# Supports shafts and axles, Rolling bearings - Applied Mechanics

## Supports shafts and axes

The shaft and axle supports are designed to support the rotational or rocking motion of the shafts and axles and transfer forces from them to the housing. The accuracy of the operation and the reliability of the mechanism as a whole largely depend on the design of the supports. Supports designed to perceive a radial or combined (radial and axial) load, it is customary to call bearings, and supports that accept only axle loads are thrust bearings.

By the form of friction, they are divided into rollers and sliding supports. The choice of one or another type of support is determined by the operating conditions, the loads acting on the support, the dimensional constraints, the required longevity and the cost of the mechanism.

## Rolling bearings

The rolling bearing is a ready-made assembly consisting of outer 1 and inner 2 rings with raceways, between which the rolling bodies 3 and the separator 4, holding the rolling bodies at a certain distance from each other and guiding their rotation (Fig. 4.72, a). The rolling bearings are the most a common finished assembly unit and used in virtually all mechanisms that have rotating parts (with the exception of mechanisms with sliding bearings).

Rolling bearings are standardized and manufactured at specialized state bearing plants (GPP). In the production of bearings, the domestic industry is one of the leading places in Europe. In the late 1980s. up to 1 billion bearings per year of various sizes - from 1 mm inner diameter to 3 m outer diameter.

Advantages : relatively small friction losses; relatively low cost of bearings during their mass production; relatively small length of the support; a lower consumption of lubricant; small starting moments; complete interchangeability, which facilitates the assembly and repair of mechanisms. In the design of shafts and axes with rolling bearings, problems of axial fixation and compensation of temperature deformations are easier to solve, they are less sensitive to distortions and deflections of shafts under load, to misalignment of supports.

Disadvantages : high sensitivity to shock loads; limited speed associated with kine -

Fig. 4.72

matika and dynamics of rolling bodies (centrifugal forces, gyroscopic moments, etc.); high cost in single or small-scale production; relatively large radial dimensions of the support; limited range of operating temperatures; noise during operation, due to errors in shape; bearings of general application do not work in aggressive environments.

Bearings of general use, which are used in general engineering, railway transport, automotive and other industries, produce five classes of accuracy, which differ in the size tolerances for the size of rings and rolling elements. As the manufacturing accuracy increases, the cost of bearings increases, so the choice of the accuracy class must have an appropriate justification. In Table. 4.22 shows the comparative cost of bearings of different accuracy classes.

Table 4.22

 Designation Accuracy class Comparative cost 0 Normal 1 6 Increased 1.92 5 High 10 4 Precision 20 2 Super Precision Up to 100

In the form of rolling bodies bearings are divided into ball and roller bearings. The rollers can be short cylindrical, barrel-shaped, conical, twisted and long cylindrical (Figure 4.72, b).

According to the way of self-alignment bearings can be non-self-aligning and self-aligning.

According to the number of rows of rolling bodies bearings are divided into single, double and multi-row.

According to the overall dimensions ratio the same type of bearings are divided into series: ultra-light, extra light

Fig. 4.73

(Figure 4.73, a), is an easy (Figure 4.73, b), a light wide (Figure 4.73, c), average (Figure 4.73, d), medium wide (Figure 4.73, d ) and heavy (Figure 4.73, e ). Bearings of the light and medium series are the most common and, correspondingly, for mass production, are of low cost.

Let's consider some basic types of bearings of general application.

Radial bearings. The ball-bearing radial single-row bearing (Fig. 4.74, a) is intended for the perception of radial load, but can also absorb the axial load within up to 70% of unused radial. These bearings fix the position of the shaft in two axial directions, at low speeds, small misalignment of the shafts (up to 8 ') is allowed, the magnitude of which depends on the internal gaps between the rings and rolling elements.

deep groove ball bearings, double-row spherical (self-aligning) (Fig. 4.74, b) receives a radial load during mutual rotation axes of the rings to 2-3 ° and an axial, component before 20% of the unused radial. Self-aligning bearings have advantages with significant deflection of shafts and misalignment of supports. When swinging, these bearings work better than radial single-row bearings.

A radial roller bearing with short cylindrical rollers (fig. 4.74, c) perceives a radial load 1.7 times greater than ball bearing of the same dimensions. In the design of such bearings, one of the rings has guide beads, and the other with respect to the rollers is not fixed. Axial load, these bearings are not perceived. If bearings are misaligned, additional pressure is created along the edges of the rollers,

Fig. 4.74

sharply reduces the life of bearings. They are used in electric motors, reducers, gas turbines and other machines.

