The technological development of human beings in mechanical issues begins with the invention of the wheel.
Today, there is usually a bearing in the hub of the wheel and everything that rotates.
For this reason, the bearing is the most used machine element in the world. SKF, the world's largest bearing manufacturer, moved from this fact to put a symbolically giant ball in front of the central government building in Gothenburg. The basic principle of rolling is based on minimizing the friction of the periphery rotating around a fixed shaft with the shaft surface.

Theoretically, a ball rolling on a surface, a wheel, etc. If it is infinitely hard, that is, it does not stretch at all, there is zero friction between the surface and the rotating object (See Figure 1). However, due to the fact that the rotating object stretches a certain amount under load and becomes flat on the touch surface (See Figure 2), the movement occurs with rotation and sliding. This creates friction. Bearings have been developed to reduce this friction.

What is meant by the above friction is the friction that occurs when the ball or wheel slides on the surface instead of rolling. Normally, the friction to keep the wheel on the ground is essential for rolling, and if this friction does not occur, the wheel will not roll, but will spin where it is (spinning). As a matter of fact, there must be a minimum load on the bearings to prevent spinning. This load is particularly important at high speeds, high accelerations or sudden changes in the direction of action of the load.
How much the minimum loads should be specified in the catalogs according to the bearing type.

FIGURE 2

There is no general rule regarding the selection of bearings. Each application has its own bearing type required by its specific conditions. These conditions can be listed as follows.

Radial load size
Axial load size
Number of revolutions
Working time and continuity
Expected life
Shaft-bearing layout design (Bearing arrangements)
The size of the volume in which the bearing can be placed
Lubrication method
Design of sealing elements
Operating temperature
Acceptable sound level
Acceptable vibration amount
Acceptable working gap size
Acceptable axial play
EQUIVALENT DYNAMIC LOAD (P)

The resultant force created by radial and axial loads is the main factor that determines the bearing life.

The resultant force is called "Equivalent Dynamic Load (P)" in the bearing literature and its formula

P (N) = Fr * cos β + Fa * sinβ (See figure 3)

The sinβ and cos β values ​​vary according to the type and size of the bearing, and they are given as X and Y coefficients in the bearing catalog. Thus;

P = X * Fr + Y * Fa.

If Fa is below a certain size, the second term is considered 0 and the formula

P = X * returns to Fr.

Whether the Fa value will be taken into account or not is determined by the coefficient "e" given in the catalog.

If Fa / Fr> e the formula P = X * Fr + Y * Fa is used.

If Fa / Fr <e the formula P = X * Fr is used.

Here Fr: Radial load (N)
Fa: Axial load (N)

FIGURE 3

The determined Equivalent dynamic load (P) is the main parameter used in calculating the life of the bearing. (See section.4 for determination of bearing life).

L10 = (C / P) p

L10: Bearing life in millions of revolutions
C: dynamic load number in Newton
P: dynamic equivalent load in Newtons
p: This value is always 3 for ball bearings and always 10/3 for roller bearings.

EQUIVALENT STATIC LOAD (P0)

The "dynamic load number (C)" used in the life calculation is taken from the table of the relevant bearing in the catalog. In the tables, next to C, “static load number (C0) is given.

Static load number (C0) is taken into consideration in cases where the bearing rotation rate is very low, in slow oscillation movements, under load when stationary, and most importantly in cases where it will be exposed to shock impacts. In these cases, not fatigue (fatigue) but permanent deformation caused by static load is effective in determining the bearing performance. This deformation causes an increase in noise, vibration and friction in the bearings. In order to ensure that the bearing operates without reaching the low performance limit, the static equivalent load P0 (N) is calculated from the following formula.

