Bearings
Types of Bearings
Learning Objectives:

Recognize the different types of rolling contact bearings and applications where they may be suitable.

Understand principles of roller bearings, tapered roller bearings, thrust bearings, and needle bearings.

Hydrodynamically lubricated bearings  If a lubricant film is enclosed in a wedge or tapered gap between the stationary and moving members, the oil film is drawn into the wedge shape generating a pressure that can support a load.

Rolling Contact Bearings These can be further classified as:

Ball Bearings A typical ball bearing has the following components:

Outer ring, which contains the outer raceway

Inner ring, which contains the inner raceway

Complement of balls

Twopiece separator (also called cage or retainer)


Roller Bearings These have more load carrying capacity as the contact area is more compared to ball bearings.

Needle Bearings– Only for radial loads.

Footstep Bearing:
Footstep bearing is used to support shaft vertically. It consists of a cast iron block into which a gunmetal bush having a collar at the top is fitted. The shaft rests on a steel pad. The pad is prevented from rotating by a pin, inserted half inside the block and half in the pad and away from the centre. The collar of the bush is made hollow to serve as an oil cup for lubrication of the bearing.
Solved Example: 94101
The usual clearance provided in hydrodynamic bearing per mm of diameter of shaft is:
A. 0.01 micron
B. 0.1 micron
C. 1 micron
D. 10 microns
Correct Answer: C
Solved Example: 94102
In hydrostatic bearings:
A. The Oil film pressure is generated only by the rotation of the journal
B. The oil film is maintained by supplying oil under pressure
C. Do not require external supply of lubricant
D. Grease is used for lubrication
Correct Answer: B
Solved Example: 94103
Oil in journal bearing should be applied at the point where load is:
A. Nil or lightest
B. Maximum
C. Average
D. Any one of the above
Correct Answer: A
Solved Example: 94104
In standard taper roller bearings, the angle of taper of outer raceway is:
A. 5$^\circ$
B. 8$^\circ$
C. 15$^\circ$
D. 25$^\circ$
Correct Answer: D
Solved Example: 94105
For fluctuating loads, well suited bearing is:
A. Ball bearing
B. Roller bearing
C. Needle roller bearing
D. Thrust bearing
Correct Answer: C
Solved Example: 94106
In a hydrodynamic lubricated bearing:
A. There is no lubricant between the journal and the bearing
B. The lubricant is forced between the journal and the bearing, by external pressure
C. There is a thin film of lubricant between the journal and the bearing
D. There is a thick film of lubricant between the journal and the bearing
In hydrodynamic lubrication hydro means (liquid) and dynamic means (relative motion) it is the combination of both liquid and relative motion to reduce the friction. In hydrodynamic lubricated bearings, a thick film of lubricant is formed between the journal and the bearing.
Correct Answer: D
Solved Example: 94107
Antifriction bearings are:
A. Sleeve bearings
B. Hydrodynamic bearings
C. Ball and roller bearings
D. None of the above.
An antifriction bearing is a bearing that contains moving elements to provide a low friction support surface for rotating or sliding surfaces. Antifriction bearings are commonly made with hardened rolling elements (balls and rollers) and races. A race is the bearing surface in an antifriction bearing that supports rolling elements during rotation. A separator is an antifriction bearing component used to maintain the position and alignment of rolling elements. Antifriction bearings reduce lubrication requirements and decrease starting and operating friction. Reduced friction results in less power required to rotate engine components and increases overall engine output.
Correct Answer: D
Basic Load Rating
Learning Objectives:

Select appropriate type of bearings and their sizes for the design being undertaken.

