Option 3 : Journal bearings

__Explanation:__

Bearing: It is a mechanical element that permits relative motion between two parts with minimum friction.

Functions of bearing:

- Free rotation of shaft with minimum friction.
- Supports shaft and holds in the correct position.
- Bears force that acts on the shaft and transmits to the foundation.
- Bearings are classified into two types :

- Sliding contact bearing (
**Journal bearings**) - Rolling contact bearing.

Sliding contact bearing it is classified as

- Thick film lubrication
- Thin-film (zero films) lubrication bearing.

Roller contact bearings

Roller contact bearings are the bearings that use spherical balls, or some other type of roller between the stationary and the moving elements.

These bearings are also called anti-friction bearing.

Roller contact bearings are classified into two types:

- Ball Bearings are used to take heavy as well as high-speed loads. It is classified into the following types.
- Deep groove ball bearing
- Angular ball bearing
- Self align ball bearing
- Thrust ball bearing

- Roller Bearing
- Cylindrical Roller Bearing
- Taper Roller Bearing
- Spherical Roller Bearing
- Needle Roller Bearing

Option 1 : 12,000 hours

__Concept:__

Load-life relationship:

The approximate rating of the service life of a ball or roller bearing is based on the given fundamental equation.

\({\rm{L_{10}}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} \)

L10 = Rated bearing life (in million revolutions)

C = Dynamic load capacity.

P = Load acting in bearing.

k = 3 for ball bearing and k = 10/3 for the roller bearing.

The relation between life in million revolutions and life in hours is given by:

\({\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} =\frac{L_{10h}\;× \;N \;× \;60}{10^6}\)

where, L10h = rated bearing life in hours and N = speed of rotation in rpm.

**Calculation:**

**Given:**

P_{1 }= 9800 N, N_{1} = 1000 rpm, L_{10h} = 3000 hrs

P_{2} = 4900 N, N_{2} = 2000 rpm,

Combining both the equation:

\({\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} =\frac{L_{10h}\;× \;N \;× \;60}{10^6}\)

∴ L10h × N × P^{k} = constant

\((L_{10h})_1× N_1× P_1^k=(L_{10h})_2× N_2× P_2^k\)

3000 × 1000 × 9800^{3} = (L_{10h})_{2} × 2000 × 4900^{3}

∴ (L10h)2 = 12000 hrs

Option 4 : Tapered roller bearings

__Concept:__

- Tapered roller bearings are capable of carrying both radial and axial loads.
- They are often used in pairs to take the thrust load in both directions.
- The taper roller bearing consists of rolling elements in the form of a frustum of cone. They are arranged in such a way that the axes of individual rolling elements intersect in a common apex point on the axis of the bearing.
- The taper roller bearing consists of rolling part and inner and outer raceways in the form of conical surfaces. The outer raceway or outer ring is called ‘cup’ and inner raceway is called ‘cone’.

**Needle roller bearing**

- These bearings are relatively slender and completely fill the space so that neither a cage nor a retainer is needed.
- These bearings are used when heavy loads are to be carried with an oscillatory motion.
- For example, piston pin bearing in heavy-duty diesel engines where the reversal of motions tends to keep the roller in correct alignment.

__Additional Information__

The following Points are to be noted about the load-carrying capacity of different types of rolling contact bearings:

- Thrust Ball Bearing: Thrust ball bearing cannot take the radial load.
- Taper Roller Bearing: can take heavy radial and thrust loads.
- Angular Contact Bearing: can take both radial and thrust loads.
- Cylindrical Roller Bearing: can take radial load only
- Deep Groove Ball Bearing: takes load in radial as well as an axial direction

Option 4 : increased 8 times

**Concept:**

The static load carrying capacity of a bearing is defined as the Static load which results in a total permanent deformation of balls and races, at the most heavily stressed point of contact, equal to 0.0001 of the ball diameter.

