All questions of Design of Machine Elements for Mechanical Engineering Exam

Explanation:

Thick film hydrodynamic journal bearings are used to support rotating shafts in various mechanical systems. These bearings work on the principle of hydrodynamic lubrication, where a thin film of lubricant is formed between the journal and the bearing surface due to the relative motion between them.

Coefficient of friction is a measure of the resistance to sliding between two surfaces in contact. In hydrodynamic journal bearings, the coefficient of friction is influenced by various factors such as load, speed, viscosity of the lubricant, surface roughness, and the geometry of the bearing.

Effect of Load on Coefficient of Friction:

- As the load on the bearing increases, the pressure on the lubricant film also increases. This causes the thickness of the lubricant film to decrease, which in turn increases the contact area between the journal and the bearing surface.
- Due to the increased contact area, the shearing forces acting on the lubricant also increase. This leads to an increase in the frictional resistance between the two surfaces, resulting in an increase in the coefficient of friction.

However, this effect is only observed up to a certain limit. Beyond this limit, the thickness of the lubricant film becomes too thin to support the load and the bearing enters into a mixed or boundary lubrication regime. In this regime, the coefficient of friction may increase or decrease depending on the lubricant properties and the surface roughness of the bearing.

Therefore, the correct option is C) Decreases with increase in load, up to a certain limit.

Conclusion:

In thick film hydrodynamic journal bearings, the coefficient of friction initially decreases with an increase in load due to the formation of a thicker lubricant film. However, beyond a certain limit, the lubricant film becomes too thin to support the load and the bearing enters into a mixed or boundary lubrication regime, where the coefficient of friction may increase or decrease depending on various factors.

-The term rolling contact bearings refers to the wide variety of bearings that use spherical balls or some other type of roller between the stationary and the moving elements. • The most common type of bearing supports a rotating shaft, resisting purely radial loads or a combination of radial and axial (thrust) loads.

The length of the key will be 

Criterion in the design of hydrodynamic journal bearings

The hydrodynamic journal bearing is a type of bearing that operates on the principle of hydrodynamic lubrication, where a film of lubricating fluid is created between the journal and the bearing surfaces. This film of lubricant helps to reduce friction, prevent wear, and provide smooth and reliable operation. In the design of hydrodynamic journal bearings, several criteria are considered, but the most important criterion is the Sommerfeld number.

Sommerfeld number

The Sommerfeld number, also known as the Sommerfeld parameter or bearing number, is a dimensionless parameter that represents the ratio of the load-carrying capacity of the bearing to the viscous dissipation of the lubricant. It is defined as the ratio of the product of the journal diameter, rotational speed, and the viscosity of the lubricant to the product of the load and the dynamic viscosity of the lubricant.

The Sommerfeld number is given by the equation:

Sommerfeld number = (d * N * μ) / (P * μ')

Where:
- d is the journal diameter
- N is the rotational speed
- μ is the viscosity of the lubricant
- P is the load
- μ' is the dynamic viscosity of the lubricant

Significance of the Sommerfeld number

The Sommerfeld number is a crucial criterion in the design of hydrodynamic journal bearings because it determines the stability and performance of the bearing. A low Sommerfeld number indicates a high load-carrying capacity and good lubrication, while a high Sommerfeld number suggests poor lubrication and potential bearing failure.

When designing a hydrodynamic journal bearing, the Sommerfeld number is used to ensure that the bearing operates within an acceptable range. If the Sommerfeld number is too low, it may result in excessive wear and failure of the bearing due to insufficient lubrication. On the other hand, if the Sommerfeld number is too high, it may lead to excessive heat generation and reduced bearing life.

Other criteria in the design of hydrodynamic journal bearings

While the Sommerfeld number is the most important criterion, other factors are also considered in the design of hydrodynamic journal bearings, including:

- Rating life: This criterion represents the expected operating life of the bearing under specified conditions. It takes into account factors such as load, speed, lubrication, and temperature.

- Specific dynamic capacity: This criterion refers to the load-carrying capacity of the bearing per unit area of the bearing surface. It indicates the ability of the bearing to support the applied load without excessive deformation or failure.

