Unit - 2

Design of Shafts, Keys and Couplings

Q1) What properties should a shaft possess to be used?

A1)

• High Strength
• Good machinability
• Low notch sensitivity factor
• Good heat treatment properties
• High wear resistant properties

Q2) What properties should a shaft possess to be used?

A2)

• Transmission shafts

Transmission shafts, such as counter shafts and line shafts, are used to transmit power between the source and the machine absorbing power. Transmit power between the source and the machine absorbing power. They are subjected to twisting as well as bending.

• Machine shafts

Machine shafts, such as crankshafts, are an integral part of the machine itself.

Q3) A line shaft rotating at 200 revolutions per minute is to transmit 20 kW. The shaft is assumed to be made of mild steel with a shear stress limit of 42 MPa. Determine the diameter of the shaft, neglecting the bending moment on the shaft.

A3) 

N = 200 r.p.m.; P = 20 kW = 20 × 103 W; τ = 42 MPa = 42 N/mm2

Also,

Q4) Determine the diameter of a solid steel shaft required to transmit 20 kW at 200 rpm. The steel's ultimate shear stress is 360 MPa, and the factor of safety is 8. If a hollow shaft is to be used instead of a solid shaft, determine the inside and outside diameters when the inside to outside diameter ratio is 0.5.

A4) Given: P = 20 kW = 20 × 103 W; N = 200 r.p.m.; τu = 360 MPa = 360 N/mm2; F.S. = 8; k = di / do = 0.5

We know that the allowable shear stress

Diameter of the solid shaft

Let d=Diameter of the solid shaft

We know that torque transmitted by the shaft

We also know that torque transmitted by the solid shaft (T)

Diameter of hollow shaft

Let Inside diameter, and

Outside diameter

We know that torque transmitted by the hollow shaft (T)

And

Q5) A railway wagon's wheels carry a load of 50 kN on each axle box, acting at a distance of 100 mm outside the wheelbase. The rails have a 1.4 m gauge. If the stress is not to exceed 100 MPa, determine the diameter of the axle between the wheels

A5) 

Given: W = 50 kN = 50 × 103 N; L = 100 mm; x = 1.4 m; σb = 100 MPa = 100 N/mm2

Q6) Solid Shaft, with Bending movement = 5000 N-m & Twisting Torque 5000√3 N-m. Ultimate tensile stress 720 Mpa. Ultimate Sheer Stress 500 Mpa. FOS = 6. Calculate Diameter?

A6)

Equivalent torsion Moment & equivalent Bending Moment

So, 86 mm as bigger value

Q7) Cross section of flat key =20 * 8 mm. Which is fitted on 1 50 mm Diameter shaft. Power transmitted = 560 N-m from shaft to hub via key. Find length of key. Given: Syc = Syt = 230 N/mm^2 & FOS = 3.

A7)

So, l = 29.2 mm or 30 mm

So, l = 73 mm

Q8) Kennedy keys of 10*10 mm is mounted on a shaft of 60mm. It is transmitting 40 Kw at 600 Rpm. Given: Syc =Syt =360 N/mm^2 & Fos =3.

A8)

Q9) Explain Involute splines.

A9)

Splines that bend inward Concentric external and internal gear teeth are used to make involute splines. They have a 30° pressure angle and are stub teeth. Modules define these splines. Because of their higher strength-to-size ratio, involute splines are more popular than straight splines. Self-centering, involute splines adjust to an even load distribution. Involute splines, on the other hand, are more expensive than straight splines.

Q10) Write Difference between rigid and flexible coupling.

A10)

Misalignment of the shaft axis is not tolerated by a rigid coupling. It can only be utilized when the two shafts are perfectly aligned. The flexible coupling, on the other hand, can tolerate 0.5° of angular misalignment and 5 mm of axial displacement between the shafts due to the provision of flexible parts such as bush or disc. Shocks and vibrations are absorbed by the flexible parts in the flexible coupling. In rigid coupling, there is no such provision. It can only be utilized in motions that are devoid of shocks and vibrations. Rigid coupling is a basic and low-cost option. Due to the additional pieces, flexible coupling is more expensive.

Q11) Write Advantages & Drawbacks of rigid flange couplings.

A11)

The advantages of rigid flange couplings are as follows:

• Rigid couplings can transmit a lot of torque.
• Rigid coupling is simple to put together and take apart.
• Rigid couplings are easy to construct. It is simple to develop and produce.

The following are the drawbacks of rigid flange couplings:

• I It is a sort of connection that is stiff. It can't stand when the axes of two shafts aren't aligned.
• It can only be utilized in motions that are devoid of shocks and vibrations.
• It necessitates a larger radial space.

Q12) Write Advantages & Drawbacks of Flexible couplings.

A12)

The advantages of Flexible couplings are as follows:

• It can withstand a lateral or axial misalignment of 0.5 mm and an angular misalignment of 1.5°.
• It absorbs vibrations and prevents shock transmission from one shaft to the other.
• It is capable of transmitting high torques.

The following are the drawbacks of Flexible couplings:

• Because of the additional parts, the cost of flexible coupling is higher than that of rigid coupling.
• It necessitates more radial space than other types of coupling.