Stribeck’s equation gives the basis static capacity of a ball bearing directly proportional to the number of balls in a row and square of the diameter of the ball. i.e.,

\({C_0} = \frac{{K{d^2}z}}{5}\) ⇒ \(C_o\propto(zd^2)\)

where Z = number of balls, C_{o} = static capacity, d = diameter of the ball

**Calculation:**

**Given:**

z_{1} = z, z_{2} = \(\frac{z}{2}\), d_{1} = d, d_{2} = 4d

Therefore, \(\frac{C_{01}}{C_{02}}=\frac{zd^2}{\frac{z}{2}(4d)^2}\)

⇒ C_{02} = 8C_{01}

Two identical ball bearings P and Q are operating at loads 30 kN and 45 kN respectively. The ratio of the life of bearing P to the life of bearing Q is

Option 2 : \(\frac{27}{8}\)

**Concept:**

**Load-life relationship:**

The approximate rating of the service life of a ball or roller bearing is based on the given fundamental equation.

\({\rm{L_{10}}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} \times {10^6}{\rm\;{revolution}}\)

L_{10} = Rated bearing life (in million revolutions)

C = Dynamic load capacity.

P = Load acting in bearing.

k = 3 for ball bearing and k = 10/3 for the roller bearing.

**Calculation:**

**Given:**

P_{P} = 30 kN, Q_{P} = 45 kN and k = 3.

\({\rm{L_{10}}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} \times {10^6}{\rm\;{revolution}}\)

∵ the dynamic load capacity of bearing is the same i.e. C_{P} = C_{Q}.

\(\left ( \frac{L_{10P}}{L_{10Q}} \right )=\left ( \frac{P_Q}{P_P} \right )^3\Rightarrow\left ( \frac{45}{30} \right )^3=\frac{27}{8}\)

Option 3 : Cylindrical (straight) roller bearing

__Explanation:__

Bearing: It is a mechanical component used to reduce the friction between two rotating or sliding surfaces.

A plain bearing is divided into two halves, usually associated with a crankcase that can be detached or supports the main bearing cap. The plain bearing is wrapped around the journal and pressurized with oil.

Plain bearings are used in main bearings and connecting rod bearing. Its main application is in the piston and connecting rod in engine.

Roller bearing: It is a type of rolling-element bearing that uses cylindrical rollers to maintain the separation between the bearing races. The load-carrying capacity is more than ball bearing.

It is having 4 types:

1. Cylindrical roller bearing:

- Cylindrical roller bearings can only support radial loads. Axial loads will cause the ends of the rollers to rub against the sides of the races. In addition, because the rollers are fairly wide,
- cylindrical roller bearings cannot accommodate much angular misalignment.

- These bearings have short roller guided in a cage.
- These bearings are relatively rigid against the radial motion and have the lowest coefficient of friction of any form of heavy-duty rolling contact bearings.
- Such types of bearings are used in high-speed service.

2. Spherical roller bearing

- These bearings are self-aligning bearings.
- The self-aligning feature is achieved by grinding one of the races in the form of a sphere.
- These bearings can tolerate angular misalignment in the order of \(\pm1 \frac 12\).
- When used with a double row of rollers, these can carry thrust load in either direction.

3. Needle roller bearing

- These bearings are relatively slender and completely fill the space so that neither a cage nor a retainer is needed.
- These bearings are used when heavy loads are to be carried with an oscillatory motion.
- For example, piston pin bearing in heavy-duty diesel engines where the reversal of motions tends to keep the roller in correct alignment.

4. Taper Roller bearing

- The roller and raceways of these bearings are truncated cones whose elements intersect at a common point.
- Such type of bearing can carry both radial and thrust loads.

Ball-bearing: It is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races.

It is having 6 types:

1. Single row deep groove ball bearing

- During assembly of this bearing, the races are offset and the maximum number of balls are placed between the races.
- The races are then centred and the balls are symmetrically located by the use of a retainer or cage.
- These bearings are used due to their high load-carrying capacity and suitability for high running speeds.

2. Filling notch ball bearing

- These bearings have notches in the inner and outer races which permits more balls to be inserted.
- The notch does not extend to the bottom of the raceway and therefore the balls inserted through the notches must be forced in position.

3. Angular contact bearing

- These bearings have one side of the outer race cut away to permit the insertion of more balls than in a deep groove bearing but without having a notch cut in both races.
- This permits the bearing to carry a relatively large axial load in one direction while carrying a relatively large radial load.
- The angular contact bearing are used in pairs so that thrust load may be carried in either direction.