- Rotation factor: This criterion represents the ratio of the circumferential speed of the journal to the speed of sound in the lubricant. It is used to ensure that the bearing operates within the limits of the lubricant film speed, as excessive speeds can lead to film breakdown and bearing failure.

In conclusion, while there are several criteria in the design of hydrodynamic journal bearings, the Sommerfeld number is the most important one. It determines the load-carrying capacity and lubrication performance of the bearing. The other criteria, such as rating life, specific dynamic capacity, and rotation factor, are also considered to ensure the overall performance and reliability of the bearing.

Pitch Circle in Spur Gears

Pitch circle is an important term used in the context of spur gears. It refers to the imaginary circle that intersects with the teeth of the gear. The pitch circle is used to calculate the gear ratio, tooth profile, and other important parameters of the gear. In this article, we will discuss the pitch circle in detail.

Definition

The pitch circle is the circle on which the involute gear tooth profile is based. It is an imaginary circle that intersects with the teeth of the gear. The diameter of the pitch circle is the reference diameter of the gear, which is used to calculate the gear ratio, tooth profile, and other important parameters of the gear.

Importance

The pitch circle is an important concept in gear design because it helps to determine the geometry of the gear teeth. The distance between the centers of two gears is called the pitch distance, and it is equal to the sum of the pitch diameters of the two gears. The pitch circle is also used to calculate the pitch angle, which is the angle between the tangent to the pitch circle and the axis of the gear.

Calculation

The pitch circle diameter (P.C.D) is calculated using the following formula:

P.C.D = N x M

where N is the number of teeth on the gear, and M is the module (size) of the gear.

The pitch circle diameter is also related to the outside diameter (O.D.) and the root diameter (R.D.) of the gear:

O.D. = P.C.D + 2 x addendum
R.D. = P.C.D - 2 x dedendum

where addendum is the distance between the pitch circle and the top of the tooth, and dedendum is the distance between the pitch circle and the bottom of the tooth.

Conclusion

In conclusion, the pitch circle is an imaginary circle that intersects with the teeth of the gear. It is an important concept in gear design because it helps to determine the geometry of the gear teeth. The pitch circle diameter is used to calculate the gear ratio, tooth profile, and other important parameters of the gear.

Statement: The length of the crossed belt increases as the sum of the diameters of the pulleys increases.

Explanation:

Belt Drives:
Belt drives are a type of power transmission mechanism used to transmit power from one shaft to another. They consist of a belt that is wrapped around two pulleys. The power is transferred through the tension in the belt, which causes friction between the belt and the pulleys.

Length of the Crossed Belt:
The length of the crossed belt refers to the total length of the belt that is in contact with the pulleys. It is important to know the length of the crossed belt in order to properly design and select a belt for a specific application.

Relation with the Sum of Diameters:
The length of the crossed belt is directly related to the sum of the diameters of the pulleys. As the sum of the diameters increases, the length of the crossed belt also increases.

Reasoning:
When a belt is wrapped around two pulleys, the length of the belt is determined by the distance it travels along the circumference of the pulleys. The distance traveled by the belt is directly proportional to the sum of the diameters of the pulleys.

To visualize this, imagine two pulleys of different sizes. If the belt is wrapped around the smaller pulley, it will travel a shorter distance compared to if it is wrapped around the larger pulley. Therefore, the length of the crossed belt increases as the sum of the diameters of the pulleys increases.

Example:
Let's consider an example to further illustrate this concept. Suppose we have two pulleys with diameters of 10 cm and 20 cm. The sum of the diameters is 30 cm. If we wrap a belt around these pulleys, the length of the crossed belt will be greater compared to if we had two pulleys with diameters of 5 cm and 10 cm, where the sum of the diameters is 15 cm.

Conclusion:
In conclusion, the statement "The length of the crossed belt increases as the sum of the diameters of the pulleys increases" is correct. The length of the crossed belt is directly proportional to the sum of the diameters of the pulleys in a belt drive system.

