Design of Machine Elements MCQ Quiz - Objective Question with Answer for Design of Machine Elements - Download Free PDF

Explanation:

Fatigue Testing and the S-N Curve

Definition: Fatigue testing is a method used to determine the durability and lifespan of a material under cyclic loading conditions. It is crucial in predicting how a material will behave when subjected to repeated stress or strain over time. The S-N curve, also known as the Wöhler curve, is a graphical representation that illustrates the relationship between the stress amplitude (S) and the number of cycles to failure (N).

Working Principle: During fatigue testing, a sample material is subjected to repeated cyclic loading until failure occurs. The stress amplitude and the number of cycles to failure are recorded. This data is then used to plot the S-N curve, where the x-axis represents the number of cycles to failure (N) on a logarithmic scale, and the y-axis represents the stress amplitude (S).

Correct Option Analysis:

The correct option is:

Option 2: The number of cycles and stress amplitude

This option accurately describes the S-N curve in fatigue testing. The S-N curve shows the relationship between the number of cycles to failure (N) and the stress amplitude (S). The curve typically displays how the material's endurance limit or fatigue limit is determined, which is the stress level below which the material can endure an infinite number of cycles without failing.

The S-N curve is critical for engineers and designers to understand the fatigue behavior of materials and to ensure the reliability and safety of components subjected to cyclic loading in various applications, such as in automotive, aerospace, and structural engineering

Concept:

• Speed of driving shaft, \( N_1 = 80 \, \text{rpm} \)
• Speed of driven shaft, \( N_2 = 150 \, \text{rpm} \)
• Diameter of driving pulley, \( D_1 = 600 \, \text{mm} \)
• Belt thickness, \( t = 5 \, \text{mm} \)

Step 1: Account for belt thickness in effective diameters

The effective diameter increases by the belt thickness:

\( D_{\text{eff1}} = D_1 + t = 600 + 5 = 605 \, \text{mm} \)

Let the effective diameter of the driven pulley be \( D_{\text{eff2}} = D_2 + t \).

Step 2: Apply the speed ratio formula for belt drives

The speed ratio is inversely proportional to the effective diameters:

\( \frac{N_2}{N_1} = \frac{D_{\text{eff 1}}}{D_{\text{eff 2}}} \)

\( \frac{150}{80} = \frac{605}{D_2 + 5} \)

\( D_2 + 5 = \frac{605 \times 80}{150} \)

\( D_2 + 5 = 322.67 \, \text{mm} \)

\( D_2 = 322.67 - 5 = 317.67 \, \text{mm} \)

Concept:

For a single plate clutch with both sides effective and assuming uniform wear, torque transmitted is:

\( T = 2 \times \mu \times W \times \frac{R_o + R_i}{2} \)

Given:

\( W = 1000~N \), \( R_i = 0.10~m \), \( R_o = 0.15~m \), \( \mu = 0.5 \)

Calculation:

\( T = 2 \times 0.5 \times 1000 \times \frac{0.15 + 0.10}{2} = 1000 \times 0.125 = 125~\text{N·m} \)

Concept:

The maximum efficiency of screw jack is when helix angle α is

\(\alpha = 45^\circ- \frac{\phi }{2}\)

Note:

If the friction angle is greater than the helix angle, the torque required to lower the load will positive, indicating that an effort is applied to lower the load. Such a screw is known as a self-locking screw.

Additional Information

Screw jack

• A screw jack is a portable device consisting of a screw mechanism used to raise or lower the load. There are two types of jack Hydraulic and mechanical
• A Hydraulic jack consists of a cylinder and piston mechanism. The movement of piston rod is used to raise or lower the load.
• Mechanical jack can be either hand operated or power driven

The maximum efficiency of screw jack is:

\(\eta = \frac{{1 - sin\phi }}{{1 + sin\phi }} \)

Explanation:

Face of a Tooth in Spur Gear

• In the context of spur gears, the "face" of a tooth refers to the surface of the tooth that lies between the pitch circle and the top land. This definition is crucial for understanding the geometry of gear teeth and their role in transmitting motion and power in mechanical systems.
• The face of a tooth in a spur gear is specifically defined as the part of the tooth's profile that extends from the pitch circle to the top land. The pitch circle is an imaginary circle that represents the effective diameter at which the gear teeth engage with a mating gear. The top land, on the other hand, is the flat or slightly rounded surface at the very top of the tooth. The face of the tooth plays a critical role during the engagement of gears as it is part of the contact surface where power transmission occurs.

Explanation of the Gear Tooth Terminology:

• Pitch Circle: The pitch circle is an imaginary circle that defines the size of the gear. It is the circle where the teeth of two mating gears make contact and effectively transmit motion and force. This circle is fundamental in determining the gear ratio and speed ratio in gear systems.
• Top Land: The top land is the flat or rounded surface at the top of the gear tooth. It is the highest point of the tooth profile and is not involved in the engagement with the mating gear teeth.
• Face: The face of the tooth is the portion of the tooth profile that extends from the pitch circle to the top land. This surface interacts with the mating gear teeth during the operation of the gear system.

