# roller bearing

Deep groove ball bearings (exemplary structure and designation of the components according to DIN 625)
1. Inner ring
2. Cage
3. Sealing washer
4. Rolling element
5. Outer ring
Ball bearing with stationary outer ring
Tapered roller bearings

Rolling bearings are bearings in which between an inner ring and an outer ring, in contrast to the lubrication in plain bearings , rolling bodies reduce the frictional resistance. They serve to fix axles and shafts . Depending on the design, they absorb radial and / or axial forces and at the same time enable the rotation of the shaft or of the components mounted on an axle (e.g. a wheel ). Rolling friction mainly occurs between the three main components of the inner ring, outer ring and the rolling elements. Since the rolling elements in the inner and outer ring roll on hardened steel surfaces with optimized lubrication , the rolling friction of these bearings is relatively low.

Rolling bearings are differentiated according to the type of rolling element (ball, roller, etc.), see section Rolling bearing designs . In particular, one speaks of a ball bearing when the rolling elements are balls. Colloquially, other types of rolling bearings are sometimes referred to as "ball bearings".

## History of the rolling bearing

The history of the roller bearing goes back over 2,700 years. During the excavations of a Celtic chariot , small pieces of cylindrical beech wood were discovered near the wheel hubs of the vehicles . Researchers conclude that the Celts as early as 700 BC. Knew the cylindrical roller bearing.

In the Roman Empire , roller bearings were described by Vitruvius and, towards the end of the Republic, ball bearings were used in hoists. When the Nemi ships of Emperor Caligula (term of office: 37-41 AD) were salvaged , a thrust bearing was found, which may have belonged to a rotating statue base.

In the course of industrialization , the need arose for a bearing that behaved better than plain bearings at low speed. The plain bearing wears very quickly at low speed and / or if there is insufficient lubrication. In old steam locomotives, for example, these wheel bearings were often replaced.

Built-in roller bearing (1904)

In the course of time, numerous other variants were added. In particular, manufacturing accuracy and lubricant development continued to develop. Numerous norms also set common standard dimensions and thus simplified design and manufacture. Today, bearings with integrated sensors such as electronic force and wear detection are offered.

## History of the German rolling bearing industry

Headquarters FAG Kugelfischer in Schweinfurt (until 2001), today Schaeffler with the FAG brand
Headquarters SKF Deutschland GmbH in Schweinfurt
• In 1883 Friedrich Fischer built the first ball grinding machine in Schweinfurt and thus laid the foundation for the industrial production of round steel balls with sufficient accuracy and the roller bearing industry. In the same year he founded the Kugelfischer company . His colleague Wilhelm Höpflinger made decisive improvements to the ball grinding machine. Höpflinger started his own business in 1890 and founded the company Fries & Höpflinger together with Engelbert Fries, also in Schweinfurt . The big three Kugelfischer, Fries & Höpflinger and Fichtel & Sachs established Schweinfurt's position as the center of the German as well as the European roller bearing industry.
• Around 1910: Other German rolling bearing manufacturers were the Deutsche Waffen- und Munitionsfabriken AG Berlin-Karlsruhe (DWM) , the Maschinenfabrik Rheinland ( Düsseldorf ), the Riebe-Werk ( Berlin ), the Deutsche Kugellagerfabrik (DKF, Leipzig), Fritz Hollmann ( Wetzlar ) , G. u. J. Jäger ( Wuppertal ).
• 1912: SKF participated in the Norma-Compagnie founded by Albert Hirth in Stuttgart-Cannstatt .
• 1929: Under pressure from SKF, six German rolling bearing manufacturers (rolling bearing division of Fichtel & Sachs, rolling bearing division of Berlin-Karlsruher Industriewerke (DWF), Fries & Höpflinger, Maschinenfabrik Rheinland, Riebe-Werke and SKF-Norma) joined the United under Swedish leadership Kugellagerfabriken AG (VKF, Schweinfurt). As the only leading German rolling bearing manufacturer, FAG Kugelfischer remained independent. The two Schweinfurt companies VKF and FAG Kugelfischer were the dominant German rolling bearing manufacturers for the next few decades.
• 1933: Kugelfischer takes over G. u. J. Jaeger GmbH, Wuppertal-Elberfeld.
• 1943–1945: During the Second World War , 15 major air raids by the British and US Americans caused severe damage to the city of Schweinfurt and its production facilities for the rolling bearing industry.
• 1946: Georg and Wilhelm Schaeffler founded the INA needle roller bearings company in Herzogenaurach .
• In 1949 Erich Franke and Gerhard Heydrich founded the company Franke & Heydrich KG - now Franke GmbH - in Aalen . In 1934 Erich Franke invented the wire race bearing based on the principle of the inserted running wires.
• 1953: The United Kugellagerfabriken AG (VKF) is renamed SKF Deutschland GmbH, based in Schweinfurt.
• 1991: FAG Kugelfischer took over the GDR roller bearing manufacturer DKF in Leipzig from the trust . This commitment proved to be economically unsustainable, and in 1993 FAG Kugelfischer found itself in an existentially dangerous situation.
• 2001: The previously generally unknown INA-Holding Schaeffler KG acquired the meanwhile restructured DAX group FAG Kugelfischer as part of the first hostile takeover of Germany after the war .
• 2006: FAG Kugelfischer and INA are merged in Schaeffler KG and thus become the second largest rolling bearing group in the world; to SKF, whose world's largest plant is also located in Germany (Schweinfurt).