Bearing roller radial spherical double-row (self-aligning) (fig. 4.74, d) perceives increased radial load and axial to 25% of unused radial. The rollers of this bearing are barrel-shaped, and the outer ring can rotate freely in the axial direction with respect to the inner ring. Such bearings can compensate misalignment and deflections of the shaft with skewed rings up to 2.5 °. They fix the shaft in the axial direction to both sides within the available gaps. These bearings are used in the supports of pumps, rolling mills and other machines where large radial loads and possible misalignment of shafts.

Needle Roller Bearing (Figure 4.74, ) perceives large radial loads at small radial dimensions. It is used at speeds of up to 5 m/s on the pallet, as well as with swinging movements. Rollers are rollers with a diameter of 1.6-6 mm and a length of 4-10 diameters of rollers, which are installed without a separator. Sometimes bearings are used without an inner ring, and the rollers roll over the surface of the shaft. These bearings are very sensitive to deflection of shafts and misalignment of seats. The needle bearing is used in the support of crank-rod and rocking mechanisms, cardans, milling machine units, etc.

The roller bearing conical (Figures 4.74, g) simultaneously perceives a significant radial and one-sided axial loads. The rolling element of this bearing is a conical roller. Apply them at speeds of up to 15 m/s. At very high loads (in rolling mills) multi-row tapered roller bearings are installed, capable of absorbing double-sided axial loads. The magnitude of the perceived axial load depends on the angle of the cone of the outer ring, with the increase of which increases the axial load and reduces the radial load capacity. When mounting these bearings, the axial clearance must be adjusted. Very small or too large gaps can lead to the destruction of the bearing parts. Apply these bearings in the wheels of aircraft, automobiles, in cylindrical and worm gearboxes, gearboxes, in spindles of metal-cutting machines.

Thrust ball bearings ( 4.74, Z ) are designed to absorb axial loads, but can also take small radial loads. The angle of inclination of the contact line is 45-60 °. Apply them at low speeds.

Thrust Bearings. The ball bearing thrust bearing (Figures 4.74, and) is intended for only axial load at shaft speeds up to 10 m/s , works better on vertical shafts. At high speeds, the operating conditions of the bearing deteriorate due to centrifugal forces and gyroscopic moments acting on the balls. Very sensitive to the accuracy of installation, allow the mutual skewing of the rings to 2 '. They are used in screw-nut gears, for jacks, crane hooks, etc.

The thrust roller bearing (Fig. 4.74, k) is intended for the perception of only the axial load, mainly on vertical shafts with low speeds . Characterized by high carrying capacity. Very sensitive to skewed rings: an allowable skew of not more than 1.

Special bearings. In addition to general-purpose bearings, special bearings are also produced, for example aircraft, corrosion-resistant, self-lubricating, low-noise, etc. Bearings include heavy-duty high-speed bearings for gas turbine engines, bearings for control mechanisms aircraft (LA), performing swinging motion under the action of high loads, bearings for electric generators with speeds of up to 100,000 rpm. Bearings for control mechanisms LA released without a separator with a full filling balls, grease and protective washers that hold the lubricant in the space between the rings. Corrosion-resistant bearings are made of chrome steel 95X18, 11X18, separator - made of PTFE-4. Self-lubricating bearings are installed in the mechanisms of special equipment operating under conditions of deep vacuum, ultra-low or ultrahigh temperatures (mechanisms of space technology). Under these conditions, plastic and liquid lubricants lose their viscosity and therefore use solid lubricants, such as molybdenum disulfite MoS2, graphite, fluoroplastic, special grades of plastics. Special coatings of silver, nickel, and gold are applied to the raceways. These bearings operate at speeds of 2 times lower than conventional ones, since there is no heat removal from the friction zone. Low-noise bearings are used in mechanisms that operate for a relatively long time in the presence of a person (life support systems for an astronaut, mechanisms for household appliances, etc.). Reducing the level of vibrations and accordingly the noise is achieved by reducing the gaps between the rolling elements and the bearing rings, increasing the accuracy of their manufacture.

Bearings are made of ball bearing high-carbon chromium steels ШХ15, ШХ15СГ with carbon content of 1-1,5%. The number in the designation of the steel grade indicates the chromium content in tenths of a percent. Also used are cemented alloyed steel 18ХГТ, 20Х2Н4А, 20НМ. Hardness of rolling bodies and bearing rings 60-65 HRC. For bearings operating in corrosive environments, corrosion-resistant steels 9X18, 9X18SH are used. Separators are most often made of stamped or riveted steel tape. At relative circumferential speeds of rings more than 10 m/s separators from bronze, brass, aluminum alloys and non-metallic materials are used.