Q13) Derive the relation between outer diameter, thickness, and internal diameter of hollow shaft. If Solid shaft & a Hollow shaft are made from same material, Día of solid = Id of hollow shaft & transmit same torque.

A13)

Therefore   is same for both and

(Neglecting the big terms of

Q14) Design rectangular key for shaft of 50mm diameter. The shearing and crushing stresses for the key are 42 Mpa & 70 Mpa.

A14)

Given d=50 mm =42MPa=42 N/;

The rectangular key is designed as discussed belo2

From Table we find that for a shaft of 50 mm diameter

Width of key, w

And thickness key

The length of key is obtained by considering the key in shearing and crushing

Let Length of key

Considering shearing of the key. We know that shearing strength (or torque transmitted) of the key.

And torsional shearing strength (or torque transmitted) of the shaft.

From equation (i) and (ii) we have

Now considering crushing of the key. We know that shearing strength (or torque transmitted) of the key

From equations(ii) and(iii), we have

Taking larger of the two values we have length of key

Q15) A 45 mm diameter shaft is made of steel with a yield strength of 400 MPa. A parallel key of size 14 mm wide and 9 mm thick made of steel with a yield strength of 340 MPa is to be used. Find the required length of key, if the shaft is loaded to transmit the maximum permissible torque. Use maximum shear stress theory and assume a factor of safety of 2.

A15) Given:  d = 45 mm; σyt for shaft = 400 MPa = 400 N/mm2; w = 14 mm; t = 9 mm; σyt for key = 340 MPa = 340 N/mm2; F.S. = 2

Let l=length of key

According to maximum shear stress theory (See Art 5.10) the maximum shear stress for the shaft.

And maximum shear stress for the key

We know that the maximum torque transmitted by the shaft and key

First of all, let us consider the failure of key due to shearing. We know that the maximum torque transmitted (T)

Now considering the failure of key due to crushing. We know that the maximum torque transmitted by the shaft and key (T)

(Taking )

Taking the larger of the tow values we have

Q16) A 15 kW, 960 r.p.m. Motor has a mild steel shaft of 40 mm diameter and the extension being 75 mm. The permissible shear and crushing stresses for the mild steel key are 56 MPa and 112 MPa. Design the keyway in the motor shaft extension. Check the shear strength of the key against the normal strength of the shaft.

A16) 

Given P=15kW=15×; N=960 r.pm d=40mm; l=75mm

;

We know that the torque transmitted by the motor,

Let Width of keyway or key

Considering the key in shearing. We know that the torque transmitted (T)

This width of keyway is too small. The width of keyway should be at least d/4

Since therefore square key of is adopted

According to H.F Moore, the shaft strength factor.

∴ Strength of the shaft with key

And shear strength of the key

Q17) What is a Key?

A17) A key is a machine component that connects the transmission shaft to spinning machine components such as pulleys, gears, sprockets, and flywheels. The key's principal role is to transmit torque from the shaft to the mating element's hub and vice versa. The key's second purpose is to prohibit relative rotational motion between the shaft and the attached machine unit, such as a gear or pulley. Except in the case of a feather key or a splined connection, the key also prohibits axial motion between two pieces in most circumstances. The keyway is a recess or groove carved on the shaft or in the hub to receive the key. A vertical horizontal milling cutter is commonly used to cut the keyway. The keyway causes tension to build up in the shaft, making the portion fragile

Q18) Explain different types of Keys.

A18) 

• Saddle key

A saddle key is a key that only fits in the hub's keyway. The shaft in this example does not have a keyway. Hollow and flat saddle keys are the two varieties of saddle keys.

• Sunk key

A sunk key is one that fits half of its thickness into the keyway on the shaft and the other half into the keyway on the hub. As a result, keyways are needed on both the shaft and the hub of the mating member. This is the most common type of key, and it can have a rectangular or square cross-section.

• Feather key

A feather key is a parallel key that is attached to either the shaft or the hub and allows relative axial movement between the two. The feather key is a sort of buried key with a uniform height and width.

• Woodruff key

A sunk key in the shape of an almost semicircular disc of uniform thickness is known as a Woodruff key. The shaft's keyway is shaped like a semicircular recess with the same curve as the key. The lower half of the Woodruff key fits into the shaft's circular keyway. The hub's keyway is created in the traditional way. The projecting section of the Woodruff key fits into the hub's keyway. The Woodruff key tilts and aligns itself on the shaft once it is in place.

Q19) When is Oldham coupling & Hooke’s coupling employed?

A19) 

The shafts that the coupling will join may have collinear axes, intersecting axes, or parallel axes with a short gap between them. When two parallel shafts are close together, an Oldham coupling is utilized to link them. To link two shafts with intersecting axes, Hooke's coupling is employed

Q20) Write Characteristics of Good Coupling

A20) 

• The coupling needs to be able to transfer torque from the driving shaft to the driven shaft.
• The connection should maintain good alignment between the two shafts.
• For repairs and adjustments, the coupling should be simple to assemble and detach. Accidents can occur when revolving bolt heads, nuts, key heads, and other projecting pieces break. They should be protected by giving the flanges a proper form or by using guards.