As elastic devices in suspensions modern cars use metallic and non-metallic elements. Most widespread received metal devices: 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 steel elastic rod round 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. IN Lately 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.

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 the parts of machines whose operation is based on the ability to change their shape under the influence of an external load and restore it to its original form after removing this load.

Or another definition:

Elastic elements – parts whose rigidity is much lower than the rest, and whose deformation is 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 “disguised” elastic element precisely by its relatively low rigidity.

Elastic elements find the widest application:

For shock absorption (reducing acceleration and inertia forces during shock and vibration due to a significantly longer deformation time of the elastic element compared to rigid parts, such as car springs);

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, clutch disc pressing force);

For the force closure of kinematic pairs in order to eliminate the influence of the gap on the accuracy of movement, for example in the cam distribution mechanism of an internal combustion engine;

For the accumulation (accumulation) of mechanical energy (clock springs, gun striker spring, bow arc, slingshot rubber, etc.);

To measure forces (spring scales are based on the relationship between weight and deformation of a measuring spring according to Hooke’s law);

To absorb impact energy, for example, buffer springs used in trains and artillery guns.

Technical devices use a large number of different elastic elements, but the most common are the following three types of elements, usually made of metal:

Springs– elastic elements designed to create (perceive) a concentrated force load.

Torsion bars- elastic elements, usually made in the form of a shaft and designed to create (perceive) a concentrated moment load.

Membranes- elastic elements designed to create (perceive) a force load (pressure) distributed over their surface.

Elastic elements find the widest application in various fields of technology. They can be found in fountain pens with which you write notes, and in small arms (for example, a mainspring), and in MGKM (valve springs of internal combustion engines, springs in clutches and main clutches, springs of toggle switches and switches, rubber knuckles in limiters turning the balancers of tracked vehicles, etc., etc.).

In technology, along with cylindrical helical single-core tension-compression springs, moment springs and torsion shafts are widely used.

This section discusses only two types of a large number of elastic elements: cylindrical tension-compression springs And torsion bars.

Classification of elastic elements

1) By type of created (perceived) load: power(springs, shock absorbers, dampers) - perceive concentrated force; momentary(moment springs, torsion bars) – concentrated torque (a couple of forces); absorbing distributed load(pressure membranes, bellows, Bourdon tubes, etc.).

2) According to the type of material used to manufacture the elastic element: metal(steel, stainless steel, bronze, brass springs, torsion bars, membranes, bellows, Bourdon tubes) and non-metallic made of rubber and plastics (dampers and shock absorbers, membranes).

3) According to the type of main stresses arising in the material of the elastic element during its deformation: tension-compression(rods, wires), torsion(coil springs, torsion bars), bending(bending springs, springs).

4) Depending on the relationship between the load acting on the elastic element and its deformation: linear(the load-strain graph represents a straight line) and

5) Depending on the shape and design: springs, cylindrical screw, single and multi-core, conical screw, barrel screw, disc, cylindrical slotted, spiral(ribbon and round), flat, springs(multi-layer bending springs), torsion bars(spring shafts), curly and so on.

6) Depending on the method manufacturing: twisted, turned, stamped, typesetting and so on.

7) Springs are divided into classes. 1st class – for large numbers of load cycles (valve springs of car engines). 2nd class for medium numbers of loading cycles and 3rd class – for small numbers of loading cycles.

8) According to accuracy, springs are divided into groups. 1st accuracy group with permissible deviations in forces and elastic movements ± 5%, 2nd accuracy group - by ± 10% and 3rd accuracy group ± 20%.

Rice. 1. Some elastic elements of machines: coil springs - A) sprains, b) compression, V) conical compression, G) torsion;

d) telescopic compression band spring; e) stacked disc spring;

and , h) ring springs; And) compound compression spring; To) spiral spring;

l) bending spring; m) spring (stacked bending spring); n) torsion roller.