Determine the life of a rolling bearing using the life equation.
Bearings are subjected to repeated stress cycles and are likely to fail by fatigue. \(L_{10}\) life is defined as the number of hours that 90% of the bearings tested will exceed, which means the probability of failure is 10% at the \(L_{10}\) life.
Average life is the number of hours that 50% of the bearings exceed.
Basic Load Rating is defined as the load for which 90% of the bearings from a given population will survive 1 million revolutions.
It is calculated as follows:
\[C = PL^{\left[\dfrac{1}{a}\right]}\]
where,
C = minimum required basic load rating
P = design radial load
L = design life (in millions of revolutions)
a = constant which is = 3 for ball bearing or \(\dfrac{10}{3}\) for roller bearings.
Solved Example: 94201
The life of a ball bearing is inversely proportional to:
A. $(\mathrm{Load})^{1/3}$
B. $(\mathrm{Load})^3$
C. $(\mathrm{Load})^{10/3}$
D. $\mathrm{Load}^2$
The industry standard usable bearing lifespan is inversely proportional to the bearing load cubed.
\[C = PL^{\left[\frac{1}{a}\right]}\]where,
C = minimum required basic load rating
P = design radial load
L = design life (in millions of revolutions)
a = constant which is = 3 for ball bearing or $\dfrac{10}{3}$ for roller bearings.
Correct Answer: B
Solved Example: 94202
The life of a ball bearing at a load of 10 kN is 8000 hrs. If the load is increased to 20 kN, what would be its life?
A. 4000
B. 2000
C. 1000
D. 500
\[\mathrm{Life} \propto \left(\dfrac{1}{P}\right)^3\] \[\dfrac{L_2}{L_1} = \left(\dfrac{P_1}{P_2}\right)^3\] \[\dfrac{L_2}{8000} = \left(\dfrac{10}{20}\right)^3\] \[L_2 = 1000 \mathrm{\ hrs}\]
Correct Answer: C
Solved Example: 94203
The expected life of a ball bearing subjected to a load of 9800N and working at 1000 rpm is 3000 hrs. What is the expected life of the same bearing for a similar load of 4900N and speed of 2000 rpm?
A. Unchanged
B. 12000 hrs
C. 1500 hrs
D. 6000 hrs
From the FE Reference Handbook, $C = PL^{\dfrac{1}{a}}$
where,C = minimum required basic load rating
P = design radial load
L = design life (in millions of revolutions)
a = 3 for ball bearings, $\dfrac{10}{3}$ for roller bearings
\begin{align*} \dfrac{L_1}{L_2} &= \left[\dfrac{P_2}{P_1}\right]\\ \dfrac{1000 \times 60 \times 3000}{2000 \times 60 \times t_2} &= \left[\dfrac{4900}{9800}\right]\\ t_2 &= 12000\ \mathrm{hrs} \end{align*}
Correct Answer: B
Equivalent Radial Load
Learning Objectives:

Factor in effect of thrust loading on the equivalent radial load in calculating the life of a bearing.
It is used when both radial as well as axial loads are applied to a ball bearing. It is calculated as:
\[P_{eq} = XVF_r + YF_a\]
where,
P = equivalent radial load
\(F_r\) = Applied constant radial load
\(F_a\) = Applied constant axial (Thrust) load
For radial contact, deep groove ball bearing:
V = 1 if inner ring rotating,
V = 1.2 if outer ring rotating
If \(\dfrac{F_a}{VF_r} > e\), \[X = 0.56, \ and \ Y = 0.840 \left(\dfrac{F_a}{C_o}\right)^{0.247}\] where, \[e= 0.513 \left(\dfrac{F_a}{C_o}\right)^{0.236}\] \(C_o\) = basic static load rating from bearing catalog
If \(\dfrac{F_a}{VF_r} \leq\)e, X = 1 and Y= 0
Solved Example: 94301
A solid shaft can resist a bending moment of 3.0kNm and a twisting moment of 4.0 kNm together, then the maximum torque which can be applied is:
A. 7.0 kNm
B. 3.5 kNm
C. 4.5 kNm
D. 5.0 kNm
Maximum tensile stress due to bending, \[f_t = \dfrac{M}{Z} = \dfrac{30.558}{d^3}\ kPa\] Maximum shear stress due to torsion, \[f_s = \dfrac{TR}{J} = \dfrac{20.7}{d^3}\ kPa\] When both stresses are acting simultaneously, maximum induced shear stress, \[f_{s_{max}} = \dfrac{1}{2}\sqrt{{f_t}^2 + 4{f_s}^2}\] Maximum torque that can be applied, \[T = \dfrac{\pi d^3}{16}f_{s_{max}} = 5\ kNm\]
Correct Answer: D
Solved Example: 94302
If p = bearing pressure on projected bearing area, Z = absolute viscosity of lubricant, and N = speed of journal, then the bearing characteristic number is given by:
A. ZN/p
B. p/ZN
C. Z/pN
D. N/Zp
Correct Answer: A