P0 = X0 * Fr + Y0 * Fa

C0 = s0 * P0, s0 = C0 / P0

C0: static load number is taken from the relevant bearing catalog

s0: static safety factor (See figure 4)

X0, Y0 are given in the relevant pages of the Bearing catalog. The number of static loads C0, how much the equivalent static load P0 ratio should be is given in the s0 static safety factor table (See Figure 4.). (This ratio is less than 1 for ball bearings if there are no shock loads.) If the calculated S0 value is smaller than the S0 value found in the table, the bearing with a larger C0 value should be selected.

FIGURE 4

CHECK THE SUITABILITY OF THE BEARING SPEED
The factors that are effective in the speed capacity of the bearing are as follows.

Type and size of bearing
Bearing design
Bearing loads
Lubrication and cooling condition
Cage design
Bearing clearances
There is a speed limit on the bearings. This limit is for the oil used and the material of the bearing.

determines the temperature it can withstand. Its temperature is created by the friction in the bearing and the heat exchange between the bearing and the environment.

Two speeds are given for the bearing on the bearing catalog pages. These;

Reference speed (Thermal speed)
Limit speed
1st REFERENCE SPEED (THERMAL SPEED)

The reference speed is given in the bearing catalog and this value is sought to be greater than the acceptable speed.
The acceptable speed (nper) is found from the formula below.

nper = nr * fp * fv
nr: Reference speed given in the catalog for the relevant bearing
fp: coefficient varying according to the P / C0 ratio and the mean diameter (dm) (See Diagram 1)
fv: Coefficient varying according to the P / C0 ratio and the viscosity of the oil used (See Diagram 1)

DIAGRAM 1

TABLE 5

FIGURE 5

Sample:

Operating conditions: Bearing speed N = 6000 rpm
Radial load Fr = 5600N, Axial load Fa = 1000N

Selected bearing SKF 6210 (See Figure 5)
From the catalog d = 50 mm, D = 90 mm,
C = 37,100N, C0 = 23,200N, f0 = 14
Reference speed nr = 15,000 rpm
Space: CN with normal clearance.
Oil to be used: ISO VG 68

f0 * Fa / C0 = 14 * 1000/23200 = 0.6
=> E = 0.25, X = 0.55, Y = 1.7 (See Table5)

Fa / Fr = 1000/5600 = 0.178 <e = 0.25
=> P = Fr = 5600N (Bkaz related bearing catalog)

To use "Diagram 1"

P / C0 = 5600/23200 = 0.24

dm = (d + D) / 2 = (50 + 90) / 2 = 70mm

See diagram 1 => fp = 0.63, fv = 0.85

nper = nr * fp * fv
nper = 15000 * 0.63 * 0.85 = 8030 rpm> n = 6000rpm => Selected bearing speed is appropriate. The maximum operating speed of the bearing should always be lower than the acceptable speed (nper). If the bearing speed is more than the reference speed, it reduces the bearing clearance and causes damage to the ball cavities. Another issue is that the bearing speed is higher than the reference speed, causing the difference between the inner ring and outer ring temperatures to increase, creating thermal stress in the bearing. (Note: The outer ring temperature is always higher than the inner ring temperature because the circumferential velocity of the ball or spool at the contact point with the outer ring is greater than the circumferential velocity at the contact point with the inner ring.)
FIGURE 6

Running the bearing above the reference speed is only possible under the following conditions. These;

Continuously controlling the oil circulation in the bearing and keeping the amount of oil circulating in a clean and appropriate amount by filtering. (Important note: Excessive amount of oil applied to the bearings increases the friction, causing the bearing to heat up, thus shortening the bearing life. Bearings should have the required amount of oil. Never too much)
Keeping the circulating oil within a certain temperature range with the air or water cooling system. In the figure on the right, the circuit that circulates the bearing oil and ensures that it is filtered and cooled (See Figure 6).
2. LIMIT SPEED

Normally the reference speed is lower than the limit speed. In this case, the appropriateness of the speed is checked with the calculation method exemplified above. However, for some bearings, the limit speed given in the catalog is lower than the reference speed. In this case, the maximum acceptable speed (nper) is calculated with the method mentioned above and the limit speed is compared. Whichever is lower, that value is accepted as the maximum speed that can be used in the enterprise.