Given:
Mass of the flywheel, m = 300 kg
Radius of gyration, k = 1 m
Spin speed about horizontal axis, ω₁ = 100 rpm
Rotation speed about vertical axis, ω₂ = 6 rad/sec

To find:
The gyroscopic couple experienced by the flywheel.

Solution:

Step 1: Calculate the spin angular velocity
The spin angular velocity, ω₁, is given in rpm. To convert it to rad/sec, we use the following formula:
ω = (2π/60) * ω₁

Substituting the given value of ω₁, we get:
ω = (2π/60) * 100
ω = (π/30) * 100
ω = (10π/3) rad/sec

Step 2: Calculate the moment of inertia (I)
The moment of inertia of the flywheel can be calculated using the formula:
I = mk²

Substituting the given values of mass (m) and radius of gyration (k), we get:
I = 300 * 1²
I = 300 kg·m²

Step 3: Calculate the gyroscopic couple (C)
The gyroscopic couple (C) can be calculated using the formula:
C = I * ω₁ * ω₂

Substituting the values of moment of inertia (I), spin angular velocity (ω₁), and rotation speed (ω₂), we get:
C = 300 * (10π/3) * 6
C = 6000π N·m
C ≈ 18850 N·m

Step 4: Convert the gyroscopic couple to kNm
To convert the gyroscopic couple from N·m to kNm, we divide by 1000:
C = 18850 N·m
C ≈ 18.85 kNm

Therefore, the gyroscopic couple experienced by the flywheel is approximately 18.85 kNm.

Friction in Oil-Lubricated Journal Bearing

Friction is a significant factor in the performance of oil-lubricated journal bearings. The coefficient of friction between the journal and the bearing is affected by various factors, such as the speed of the journal, the viscosity of the lubricant, the surface roughness of the journal and the bearing, and the pressure distribution in the lubricating film. The coefficient of friction can be defined as the ratio of the frictional force between the journal and the bearing to the normal force between them.

Behavior of Coefficient of Friction with Speed

The behavior of the coefficient of friction with speed depends on the operating conditions and the design of the bearing. Generally, the coefficient of friction decreases with an increase in speed due to the following reasons:

- The viscosity of the lubricant decreases with an increase in temperature, and the shear rate increases with an increase in speed, leading to a decrease in the viscosity of the lubricant.
- The pressure distribution in the lubricating film changes with an increase in speed, and the pressure peaks shift towards the center of the bearing, reducing the frictional force between the journal and the bearing.

However, the coefficient of friction may not always decrease with an increase in speed and may reach a minimum value at an optimum speed and then increase with further increase in speed. This behavior is due to the following reasons:

- At low speeds, the lubricating film is thick, and the pressure distribution is more uniform, resulting in a high coefficient of friction.
- At high speeds, the lubricating film is thin, and the pressure distribution is non-uniform, resulting in a high coefficient of friction.
- At an optimum speed, the lubricating film is neither too thick nor too thin, and the pressure distribution is more uniform, resulting in a low coefficient of friction.

Conclusion

In conclusion, the coefficient of friction between the journal and the bearing in an oil-lubricated journal bearing becomes minimum at an optimum speed and then increases with further increase in speed due to the changes in the viscosity of the lubricant and the pressure distribution in the lubricating film.

Worm Gearing for Large Speed Reductions

Worm gearing is a type of gear system that is used to achieve large speed reductions in a single stage. This is possible due to the unique design of the worm gear, which consists of a worm and a worm wheel. The worm is a screw-like gear that engages with the teeth of the worm wheel, which is a cylindrical gear with teeth around its circumference.

Advantages of Worm Gearing

There are several advantages of using worm gearing for large speed reductions:

1. High Reduction Ratio: Worm gears can achieve high reduction ratios of up to 300:1 in a single stage, which makes them ideal for applications that require large speed reductions.

2. Self-Locking: Worm gears are self-locking, which means that they can hold a load in place without the need for a brake or other locking mechanism.

3. Compact Design: Worm gears have a compact design that allows them to be used in applications where space is limited.

4. Smooth Operation: Worm gears have a smooth operation due to the rolling contact between the worm and the worm wheel, which reduces friction and wear.