Importance of the Face:

• The face of the tooth is crucial in power transmission as it makes contact with the mating gear's teeth during engagement.
• The surface finish, shape, and accuracy of the face directly influence the efficiency, noise, and wear characteristics of the gear system.
• Proper design and manufacturing of the face ensure smooth and reliable operation of the gear system, reducing the chances of failure or excessive wear.

Explanation:

Explanation:

Vee- Belt

• The Vee belts are made up of rubber with fabric cords to transmits power and it's covered with a protective layer.
• The cords transmit the force from the driver to the driven pulley, thereby transmit the power.
• Vee belts are widely used in industry and automobiles because of their power transmitting capacity.
• The wedge shape of the belt increases the area of contact with the pulley thereby increasing more friction, which makes it carry more power without slip.

Vee belt cross-sections

• There are different sizes of Vee belt cross-sections named A, B, C, D, and E (based on the width of the belts).
• These are standard sizes manufactured by belt manufacturers.

• As we move from A to E, The power transmitted by the Vee belt drive increases. Hence Vee-belt drive with E-type cross-sections is used in the heavy-duty machine.

Additional Information

Vee belts are preferred over the flat belts the reasons follow.

• Power transmitted is more due to wedging action in the grooved pulley.
• Higher velocity ratio (Upto 10) can be obtained.
• Vee-belt drive is more compact, quiet and shock absorbing.
• The Vee belt drive is positive because the slip is negligible.
• Clean and requires no lubrication.
• They are efficient - performing with an average of 94 - 98 % efficiency.

Explanation:

Clutch:

A clutch is a mechanical device that is used to connect or disconnect the source of power from the remaining part of the power transmission system at the will of the operator. The clutch design took the help of two theories which are mentioned as follows.

Explanation:

The sliding contact bearing, according to the thickness layer of lubricant between bearing and journal are mentioned as follows.

Explanation:

Crowning of pulley:

• The rim of the pulley of a flat belt drive is slightly crowned to prevent the slipping off the belt from the pulley.
• The crowning can be in the form of a conical surface or a convex surface.
• Generally, if a pulley is made up of two equal cones or a convex surface, the belt will tend to climb on the slope and will run with its center line on the mid-plane of the pulley.

Explanation:

Belt Drive

• The belt drive is the most common method of power transmission.
• The belts are made from leather, cotton, rubber, and synthetic materials.

There are four types of belts:

1. Flat belt
2. V - belt and multiple V - belt
3. Ribbed belt
4. Toothed or timing belt

V - Belt drive

• V - belt drives are generally used when the distance between the shafts is short for flat belt drives.
• Owing to the wedge action between the belt and the sides of the groove in the pulley, the V belt is less likely to slip, hence more power can be transmitted.

Advantages of V -belt drive

• It is compact, so installation is possible in limited space
• It is used when the center distance between the drive and the driven pulleys is short.
• Less vibration and noise
• Cushions the motor and bearings against load fluctuation
• Easy replacement and maintenance

Explanation:

Function of a washer:

• A washer is a thin plate (typically disk-shaped) with a hole (typically in the middle) that is normally used to distribute the load of a threaded fastener, such as a screw or nut. 
• Washers are used to distribute the clamping pressure over a larger area and prevent surface damage. They also provide an increased bearing surface for bolt heads and nuts.

Types of Washers:

Figure: Lock Washer

Concept:

When the frictional force helps the applied force in applying the brake, such type of brakes are said to be self-energizing brakes.

Self-energizing brake is the one in which torque due to Fr supports torque due to F.

Calculation:

Given:

The torque due to F is clockwise. The torque due to Fr = μR_N is clockwise. So, it is a self-energizing brake.

Let consider clockwise rotation

∑M_pivot = 0

F × ℓ - R_N × a + μ R_N × b = 0

When the wheel rotates in a clockwise direction we can see that friction is helping the applied force in applying the brake. Hence it is called a self-energizing brake.

Explanation:

Reduction of stress concentration:

Although it is not possible to completely eliminate the effect of stress concentration, there are methods to reduce stress concentration. They are:

Additional notches and holes in tension member:

A single notch results in a high degree of stress concentration. The impact is reduced by three methods:

• use of multiple notches
• drilling additional holes
• removal of undesired material

Fillet radius, undercutting, and notch for members in bending:

Drilled additional holes in shaft:

Addition of washer:

Simple washers are thin annular-shaped metallic disks. Its functions are as follows:

• Distributes the load over a large area on the surface of clamped parts.
• It provides bearing surfaces over large clearance holes.

Explanation:

Square and trapezoidal threads are most commonly used threads.

Square thread: In this thread the flanks are perpendicular to the axis of the thread. This is used for transmitting motion or power. E.g. Fly presses, Screw jack, vice handles, cross-slide and compound slide etc.

Trapezoidal threads: These threads have a profile which is neither square nor V thread form and have a form of trapezoid. Different forms of trapezoidal threads are ACME thread, Buttress thread, Saw-tooth thread, Worm thread

• ACME thread: It has an included angle of 29°. These are used in lathe lead screws.
• Buttress Thread: In this thread, one flank is perpendicular to the axis of the thread and other flank is at 45°. These threads are used in power press, carpentry vices, gun breeches, ratchets etc.
• Knuckle thread: The shape of the knuckle thread is not trapezoid, but it has a rounded shape. It has limited applications. It is used for valve spindles, railway carriage coupling, hose connections etc.