Typically, elastic elements are made in the form of springs of various designs (Fig. 1.1).

Rice. 1.1.Spring designs

Elastic tension springs are the most common type in machines (Fig. 1.1, A), compression (Fig. 1.1, b) and torsion (Fig. 1.1, V) with different wire cross-section profiles. Shaped ones are also used (Fig. 1.1, G), stranded (Fig. 1.1, d) and composite springs (Fig. 1.1, e) having a complex elastic characteristic and used under complex and high loads.

In mechanical engineering, the most widespread are single-core screw springs twisted from wire - cylindrical, conical and barrel-shaped. Cylindrical springs have a linear characteristic (force-deformation relationship), the other two have a nonlinear characteristic. The cylindrical or conical shape of the springs is convenient for placing them in machines. In elastic compression and extension springs, the coils are subject to torsion.

Coil springs are usually made by winding wire onto a mandrel. In this case, springs from wire with a diameter of up to 8 mm are wound, as a rule, in a cold way, and from wire (rod) of a larger diameter - in a hot way, that is, with preheating of the workpiece to the plasticity temperature of the metal. Compression springs are wound with the required pitch between turns. When winding tension springs, the wire is usually given additional axial rotation, ensuring a tight fit of the turns to each other. With this method of winding, compression forces arise between the turns, reaching up to 30% of the maximum permissible value for a given spring. To connect to other parts, various types of trailers are used, for example in the form of curved coils (Fig. 1.1, A). The most advanced are fastenings using screw-in screw plugs with hooks.

Compression springs are wound with open coiling with a gap between the coils 10...20% greater than the calculated axial elastic displacements of each coil at maximum operating loads. The outermost (support) coils of compression springs (Fig. 1.2) are usually pressed and sanded off to obtain a flat bearing surface perpendicular to the longitudinal axis of the spring, occupying at least 75% of the circular length of the coil. After cutting to the required size, bending and grinding the end coils of the spring, they undergo stabilizing annealing. To avoid loss of stability, if the ratio of the height of the spring in the free state to the diameter of the spring is more than three, it should be placed on mandrels or mounted in guide cups.

Fig.1.2. Coil compression spring

To obtain increased compliance with small dimensions, multi-strand twisted springs are used (in Fig. 1.1, d) cross-sections of such springs are shown). Made from high grade patented wires they have increased elasticity, high static strength and good shock-absorbing ability. However, due to increased wear caused by friction between wires, contact corrosion and reduced fatigue strength, it is not recommended to use them for variable loads with a large number of loading cycles. Both springs are selected according to GOST 13764-86... GOST 13776-86.

Composite springs(Fig. 1.1, e) used under heavy loads and to weaken resonance phenomena. They consist of several (usually two) concentrically located compression springs that absorb the load simultaneously. To eliminate twisting of the end supports and misalignment, the springs must have a right and left winding direction. There must be sufficient radial clearance between them, and the supports are designed so that there is no lateral sliding of the springs.

To obtain a nonlinear load characteristic, use shaped(specifically conical) springs(Fig. 1.1, G), the projections of the turns of which onto the reference plane have the form of a spiral (Archimedean or logarithmic).

Twisted cylindrical torsion springs made from round wire similar to tension and compression springs. They have a slightly larger gap between the turns (to avoid friction during loading). They have special hooks, with the help of which an external torque loads the spring, causing rotation of the cross sections of the coils.

Many designs of special springs have been developed (Fig. 2).

Fig. 2. Special springs

The most commonly used are disc-shaped (Fig. 2, A), ring (Fig. 2, b), spiral (Fig. 2, V), rod (Fig. 2, G) and leaf springs (Fig. 2, d), which, in addition to shock-absorbing properties, have a high ability to extinguish ( dampen) vibrations due to friction between the plates. By the way, stranded springs also have the same ability (Fig. 1.1, d).

For significant torques, relatively low compliance and freedom of movement in the axial direction, torsion shafts(Fig. 2, G).

