Shafts Keys and Couplings MCQ Quiz - Objective Question with Answer for Shafts Keys and Couplings - Download Free PDF

Explanation:

Line shaft:

• A shaft directly coupled to a power source is referred to as a Line Shaft. This type of shaft is used to transmit power from the primary source to various machine components or systems in mechanical operations. The term specifically denotes the direct connection between the power source and the shaft, ensuring efficient power transmission without intermediate mechanisms.
• The Line Shaft operates by being physically connected to the power source, such as an engine or motor. This connection allows the rotational motion generated by the power source to be directly transmitted to the shaft. The shaft then distributes this mechanical energy to other connected components, such as pulleys, gears, or belts, which perform specific tasks or operations. Its direct coupling eliminates the need for secondary power transmission systems, enhancing efficiency and minimizing energy losses.

Applications: Line Shafts are commonly used in industries that require direct and robust power transmission systems, such as:

• Textile manufacturing units for operating multiple machines simultaneously.
• Conveyor systems in material handling processes.
• Machining operations in workshops and factories.
• Power transmission setups in agricultural equipment.

Important InformationCounter Shaft

• A Counter Shaft is used as an intermediate shaft in power transmission systems. It typically connects the main power source to other shafts or components, allowing for speed or torque adjustments.

Jack Shaft:

• A Jack Shaft is another type of intermediate shaft used in power transmission systems. It often serves as a connecting shaft between two main shafts or between the power source and the final driven component. Similar to the Counter Shaft, its function involves intermediate transmission rather than direct coupling to the power source.

Flexible Shaft

• A Flexible Shaft is designed to transmit rotary motion between components that are not perfectly aligned or have relative motion between them. It is commonly used in applications requiring flexibility in power transmission, such as handheld tools or equipment.

Explanation:

Knuckle Joint:

• A knuckle joint is a type of mechanical joint used to connect two rods or components that are subjected to tensile or compressive forces. It allows a small degree of angular movement between the connected components, making it suitable for applications where the connected rods are not perfectly aligned or where some flexibility is required. In the context of a steam engine, the knuckle joint is specifically used to connect the valve rod to the eccentric rod, ensuring smooth and efficient operation of the valve mechanism.

Working Principle:

The knuckle joint consists of three main components:

• Fork: One of the rods to be connected has a fork-shaped end, which provides two parallel lugs with a hole in each lug.
• Eye: The other rod to be connected has an eye-shaped end, which fits between the lugs of the fork. The eye also has a hole that aligns with the holes in the fork.
• Knuckle Pin: A pin is inserted through the aligned holes in the fork and eye, securing the connection. The knuckle pin is often secured with a collar or split pin to prevent it from slipping out during operation.

When tensile or compressive forces are applied, the knuckle joint transmits these forces from one rod to the other. The design of the joint allows for slight angular movement between the rods, accommodating any misalignment or dynamic motion during operation.

Applications:

• Connecting rods in steam engines, as in the valve mechanism mentioned in the question.
• Linkages in mechanical systems where some angular movement is required.
• Structural applications where two components need to be connected flexibly.

Important InformationUniversal Joint

• A universal joint is used to connect two shafts that are inclined at an angle to each other, allowing for the transmission of rotary motion. It is commonly used in drive shafts and other rotary systems. However, it is not suitable for connecting the valve rod to the eccentric rod in a steam engine, as this connection requires the transmission of linear motion with slight angular flexibility.

Flange Coupling

• A flange coupling is used to connect two shafts rigidly for the transmission of rotary motion. It consists of two flanges that are bolted together. This type of coupling is not suitable for connecting the valve rod to the eccentric rod in a steam engine, as it does not allow for any angular movement or flexibility, which are essential in this application.

Cotter Joint

• A cotter joint is used to connect two rods that are aligned and subjected to axial forces. It consists of a cotter pin that passes through the rods to secure the connection. While cotter joints are suitable for transmitting tensile or compressive forces, they do not allow for any angular movement, making them unsuitable for connecting the valve rod to the eccentric rod in a steam engine.