## Rolling elements and rolling element cage

Ball bearings:
1. Outer ring
2. Guide
3. Rolling elements
4. Cage
5. Guide
6. Inner ring

The colloquially known ball bearings are a subgroup of rolling bearings in which balls serve as rolling elements .

In modern rolling bearings, the rolling elements (balls, cylinders, needles, barrels or cones) are kept at the same distance by a cage . Older roller bearing types and special designs manage without a cage. Rolling bearings in aircraft control systems in particular do not have a cage. This means that more rolling elements can be used per bearing, which significantly increases the load capacity. However, they are only suitable for higher speeds to a limited extent.

The cage material used to be brass because it ran more smoothly . Today the cage is often made of (mostly glass fiber reinforced) plastic ( polyamide ) for reasons of cost and weight . A cage made of low-alloy, unhardened steel is used in many types of rolling bearings. Brass cages still exist; especially for larger bearings where the tool costs for plastic or sheet steel cages are not worthwhile.

## Assembling a ball bearing

A simple radial deep groove ball bearing is composed as follows:

Assembly step Illustration description
1. The balls are placed in the outer ring so that they rest against one another.
2. The inner ring is first inserted from an eccentric position. The number of balls is essentially limited by the fact that the inner ring can be inserted in this constellation with balls resting against one another.
3. The inner ring is pressed down so that it is approximately concentric.
4th The balls are distributed so that they are evenly spaced from one another.
5. The cage is inserted. The cage is either elastic and one-piece or it is composed of two parts which are inserted from both sides and connected to one another by a suitable method.

The ball bearings are then greased or oiled and, if necessary, provided with cover or sealing washers.

## Bearing materials

Rolling bearings are usually made of chrome steel, very hard but easily rusting, in the steel grade 100Cr6 (material no. 1.3505), a steel with a content of approx. 1% carbon and 1.5% chromium. Other steels are for example 100CrMnSi6-4 and 100CrMo7, the alloying elements manganese (Mn) and molybdenum (Mo) are used for better hardenability.

For applications in a corrosive environment, the high-alloy steels X65Cr13 (material no. 1.4037) and X30CrMoN15-1 (material no. 1.4108) are also used. The latter can also be used in the human organism, at least for a few days. Hardenable steels are never completely “rust-free”, but only have increased corrosion resistance for a certain period of time.

The following roller bearings are available in the following designs for special operating conditions:

• Made of stainless steel (for example ball bearings S6204 or W6204)
• Hybrid bearings (two materials) in which the bearing rings are made of steel and the rolling elements are made of ceramic ( silicon nitride or zirconium dioxide), for example spindle bearings for machine tools
• Ceramic bearings, in which both the bearing rings and the rolling bodies from silicon nitride , zirconium oxide or silicon carbide exist
• Plastic bearings with rolling elements made of glass or ceramic against aggressive acids or bases in the chemical and food industries
• Bearings with a plastic cage ( e.g. ball bearing 6205 TN9 .C3) for low-noise operation
• Bearings with a current-insulating coating on the outer or inner ring in order to prevent undesired passage of current through the bearing and thus damage from electrical erosion , for example when using frequency converters to control the speed of three-phase motors

## Installation of rolling bearings

Rolling bearings are usually mounted on shafts or axles .

In the case of special designs (without a separate inner and outer ring), the ground or rolled and hardened running surfaces can be pressed directly onto the shaft or axle and / or into the bearing housing and the rolling bearing can thus be integrated into these components. This variant is mainly chosen for reasons of space. Therefore, needle rollers in particular are predestined for this task.

The bearings are often secured against slipping with a retaining ring, a lock nut or a spacer sleeve. To protect against contamination, bearings are built into a bearing housing or covered with a shaft seal .

In order not to damage the bearing, the press-in force must not be applied via the rolling elements during installation. With special tools such as a drive-in sleeve, for example, the bearing is only driven in via the outer ring. Needle roller bearings must be pressed in with a mandrel.

In the case of large bearings, the press-in forces are also greater, which is why they are heated to 80–100 ° C in an oil bath or an electric heater before assembly. The rings expand minimally and can thus be more easily pressed onto the shaft or axle.

When removing the bearings, care must be taken to use the appropriate tool, for example a puller.

Defective bearings can be recognized by sluggishness when turning slowly by hand, noticeable bearing play as well as running noises and vibrations at operating speed. Unlubricated bearings fail immediately.

## Life of rolling bearings

The inner race ("cone") of the cone bearing of a bicycle. The tread, which is probably too
brittle due to surface hardening, has flaked off.

The bearing life depends on many factors. Some influencing variables can be measured or calculated (such as bearing load or surface quality of the components). Others cannot be determined numerically (contamination or precise lubrication condition). Simple calculation tools are available on the manufacturers' websites (see web links ).

The lifetimes required of rolling bearings range from a few hundred hours, for example for household appliances or medical-technical equipment, to approx. 100,000 hours for running bearings of ocean-going ships, mine pumps and blowers and paper machines. Expressed in revolutions, bearings can withstand 3 billion revolutions and more, depending on the load. For example, SKF specifies a service life of 2 billion revolutions for some bearings, but this is often far exceeded.

Whether a bearing reaches its service life depends heavily on the operating conditions. High bearing loads should be avoided as far as possible, as well as dirty operating conditions, high operating temperatures or the ingress of water into the bearing. Many bearings are also available in an encapsulated design, especially to make it more difficult for dirt and water to penetrate.

One-time lubrication by the manufacturer over a specified service life is also common for rolling bearings .