Can be used for large axial loads and small movements disc and ring springs(Fig. 2, a, b), Moreover, the latter, due to their significant energy dissipation, are also widely used in powerful shock absorbers. Belleville springs are used for large loads, small elastic movements and limited dimensions along the axis of load application.

For limited axial dimensions and small torques, flat spiral springs are used (Fig. 2, V).

To stabilize load characteristics and increase static strength, critical springs undergo surgery bondage , i.e. loading, under which plastic deformations occur in some cross-sectional zones, and during unloading, residual stresses occur with a sign opposite to the sign of the stresses arising under working loads.

Non-metallic elastic elements (Fig. 3), usually made of rubber or polymer materials, are widely used.

Fig.3. Typical rubber elastic elements

Such rubber elastic elements are used in the designs of elastic couplings, vibration-isolating supports (Fig. 4), soft suspensions of units and critical loads. In this case, distortions and misalignments are compensated. To protect rubber from wear and load transfer, metal parts are used - tubes, plates, etc. element material – technical rubber with tensile strength σ ≥ 8 MPa, shear modulus G= 500...900 MPa. In rubber, due to its low elastic modulus, 30 to 80 percent of the vibration energy is dissipated, which is about 10 times more than in steel.

The advantages of rubber elastic elements are as follows: electrically 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).

Rice. 4. Elastic shaft support

Springs and rubber elastic elements are used in the designs of some important gears, where they smooth out the pulsations of the transmitted torque, significantly increasing the service life of the product (Fig. 5).

Fig.5. Elastic elements in gears

A– compression springs, b– leaf springs

Here, elastic elements are integrated into the gear structure.

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 laminated springs (springs) deform, energy is dissipated due to mutual friction of the elements, as happens in laminated springs and strand springs.

Leaf packet springs (Fig. 2. d) due to their high damping, were successfully used from the first steps of transport engineering even in the suspension of carriages, they were used on electric locomotives and electric trains of the first production, where, due to the instability of friction forces, they were later replaced by coiled springs with parallel dampers, they can be found in some models of cars and road construction machines.

Springs are made from materials with high strength and stable elastic properties. High-carbon and alloyed (carbon content 0.5...1.1%) steel grades 65, 70 have such qualities after appropriate heat treatment; manganese steels 65G, 55GS; silicon steels 60S2, 60S2A, 70SZA; chrome vanadium steel 51HFA, etc. Modulus of elasticity of spring steels E = (2.1…2.2)∙ 10 5 MPa, shear modulus G = (7.6…8.2)∙ 10 4 MPa.

For work in aggressive environments, stainless steels or alloys of non-ferrous metals are used: bronze BrOTs4-1, BrKMts3-1, BrB-2, Monel metal NMZhMts 28-25-1.5, brass, etc. Modulus of elasticity of copper-based alloys E = (1.2…1.3)∙ 10 5 MPa, shear modulus G = (4.5…5.0)∙ 10 4 MPa.

Blanks for making springs are wire, rod, strip steel, tape.

Mechanical properties Some materials used for the manufacture of springs are presented in table 1.

Table 1. Mechanical properties materials for springs

Material	Brand	Ultimate tensile strengthσ V , MPa	Torsional strengthτ , MPa	Elongationδ , %
Iron-based materials
Carbon steels	65 70 75 85	1000 1050 1100 1150	800 850 900 1000	9 8 7 6
Piano wire		2000…3000	1200…1800	2…3
Cold-rolled spring wire (normal - N, high - P and high - B strength)	N P IN	1000…1800 1200…2200 1400…2800	600…1000 700…1300 800…1600
Manganese steels	65G 55GS	700 650	400 350	8 10
Chrome vanadium steel	50HFA	1300	1100
Corrosion resistant steel	40Х13	1100
Silicon steels	55С2 60С2А 70С3А	1300 1300 1800	1200 1200 1600	6 5 5
Chrome-manganese steels	50ХГ 50HGA	1300	1100 1200	5 6
Nickel-silicon steel	60С2Н2А	1800	1600
Chrome-silicon-vanadium steel	60S2HFA	1900	1700
Tungsten-silicon steel	65S2VA
Copper alloys
Tin-zinc bronze Siliceous manganese bronze	BrO4Ts3 BrK3Mts1	800…900	500…550	1…2
Beryllium bronzes	BrB 2 BrB2.5	800…1000	500…600	3…5

