
In addition to shot blasting, coercion can be used to strengthen springs, which consists of keeping the springs in a deformed state for a certain time. The spring is coiled in such a way that the distances between the coils in the free state are made by some amount larger than according to the drawing. After heat treatment, the spring is removed until the coils touch and kept in this state for 20 to 48 hours, then it is heated. During compression, residual stresses of the opposite sign are created in the outer zone of the cross section of the rod, as a result of which, during its operation, the true stresses turn out to be less than they would be without captivity.

Pictured are new coil springs

Winding springs in a heated state

Checking spring elasticity

Cylindrical springs, depending on the load they absorb, are made single-row or multi-row. Multi-row springs consist of two, three or more springs nested one inside the other. In double-row springs, the outer spring is made from a rod of larger diameter, but with a small number of turns, and the inner spring is made from a rod of smaller diameter and with a large number of turns. To ensure that when compressed, the coils of the inner spring are not pinched between the coils of the outer one, both springs are curled in different directions. In multi-row springs, the dimensions of the rods also decrease from the outer spring to the inner one, and the number of turns increases accordingly.

Multi-row springs allow, with the same dimensions as a single-row spring, to have greater rigidity. Double-row and three-row springs are widely used in bogies of freight and passenger cars, as well as in the draft gears of automatic couplers. The force characteristic of multi-row springs is linear.
In some designs of double-row springs (for example, in bogies 18-578, 18-194), the outer springs of the spring set are higher than the inner ones, due to which the suspension rigidity of an empty car is 3 times less than that of a loaded one.

Springs installed on the carriage

SPRINGS AND ELASTIC ELEMENTS n n n 1. General characteristics of springs Springs are widely used in structures as vibration-isolating, shock-absorbing, return-feeding, tensioning, dynamometer and other devices. Types of springs. Based on the type of external load perceived, springs are divided into tension, compression, torsion and bending springs.

SPRINGS AND ELASTIC ELEMENTS n n coiled springs (cylindrical - tension, Fig. 1 a, compression, Fig. 1 b; torsion, Fig. 1 c, shaped compression, Fig. 1 d-f), special springs (disc and ring, Fig. 2 a and b, - compression; springs and springs, Fig. 2 c, - bending; spiral, Fig. 2 d - torsion, etc.) The most common are twisted cylindrical springs made of round wire.

SPRINGS AND ELASTIC ELEMENTS n Tension springs (see Fig. 1 a) are wound, as a rule, without gaps between the turns, and in most cases - with an initial tension (pressure) between the turns, partially compensating for the external load. The tension is usually (0.25 - 0.3) Fpr (Fnp is the maximum tensile force at which the elastic properties of the spring material are completely exhausted).

SPRINGS AND ELASTIC ELEMENTS n n To transmit external load, such springs are equipped with hooks. For example, for springs of small diameter (3-4 mm), the hooks are made in the form of bent last turns (Fig. 3 a-c). However, such hooks reduce the resistance of fatigue springs due to the high stress concentration in the bend areas. For critical springs with a diameter of over 4 mm, embedded hooks are often used (Fig. 3 d-e), although they are less technologically advanced.

SPRINGS AND ELASTIC ELEMENTS n n n Compression springs (see Fig. 1 b) are wound with a gap between the turns, which should be 10-20% greater than the axial elastic movements of each turn at the greatest external load. The supporting planes of the springs are obtained by pressing the last turns against the adjacent ones and grinding them perpendicular to the axis. Long springs may become unstable (bulge) under load. To prevent bulging, such springs are usually placed on special mandrels (Fig. 4 a) or in glasses (Fig. 4 b).

SPRINGS AND ELASTIC ELEMENTS n n n The alignment of the springs with the mating parts is achieved by installing support coils in special plates, bores in the body, grooves (see Fig. 4 c). Torsion springs (see Fig. 1c) are usually wound with a small angle of elevation and small gaps between the coils (0.5 mm). They perceive external load with the help of hooks formed by bending the end turns.

SPRINGS AND ELASTIC ELEMENTS n n Basic parameters of coil springs. Springs are characterized by the following main parameters (see Fig. 1 b): wire diameter d or cross-sectional dimensions; average diameter Do, index c = Do/d; number n of working turns; length Ho of the working part; step t = Ho/n turns, angle =arctg rise of turns. The last three parameters are considered in unloaded and loaded states.