BEARING TYPES

There are generally two types of bearings. These;

Ball bearings
Roller bearings
1. BALL BEARINGS
As the name suggests in ball bearings, rolling elements are balls. Ball bearings can be used at very high speeds, but their biggest drawback is their limited capacity to carry high loads.

Click on the relevant group name for ball bearing features and application areas where they can be used.

1.1 Deep Groove ball bearings
1.2 Self aligning ball bearings
1.3 Angular contact ball bearings
1.4 Thrust ball bearings

2. ROLLER BEARINGS
Roller bearings can carry much higher loads than ball bearings. The biggest disadvantages of these are that they run at lower speeds and are more noisy and vibrating. Rollers are of cylindrical, conical, needle type (thin diameter) as stated below. Click on the relevant group name for the properties of roller bearings and their application areas. 2.1 Cylindirical roller bearings
2.2 Spherical roller bearings
2.3 Taper roller bearings
2.4 Cylindirical roller thrust bearings

NUMBERING SYSTEMATICS IN BEARINGS
Bearings are produced by major companies in the world and the same type of bearings are put on the market with a standard numbering system.
This systematic has been standardized and published by ISO. These standard notations are adhered to even in countries that do not use the metric system.

The size systematic standardized by ISO is simply realized as follows.

The last two digits (rightmost) of the representation indicate the inner diameter.

It has been used for tilling. (See 3.1 inside diameter notation)
The number to the left of the inside diameter notation (third from the right) is used to indicate the outer diameter.
In this digit, the smallest outer diameter of the same inner diameter is indicated by 8, and as the outer diameter grows, the digit in the digit changes to 8, 9, 0, 1, 2, 3, 4.
The number to the left of the outer diameter notation (fourth from the right) is used to indicate the bearing width. The number 0 is used for the thinnest bearing width with the same inside diameter. As the bearing width increases, this number is specified as 0, 1, 2, 3, 4, 5.
(For thrust bearings, these numbers vary from thin to thick 7, 9, 1.)
The letter or numbers at the beginning (leftmost) of the bearing designation indicate the bearing type. (See 3.2 Bearing type designation)
After leaving a space to the right of the two numbers on the right reserved for the inner diameter in the bearing representation, the special shapes of that bearing are indicated with various numbers or letters. (See 3.3 bearing special figure designations

3.1 BEARING INNER DIAMETER INDICATION

There is a very simple rule regarding the bearing bore.
For bore diameters greater than 19 mm and smaller than 496 mm, it gives 5 times the inner diameter of the bearing than the last two figures in the bearing designation.
Example: NU 1088 cylindrical bearing bore d = 88 * 5 = 440 mm.

Since the last two digits in the display can be the largest 99, if the inner diameters are larger than 5X99 = 495mm, the last digits are written directly after the "/" sign. Example: 618/750 single row ball bearing with an inside diameter of 750 mm. These rules apply to all bearing types.

3.2 BEARING TYPE DESCRIPTION The starting characters in the display determine the bearing type. Accordingly, if the first characters start with 6 or 16, the bearing is a single row ball bearing.

If it starts with 4, the bearing is a double row ball bearing.

If it starts with 1 or 2, the bearing is a self-aligning ball bearing.

If it starts with 7, the bearing is an angular contact ball bearing.

If it starts with 3, the bearing is a double row angular contact ball bearing.

If it starts with Q, the bearing is a four-point contact ball bearing.

If it starts with N or 319, the bearing is a cylindrical roller bearing.

If it starts with HK or N or RNA, the bearing is a needle roller bearing.

If it starts with K or T or 3, the bearing is a tapered roller bearing.

If it starts with 2, the bearing is a spherical roller bearing.

If it starts with 5, the bearing is an axial ball bearing.

If it starts with 8, the bearing is an axial roller bearing.