Design and calculation of cylindrical helical tension and compression springs

Springs made of round wire are mainly used in mechanical engineering due to their lowest cost and their better performance under torsional stresses.

Springs are characterized by the following basic geometric parameters (Fig. 6):

Diameter of wire (rod) d;

Average spring coil diameter D.

The design parameters are:

Spring index characterizing the curvature of its coil c =D/d;

Turn pitch h;

Helix angle α,α = arctg h /(π D);

Length of the working part of the spring N R;

Total number of turns (including end bent and support turns) n 1 ;

Number of working turns n.

All listed design parameters are dimensionless quantities.

Strength and elastic parameters include:

- spring stiffness z, spring stiffness of one coilz 1 (usually the unit of stiffness is N/mm);

- minimum workingP 1 , maximum workingP 2 and limit P 3 spring forces (measured in N);

- the amount of spring deformationF under the influence of applied force;

- the amount of deformation of one turnf under load.

Fig.6. Basic geometric parameters of a coil spring

Elastic elements require very precise calculations. In particular, they must be designed for rigidity, since this main characteristic. In this case, inaccuracies in calculations cannot be compensated for by rigidity reserves. 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.

The more flexible the spring should be, the greater the spring index and the number of turns. Typically, the spring index is selected depending on the wire diameter within the following limits:

d , mm...Up to 2.5...3-5....6-12

With …… 5 – 12….4-10…4 – 9

Spring stiffness z is equal to the magnitude of the load required to deform the entire spring per unit length, and the stiffness of one turn of the spring z 1 equal to the magnitude of the load required to deform one turn of this spring per unit length. Assigning a symbol F, denoting the deformation, the necessary subscript, we can write down the correspondence between the deformation and the force that caused it (see the first of the relations (1)).

The force and elastic characteristics of the spring are interconnected by simple relationships:

Coil springs made cold-rolled spring wire(see Table 1), standardized. The standard specifies: outer diameter of the spring D N, The diameter of the wire d, maximum permissible deformation force P 3, limiting deformation of one turn f 3, and the rigidity of one turn z 1. The design calculation of springs made from such wire is carried out using the selection method. To determine all spring parameters, it is necessary to know as initial data: maximum and minimum operating forces P2 And P 1 and one of three values ​​characterizing the deformation of the spring - the magnitude of the working stroke h, the magnitude of its maximum working deformation F 2, or hardness z, as well as the dimensions of the free space for installing the spring.

Usually taken P 1 =(0,1…0,5) P2 And P 3 =(1,1…1,6) P2. Next in terms of maximum load P 3 select a spring with suitable diameters - outer spring D N and wires d. For the selected spring, using relations (1) and the deformation parameters of one turn specified in the standard, it is possible to determine the required spring stiffness and the number of working turns:

The number of turns obtained by calculation is rounded to 0.5 turns at n≤ 20 and up to 1 turn at n> 20. Since the outermost turns of the compression spring are bent and ground (they do not participate in the deformation of the spring), the total number of turns is usually increased by 1.5...2 turns, that is

n 1 =n+(1,5 …2) . (3)

Knowing the stiffness of the spring and the load on it, you can calculate all its geometric parameters. The length of the compression spring in a fully deformed state (under the influence of force P 3)

H 3 = (n 1 -0,5 )d.(4)

Free length of spring

Next, you can determine the length of the spring when loaded with working forces, pre-compression P 1 and maximum working P2

When making a working drawing of a spring, a diagram (graph) of its deformation must be drawn parallel to the longitudinal axis of the spring, on which permissible length deviations are noted H 1, H 2, H 3 and strength P 1, P2, P 3. In the drawing, reference dimensions are indicated: spring winding pitch h =f 3 +d and the angle of rise of turns α = arctg( h/p D).