SPRINGS AND ELASTIC ELEMENTS n n The spring index characterizes the curvature of the coil. Springs with index 3 are not recommended for use due to the high stress concentration in the coils. Typically, the spring index is selected depending on the wire diameter as follows: for d 2.5 mm, d = 3--5; 6-12 mm respectively c = 5-12; 4-10; 4-9.

SPRINGS AND ELASTIC ELEMENTS n n Materials. Twisted springs are made by cold or hot coiling, followed by finishing of the ends, heat treatment and control. The main materials for springs are high-strength special spring wire of classes 1, II and III with a diameter of 0, 2-5 mm, as well as steel: high-carbon 65, 70; manganese 65 G; silicon 60 C 2 A, chrome vanadium 50 CFA, etc.

SPRINGS AND ELASTIC ELEMENTS n n Springs intended for operation in a chemically active environment are made of non-ferrous alloys. To protect the surfaces of the coils from oxidation, springs for critical purposes are varnished or oiled, and springs for especially critical purposes are oxidized and also coated with zinc or cadmium.

SPRINGS AND ELASTIC ELEMENTS n n 2. Calculation and design of twisted cylindrical springs Stresses in sections and displacement of coils. Under the action of an axial force F (Fig. 5 a), a resultant internal force F appears in the cross section of the spring coil, parallel to the spring axis, and a moment T = F D 0/2, the plane of which coincides with the plane of the pair of forces F. The normal cross section of the coil is inclined to moment plane at an angle.

SPRINGS AND ELASTIC ELEMENTS n n Projecting force factors in the cross section of a loaded spring onto the x, y and z axes (Fig. 5, b), associated with the normal section of the coil, force F and moment T, we obtain Fx = F cos ; Fn = F sin (1) T = Mz = 0.5 F D 0 cos ; Mx = 0.5 F D 0 sin ;

SPRINGS AND ELASTIC ELEMENTS n n n The angle of elevation of the turns is small (usually 12). Therefore, we can assume that the cross section of the spring works for torsion, neglecting other force factors. In the coil section, the maximum tangential stress (2) where Wk is the moment of resistance to torsion of the coil section

SPRINGS AND ELASTIC ELEMENTS n Taking into account the curvature of the coils and relation (2), we write in the form equality (1), (3) n where F is the external load (tensile or compressive); D 0 - average spring diameter; k - coefficient taking into account the curvature of the turns and the shape of the section (amendment to the formula for torsion of a straight beam); k is the permissible punitive stress during torsion.

SPRINGS AND ELASTIC ELEMENTS n The value of the coefficient k for springs made of round wire with index c 4 can be calculated using the formula

SPRINGS AND ELASTIC ELEMENTS n n Taking into account that for a wire of round cross-section Wk = d 3 / 16, then (4) A spring with an elevation angle of 12 has axial displacement n F, (5)

SPRINGS AND ELASTIC ELEMENTS n n where n is the coefficient of axial compliance of the spring. The compliance of a spring is most simply determined from energy considerations. Potential energy of the spring: where T is the torque in the spring cross-section due to force F, G Jk is the torsional rigidity of the coil section (Jk 0, 1 d 4); l D 0 n - total length of the working part of the turns;

SPRINGS AND ELASTIC ELEMENTS n and coefficient of axial compliance of the spring (7) n where is the axial compliance of one turn (settlement in millimeters under the action of force F = 1 N),

SPRINGS AND ELASTIC ELEMENTS n determined by formula (8) n where G = E/ 0.384 E is the shear modulus (E is the elastic modulus of the spring material).

SPRINGS AND ELASTIC ELEMENTS n From formula (7) it follows that the spring compliance coefficient increases with an increase in the number of turns (spring length), its index (outer diameter) and a decrease in the shear modulus of the material.

SPRINGS AND ELASTIC ELEMENTS n n Calculation and design of springs. The wire diameter is calculated from the strength condition (4). For a given index value c (9) n where F 2 is the greatest external load.

SPRINGS AND ELASTIC ELEMENTS n The permissible stresses [k] for springs made of steels 60 C 2, 60 C 2 N 2 A and 50 HFA are: 750 MPa - under the action of static or slowly changing variable loads, as well as for springs of non-critical purposes; 400 MPa - for critical dynamically loaded springs. For dynamically loaded bronze responsible springs [k] are assigned (0.2-0.3) in; for non-responsible bronze springs - (0.4-0.6) c.