In rolling bearings are sudden changes in load, as z. B. can occur in wheel bearings in cars, to be avoided if possible, since these forces can lead to a brief overload of the bearing and thus significantly affect the quality of the bearings and the service life.

To calculate the service life of rolling bearings, see: Bearing selection .

## Rigidity and damping behavior of rolling bearings

To determine the static stiffness of rolling bearings, relatively precise and experimentally well-proven calculation methods are available based on Hertzian theory, see e.g. B. the statements in the book "Rolling Bearing Analysis" by Tedric A. Harris (4th ed., 2000, Wiley-Interscience. ISBN 0-471-35457-0 ).

From recent scientific studies, there are also experimentally verified computer models for describing the dynamic rolling bearing properties, including the bearing damping properties, see e.g. B. the extensive literature review in the work "Damping and Stiffness Characteristics of Rolling Element Bearings" (Paul Dietl, Dissertation TU Wien, 1997).

The starting point of the mathematical models is usually a linearized spring-damper model of the elasto-hydrodynamic EHD rolling contact. Using a computer program to solve the transient EHD contact problem, equivalent damping coefficients for the highly stressed lubricating film in the rolling contact can then be determined numerically. From the numerical results, an empirical law of approximation for estimating the oil film damping in the rolling contact was derived in the above-mentioned work by Dietl.

The effective damping of material and dry friction in the rolling contacts can be described by a loss factor that is frequently used in the theory of material damping, which, according to measurements in the above-mentioned work by Dietl, is around 1 to 2%, depending on the influence of the joint fails between the outer ring and the housing.

## Applications

Rolling bearings are used in areas of application where bearings have to work with low friction at low speeds and high loads and where speeds change frequently.

Advantages of roller bearings over plain bearings Disadvantages of roller bearings compared to plain bearings
• low friction, therefore low heat generation
• no stick-slip effect (starting torque hardly greater than the operating torque)
• low lubricant requirement
• hardly any care and maintenance required
• good standardization and assessment bases, therefore easily interchangeable
• Change of direction of rotation possible without structural modification
• at standstill and at low speed sensitive to shocks and vibrations
• limited maximum speed and service life
• Sensitivity to soiling
• complex construction
• higher noise development

## Rolling bearing designs

Classification according to rolling elements, load direction and possible absorption of axis misalignment:

 radial radially spherical aslant obliquely spherical axial axially spherical ball-bearing Deep groove ball bearings, self-aligning ball bearings Angular contact ball bearings or cone bearings (single, double), four-point bearings Axial deep groove ball bearings Roller bearings cylindrical roller bearings and needle roller bearings, spherical roller bearings (barrel bearings) Tapered roller bearings, crossed roller bearings, spherical roller thrust bearings Thrust roller bearings

Depending on the direction of load, a distinction is made between radial and axial bearings . The pressure angle is used to help classify these two categories . Pressure angle is the angle between the radial plane and the pressure line , whereby the position of the pressure line is heavily dependent on the rolling elements and runways used. ${\ displaystyle \ alpha}$

• Radial bearing: ${\ displaystyle 0 ^ {\ circ} <\ alpha <45 ^ {\ circ}}$
• Thrust bearing: ${\ displaystyle 45 ^ {\ circ} <\ alpha <90 ^ {\ circ}}$

There are six basic forms of rolling bearings:

1. ball-bearing
2. Cylindrical roller bearings
3. Needle roller bearings
4. Tapered roller bearings
5. Barrel storage
6. Toroidal roller bearings (SKF CARB, FAG TORB)

Ball bearings are the most commonly used rolling bearings. There is the widest selection of different dimensions here. They are inexpensive, but due to their design they have a limited load-bearing capacity.

Various roller bearings: (from inside to outside) needle roller bearings, axial cylindrical roller bearings and ball bearings in a torque converter

#### Deep groove ball bearings ( DIN 625 )

Open single row deep groove ball bearing

The best known type is the deep groove ball bearing . It is designed to absorb predominantly radial forces. Since the balls also lie tightly against the running grooves at the sides, so that the rings and balls cannot be axially displaced against one another, this bearing can also absorb small axial forces. A rule of thumb is that the axial load capacity is approximately 50% of the radial load capacity. According to the SKF 2005 catalog, the axial load should generally not exceed 0.5 C 0 , and 0.25 C 0 for small and light bearings . Contact angle deep groove ball bearings are available as miniature ball bearings from dimensions of 0.6 × 2.5 × 1 mm (d × D × W). Of course, these deep groove ball bearings are also suitable for an axial load, e.g. B. when storing spindles in small CNC machines. As has already been written, the performance of such bearings is then limited to around 50% of the radial load capacity. But larger bearings certainly have no problems at all with a 50% load in providing a secure bearing in the axial direction. C 0 is the radial load capacity of a bearing. For small bearings (bore diameter up to approx. 12 mm) and for light bearings with the last digits 0, 1, 8 and 9, the axial load should be  limited to 0.25 times C 0 . Excessive axial loads can result in a significant reduction in bearing life. ${\ displaystyle \ alpha = 0 ^ {\ circ}}$

#### Angular contact ball bearings ( DIN 628 )

Angular contact ball bearings
(DIN 628)
##### Single row

The angular contact ball bearing can absorb radial forces and axial forces in one direction.

An angular contact ball bearing in vehicle construction is referred to as a cone bearing or cone bearing , which consists of two individually mounted running surfaces, the outer bearing shell and the inner cone . Often the cone is screwed onto the axle , which enables easy adjustment of the bearing clearance. In the inner bearing of the bicycle, the inner running surface is often forged onto the axle and the outer bearing shell is adjustable.

