ROLLING CONTACT BEARING Objective: By the end of the courses, student must be able to select bearing. There are two types of bearings we have to learn: cylindrical and roller contact bearing. Background The invention of bearing started from textile industries that demands long shaft. To eliminate the bending on the shaft bearing is used.

Bearing Manufacturer: SKF (famous in Malaysia), Timken (Shigley’s).

Bearing Nomenclature

1

Bearing Types Ball bearing

Roller and tapered bearing

Load type Radial load Thrust or axial load

2

Bearing life and load Bearing Life Is the cycle of bearing on constant speed before any sign of fatigue failure to occur. The relationship between life (cycles) and load or force is 1 a

FL = c a = 3 for ball bearings a = 10/3 for roller (cylindrical and tapered roller)

Catalogue: Bearing manufacturer may choose a rated value (ie Timken 106 cycles) A test is carried out on a group of similar bearings. When 90% of the bearings survive the rated life (106), the load that is used in the test is called Catalogue-Load Rating (C10). The C10 is used as the foundation to select the bearing. However, our design might not be having rated life of 106, therefore we must find relation of the rated life and our design life. 1 a

FL = C 1 a 1 1

1 a 2 2

FL = F L Similarly, for the tested condition 1 a 10 R

C L =c

3

When we are using the same bearing from the catalogue 1 a D

FD L = c 1 a

1 a R

FD L = C10 L

⎡L ⎤ C10 = FD ⎢ ⎥ ⎣ LR ⎦

1 a

* Converting cycles to hours

⎡ L n 60 ⎤ C10 = FD ⎢ D D6 ⎥ ⎣ 10 ⎦

1 a

L = life in cycles LD = rating life in hours (operation hours) nD = speed in rpm RELATIONSHIP DESIGN LOAD (FD) AND RADIAL AND THRUST LOAD

FD = X. V. FR + Y.Fa Refer Table 11-1 FR = radial load Fa = thrust or axial load X = radial load factor Y = thrust load factor V = rotation factor V = 1 : inner ring rotates V = 1.2: outer ring rotates V = 1.0: misalignment bearings C0 and C10 is based on the bearings (Refer Table 11-2, 11-3). How can choose a bearing based on C10 and at the same time, we need the value C0 from the catalogue as well? 4

MATTERS TO BE CONSIDERED WHEN DOING THE BEARING SELECTION. Selection of bearing based on design load is simply following the step or procedure. However, the real design world is quite critical. 1. Wide range of bearing selection ⇒ A number of bearing types: SKF deep grove ball bearing (single and

double row), angular contact ball bearings (6 types) … ⇒ Within each type a number of series 2. ⇒ ⇒ ⇒

Parameters that are important in bearing selection.

Inner diameter: must fit the shaft Outer diameter: must according to the dimensional constraint Deflection of the shaft (must be very minimal). For misalignment bearing, the allowable deflection is 1.50 to 3.00 depends on the bearing size and type

3. Bearing load and its possible selection ⇒ Type of loads: depends on the configuration of the bearing. ⇒ Direction of thrust: depends on the direction of contact. Single row

Æ one direction, double row Æ both direction

4.

Bearing Recommendation life (Table 11-4 pp 563) and load application factor (Table 11.5 pp 563)

5.

Reliability other than 90% (refer to Figure 11-5 pp 556)

⎡ ⎤ xD C10 = FD ⎢ 1/ b ⎥ x + ( − x )( 1 − R ) θ 0 D ⎣ 0 ⎦ L 60LDnD 60LDnD xD = = = L10 6LRnR 106

1 a

Weibull Parameter: x0, (-x0),b

5

6.

Bearing reliability (or combined reliability) for multi-bearings system

R=n R

Individual reliability

Overall reliability, R = 0.99 for 3 bearing supporting a shaft

R = 3 0.99 = 0.9967 STEPS IN BEARING SELECTION 1.

FBD on point where the bearing to be installed.

2.

Determine radial load Fr and thrust load Fa

3.

Estimate value C0. * initial estimation: use FD = CFS FR and based on the calculated C10 select bearing from respective tables.

4.

From initial selection from step 3, find the value C0. Then use the C0 to calculate Fa/C0. Based on the value e and Fa/C0, determine X and Y. (Do the interpolation if it is required).

5.

Calculate the FD

= X. V. FR + Y.Fa

Radial load only FD = FR * application factor (CFS) is needed. 6.

Calculate the C10

6

⎡ L n 60 ⎤ C10 = (CFS ) FD ⎢ D D6 ⎥ ⎣ 10 ⎦

1 a

• Please note that the reliability is 90%, other than that use

⎡ ⎤ xD C10 = (CFS )FD ⎢ 1/ b ⎥ ⎣ x 0 +(θ − x 0 )(1 − RD ) ⎦ L 60LDnD 60LDnD xD = = = L10 6LRnR 106 7.

1 a

Compare the calculated value of C10 with the estimated C10 value.

If C10 [calculated] >> C10 [initial estimation], repeat step no 4 – 6, by choosing larger C0 (or the next larger bearing). The iteration is finished when the C10 [calculated]