SPRINGS AND ELASTIC ELEMENTS n n The required number of working turns is determined from relation (5) according to the given elastic movement (stroke) of the spring. If the compression spring is installed with pre-tensioning (load) F 1, then (10) Depending on the purpose of the spring, force F 1 = (0.1-0.5) F 2. By changing the value of F 1, the working draft of the spring can be adjusted. The number of turns is rounded to half a turn for n 20 and to one turn for n > 20.

SPRINGS AND ELASTIC ELEMENTS n Total number of turns n n H 0 = H 3 + n (t - d), (12) where H 3 = (n 1 - 0. 5) d is the length of the spring, compressed until adjacent working turns touch; t - spring pitch. n n n 1 = n + (l, 5 -2, 0). (11) An additional 1.5-2 turns are used for compression to create supporting surfaces for the spring. In Fig. Figure 6 shows the relationship between load and compression spring upset. Total length of unloaded spring n

SPRINGS AND ELASTIC ELEMENTS n n The total number of turns is reduced by 0.5 due to the grinding of each end of the spring by 0.25 d to form a flat bearing end. The maximum spring settlement, i.e. the movement of the end of the spring until the coils are in full contact (see Fig. 6), is determined by the formula

SPRINGS AND ELASTIC ELEMENTS n n n The spring pitch is determined depending on the value 3 from the following approximate ratio: The length of wire required for the manufacture of the spring where = 6 - 9° is the angle of elevation of the turns of the unloaded spring.

SPRINGS AND ELASTIC ELEMENTS n n To prevent the spring from buckling due to loss of stability, its flexibility H 0/D 0 should be less than 2.5. If, for design reasons, this limitation is not met, then the springs, as indicated above, should be placed on mandrels or mounted in sleeves .

SPRINGS AND ELASTIC ELEMENTS n n n The installation length of the spring, i.e. the length of the spring after tightening it with force F 1 (see Fig. 6), is determined by the formula H 1 = H 0 - 1 = H 0 - n F 1 under the action of the greatest external load, spring length H 2 =H 0 - 1 = H 0 - n F 2 and the smallest spring length will be at force F 3 corresponding to length H 3 = H 0 - 3

SPRINGS AND ELASTIC ELEMENTS n The angle of inclination of the straight line F = f() to the abscissa axis (see Fig. 6) is determined from the formula

SPRINGS AND ELASTIC ELEMENTS n For heavy loads and cramped dimensions, use Compound compression springs (see Fig. 4, c) - a set of several (usually two) concentrically located springs that simultaneously perceive external load. To prevent strong twisting of the end supports and distortions, the coaxial springs are wound in opposite directions (left and right). The supports are designed to ensure mutual alignment of the springs.

SPRINGS AND ELASTIC ELEMENTS n n To evenly distribute the load between them, it is desirable that the composite springs have the same settlements (axial movements), and the lengths of the springs compressed until the coils touch each other are approximately the same. In the unloaded state, the length of the tension springs Н 0 = n d+2 hз; where hз = (0, 5- 1, 0) D 0 is the height of one hook. At maximum external load, the length of the tension spring H 2 = H 0 + n (F 2 - F 1 *) where F 1 * is the force of the initial compression of the turns during winding.

SPRINGS AND ELASTIC ELEMENTS n n The length of the wire for making a spring is determined by the formula where lз is the length of the wire for one trailer.

SPRINGS AND ELASTIC ELEMENTS n Common springs are those in which, instead of wire, a cable twisted from two to six wires of small diameter (d = 0.8 - 2.0 mm) is used - stranded springs. In terms of design, such springs are equivalent to concentric springs. Due to their high damping capacity (due to friction between the strands) and compliance, stranded springs work well in shock absorbers and similar devices. When exposed to variable loads, stranded springs quickly fail due to wear of the strands.

SPRINGS AND ELASTIC ELEMENTS n In structures operating under conditions of vibration and shock loads, shaped springs are sometimes used (see Fig. 1, d-e) with a nonlinear relationship between the external force and the elastic movement of the spring.