Conical bearings are usually installed and preloaded in pairs. They can be installed in pairs in the form of tandem, O or X versions. The axially absorbable forces change depending on the type of installation. The inclination of the runway creates an (internal) axial force that cannot be ignored, even with purely radial loads. Pressure angle${\ displaystyle \ alpha \ approx 40 ^ {\ circ}}$

##### Double row

The double row angular contact ball bearing corresponds to two single row angular contact ball bearings in an O arrangement. It can withstand high loads radially and axially in both directions. Pressure angle${\ displaystyle \ alpha \ approx 25 ^ {\ circ}}$

#### Four point bearings ( DIN 628 )

This roller bearing is a special form of angular contact ball bearing with a contact angle of . There are four points of contact between the rolling elements and the raceways. The split inner ring or outer ring means that more balls can be used with smaller dimensions. For this reason, both the axial and radial forces that can be absorbed increase in both directions. ${\ displaystyle \ alpha \ approx 35 ^ {\ circ}}$

#### Shoulder ball bearings ( DIN 615 )

The shoulder ball bearing is a special form of deep groove ball bearing that can be dismantled. It has only a low load-bearing capacity in the radial direction and in the axial direction on one side and is used for devices with low loads, such as measuring devices and household appliances. With double bearings (bearing-flinger-disk-bearing) loads of up to 2000 kg are possible. It can usually be dismantled. Contact angle shoulder ball bearings are standardized up to 30 mm and suitable for high speeds. ${\ displaystyle \ alpha \ approx 0 ^ {\ circ}}$

#### Self-aligning ball bearings ( DIN 630 )

The self-aligning ball bearing has two rows of balls. The roller track of the outer ring has a hollow spherical shape. The inner ring, cage and balls can be swiveled a few degrees from the center position. In this way, misalignments or deflections in the shaft can be compensated for by the self-aligning bearing. The load can be axial as well as radial in both directions.

#### Cylindrical roller bearings (DIN 5412)

Cylindrical roller bearings of type NU (DIN 5412). The inner ring can be pulled out on both sides.

The cylindrical roller bearing has a large radial load-bearing capacity, but it is not or only very little loadable in the axial direction. The rolling elements of cylindrical roller bearings are circular cylinders. Cylindrical roller bearings are manufactured in different designs (see table below).

Depending on the design, they can only absorb radial (e.g. NU as shown) or additional axial forces (e.g. one-sided with type NJ). The designs differ in the arrangement of the "ribs" on the inner and outer ring. If the ribs are missing, the inner ring can be pulled off, with the NU variant even from both sides. Cylindrical roller bearings are therefore suitable as floating bearings in fixed-floating bearings, because axial displacements are possible within certain limits.

Standard designs of single row cylindrical roller bearings:

1. NU: two fixed ribs on the outer ring, no rib on the inner ring
2. N: no rib on the outer ring, two ribs on the inner ring
3. NJ: two ribs on the outer ring, one rib on the inner ring
4. NUP: two ribs on the outer ring, one rib on the inner ring and a loose flange washer on the inner ring

A bearing without the removable ring is given the prefix “R”, so RNU202 designates a cylindrical roller bearing outer ring including rolling element set and cage from the complete bearing NU202. If necessary, an NJ202 inner ring can also be inserted into this. This leads to confusion during repairs. The prefix “R” can also be found on many types of needle roller bearings and support rollers.

#### Tapered roller bearings ( DIN 720 , ISO 355)

Tapered roller bearings

This bearing can withstand very high loads both in the radial and in the axial direction. It is usually installed in pairs: two bearings are set against each other, because the bearing consists of two loose elements: the inner ring (cone) with rolling elements, and the outer ring (cup) as a bearing shell. Common applications are: wheel bearings in cars and trucks ; Steering head bearings for motorcycles .

The rolling elements on the inner ring have the shape of a truncated cone, and they are slightly inclined towards the shaft axis. The game is adjustable. The cone tips (and any generators of the conical surfaces) of the inner ring, outer ring and all tapered rollers meet at one point on the axis of rotation, because only then can the tapered rollers roll without slippage .

Two tapered roller bearings ([<) can be mounted in an "O" ([<>]) or "X" arrangement ([> <]) as bearings. Example: The back-to-back arrangement is common for motorcycle steering head bearings, as external tilting moments can be better absorbed by the front wheel. The outer ring is pressed in at the top under the handlebar, the inner ring is placed in the outer ring pointing downwards. The lower counter bearing is mounted with the inner ring pointing upwards.

Bearings in metric and inch sizes are common, the latter have a completely different designation scheme.

#### Barrel and spherical roller bearings ( DIN 635 )

##### Barrel roller bearings DIN 635-1

This single-row barrel roller bearing is designed for high shock-like radial forces, but can only be subjected to low loads in the axial direction. It is well suited for compensating for misalignments. These are angle adjustable (up to 4 ° from the central position), since the outer ring has a spherical running surface. The rolling bodies, the so-called barrel rollers, are barrel-shaped . Barrel bearings are single-row, i.e. that is, they have a number of barrel rollers in a cage.

##### Spherical roller bearings DIN 635-2

The spherical roller bearing withstands axial and radial loads and is well suited to compensate for misalignments. Like barrel bearings, spherical roller bearings can be angularly adjustable (up to 2 ° with low load, otherwise up to 0.5 °), but in two rows. They are suitable for the heaviest loads, so they have high load ratings.