5. High Efficiency: Worm gears are highly efficient, with efficiencies of up to 90%, which makes them ideal for applications where energy efficiency is important.

Applications of Worm Gearing

Worm gearing is used in a wide range of applications, including:

1. Conveyor systems

2. Elevators

3. Packaging machinery

4. Material handling equipment

5. Printing presses

Conclusion

In conclusion, worm gearing is an excellent choice for achieving large speed reductions in a single stage. Its self-locking, compact design, smooth operation, high efficiency, and wide range of applications make it a popular choice for engineers and designers.

S-N for steel becomes a sympetric at 10^6 cycles.Hence, the correct option is (c)

Given data:
- Outer diameter of clutch (D1) = 100 mm
- Inner diameter of clutch (D2) = 40 mm
- Uniform pressure (P) = 2 MPa
- Coefficient of friction (μ) = 0.4

To calculate the torque carrying capacity of the clutch, we can use the formula:

T = (π/2) * (D1^2 - D2^2) * P * μ

Let's break down the solution into steps:

Step 1: Convert the diameters from millimeters to meters
- D1 = 100 mm = 0.1 m
- D2 = 40 mm = 0.04 m

Step 2: Calculate the torque carrying capacity using the formula
- T = (π/2) * (0.1^2 - 0.04^2) * 2e6 * 0.4
- T = (π/2) * (0.01 - 0.0016) * 2e6 * 0.4
- T = (π/2) * 0.0084 * 2e6 * 0.4
- T = 0.0084 * π * 2e6 * 0.4
- T = 2680832 Nmm

Step 3: Convert the torque from Newton-millimeters to Newton-meters
- 1 Nm = 1 Nmm / 1000
- T = 2680832 / 1000
- T ≈ 2680.832 Nm

Therefore, the torque carrying capacity of the clutch is approximately 2680.832 Nm, which is closest to option B (196 Nm).

In conclusion, option B is the correct answer.

Understanding the Design Considerations for Rocker Arm Pins
When designing the pin of a rocker arm in an internal combustion (I.C.) engine, several failure modes should be considered. The correct answer, option 'D', focuses on bearing failure, shearing failure, and bending failure. Here’s a detailed breakdown:
Tensile Failure
- This failure mode occurs when the material experiences excessive tensile stress.
- While important, tensile failure is not the primary concern for the pin in this context.
Creep Failure
- Creep failure happens over time under constant stress at elevated temperatures.
- Although creep is relevant in high-temperature applications, it is less critical for rocker arm pins, which operate under variable loads and temperatures.
Bearing Failure
- Bearing failure is crucial since the pin acts as a pivot point in the rocker arm assembly.
- Proper design must account for the loads transferred through the pin to prevent excessive wear or seizure.
Shearing Failure
- Shearing failure occurs when the pin is subjected to lateral forces that cause it to slide or fail along its cross-section.
- This type of failure is significant in rocker arms due to the dynamic forces at play.
Bending Failure
- Bending failure arises when the pin is subjected to moments causing it to bend beyond its elastic limit.
- Given the rocker arm's motion and the forces it experiences, ensuring the pin can withstand bending stresses is vital for longevity and performance.
Conclusion
Selecting option 'D' (bearing, shearing, and bending failures) emphasizes the critical design aspects that will ensure the pin's durability and functionality in an I.C. engine rocker arm. Proper consideration of these factors leads to safer and more efficient engine operation.

Explanation:
- Belt drives are used to transmit power from one shaft to another.
- When the belt is in motion, it tends to slide over the pulleys due to the frictional force between the belt and the pulley surface.
- The amount of slip that occurs in a belt drive depends on the angle of rest and angle of creep.
- The angle of rest is the maximum angle at which the belt will remain in contact with the pulley surface without slipping, when the pulley is at rest.
- The angle of creep is the maximum angle at which the belt will remain in contact with the pulley surface without slipping, when the pulley is in motion.
- Total slip refers to the difference between the linear distance traveled by the belt and the distance traveled by the pulley surface during a complete revolution of the pulley.
- Total slip occurs when the belt slips on the pulley surface due to insufficient frictional force.