SPRINGS AND ELASTIC ELEMENTS n n Safety margins. When exposed to static loads, springs may fail due to plastic deformations in the coils. According to plastic deformations, the safety factor is where max is the highest tangential stress in the spring coil, calculated by formula (3), at F=F 1.

SPRINGS AND ELASTIC ELEMENTS n Springs that operate for a long time under variable loads must be designed for fatigue resistance. Springs are characterized by asymmetric loading, in which the forces vary from F 1 to F 2 (see Fig. 6). At the same time, in the cross sections of the voltage turns

SPRINGS AND ELASTIC ELEMENTS n amplitude and average cycle stress n For tangential stresses, safety factor n where K d is the scale effect coefficient (for springs made of wire d 8 mm is equal to 1); = 0, 1 - 0, 2 - cycle asymmetry coefficient.

SPRINGS AND ELASTIC ELEMENTS n n Fatigue limit - 1 wire with variable torsion in a symmetrical cycle: 300-350 MPa - for steels 65, 70, 55 GS, 65 G; 400-450 MPa - for steels 55 C 2, 60 C 2 A; 500-550 MPa - for steels 60 C 2 HFA, etc. When determining the safety factor, the effective stress concentration coefficient K = 1 is taken. The stress concentration is taken into account by the coefficient k in the formulas for stresses.

SPRINGS AND ELASTIC ELEMENTS n In the case of resonant oscillations of springs (for example, valve springs), an increase in the variable component of the cycle may occur while m remains unchanged. In this case, the safety factor for alternating stresses

SPRINGS AND ELASTIC ELEMENTS n To increase fatigue resistance (by 20-50%), the springs are strengthened by shot peening, which creates compressive residual stresses in the surface layers of the coils. To process springs, balls with a diameter of 0.5-1.0 mm are used. It is more effective to treat springs with balls of small diameters at high flight speeds.

SPRINGS AND ELASTIC ELEMENTS n n Calculation for impact load. In a number of structures (shock absorbers, etc.), springs operate under shock loads applied almost instantly (at high speed) with known impact energy. The individual coils of the spring receive significant speed and can collide dangerously. The calculation of real systems for impact loading is associated with significant difficulties (taking into account contact, elastic and plastic deformations, wave processes, etc.); Therefore, for the engineering application we will limit ourselves to the energy calculation method.

SPRINGS AND ELASTIC ELEMENTS n n n The main task of shock load analysis is to determine the dynamic settlement (axial movement) and static load equivalent to the impact action on a spring with known dimensions. Let us consider the impact of a rod of mass m on a spring shock absorber (Fig. 7). If we neglect the deformation of the piston and assume that after an impact, elastic deformations instantly cover the entire spring, we can write the energy balance equation in the form where Fd is the gravity force of the rod; K is the kinetic energy of the system after the collision,

SPRINGS AND ELASTIC ELEMENTS n determined by formula (13) n where v 0 is the speed of movement of the piston; - coefficient of reduction of the spring mass to the point of impact

SPRINGS AND ELASTIC ELEMENTS n n n If we assume that the speed of movement of the coils of the spring changes linearly along its length, then = 1/3. The second term on the left side of equation (13) expresses the work of the piston after a collision during dynamic upsetting of the spring. The right side of equation (13) is the potential energy of deformation of the spring (with compliance m), which can be returned by gradually unloading the deformed spring.

SPRINGS AND ELASTIC ELEMENTS With instantaneous application of load v 0 = 0; d = 2 tbsp. A static load, equivalent in effect to impact, can. calculated from the relation n n

SPRINGS AND ELASTIC ELEMENTS n n Rubber elastic elements are used in the designs of elastic couplings, vibration and noise insulating supports and other devices for obtaining large movements. Such elements usually transmit the load through metal parts (plates, tubes, etc.).

SPRINGS AND ELASTIC ELEMENTS n Advantages of rubber elastic elements: electrical insulating ability; high damping capacity (energy dissipation in rubber reaches 30-80%); the ability to accumulate more energy per unit mass than spring steel (up to 10 times). In table Figure 1 shows calculation diagrams and formulas for approximate determination of stresses and displacements for rubber elastic elements.

SPRINGS AND ELASTIC ELEMENTS n n The material of the elements is technical rubber with a tensile strength (8 MPa; shear modulus G = 500-900 MPa. In recent years, pneumoelastic elastic elements have become widespread.