4. Double row deep groove ball bearing

- These bearings may be made with radial or angular contact between the balls and the races.
- The double row bearing is appreciably narrower than two single-row bearings.
- The load-carrying capacity of such bearing is slightly less than twice that of a single-row bearing.

5. Self-aligned bearing

- These bearings permit shaft deflections with 2-3 degrees.

6. Thrust bearing

- The thrust bearing is used for carrying thrust loads exclusively and at speeds below 2000 rpm.
- It doesn't take any radial load.
- At high speeds, centrifugal force causes the balls to be forced out of the races.

Option 4 : 1000

__Concept:__

Life of a bearing

The approximate rating of the service life of a ball or roller bearing is based on the given fundamental equation.

\({\rm{L}} = {\left( {\frac{{\rm{C}}}{{\rm{W}}}} \right)^{\rm{k}}} \times {10^6}{\rm{revolution}}\)

where L is rating life, C is a basic dynamic load, W is the equivalent dynamic load

k = 3 for ball bearing

k = 10/3 for roller bearing

∴ For a ball bearing,

\(L \propto \frac{1}{{{W^3}}}\;or~Life \propto \frac{1}{{{{\left( {Load} \right)}^3}}}\)

__Calculation:__

__Given:__

Initial load = F, Final load = 2F, Initial life = 8000 hours

As we know,

\(Life\;\;\alpha \;\;\frac{1}{{{{\left( {Load} \right)}^3}}}\)

\(\frac{{final\;life}}{{initial\;life}} = {\left( {\frac{{initial\;load}}{{final\;load}}} \right)^3}\)

\(\frac{{final\;life}}{{8000}} = {\left( {\frac{F}{{2F}}} \right)^3}\)

\(final\;life = \frac{{8000}}{8} = 1000\;hours\)

Option 1 : \(\frac{C}{P} = (\frac{L}{L_{10}})^{\frac{1}{K}}\)

**Explanation:**

Dynamic Load capacity:

- It is the radial load at which the 90% of the group of apparently identical bearings run for 1 million revolutions before the evidence of the first crack.
- The fatigue life of bearing at which 90% of a sufficiently large group of identical
**bearings**operating under identical conditions fails is called**rated life.**

Bearing rated life in million revolutions can be calculated by:

\(\frac{L}{L_{10}} = {\left( {\frac{C}{P}} \right)^k}\)

\((\frac{L}{L_{10}})^\frac{1}{k} = {\frac{C}{P}}\)

where, L = Life of bearing in Million revolution L10 = Rated life in Million revolutions, C = Dynamic load capacity/Basic load rating, P = Equivalent dynamic load

k = 3 for ball bearing, k = \(\frac{10}{3}\) for roller bearing

Option 2 : Plain bearings

**Concept:**

**Bearing**: It is a mechanical component used to reduce the friction between two rotating or sliding surfaces.

**A plain bearing** is divided into two halves, usually associated with a crankcase that can be detached or supports the main bearing cap. The plain bearing is wrapped around the journal and pressurized with oil.

Plain bearings are used in main bearings and connecting rod bearing.** Its main application is in the piston and connecting rod in engine.**

**Ball-bearing:** It is a type of rolling-element bearing that uses **balls** to maintain the separation between the bearing races.

It is having 6 types:

**1. Single row deep groove ball bearing**

- During assembly of this bearing, the races are offset and the maximum number of balls are placed between the races.
- The races are then centred and the balls are symmetrically located by the use of a retainer or cage.
- These bearings are used due to their high load-carrying capacity and suitability for high running speeds.

**2. Filling notch ball bearing**

- These bearings have notches in the inner and outer races which permits more balls to be inserted.
- The notch does not extend to the bottom of the raceway and therefore the balls inserted through the notches must be forced in position.

**3. Angular contact bearing**

- These bearings have one side of the outer race cut away to permit the insertion of more balls than in a deep groove bearing but without having a notch cut in both races.
- This permits the bearing to carry a relatively large axial load in one direction while carrying a relatively large radial load.
- The angular contact bearing are used in pairs so that thrust load may be carried in either direction.