Explanation:

Key:

• In mechanical engineering, a key is a machine element used to connect a rotating machine component (like a gear or pulley) to a shaft. This connection prevents relative motion between the two components and allows for torque transmission. The failure of a key is often attributed to shearing, which occurs when the material of the key is subjected to excessive shear stress, exceeding its shear strength. This leads to the key material being physically separated or sheared off.
• A key is inserted between the shaft and the hub of a rotating component. When torque is transmitted, the key experiences forces in the form of shear and compressive stresses. The key must be designed to withstand these stresses within the material's permissible limits. If the applied torque generates a shear force greater than the shear strength of the key material, the key fails by shearing.

Why Shearing is the Primary Cause of Key Failure:

• Stress Concentration: The keyway (slot in which the key is inserted) introduces stress concentration points, making the key more susceptible to shearing compared to other types of failure.
• Design Considerations: The dimensions of the key (length, width, and height) and the material used are designed primarily to resist shearing forces. If these are not adequately designed, the key will fail under shear stress.
• Overloading: If the torque transmitted exceeds the design specifications, the key experiences excessive shear stress, leading to failure.
• Material Properties: The shear strength of the material used for the key plays a crucial role. Low-quality materials or improper material selection can result in shearing failure.

Preventive Measures:

• Proper material selection with sufficient shear strength.
• Accurate design and dimensioning of the key and keyway to distribute stress evenly.
• Avoiding overloading of the system to prevent excessive torque transmission.
• Regular inspection and maintenance of the key and keyway for wear and tear.

Applications: Keys are widely used in mechanical systems for torque transmission, such as in gears, couplings, pulleys, and flywheels. Ensuring that the key does not fail under normal operating conditions is critical to the reliability of these systems.

Explanation:

Flexible Coupling

• A flexible coupling is a type of coupling used to connect two shafts while accommodating minor misalignments, whether angular, axial, or radial, between the shafts. This coupling is specifically designed to transmit torque while allowing for flexibility, which helps in protecting the machinery components from stress and potential damage caused by misalignment.
• Flexible couplings work by incorporating elements that can deform or adjust to accommodate misalignment. These elements may include elastomers, springs, or other flexible components. When the shafts are slightly misaligned, the flexible coupling compensates for the misalignment by absorbing the resulting stresses and vibrations, ensuring smooth transmission of torque.

Applications: Flexible couplings are widely used in applications where minor misalignments are expected, such as in pumps, compressors, blowers, and conveyor systems. They are also employed in systems that require vibration damping or shock absorption.

Important Information

To further understand the analysis, let’s evaluate the other options:

Rigid coupling

• Rigid couplings are designed to connect perfectly aligned shafts. They do not allow for any misalignment and will transmit torque directly. If rigid couplings are used in a system where the shafts are slightly misaligned, it can lead to excessive stress on the shafts, bearings, and other components, causing premature failure and operational issues.

Oldham-hook coupling

• Oldham couplings are a type of flexible coupling specifically designed to accommodate large radial misalignments. However, they are not as commonly used for minor misalignments and are typically employed in applications requiring precise alignment adjustments. While they can handle slight misalignments, they are less efficient compared to standard flexible couplings for general-purpose applications.

Concept:

We use torque transmission and shear stress principles in a flange coupling to determine the required core diameter of the bolts.

Given:

• Torque, \( T = 30 \, \text{N-m} = 30 \times 10^3 \, \text{N-mm} \)
• Number of bolts, \( n = 4 \)
• Radius of bolt circle, \( R = 30 \, \text{mm} \)
• Allowable shear stress, \( \tau = 30 \, \text{MPa} = 30 \, \text{N/mm}^2 \)

Step 1: Calculate shear force per bolt

The torque is transmitted through shear forces on the bolts. The shear force \( F \) on each bolt is:

\( T = F \times R \times n \)

\( F = \frac{T}{R \times n} = \frac{30 \times 10^3}{30 \times 4} = 250 \, \text{N} \)

Step 2: Relate shear force to shear stress

The shear stress \( \tau \) on each bolt is given by:

\( \tau = \frac{F}{A} \)

where \( A = \frac{\pi d^2}{4} \) is the cross-sectional area of the bolt core (diameter \( d \)).