Helical coil springs, made from other materials, not standardized.

The force factors acting in the frontal cross section of tension and compression springs are reduced to the moment M =FD/2, whose vector is perpendicular to the axis of the spring and the force F, acting along the axis of the spring (Fig. 6). This moment M expands to torque T and bending M I moments:

In most springs, the angle of elevation of the coils is small, does not exceed α < 10…12°. Therefore, the design calculation can be carried out using the torque, neglecting the bending moment due to its smallness.

As is known, when the tension rod is torsioned in a dangerous section

Where T– torque, and W ρ =π∙ d 3 /16 – polar moment of resistance of the section of a coil of a spring wound from a wire with a diameter of d, [τ ] – permissible torsional stress (Table 2). To take into account the uneven distribution of stress over the cross section of the turn, due to the curvature of its axis, a coefficient is introduced into formula (7) k, depending on the spring index c =D/d. At normal helix angles lying within 6...12°, the coefficient k with sufficient accuracy for calculations can be calculated using the expression

Taking into account the above, dependence (7) is transformed to the following form

Where N 3 – length of the spring, compressed until adjacent working coils touch, H 3 =(n 1 -0,5)d, 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 supporting end.

n 1 – total number of turns, n 1 =n+(1.5…2.0), an additional 1.5…2.0 turns are used for compression to create the supporting surfaces of the springs.

Axial elastic compression of springs is defined as the total angle of twist of the spring θ, multiplied by the average radius of the spring

The maximum spring settlement, i.e., the movement of the end of the spring until the coils are in full contact, is,

The length of wire required to wind the spring is indicated in the technical requirements of its drawing.

Free length ratio of springH to its average diameterD is called spring flexibility index(or just flexibility). Let us denote the flexibility index γ, then by definition γ = H/D. Usually, at γ≤ 2.5, the spring remains stable until the coils are completely compressed, but if γ >2.5, loss of stability is possible (the longitudinal axis of the spring can bend and bulge sideways). Therefore, for long springs, either guide rods or guide sleeves are used to keep the spring from bulging to the side.

Load nature	Allowable torsional stresses [ τ ]
Static	0,6 σ B
Zero	(0,45…0,5) σ Design and calculation of torsion shafts Torsion shafts are installed in such a way as to exclude the influence of bending load on them. The most common is to connect the ends of the torsion shaft with parts that are mutually movable in the angular direction using a spline connection. Therefore, the material of the torsion shaft works in pure torsion, therefore the strength condition (7) is valid for it. This means that the outer diameter D the working part of the hollow torsion bar can be selected according to the ratio Where b =d/D– relative value of the diameter of the hole made along the axis of the torsion bar. With known diameters of the working part of the torsion bar, its specific angle of twist (the angle of rotation around the longitudinal axis of one end of the shaft relative to its other end, related to the length of the working part of the torsion bar) will be determined by the equality and the maximum permissible angle of twist for the torsion bar as a whole will be Thus, during the design calculation (determining the structural dimensions) of the torsion bar, its diameter is calculated based on the limiting moment (formula 22), and the length is calculated from the maximum twist angle using expression (24). The permissible stresses for helical compression-tension springs and torsion bars can be assigned the same in accordance with the recommendations in Table. 2. This section provides brief information regarding the design and calculation of the two most common elastic elements of machine mechanisms - cylindrical helical springs and torsion bars. However, the range of elastic elements used in technology is quite large. Each of them is characterized by its own characteristics. Therefore, to obtain more detailed information on the design and calculation of elastic elements, you should refer to the technical literature. Self-test questions By what criteria can elastic elements be found in the design of a machine? For what purposes are elastic elements used? What characteristic of an elastic element is considered the main one? What materials should elastic elements be made of? What type of stress does the tension-compression spring wire experience? Why choose materials for springs of high strength? What are these materials? What does open and closed winding mean? What is the calculation of coil springs? What is the unique characteristics of disc springs? Elastic elements are used as..... 1) power elements 2) shock absorbers 3) engines 4) measuring elements when measuring forces 5) elements of compact structures A uniform stress state along the length is inherent in ..... springs 1) twisted cylindrical 2) twisted conical 3) disc-shaped 4) leafy For the manufacture of twisted springs from wire with a diameter of up to 8 mm, I use ..... steel. 1) high carbon spring 2) manganese 3) instrumental 4) chromium-manganese The carbon steels used to make springs differ...... 1) high strength 2) increased elasticity 3) stability of properties 4) increased hardenability For the manufacture of twisted springs with coils with a diameter of up to 15 mm, .... steel is used 1) carbon 2) instrumental 3) chromium-manganese 4) chrome vanadium For the manufacture of twisted springs with coils with a diameter of 20...25 mm, .... is used.