#### Needle roller bearings (DIN 617)

Needle roller and cage assembly: needle cage without housing and inner ring

A needle roller bearing has circular cylindrical rolling elements (needles) with very long lengths in relation to the rolling element diameter (> 2.5). It has a very small size and is often used in gearboxes and motors. Needle roller bearings in particular often do without an inner ring, in which case the appropriately designed shaft (hardened surface) serves as a raceway. Needle roller bearings are not suitable for absorbing tilting of the shaft, since high edge pressure occurs here, which greatly reduces the service life.

Needle roller bearings is the generic term for a whole range of special types:

• Needle roller and cage assemblies
• Needle sleeves, needle sleeves
• Needle roller bearings with a solid outer ring
• combined needle roller bearings (needle roller bearings and thrust bearings in one unit)
• Special forms such as support rollers with needle bearings

#### Toroidal roller bearings

Toroidal roller bearings are similar to spherical roller bearings, but have slightly convex rollers. Together with appropriately shaped roller tracks, they can compensate for both axial and angular misalignments without increasing the frictional torque of the bearing. Thus, a toroidal roller bearing can simultaneously function as a cylindrical roller bearing and a spherical roller bearing.

#### Ball roller bearings

Ball roller bearings are roller bearings related to deep groove ball bearings. They use laterally flattened balls and, thanks to their smaller width, offer advantages in terms of installation space compared to deep groove ball bearings. Another advantage of this type of bearing is the higher load capacity, since the design of the rolling elements means that a greater number can be installed than with a deep groove ball bearing of the same size.

This type of bearing was only developed a few years ago; it is currently not yet standardized (as of December 2012).

### Thrust bearings

Axial ball bearings in several designs

#### Axial deep groove ball bearings (DIN 711)

With axial deep groove ball bearings, the balls run between two or three disks, depending on whether the axial force occurs in both directions or only in one. When force is applied on both sides, the middle disk is held on the shaft, the two outer ones in the housing. These bearings can only absorb axial forces.

#### Axial cylindrical roller bearings (DIN 722)

This type of bearing is made up of a shaft washer, a housing washer and a unit with cylindrical rollers and cage. It is particularly suitable for heavy axial loads. Due to the speed differences between the inside and outside of the rollers, these bearings are only suitable for low speeds.

#### Axial spherical roller bearings (DIN 728)

The construction of the axial spherical roller bearing is similar to the radial spherical roller bearing, but only a number of rolling elements are used. Due to the spherical shape of the raceways, both high axial loads and misalignments (up to 3 ° with low loads) can be corrected.

## Bearing selection

### Rating

Values ​​that are necessary to dimension a bearing are:

• Axial force
• Speed or
• Speed (especially with linear bearings )
• Deflection and misalignment of the shaft or axis
• Environmental values, such as
• Installation conditions, such as B. the rigidity of a machine housing in the area of ​​the bearing point

Step 1

Input variables:

${\ displaystyle X, Y}$ = Adjustment factors, taken from a warehouse catalog
${\ displaystyle F_ {r}}$ = Determine the radial force on the bearing, in kN, yourself
${\ displaystyle F_ {a}}$ = Determine the axial force on the bearing, in kN, yourself

Calculate formula: ${\ displaystyle P = X \ times F_ {r} + Y \ times F_ {a}}$

Result:

${\ displaystyle P}$ = Dynamic equivalent load in kN

2nd step

Input variables:

${\ displaystyle C}$= Dynamic load rating in kN (= kilonewtons . Load rating for a given bearing can be taken from the manufacturer's bearing table)
${\ displaystyle P}$ = Dynamic equivalent load in kN (must be calculated first, see 1st step above)
${\ displaystyle p}$= Life exponent , = 3 (for ball bearings), = 10/3 (for all other bearings)${\ displaystyle p}$${\ displaystyle p}$
${\ displaystyle n}$ = Speed ​​in 1 / min (revolutions per minute)

Results: Service life in millions of revolutions with a 10% failure probability ${\ displaystyle L_ {10} = \ left ({\ frac {C} {P}} \ right) ^ {p}}$

${\ displaystyle L_ {10h} = {\ frac {10 ^ {6}} {60 \ cdot n}} \ cdot L_ {10} = \ left ({\ frac {16666} {n}} \ right) \ cdot \ left ({\ frac {C} {P}} \ right) ^ {p}}$Lifetime in hours with 10% probability of failure

The service life for other failure probabilities is calculated by multiplying by a factor: ${\ displaystyle L_ {10}}$

${\ displaystyle L_ {5} = 0 {,} 64 \ cdot L_ {10}}$ in millions of revolutions with 5% failure probability
${\ displaystyle L_ {4} = 0 {,} 55 \ cdot L_ {10}}$ in millions of revolutions with 4% failure probability
${\ displaystyle L_ {3} = 0 {,} 47 \ cdot L_ {10}}$ in millions of revolutions with 3% probability of failure
${\ displaystyle L_ {2} = 0 {,} 37 \ cdot L_ {10}}$ in millions of revolutions with 2% probability of failure
${\ displaystyle L_ {1} = 0 {,} 25 \ cdot L_ {10}}$ in millions of revolutions with 1% probability of failure

If the speed n is variable, the average speed must be used. This mean speed is calculated from the individual speeds and the respective duration of action in%: ${\ displaystyle n _ {\ text {m}}}$${\ displaystyle q}$