Substituting values:

\( 30 = \frac{250}{\frac{\pi d^2}{4}} \)

\( 30 = \frac{1000}{\pi d^2} \)

Step 3: Solve for core diameter

Rearranging for \( d^2 \):

\( d^2 = \frac{1000}{30 \pi} = \frac{100}{3 \pi} \)

Taking the square root:

\( d = \left( \frac{100}{3 \pi} \right)^{1/2} \, \text{mm} \)

Explanation:

A flange coupling consists of two flanges one keyed to the driving shaft and other keyed to the driven shaft as shown in the figure.

The two flanges are connected together by means of bolts.

Power is transmitted from driving shaft to the flange through the key and then one flange to another flange through bolts and finally, power is transmitted to the flange to driven haft through the key.

Bolts of flange coupling fail under two modes

• By shearing of bolts

Force acting on individual bolt due to transmission of torque

\({M_t} = P \times \frac{D}{2} \times n\)

Where M_t = Torque transmitted by the coupling (N-mm)

P = force on each bolt

D = Pitch circle diameter of the bolts

N = Number of bolts

Bolts are subjected to direct shear stress due to force P and not torsional shear stress.

Direct shear stress in the bolt

 \(\tau = \frac{P}{{\left( {\frac{\pi }{4} \times d_1^2} \right)}}\)

 d₁ = nominal diameter of the tube.

Equating above two equations

\(\tau = \frac{{8{M_t}}}{{\pi Dnd_1^2}}\)

The above equation is used to find the safe nominal diameter of the bolt.

By crushing (Bending) of the bolt

The safe diameter of the bolt can be found by using the design criteria.

\(\frac{P}{{n \times {d_1} \times t}} < {\sigma _b}\)

where t = thickness of the flange, σ_b = Bending strength of the bolt

d₁ × t = Crushing area of the bolt

Explanation:

The woodruff key is an easily adjustable key. It is a piece from a cylindrical disc having segmental cross-section. This key is largely used in machine tool and automobile construction.

A key attached to one member of a pair and which permits relative axial movement is known as feather key. It is a special type of parallel key which transmits a turning moment and also permits axial movement.

A flat saddle key is a taper key which fits in a keyway in the hub and is flat on the shaft. A hollow saddle key is a taper key which fits in a keyway in the hub and the bottom of the key is shaped to fit the curved surface of the shaft.

Gib-head key is a rectangular sunk key with a head at one end known as gib head. It is usually provided to facilitate the removal of key.

Explanation:

Coupling:

Coupling is a device that is used to connect two shafts permanently.

Sleeve / Muff Coupling:

• This coupling consists of cast iron sleeves that are fitted over both shafts ends by means of keys.
• Simple in design and manufacture.
• Dis-assembly is difficult.
• Used with small diameter shafts only.

Flange Coupling:

• It consists of two cast-iron flanges.
• The flanges are keyed to the shaft ends and then bolted together to make a joint.
• The coupling is widely used and is capable of transmitting large torques.
• Design is simple, easy to assemble and dis-assemble and the cost is low just requires proper alignment. 

Oldham Coupling:

• This is used to join two laterally non-aligned shafts which are parallel.
• It consists of two flanges with slots and a central floating part is held by means of a pin passing through the flanges.

Universal Joint:

• It permits substantial angular misalignment of the shafts having intersecting axes.
• A common example is the joint used at the end of the drive shaft on rear-wheel-drive automobiles.

Explanation:

• A knuckle joint is used to connect two rods under tensile load. This joint permits angular misalignment of the rods and may take the compressive load if it is guided.
• The automotive engine piston is connected to the small end of the connecting rod by means of the piston pin. This is one major application of the knuckle joint.
• The valve rod in a steam engine is connected to an eccentric rod by the Knuckle joint.

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Explanation:

Coupling:

Coupling is a device that is used to connect two shafts permanently.

Additional Information

Sleeve / Muff Coupling:

• This coupling consists of cast iron sleeves that are fitted over both shafts ends by means of keys.
• Simple in design and manufacture.
• Dis-assembly is difficult.
• Used with small diameter shafts only.