4. Double row deep groove ball bearing

- These bearings may be made with radial or angular contact between the balls and the races.
- The double row bearing is appreciably narrower than two single-row bearings.
- The load-carrying capacity of such bearing is slightly less than twice that of a single-row bearing.

**5. Self-aligned bearing**

- These bearings permit shaft deflections with 2-3 degrees.

**6. Thrust bearing**

- The thrust bearing is used for carrying thrust loads exclusively and at speeds below 2000 rpm.
- At high speeds, centrifugal force causes the balls to be forced out of the races.

**Roller bearing:** It is a type of rolling-element bearing that uses **cylindrical rollers** to maintain the separation between the bearing races. The load-carrying capacity is more than ball bearing.

It is having 4 types:

**1. Cylindrical roller bearing:**

- These bearings have short roller guided in a cage.
- These bearings are relatively rigid against the radial motion and have the lowest coefficient of friction of any form of heavy-duty rolling contact bearings.
- Such types of bearings are used in high-speed service.

**2. Spherical roller bearing**

- These bearings are self-aligning bearings.
- The self-aligning feature is achieved by grinding one of the races in the form of a sphere.
- These bearings can tolerate angular misalignment in the order of \(\pm1 \frac 12\).
- When used with a double row of rollers, these can carry thrust load in either direction.

**3. Needle roller bearing**

- These bearings are relatively slender and completely fill the space so that neither a cage nor a retainer is needed.
- These bearings are used when heavy loads are to be carried with an oscillatory motion.
- For example, piston pin bearing in heavy-duty diesel engines where the reversal of motions tends to keep the roller in correct alignment.

4. Taper Roller bearing

- The roller and raceways of these bearings are truncated cones whose elements intersect at a common point.
- Such type of bearing can carry both radial and thrust loads.

Option 4 : Taper roller bearing

__Concept:__

- Tapered roller bearings are capable of carrying both radial and axial loads.
- They are often used in pairs to take the thrust load in both directions.
- The taper roller bearing consists of rolling elements in the form of a frustum of cone. They are arranged in such a way that the axes of individual rolling elements intersect in a common apex point on the axis of the bearing.
- The taper roller bearing consists of rolling part and inner and outer raceways in the form of conical surfaces. The outer raceway or outer ring is called ‘cup’ and inner raceway is called ‘cone’.

Needle roller bearing

- These bearings are used when heavy loads are to be carried with an oscillatory motion.

__Additional Information__

The following Points are to be noted about the load-carrying capacity of different types of rolling contact bearings:

- Thrust Ball Bearing: Thrust ball bearing cannot take the radial load.
- Taper Roller Bearing: can take heavy radial and thrust loads.
- Angular Contact Bearing: can take both radial and thrust loads.
- Cylindrical Roller Bearing: can take radial load only
- Deep Groove Ball Bearing: takes load in radial as well as an axial direction

Two identical ball bearings P and Q are operating at loads 15 kN and 45 kN respectively. The ratio of life bearing P to Q is

Option 2 : 27

__Concept:__

Load-Life relationship of a Bearing:

\({L_{10}} = {\left( {\frac{C}{P}} \right)^n}\)

L10 = Rated bearing life (in million revolutions), C = Dynamic load-carrying capacity, P = Load acting on the bearing

n = 3 for ball bearing and n = 10/3 for roller bearing.

__Calculation:__

__Given:__

PP = 15 kN, PQ = 45 kN, n = 3 (∵ ball bearing) and CP = CQ (∵ identical bearing).