${\ displaystyle n_ {m} = n_ {1} \ cdot {\ frac {q_ {1}} {100}} + n_ {2} \ cdot {\ frac {q_ {2}} {100}} + \ dotsb }$

As can be seen from the second formula, the load on the bearing due to the power has a very strong influence on the service life. When the load changes, high loads that are effective for only a short period of time therefore have a considerable influence on the service life. The following then applies to the equivalent dynamic bearing load:

${\ displaystyle P = {\ sqrt [{p}] {P _ {\ text {1}} ^ {p} \ cdot {\ frac {n _ {\ text {1}}} {n _ {\ text {m}} }} \ cdot {\ frac {q _ {\ text {1}}} {100}} + P _ {\ text {2}} ^ {p} \ cdot {\ frac {n _ {\ text {2}}} { n _ {\ text {m}}}} \ cdot {\ frac {q _ {\ text {2}}} {100}} + \ dotsb}}}$

### Calculation example

The shaft absorbs 12 kN radial force at one bearing point. The shaft rotates at 6000 rpm during operation. As part of a fixed / loose bearing, this bearing should be axially displaceable as the floating bearing, i.e. it should not absorb any axial forces. This bearing should be a cylindrical roller bearing. It should have a lifespan of at least 10,000 hours.

In order to select a bearing that can carry this load, one must first determine the necessary dynamic load rating. To do this, first calculate the dynamic equivalent load.

For the bearing type cylindrical roller bearing, the values and can be found in the bearing catalog ${\ displaystyle X = 1}$${\ displaystyle Y = 0}$

In other words: ${\ displaystyle P = F_ {r}}$

In the formula for we now insert the required operating time of 10,000 hours, the number of revolutions and our determined . This formula then only has to be transformed to obtain the necessary dynamic load rating: ${\ displaystyle L_ {10h}}$${\ displaystyle P}$${\ displaystyle C}$

Out

${\ displaystyle L_ {10h} = {\ frac {10 ^ {6}} {60 \ cdot n}} \ cdot \ left ({\ frac {C} {P}} \ right) ^ {p}}$

becomes

${\ displaystyle C = \ left ({\ frac {L_ {10h} \ cdot 60 \ cdot n} {10 ^ {6}}} \ right) ^ {\ frac {1} {p}} \ cdot P}$

With

${\ displaystyle L_ {10h} = 10000}$
${\ displaystyle n = 6000 \, \ mathrm {min} ^ {- 1}}$
${\ displaystyle p = 10/3}$

and

${\ displaystyle P = 12 \ \ mathrm {kN}}$

follows

${\ displaystyle C = \ left ({\ frac {10000 \ cdot 60 \ cdot 6000} {10 ^ {6}}} \ right) ^ {\ frac {3} {10}} \ cdot 12 \ \ mathrm {kN }}$

or.

${\ displaystyle C = 140 \ \ mathrm {kN}}$

The dynamic load rating should therefore at least be. A suitable bearing with a suitable shaft diameter can now be found in the bearing catalog. ${\ displaystyle C = 140 \ \ mathrm {kN}}$

The following guide values ​​can be used to estimate the load on the bearings:

${\ displaystyle {\ frac {C} {P}}> 15}$ low load
${\ displaystyle {\ frac {C} {P}} <15}$ medium load
${\ displaystyle {\ frac {C} {P}} <6}$ high load
${\ displaystyle {\ frac {C} {P}} <3}$ very high load on the bearing

When designing the bearing, it is essential to avoid very high loads, even at low speeds. Low loads should also be avoided, since the rolling elements will not roll, but slide. Sliding friction must be avoided at all costs, as it causes heavy wear and a shortened service life.

In the case of angular contact ball bearings or tapered roller bearings in an adjusted bearing, a radial force to be absorbed by the bearing causes an internal axial force, which is taken into account in the service life calculation using appropriate and factors. ${\ displaystyle X}$${\ displaystyle Y}$

For most applications in general mechanical engineering, the above service life calculation method is sufficient. In certain cases, however, it may be necessary to carry out an extended service life calculation, which takes into account other influences such as the viscosity of the lubricant, operating temperature, probability of experience and cleanliness. The corresponding regulation is also contained in DIN ISO 281.

### Designation scheme

Rolling bearings are almost exclusively selected from books of tables or online catalogs.

The designations consist of combinations of letters and numbers that are structured according to a logical principle standardized in DIN 623 . This means that bearings with the same designation can be used regardless of the manufacturer.

The designation scheme includes prefixes, basic identifiers and suffixes. An S608 2RS is broken down as follows: a stainless steel bearing (prefix "S") with the main dimensions 8 × 22 × 7 mm (basic code "608"), which is sealed on both sides (suffix "2RS").

#### Bearing dimensions

Rolling bearings are largely standardized both in terms of their dimensions (bore, outside diameter, width) and their load capacities .

In addition, these bearings are also available in finished bearing blocks (see bearing units, housing bearings ), which can be pivoted or have rubber buffers for shock absorption .

Some designs are also supplied with sealing washers and permanent lubrication or cover washers (see sealing; suffix: 2RS, or 2Z or, depending on the manufacturer, ZZ) so that the running surfaces are protected from dirt or dust.

A simple assignment of the bearing designation to the main dimensions: Shaft diameter (d) and outer ring diameter (D) for bearings with a shaft diameter of 10 to 80 mm can be taken from the following table. Some bearing types are also built in different widths and can therefore be looked up in warehouse catalogs (see web link).