Select the bearing type. When choosing a rolling bearing, the magnitude, nature of the action and direction of the load, the speed of rotation, the required longevity, installation conditions, environmental effects, etc. are taken into account. For the same working conditions, bearings of various types can be used, and when they are selected, economic factors and operating experience of similar structures are taken into account. First consider the possibility of using radial single-row ball bearings of light or medium series as the cheapest and easiest to operate. The choice of other types of bearings should be justified. The dimensions of the bearing are determined by the requirements for load-carrying capacity, diameter of the shaft journal (determined by strength), conditions for placing the supports. Thus, the choice of bearing is an important and crucial moment in the design phase of the mechanism.

Calculation of bearings. Calculation of the bearing life is based on its dynamic load capacity. When the bearing rotates, contact stresses that vary in the zero-point cycle arise at the point of interaction of the rolling element with the ring. The criterion for their performance is resistance to fatigue failure of the contact surface. Based on the experimental data, the following relationship is established between the acting load and the durability:

where L - bearing life, million revolutions; - coefficients; C - dynamic load carrying capacity, which is a constant radial load, which the bearing with a stationary outer ring can withstand 1 million revolutions; P - the equivalent load acting on the bearing; - exponent ( for ball bearings and for roller bearings).

Reliability of bearings of general application corresponds to the probability of failure-free operation . If it is necessary to increase the reliability, a durability factor is introduced (Table 4.23).

Table 4.23

 P 0.9 0.95 0.96 0.97 0.98 0.99 a. 1 0.62 0.53 0.44 0.33 0.21

The coefficient depends on the material of the bearing and the operating conditions. For general mechanisms, you can take

where X and Y are the radial and axial load factors (see Table 4.16); V - the rotation coefficient equal to 1 if the inner ring rotates and 1,2 - when the outer ring rotates; and - radial and axial loads; - safety factor that takes into account the nature of the current load; - temperature coefficient equal to unity at the working temperature of the bearing C.

Safety factor with a shock-free load with light shocks and vibrations; with moderate shocks and vibrations, with strong shocks and high overloads.

Equivalent load for bearings with short cylindrical rollers is found by the formula

and for thrust bearings - according to the formula

If the equivalent load P is increased by a factor of 2, the durability is reduced by 8-10 times, therefore it is necessary to determine the load acting on the bearing as accurately as possible.

Bearing durability (in h) is compared with the mechanism resource:

where n - rotation frequency of the bearing ring, rpm; D - resource of the mechanism, h.

The calculation of durability for dynamic load is carried out for bearings with a speed of rotation; rpm. In bearings of oscillatory motion or rotating at a frequency rpm, the acting load is treated as static and is compared to the static load capacity Q. By static load capacity at which the residual deformation of the rolling bodies and rings does not exceed the permissible , where D is the diameter of the rolling element. The static and dynamic load ratings are given in the bearing catalogs.

Lubricants. Of great importance is the correct choice of lubricant, the presence of which reduces frictional losses, contributes to the removal of heat from the friction zone, softens the impact of rolling elements on the separator and rings, protects against corrosion, and reduces noise. The choice of this or that type of lubricant for bearings depends on the operating conditions and conditions, the design of the mechanism, the environment, special requirements, etc. For lubrication, plastic and liquid lubricants are used. Plastic lubricants of CILTIM-201 grades,

Litol-24, VNII NP-207 and others are used in the temperature range -60 ... +150 ° C, moderate loads and rotation frequencies; Liquid lubricants (oils) - for high-speed and heavy-loaded bearings. The latter provide more efficient heat removal, have better penetration to friction surfaces. They are also used in hard-to-replace lubricant friction units and, if necessary, constant monitoring of the presence of a lubricant. The main brands of liquid oils: industrial И-5А, И-12А, transmission TAD-17, aviation МС-14, МК-22, etc.

Sealing of bearing assemblies . An important condition for reliable operation of bearings is a reasonable choice of seals that protect the bearing cavity from penetration of dust, moisture, abrasive particles from the environment and prevent the lubricant from escaping. The design of the selected seal depends on the type of lubricant, conditions and operating conditions of the bearing assembly, and also the degree of its tightness.

According to the principle of action, the seals are divided into contact, in which sealing is carried out by tight fitting of the sealing elements to the movable surface of the shaft; contactless - sealing in which is carried out due to small gaps of conjugate elements; combined, consisting of a combination of contact and non-contact seals.