\({L_{10}} = {\left( {\frac{C}{P}} \right)^n}\)

\(\therefore \frac{{{L_P}}}{{{L_Q}}} = {\left( {\frac{{{P_Q}}}{{{P_P}}}} \right)^3} = {\left( {\frac{{45}}{{15}}} \right)^3} = 3^3 =27 \)

Option 1 : 65 kN

__Concept:__

**Equivalent bearing load (W)** is given by:

**W = XVFr + YFa**

where X = radial factor, V = service factor, F_{r} = radial load, Y = thrust factor, F_{a} =thrust load

**Life of a bearing is given by:**

\({L_{10}} = {\left( {\frac{C}{W}} \right)^n}\)

where

L_{10} = basic life rating in million revolutions

C = dynamic load-carrying capacity

W = equivalent dynamic load

n = constant = 3 for ball bearing and \(\frac{{10}}{3}\) for roller bearing

__Calculation:__

__Given:__

F_{r} = 7000 N, F_{a} = 2100 N, X = 0.65, V = 1, Y = 3.5, L_{10} = 160 million revolutions

Equivalent bearing load (W) is given by:

**W = XVFr + YFa**

W = (0.65 × 1 × 7000) + (3.5 × 2100) = 11900 N

Now,

Life of a bearing is:

\({L_{10}} = {\left( {\frac{C}{W}} \right)^n}\)

\(C = W \times {\left( {{L_{10}}} \right)^{\frac{1}{n}}}\)

C = 11900 × (160)^{1/3} = 64603.14 N = **64.6 kN ≈ 65 kN**

Option 4 : 3.4 times its earlier life

__Concept: __

The life of ball bearing is given by,

\({L_{90}} = {\left( {\frac{c}{P}} \right)^3}\)

L_{90} means that 90% of the bearing will complete or exceed this number of cycles before the indication of any failure.

Where C – dynamic load capacity and, P is equivalent load

__Calculation:__

When dynamic capacity is increased by 1.5 times then,

\({L_{90}} = {\left( {\frac{c}{P}} \right)^3}\)

New life will be \(L_{90}' = {\left( {\frac{{1.5\;C}}{P}} \right)^3} = {1.5^3}{\left( {\frac{C}{P}} \right)^3} = {1.5^3}\;{L_{90}}\)

\(L_{90}' = 3.375\;{L_{90}} \approx 3.4\;{L_{90}}\)

**Concept:**

For ball bearing,

FL^{1/3 }= K

F = Radial Load

L = Life in number of revolutions

**Calculation:**

Given:

F_{1} = 2 kN, L_{1} = 540 million revolutions, L_{2} = 1 million revolutions

\({F_1}L_1^{\frac{1}{3}} = {F_2}L_2^{\frac{1}{3}}\)

2 × 540^{1/3} = F_{2}(1)^{1/3}

∴ F_{2} = 16.286 kN

Option 2 : 0.125

Given that :

Radial clearance, λ = 50 μm

Load, F = 2 kN, N = 20 rps

diameter, d = 50 mm

viscosity, μ = 20 mPa-s

length, L = 50 mm

\(P = \frac{F}{A} = \frac{F}{{L \times d}} \\= \frac{{2000}}{{50 \times 50}} = 0.8\;\frac{N}{{m{m^2}}}\)

sommerfield number

\(Z = \frac{{\mu N}}{P}{\left( {\frac{r}{\lambda}} \right)^2}\)

\(= \frac{{\left( {20 \times {{10}^{ - 3}}} \right) \times 20}}{{\left( {0.8 \times {{10}^6}} \right)}} \times {\left( {\frac{{25\times10^{-3}}}{{50\times10^{-6}}}} \right)^2}\)

= 0.125

Option 4 : Deep groove type ball bearing

__Explanation:__

**Deep groove ball bearing**

**Deep groove ball bearing takes loads in the radial as well as the axial direction.**- Due to the relatively large size of the balls, deep groove ball bearing has a high load-carrying capacity.
- It gives excellent performance in high-speed applications due to less resultant temperature rise.

Needle roller bearing

- These bearings are used when heavy loads are to be carried with an oscillatory motion.

Cylindrical roller bearing:

- Cylindrical roller bearings can only support radial loads. Axial loads will cause the ends of the rollers to rub against the sides of the races. In addition, because the rollers are fairly wide,
- cylindrical roller bearings cannot accommodate much angular misalignment.

- These bearings have short roller guided in a cage.
- These bearings are relatively rigid against the radial motion and have the lowest coefficient of friction of any form of heavy-duty rolling contact bearings.
- Such types of bearings are used in high-speed service.