The designation of the different bearing types can be determined as follows (whereby "xxx" can be found in the table): To do this, first identify the bearing type and then the inner ring inner diameter and the outer ring outer diameter. Rolling bearings are therefore defined by two nominal diameters .

Now follow the inside diameter column in the table downwards and the outside diameter row to the right to the point of intersection. The number is added to the type designation.

Example: A single row deep groove ball bearing, the type designation begins with 6, has d = 25 mm and D = 52 mm, at the point of intersection is the number 205. The suitable replacement bearing is therefore a type 6205 with possibly a suffix for cover or sealing washers.

#### Common rolling bearing series

Special types and rare roller bearings are not listed. A distinction is made between

• 1xx = self-aligning ball bearing, two rows (108, 126 to 129 and 135)
• 6xx = deep groove ball bearings, single row (603 to 609 and 617 to 630)
• 7xx = angular contact ball bearings, single row (706 and 709xx)
• 1xxx = spherical roller bearing, double row, narrow design (12xx to 14xx)
• 2xxx = self-aligning ball bearings, two rows, wide design (22xx and 23xx)
• 3xxx = angular contact ball bearings, double row (30xx, 32xx and 33xx, 38xx and 39xx)
• 4xxx = deep groove ball bearing, double row (42xx and 43xx)
• 5xxx = cylindrical roller bearing (see Nxxx and NNxxxx)
• 6xxx = deep groove ball bearings, single row (60xx to 64xx)
• 7xxx = angular contact ball bearings, single row (70xx, 72xx to 74xx)
• 11xxx = self-aligning ball bearings with a wide inner ring (112xx and 113xx)
• 16xxx = deep groove ball bearings, single row, narrow (160xx and 161xx)
• 2xxxx = spherical roller bearings, two rows (222xx, 223xx, 223xx, 230xx to 233xx, 238xx to 241xx)
• 20xxx = barrel bearing = single row spherical roller bearing (202xx to 204xx)
• 29xxx = spherical roller thrust bearing (292xx - 294xx)
• 3xxxx = tapered roller bearings (302xx, 303xx, 313xx, 320xx, 322xx, 323xx, 329xx to 332xx)
• 51xxx = axial deep groove ball bearing, single-sided (511xx to 514xx)
• 52xxx = axial deep groove ball bearing, double-acting (522xx to 524xx, 542xx to 544xx)
• 53xxx = axial deep groove ball bearing, single-sided with spherical housing washer (532xx to 534xx)
• 54xxx = axial deep groove ball bearing, double-acting with spherical housing washer (542xx to 544xx)
• 6xxxx = deep groove ball bearings, single row (617xx to 619xx, 622xx and 623xx, 630xx, 632xx to 633xx 638xx)
• 7xxxx = angular contact ball bearings, single row (718xx and 719xx)
• 81xxx = axial cylindrical roller bearings, single row (811xx to 812xx)
• 89xxx = axial cylindrical roller bearings, single row (893xx to 894xx)
• 234xxx = axial angular contact ball bearings, double-acting (2344xx and 2347xx)
• 76xxxxx = axial angular contact ball bearings, single direction (7602xxx and 7603xxx)
• Nxxx = single row cylindrical roller bearings (NU, NJ, NUP - see below, RNU, NUB, NUC, NJP, NH, NUJ, RN, N, NF, NP, NCF; NJF)
• NNxx = double row cylindrical roller bearing (NN, NNU, NNC, NNCF, NNCL, NNF)
• Qxxx (x) = 4-point bearing = angular contact ball bearing with split outer ring (Q2xx, Q3xx, Q10xx and Q12xx)
• QJxxx (x) = 4-point bearing = angular contact ball bearings with split inner ring (QJ2xx, QJ3xx, QJ10xx and QJ12xx)

This makes it easy to identify any rusted bearing.

#### Combination table inside and outside diameter

d 10 12 15th 17th 20th 25th 30th 35 40 45 50 55 60 65 70 75 000 001 200 201 002 300 202 003 301 203 302 004 303 204 005 304 205 006 403 305 206 007 008 404 306 207 009 405 307 208 010 209 406 308 210 011 012 407 309 211 013 408 310 212 014 015 409 311 213 214 016 410 312 215 411 216 412 313 314 315 413 316

#### seal

Many rolling bearings are available in sealed designs. The seal is based on the principle of the shaft seal . The following manufacturer-specific seal designations are possible:

• Z = one-sided sheet metal cover plate with gap seal
• ZZ / 2Z = as above, on both sides
• RS = one-sided, rubbing rubber seal
• LB = as above
• 2RS = as above, on both sides
• LLU = as above, non-contact rubber seal, on both sides
• EE = as above, touching on both sides, dragging
• RZ = one-sided, non-contact rubber seal
• LB = as above
• 2RZ = as above, on both sides
• LLB = as above

#### Axial clearance

Axial clearance is described as follows: Axial clearance is the amount of non-installed bearings by which the bearing rings can be shifted against each other in the axial direction from one end position to the other until they are stress-free. The bearings are rotated. In practice, the bearings are measured individually. The distance between the two end faces (inner and outer ring) is measured. Adding them together results in the intermediate ring width or how much of the corresponding rings (including inner or outer bearing ring) has to be ground off. During operation, the bearing should run under zero axial clearance or with a slight preload. As a result, the external forces are distributed over more or all of the rolling elements.

## Installation

### Attachment

Depending on whether the bearing is a fixed bearing or a floating bearing, the outer ring and / or inner ring are firmly connected to the housing or to the shaft.