Option A:
- If the angle of rest is zero, it means that the belt will remain in contact with the pulley surface even when the pulley is at rest.
- This indicates that there will be sufficient frictional force between the belt and the pulley surface to prevent slip.
- Therefore, in this case, total slip will not occur in the belt drive.

Option B:
- If the angle of creep is zero, it means that the belt will remain in contact with the pulley surface even when the pulley is in motion.
- This indicates that there will be sufficient frictional force between the belt and the pulley surface to prevent slip.
- However, this does not guarantee that total slip will not occur in the belt drive, as there may be other factors such as belt tension, pulley diameter, and belt material that can affect slip.

Option C and D:
- If the angle of rest is greater than the angle of creep, it means that the belt will slip on the pulley surface when the pulley is in motion, as the angle of creep is the maximum angle at which the belt can remain in contact with the pulley surface without slipping.
- Similarly, if the angle of creep is greater than the angle of rest, it means that the belt will slip on the pulley surface even when the pulley is at rest, as the angle of rest is the maximum angle at which the belt can remain in contact with the pulley surface without slipping.
- In both these cases, there will be insufficient frictional force between the belt and the pulley surface to prevent slip, and total slip will occur in the belt drive.

To determine the ratio of the length of the key (l) to the diameter of the shaft (d), we need to compare the shearing strengths of the key and the shaft.

1. Shearing Strength of the Key:
The shearing strength of a rectangular sunk key can be calculated using the formula:

Shearing Strength of Key = (Width of Key * Length of Key * Shear Stress) / (Factor of Safety)

Given that the width of the key is d/4, we can substitute this value into the formula:

Shearing Strength of Key = ((d/4) * l * Shear Stress) / (Factor of Safety)

2. Shearing Strength of the Shaft:
The shearing strength of a shaft can be calculated using the formula:

Shearing Strength of Shaft = (π/16) * (d^3) * Shear Stress

3. Equating the Shearing Strengths:
Since the shearing strength of the key is equal to the shearing strength of the shaft for full power transmission, we can set the two equations equal to each other:

((d/4) * l * Shear Stress) / (Factor of Safety) = (π/16) * (d^3) * Shear Stress

4. Simplifying the Equation:
To simplify the equation, we can cancel out the shear stress terms:

(d/4) * l / (Factor of Safety) = (π/16) * (d^3)

5. Determining the Ratio (l/d):
To find the ratio of l/d, we can rearrange the equation:

l/d = (π/16) * (d^2) / ((d/4) * (Factor of Safety))

Simplifying further:

l/d = (4π/16) * (d^2) / (d * (Factor of Safety))

l/d = (π/4) * (d/Factor of Safety)

Since the width of the key is taken as d/4, we can substitute this value into the equation:

l/d = (π/4) * (Width of Key/Factor of Safety)

Therefore, the ratio of l/d is given by (π/4), which is equal to option 'C'.

Band Brake and its Working Principle
A band brake is a type of brake that uses a flexible band to wrap around a rotating drum to stop the motion. The band is tightened around the drum by applying tension to one end of the band. The tension on the other end of the band is kept slack. When the brake is applied, the friction between the band and the drum generates a force that resists the motion of the drum.

Calculating the Coefficient of Friction
Given data:
- Ratio of tight side band tension to slack side = 3
- Angle of overlap of band on drum = 180 degrees

Formula:
Coefficient of friction = (Ratio of tension - 1) / (2 x sin(angle of overlap))

Substituting the values, we get:
Coefficient of friction = (3 - 1) / (2 x sin(180)) = 0.35

Therefore, the correct answer is option 'D' (0.35).

Explanation:
The ratio of tight side band tension to slack side is 3, which means the tight side tension is three times greater than the slack side tension. The angle of overlap of the band on the drum is 180 degrees, which means the band wraps around the drum completely. The coefficient of friction is calculated using the formula, which takes into account the ratio of tension and the angle of overlap. Substituting the values, we get the coefficient of friction as 0.35. This means that the friction between the band and the drum must be 0.35 to stop the motion of the drum effectively.