__Additional Information__

The following Points are to be noted about the load-carrying capacity of different types of rolling contact bearings:

- Thrust Ball Bearing: Thrust ball bearing cannot take the radial load.
- Taper Roller Bearing: can take heavy radial and thrust loads.
- Angular Contact Bearing: can take both radial and thrust loads.
- Cylindrical Roller Bearing: can take radial load only

__Concept__:

**Life of a bearing is given by:**

**\({L_{10}} = {\left( {\frac{C}{W}} \right)^n}\)**

where

L_{10} = basic life rating in million revolutions

C = dynamic load-carrying capacity

W = equivalent dynamic load

n = constant = 3 for ball bearing and \(\frac{{10}}{3}{\rm{\;}}\)for roller bearing

__Calculation:__

__Given:__

C = 16kN, W = 2kN, n = 3 (ball bearing)

Life of bearing

\({L_{10}} = {\left( {\frac{C}{W}} \right)^n} = {\left( {\frac{{16}}{2}} \right)^3} = 512\;million\;revolutions = 512 \times {10^6}\;revolutions\)

∴ p = 512

Find the dynamic load-carrying capacity of a roller bearing if the shaft rotates at 1500 rpm, the radial load acting on the bearing is 6 kN and the expected life for 90% life of the bearing is 8100 hours.

Option 2 : 44 kN

__Concept:__

Load-life relationship:

\({\rm{L_{10}}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} \)

L10 = Rated bearing life (in million revolutions)

C = Dynamic load capacity.

P = Load acting in bearing.

k = 3 for ball bearing and k = 10/3 for the roller bearing.

The relation between life in million revolutions and life in hours is given by:

\(L_{10}=\frac{L_{10h}\;\times \;N \;\times \;60}{10^6}\)

where, L_{10h }= rated bearing life in hours and N = speed of rotation in rpm.

__Calculation: __

__Given:__

N = 1500 rpm, P = 6 kN, L_{10h} = 8100 hours, roller bearing k = 10/3

We know that;

\({\rm{L_{10}}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} \times {10^6}{\rm\;{revolution}}\) and;

\(L_{10}=\frac{L_{10h}\;\times \;N \;\times \;60}{10^6}\)

Combining both equations:

\(\frac{L_{10h}\;\times \;N \;\times \;60}{10^6}= {\left( {\frac{{\rm{C}}}{{\rm{6}}}} \right)^{{\frac{10}{3}}}} \)

\(\frac{8100\;\times \;1500 \;\times \;60}{10^6}= {\left( {\frac{{\rm{C}}}{{\rm{6}}}} \right)^{{\frac{10}{3}}}} \)

C = 43.34 kN

Option 2 : 27/8

__Concept:__

**Load-Life relationship of a Bearing:**

\({L_{10}} = {\left( {\frac{C}{P}} \right)^n}\)

L10 = Rated bearing life (in million revolutions), C = Dynamic load-carrying capacity, P = Load acting on the bearing

n = 3 for ball bearing and n = 10/3 for roller bearing.

__Calculation:__

__Given:__

P_{P} = 30 kN, P_{Q} = 45 kN, n = 3 (∵ ball bearing) and C_{P} = C_{Q} (∵ identical bearing).

\({L_{10}} = {\left( {\frac{C}{P}} \right)^n}\)

\(\therefore \frac{{{L_P}}}{{{L_Q}}} = {\left( {\frac{{{P_Q}}}{{{P_P}}}} \right)^3} \Rightarrow {\left( {\frac{{45}}{{30}}} \right)^3} = {\left( {\frac{3}{2}} \right)^3} \Rightarrow \frac{{27}}{8}\)

Option 4 : spherical roller bearing

__Concept:__

- Thrust ball bearings are used for medium thrust loads whereas for heavy thrust loads.
- Rigidity controls the selection of bearings in certain applications like machine tool spindles. taper roller bearings are used under these conditions. The line of contact in these bearings, as compared with the point of contact in ball bearings, improves the rigidity of the system.
- For low and medium radial loads, ball bearings are used.
- Spherical roller bearings are suitable in applications where the load acting on the bearing consists of two components— radial and thrust.

Hence option (4) is correct.