If it starts with 29, the bearing is an axial spherical roller bearing.

3.3 DESIGNATION OF SPECIAL SHAPES OF BEARINGS

The alphabetic letters at the end of the bearing designation mean:

K: inner diameter taper roller bearing

Z: Ball bearing closed on one side

2Z: Ball bearing sealed on both sides

N: Bearing has circlip slot on one side

NR: The bearing has circlip with circlip slot on one side

M: Balls or rollers in bronze cage

L: Balls or rollers inside alloy cage

T: Balls or rollers in a synthetic resin cage

3.4 BEARING SPACE

Normally, bearings are produced with a gap. If this gap is not left, the bearing will not be able to rotate due to thermal expansions that occur as a result of heating during operation and particles entering the bearing housing from outside. For the aforementioned reasons, the space before the bearing is used is greater than the space after it is used. Bearing clearance is also a factor that affects the even distribution of the load in the bearing.

The clearance level in the bearing directly affects the following situations. These

Noisy work
Vibrating work
Heating of the rolling bearing
Fatigue life
There are two kinds of gaps in the bearing. These;

Radial clearance (Inner and outer rings can move in a radial direction relative to each other).
Axial clearance (Inner and outer rings can move in axial direction relative to each other).
As the radial clearance increases in ball bearings, the clearance in the axial direction increases accordingly.

No additional information should be given to the supplier when ordering normal clearance bearings. However, if there is a need for bearings with more or less clearance than normal, the clearance amount must be reported to the supplier company together with the type number of this bearing. Gaps in the order are specified as follows;

C1: Bearing tighter than tight bearing

C2: Bearing with less clearance (tight) than normal clearance bearing

CN: Normal clearance (No need to be specified in the bearing specifications.)

C3: Bearing with more clearance (loose) than normal clearance bearing

C4: Bearing with more clearance (too loose) than C3 clearance bearing

C5: Bearing with more clearance (very, very loose) than C4 clearance bearing

In which situations are bearings with different gaps requested?

C1, C2 cavity bearings are used where noise and vibration should be minimal. However, in this case the bearing gets much hotter. Therefore, they are suitable for low speed bearings.

C3, C4, C5 clearances are evaluated in order to eliminate the thermal expansions that will occur due to overheating in high speed bearings. At the same time, in cases where the environment is very hot, or in vibratory working environments, empty 

Sleeve bearings are used.
(For example: in vibrating and hot working conditions that will arise due to unbalance in large-diameter fans that evacuate hot flue gas and dust, C3 or C4 bearing with gaps must be used)

4. DETERMINATION OF BEARING LIFE

In a designed system, a shaft diameter arises due to load sizes and a bearing is selected in accordance with that diameter. The life of the selected bearing is determined by the number of cycles, operating conditions, oil used, ball gaps, axial and radial loads. Bearing life is measured not in years, but by how many million revolutions (L10) it can perform.

Bearing life is calculated with different methods according to the specified bearing type. These methods are specified in the relevant bearing catalog pages. Let's try to explain how life calculation is done with an example here. In this example, the values ​​given in the SKF catalog are taken as a reference.

Let the diameter of the shaft arising due to the loads coming from my system be d = 40 mm.

Radial load Fr = 7000 N
Axial Load Fa = 2470 N
Number of revolutions: 3000 rpm
Oil to be used: ISO VG 46

Since there is an axial load of approximately 30% of the radial load in the system, the bearing with the code number SKF 22208E is chosen. From the related catalog page;

SKF 22208E
d = 40 mm,
D = 80 mm
B = 23 mm.
Dynamic load number (C) = 89,700 N
Static load number (C0) = 98,000 N
Fatigue load limit Pu = 10,600N
e = 0.28
Y1 = 2.4
Y2 = 3.6
Can this bearing bear the axial load given first? Let's check it out.