In instrument making, springs of various geometric shapes are widely used. They are flat, curved, spiral, screw.

6.1. Flat springs

6.1.1 Applications and designs of flat springs

A flat spring is a plate that bends and is made of an elastic material. During manufacturing, it can be given a shape that is convenient for placement in the device body, while it may take up little space. A flat spring can be made from almost any spring material.

Flat springs are widely used in various electrical contact devices. The most widespread is one of the simplest forms of a flat spring in the form of a straight rod clamped at one end (Fig. 6.1, a).

A - contact group of the electromagnetic relay; b - changeover contact;

V - sliding contact springs

Rice. 6.1 Contact springs:

Using a flat spring, a reversible elastic microswitch system can be made, providing a sufficiently high response speed (Fig. 6.1, b).

Flat springs are also used in electrical contact devices as sliding contacts (Fig. 6.1, c).

Elastic supports and guides made of flat springs have no friction or backlash, do not require lubrication, and are not susceptible to contamination. The disadvantage of elastic supports and guides is the limited linear and angular movements.

Significant angular movements are allowed by a spiral-shaped measuring spring - a hair. Hairs are widely used in many indicating electrical measuring instruments and intended for selecting backlashes in the transmission mechanism of the device. The twist angle of the hair is limited both for reasons of strength and due to the loss of stability of the flat shape of the bend of the hair at sufficiently large twist angles.

The mainsprings have a spiral shape and act as a motor.

Rice. 6.2 Methods for securing flat springs

6.1.2 Calculation of flat and spiral springs

Flat straight and curved springs are a plate of a given shape (straight or curved), which elastically bends under the influence of external loads, i.e., bends. These springs are usually used in cases where the force acts on the spring within a small stroke.

Depending on the methods of fastening and places where loads are applied, flat springs are distinguished:

- working as cantilever beams with a concentrated load at the free end (Fig. 6.2 a);

- working like beams, freely lying on two supports with a concentrated load (Fig. 6.2 b);

- working like beams, one end of which is fixed, and the other freely lies on a support with a concentrated load (Fig. 6.2 c);

- working like beams, one end of which is hinged, and the other freely lies on a support with a concentrated load (Fig. 6.2 d);

- which are round plates fixed at the edges and loaded in the middle (membranes) (Fig. 6.2 d).

A) c) d)

When designing flat leaf springs, you should, if possible, choose the most simple shapes, facilitating their calculation. Flat springs are calculated using the formulas

Spring deflection from load in, m
Spring thickness in m
Spring width in m
	Set according to operating conditions
RR	Selected by
Working deflection of the spring in m		constructive
Working length of spring in m		considerations

Coil springs are usually placed in a drum to give the spring certain external dimensions.