Flange Coupling:

• It consists of two cast-iron flanges.
• The flanges are keyed to the shaft ends and then bolted together to make a joint.
• The coupling is widely used and is capable of transmitting large torques.
• Design is simple, easy to assemble and dis-assemble and the cost is low just requires proper alignment. 

Oldham Coupling:

• This is used to join two laterally non-aligned shafts which are parallel.
• It consists of two flanges with slots and a central floating part is held by means of a pin passing through the flanges.

Universal Joint:

• It permits substantial angular misalignment of the shafts having intersecting axes.
• A common example is the joint used at the end of the drive shaft on rear-wheel-drive automobiles.

Explanation:

Sleeve or Muff coupling:

• It is also called the box coupling.
• It is made of a sleeve or hollow cylinder, which is fitted over the ends of input and output shafts by means of a sunk key.
• This coupling consists of a cast iron sleeve that is fitted over both shaft ends by means of keys. It is simple in design and manufacture and has a smooth exterior. But the disassembly is rather difficult.
• This coupling is used with small diameter shafts only.

Additional Information

Thin vessel: If the thickness of the wall of the vessel is less than 1/10 to 1/20 of the diameter, then the vessel is a thin vessel.

Thick vessel: If the thickness of the wall of the vessel is greater than 1/10 to 1/20 of the diameter, then the vessel is a thick vessel.

Concept:

For a rectangular key shear stress \(\tau = \frac{F}{A} = \frac{F}{{b\; × \;l}}\)

where F = force acting on key, b = width, l = length

The torque transmitted by the shaft is given by, \(T = F × \frac{d}{2}\)

where d = diameter of the shaft

Calculation:

Given:

b = 14 mm, l = 100 mm, d = 50 mm = 0.05 m, allowable stress of key = 50 MPa

For rectangular key shear stress is

\(\tau = \frac{F}{A} = \frac{F}{{b\; × \;l}}\)

\( \frac{F}{{b\; × \;l}}≤ 50~ MPa\)

F ≤ 50 × b × l 

F = 50 × 14 × 100 = 70000 N = 70 kN

The torque transmitted by the shaft

 \(T = F × \frac{d}{2}\)

T = 70000 × 0.025 = 1750 Nm

Hence max torque that can be transmitted is 1750 Nm.

Concept:

For a rectangular key Allowable shear stress \(\tau = \frac{F}{A} = \frac{F}{{b\; \times \;l}}\)

The torque transmitted by the shaft is given by, \(T = F \times \frac{d}{2}\)

Calculation:

Given, T = 800 N-m, d = 50 mm, b = 10 mm, τ_per = 40 MPa

\(T = F \times \frac{d}{2}\)

\( \Rightarrow 800 = F \times \frac{{50}}{2} \times {10^{ - 3}}\)

∴ Force on key F = 800/25 = 32 kN

Allowable shear stress \(\tau = \frac{F}{A} = \frac{F}{{b \times l}}\)

\( \Rightarrow 40 = \frac{{32000}}{{10\; \times \;l}}\)

⇒ l = 3200/40 = 80 mm

Explanation:

Key:
Key is a metallic piece of a wedge inserted between a shaft and hub, parallel to the axis of the shaft. It is proportionate to the shaft diameter.

• A keyway is a slot or recess in a shaft or hub of the pulley to accommodate a key.

• Key is the weakest member in the assembly of shaft, pulley and key.
• Key acts as a safety device, whenever there is excess load appears on the pulley key fails first and it keeps safer to shaft and pulley.
• It is always inserted parallel to the axis of the shaft.
• Keys are used as temporary fastenings and are subjected to considerable crushing and shearing stresses.

Concept:

• A cotter is a flat wedge-shaped piece of steel.
• This is used to connect rigidly two rods that transmit motion in the axial direction, without rotation.
• These joints may be subjected to tensile or compressive forces along the axes of the rods.
• Examples of cotter joint connections are the connection of piston rod to the crosshead of a steam engine, valve rod, and its stem, etc.

Additional Information

• Knuckle joint is a type of mechanical joint used in structures, to connect two intersecting cylindrical rods, whose axes lie on the same plane. It permits some angular movement between the cylindrical rods (in their plane).
• It is specially designed to withstand tensile loads. It facilitates rotation about the axis but arrests displacement.