Contact Seals. The main types of contact seals are stuffing boxes and cuffs. Felt seals (stuffing boxes) are used to seal cavities of bearings operating on ductile lubricant to circumferential velocities v = 8 m/s and T = 90 ° C . The contact of the ring 2 with the shaft 1 (Fig. 4.75, a) is provided by pre-tensioning. Before installation in the groove in the body part, the felt rings are impregnated with a heated mixture of lubricant (85%) and graphite. It is not recommended to use these seals with excessive pressure and increased dust content of the environment. The efficiency and durability of the stuffing box seals increases when installed in combination with other seals (slotted and labyrinth seals).

The lip seals (Figure 4.75, b) have a sealing ring 3, made of rubber having a protruding work edge that contacts the surface of the shaft 1. The contact edge of the cuff with a width of 0.2-0.5 mm with the shaft is provided by pre-tensioning, and also by pressing it against the shaft by a bracelet spring 2. The seal is set so that the working edge is pressed to the shaft by the excess pressure of the medium to be sealed. The cuffs for working in a clogged environment are made with an additional dust lip 5. To increase rigidity, the cuff housing can be reinforced with a steel ring 4. The lip seals in the bearing assemblies are used at speeds V = 25 to 30 m/s and an overpressure of

P = <0.2> 0.3 MPa. Efficiency of work is increased by the sequential installation of two cuffs at a distance of 3-8 mm.

Fig. 4.75

Sealing of bearing assemblies for any lubricant and speeds v> 5 m/s can be provided by shaped washers 2 (Fig. 4.75, c). The thickness of the washers depends on their size and is 0.3-0.5 mm. Fixation of the washer is carried out with a nut 1. It is not recommended to seal self-aligning bearings with large axial clearances by means of shaped washers because of the possibility of breaking the contact between the washer and the bearing ring.

Lack of contact seals - the presence of friction between the contacting surfaces, which leads to additional energy costs, as well as heating and wear of the surfaces. Friction and wear of the contact pair limit the durability and the field of application of the contact seals.

Non-contact seals. These seals work by resisting the flow of lubricant through narrow slots or channels with sharply varying cross-sections. They do not provide absolute tightness, but serve to limit leaks. The main advantage of non-contact seals is increased durability and reliable operation at all temperatures and speeds. By the principle of action, they can be divided into static and dynamic. In static seals, slotted and labyrinth, the amount of leakage depends only on the geometric characteristics of the connection of the conjugate elements. The effectiveness of dynamic seals depends on the geometry of the connection and the relative speed of rotation of the conjugate elements.

The slit seal (Fig. 4.75, r) is used with a plastic lubricant and velocities v = 5 m/s. The degree of seal sealing depends on the size of the gap and the length of the slit. The clearance is determined by the deflection of the shaft at the location of the seal, the eccentricity of the surfaces of the shaft 2 and the body 1 with respect to the axis of rotation, bearing clearance, etc. Reduction of the gap is achieved by applying a mastic 3 , prepared on powdered graphite, to a fixed piece.

Sealing of bearing assemblies operating on a plastic and liquid lubricant at temperatures T = <80> 400 ° C and velocities v = 30 m/s can be ensured by fat grooves (Figure 4.75, E), which, when assembled, is filled with a plastic lubricant. The dimensions of the grooves and the size of the clearance are determined depending on the diameter of the shaft. For example, with d = 20> 95 mm r = 1 or 1.25 mm and δ = 0.3 or 0.4 mm.

Labyrinth seal is used at speeds of v & gt; 30 m/s. Depending on the number of gaps, they can be single- and multistage. The radial seal (Figure 4.75, e) allows relative displacement of the sleeve 2 relative to the bearing cover 1, so it is used for floating bearing supports. In the axial labyrinth seal (Fig. 4.75, g) for a non-detachable casing 3 a composite labyrinth sleeve 4 is used. This seal is established with axial displacements of the shaft.

In bearing bearings with liquid lubricant , dynamic seals are used that work with the rotation of cotton wool, but lose effectiveness when stopped. To prevent leaks in non-working mechanisms, such seals are often used in combination with static contact or non-contact seals. The spiral ( threaded ) compaction (Figure 4.75, h) is performed in the form of single- or multi-thread cutting of a rectangular or triangular profile. When the shaft rotates, the lubricant is thrown into the gearbox cavity. On -

Fig. 4.76

Cutting board must be coordinated with the direction of rotation of the shaft. The spiral seal can not be used in reversible mechanisms.

In Fig. 4.76 shows the combined seal of the bearing assembly of the AI-14B aircraft engine gearbox, consisting of an oil-bearing ring 2 and elastic metal rings 1. In the non-working gearbox, sealing is provided by contact of the elastic rings with a cover bearing 4. When the shaft rotates under the action of centrifugal forces, the liquid lubricant is thrown to the periphery of the ring 2 and flows down to the lower part of the housing where there is a channel 3 for its drainage.

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