The simplest way is to press in or on both rings. To do this, the shaft and housing must have a certain dimensional tolerance.

Basically, one can assume that the rotating ring (one speaks here of circumferential load, outside or inside) is executed in a tight fit ( interference fit ) and the standing ring (point load) in a loose fit ( clearance to transition fit ) . If shocks act on the bearing, both rings are stuck. A compromise has to be found between easy (dis) assembly and preventing the ring from rotating.

On a shaft, the inner ring can also be clamped between a stop collar (shoulder) and a clamping screw or nut, or it can be pressed with a clamping sleeve .

In the process of shrink fitting , the bearing is brought to a high temperature (to prevent a change in the steel structure, max. Approx. 125 ° C, depending on the manufacturer) (ideally with an induction device). As a result of the heating, the entire bearing expands, the heated bearing is now quickly pushed over the cold shaft. When the bearing cools, it contracts again and sits extremely tight on the shaft. The temperature limits must be observed when heating.

In the housing, the outer ring with the cover is usually pressed against a stop collar (shoulder) or held with a locking ring . With floating bearings, the outer ring is given a certain amount of longitudinal play, but the ring must be pressed in so that it does not rotate.

special cases

Adhesive connections have also proven effective in precision bearings. Anaerobic adhesives with adhesive gaps of 0.0004 to 0.001 x the diameter of the shaft or the housing bore are used. The temperature limits are between approx. −20 ° C and +100 ° C. Adhesive dosing appropriate for the application is important; overdosed adhesive can get into the bearings and fix them.

### Storage concepts

The arrangement of the bearings is divided into fixed-lot storage and support-support storage . The support-support storage can in turn be designed as a floating storage and adjusted storage .

The bearing arrangements take into account that the element to be stored ( shaft , axis , ...) expands when heated. With the exception of the raised bearing , the thermal expansion is permitted without the bearings becoming warped. When choosing the arrangement, the manufacturing tolerances must also be taken into account.

#### Fixed-lot storage

With the classic fixed-lot storage, one of the bearings can be moved and the other is fixed. The fixed bearing is mounted on the element to be supported in such a way that it cannot move in the axial direction. The fixed bearing thus absorbs both radial and axial forces. The size of the maximum axial force that can be absorbed depends on the design of this bearing.

In contrast to the fixed bearing , the floating bearing can move in the axial direction. No axial forces are absorbed by the floating bearing.

#### Support-support storage

With this type of storage, each of the two bearings absorbs the axial force in only one direction.

In the case of the floating mounting , an axial play is provided between the inner or outer races of the two bearings in order to be able to compensate for the thermal expansion and to avoid tension in the bearings.

In the bearing arrangement angular contact ball bearings or tapered roller bearings are used and designed so that they are able to schedule the thermal expansion occurring due to axial standard voltage take.

### Storage units

Bearing units are a particularly simple option for storing shafts. They are mainly used in special machine construction and in agricultural machines. They consist of a radial deep groove ball bearing with a spherical (spherical) outer ring and a bearing housing.

In the housing, the bearing can be adjusted by a few degrees in order to compensate for misalignments. The bearing housings are made of gray cast iron , light metal cast , plastic or sheet steel , depending on the intended use , and can be easily attached to the machine frame.

Common housing forms are:

• UCP and UCPE = pillow block bearings
• UCF and UCFE = square flange bearings , four mounting holes,
• UCFL and UCFLE = flange bearing, two mounting holes (FD),
• UCT = radial insert ball bearing.

Other designs are also available, such as clampable flange bearings.

The shaft is fastened either with grub screws in an inner ring extended on one side or with the aid of a clamping ring. For this purpose, the inner ring of the bearing unit and the clamping ring each have an eccentric- conical recess.

## Other designs

Rolling bearings can also take place differently than by the replaceable component rolling bearing. The - simpler - majority of bicycles have had cone bearings on wheels, crankshafts (also: central bearings ), pedals and controls (fork bearings in the control head of the frame), which usually also have to be adjusted and re-greased for more than a hundred years . The cones are screwed onto the fine thread of the wheel axles and, with their conical groove, press the balls (possibly grouped in ball rings) into the groove of the bearing shells that are firmly pressed into the hubs. The cones are fixed by lock nuts with little or no bearing play, depending on the design and state of wear. Pedal axles taper outwards and have a conical bearing groove rolled into the thicker side. The outer small cone of fiberglass pedals can be screwed on and yet riveted to the axle. Most head and bottom brackets are adjusted by screwing one of the bearing cups, but there is also an inverse design.

In order to make the formerly heavy computer monitors , a cake stand and other rotatable, turntables with ball guides between two thin metal rings with a diameter of 20 to 30 cm were developed. Linear bearings with two rows of balls each also guide many telescopic drawers. These components are neither adjustable nor separable in the warehouse.

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## Individual evidence

1. Bernd Künne: Introduction to machine elements - design, calculation, construction. 2nd Edition. Teubner, 2001, p. 147.
2. ^ Fritz Kretzschmer: Pictorial documents of Roman technology . 5th edition. Verlag des Verein Deutscher Ingenieure, Düsseldorf 1983, ISBN 3-18-400598-4 , p. 113-116 .
3. nmm.ac.uk ( Memento from September 6, 2012 in the web archive archive.today )
4. ^ Schaeffler in Germany. Retrieved October 23, 2018 .
5. * Rolling and plain bearings. Catalog from Schaeffler Technologies AG & Co. KG
6. schaeffler.com
7. skf.com