FIGURE 5

Acceptable axial load on spherical roller bearings Fap = 3 * B * d = 3 * 23 * 40 = 2760N
Must be Fa <Fap. 2470 N <2760 N required condition is met.
If Fa / Fr <e P = Fr + Y1 * Fa
If Fa / Fr> e P = 0,67 * Fr + Y2 * Fa
Fa / Fr = 7000N / 2470N = 0.35> e = 0.28 => P = 0.67 * Fr + Y2 * Fa Here P: Equivalent dynamic bearing load and it is the main parameter of the life calculation.
P = 0.67 * 7000+ 3.6 * 2470
P = 13,582 N
L10 = (C / P) 3.33
L10 = (89,700 / 13,582) 3,33
L10 = 540 million cycles
Here, L10 is the parameter that shows how many revolutions the bearing can make in millions of revolutions.

FIGURE 6

It is possible to convert the life cycle calculated in cycles to hours. However, in this case, the thing that should not be ignored is that the result obtained may be correct if the bearing rotates at the same number of revolutions continuously and the rotation continues without interruption.

The parameter that indicates the bearing life in hours is shown as L10h.
L10h = (1,000,000 * L10) / (60 * N)
If we accept that the bearing we choose will rotate at 3000 rpm without stopping
L10h = (1,000,000 * 540) / (60 * 3000) = 3,000 hours bearing rotation time.
This value is equivalent to a very short life for today's bearings (3,000 hours = approximately 4 months).

However, a SKF bearing provides approximately 15-20 times this life. Therefore, SKF developed a new life theory equation for the bearings it produced. Accordingly, it is necessary to take into account a coefficient (aSKF) to be used for SKF bearings in the above formula, together with the bearing's ball clearance, lubrication condition, reliability (a1) criteria. According to this
New life calculation for SKF bearings (Lnna) = a1 * aSKF * L10

If we take the reliability coefficient from the catalog for 90% reliability (See. Figure 5)

We can accept a1 = 1 (The higher the reliability, the lower the coefficient.)

FIGURE 7

For aSKF we need to use the diagram for roller bearings in the catalog.

In order to use this diagram, we need to decide which of the ɳc * (Pu / P) value on the horizontal axis and which of the curves we will use.

ɳc is the cleaning coefficient of the oil used and ɳc = 1 for very clean oils. (See Figure 6)
(ɳc * Pu / P) = 1 * 10,600 / 13,582 = 0.78

K = ν / ν1

ν: is the viscosity of the selected oil and this value is found as 46 mm2 / s from the table for ISO VG 46.

ν1: It is found from the rotation and mean diameter diagram of the bearing. (See Figure 7)
dm = (d + D) / 2
dm = (40 + 80) / 2 = 60mm.

It is determined as dm = 60 mm and ν1 = 12 at 3000 rpm.

From the diagram with the values ​​of K = 46/12 = 3.8 and (ɳc * Pu / P) = 0.78 (See Figure 8)

It is found as aSKF = 20.

(Lnna) = a1 * aSKF * L10 = 1 * 20 * 540 = 10,800 Million revolutions.

Converting this value to hours for 3000 rpm
Lnnah = (1,000,000 * L10) / (60 * N)
Lnnah = (1,000,000 * 10,800) / (60 * 3,000) = 60,000 hours = about 7 years, we have determined that this bearing can operate continuously under the specified conditions.

FIGURE 8

You can get the life account we have given above from the ready program on the SKF website. However, you must first become a member of the SKF site.
After becoming a member, you can access the life program from the link below.

5. SHAFT BEARING ARRANGEMENTS

Proper bearing selection is not enough for the design to be successful on its own. The arrangement of the selected bearings on the shaft is extremely important in terms of shaft and bearing life, reliability of the design, ease of assembly, disassembly and maintenance.

Sample designs for the arrangement of the bearings on the shaft (bearing arrangements), the placement of the sealing elements and the appropriate fit tolerances of the bearing on the shaft are included in the SHAFT BEARING DESIGN page.