Explanation:

1. Endurance strength of a component is not affected by its surface finish and notch sensitivity of the material:
- The statement is incorrect. The endurance strength of a component can be significantly affected by its surface finish and the material's notch sensitivity.
- Surface finish can introduce stress concentrations, which can lead to premature failure of a component.
- Notch sensitivity refers to how susceptible a material is to stress concentration effects, with highly sensitive materials experiencing a greater decrease in endurance strength.

2. For ferrous materials like steel, S-N curve becomes asymptotic at 10^6 cycles:
- The statement is correct. In the case of ferrous materials like steel, the S-N curve typically becomes asymptotic at around 10^6 cycles.
- This means that beyond this point, the material experiences a much lower rate of decrease in endurance strength with increasing cycles, indicating a higher fatigue life.
Therefore, the correct answer is option B - 2 only.

It is used in connecting rods. Now, the connecting rod is subjected to tensile as well as compressive load.

Explanation:

In a 6 x 20 wire rope, the number 6 indicates the number of strands in the wire rope.

Wire Rope Construction:

A wire rope is constructed by combining multiple strands of wires together. Each strand consists of multiple wires twisted together. The construction of a wire rope is denoted by two numbers separated by an 'x', such as 6 x 20.

- The first number (6 in this case) represents the number of strands in the wire rope.
- The second number (20 in this case) represents the number of wires in each strand.

Interpretation of the Numbers:

To interpret the numbers correctly, let's consider the example of a 6 x 20 wire rope.

- The number of strands (6) indicates that there are 6 individual strands twisted together to form the wire rope. These strands are typically helically laid around a central core.
- Each strand consists of a certain number of wires, which are twisted together. In this case, there are 20 wires in each strand. These wires are typically laid in a helical pattern around a central core within each individual strand.

Significance of the Number of Strands:

The number of strands in a wire rope affects its strength, flexibility, and resistance to wear. Generally, a wire rope with a higher number of strands provides better flexibility and resistance to wear. It also tends to have a higher breaking strength compared to a wire rope with a lower number of strands.

Conclusion:

In summary, in a 6 x 20 wire rope, the number 6 indicates the number of strands in the wire rope. The higher the number of strands, the greater the flexibility, resistance to wear, and breaking strength of the wire rope.

CORRECT OPTION IS (A).
Due to slip present, the velocity ration will not remain constant and hence, belt drive is not a positive drive

Assertion (A): Uniform-strength bolts are used for resisting impact loads.

Reason (R): The area of cross-section of the threaded and unthreaded parts is made equal.

The correct answer is option C: A is true but R is false.

Explanation:

Uniform-strength bolts are designed to have the same strength in both the threaded and unthreaded sections. This allows for a more balanced distribution of load along the length of the bolt, which helps in resisting impact loads. However, the reason given for this assertion is not correct.

The area of cross-section of the threaded and unthreaded parts of a bolt is not necessarily made equal in uniform-strength bolts. In fact, the threaded section of the bolt is usually weaker than the unthreaded section due to the reduction in cross-sectional area caused by the threads. This reduction in cross-sectional area results in a decrease in the strength of the threaded section compared to the unthreaded section.

The main reason for using uniform-strength bolts in applications where impact loads are expected is to prevent stress concentration. Stress concentration occurs when there is a change in cross-sectional area along the length of a component, such as a bolt. This change in cross-sectional area can lead to high localized stresses, which can cause the component to fail under impact loads.

Uniform-strength bolts are designed to have a gradual transition from the unthreaded section to the threaded section, resulting in a more uniform distribution of stress along the length of the bolt. This helps to reduce stress concentration and improve the overall strength of the bolt under impact loads.

In conclusion, while uniform-strength bolts are indeed used for resisting impact loads, the reason given for this assertion is incorrect. The area of cross-section of the threaded and unthreaded parts of a bolt is not made equal in uniform-strength bolts.