Page: Design of shafts and couplings
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Q.1 Why the hollow shaft is beneficial over the solid shaft?

Or

A hollow shaft has greater strength and stiffness than solid shaft of equal weight. Explain

Ans :-

1st Statement :- Hollow shaft has greater strength than the solid shaft of equal weigth

Explaination :- The tensile shear stress and bending stress in the shaft is given by,

$t = \frac{T.r}{J}$ and $\sigma_b = \frac{M.Y}{I}$

From the diagram it is clear that, the torsional shear stress as well as the bending stress is zero at the centre of shaft [i.e. at $r=0\ or \ Y=0$] and negligibly small in the vicinity of shaft centre, where radius is small. As the radius is increases, the stresses also increase. Therefore, the outer fibres are more effective in resisting the applied moments.

In hollow shafts, the material at the centre is removed and spread at large radius. Therefore, hollow shafts are stronger than solid shafts having same weight.

2nd Statement :- Hollow shaft has greater rigidity than the solid shaft of equal weight

Explaination :- The torsional rigidity or torsional stiffness of the shaft is given by,

$K_t$ = $\frac{T}{\theta}$ = $\frac{GJ}{L}$

Therefore, for the same material and same length, the torsional rigidity or torsional stiffness of the shaft is proportional to ‘J’. for the same weight, the polar moment of inertia 'J' is higher for the hollow shaft as compared to the solid shaft.

Hence, hollow shaft has greater torsional rigidity or torsional stiffness than the solid shaft of same weight.

Note :-

Limitations of hollow shafts :-

1) The hollow shafts are difficult to manufacture as compared to the solid shafts.

2) The hollow shafts are costlier than the solid shafts.

3) The outer diameter of hollow shaft is more than the diameter of solid shaft. Hence, requires more space.

• Hollow shaft are used to provide passage for coolants and control cables in case of deep hole drilling and bore well drilling. They are also used as propeller shafts in automobiles and for axles of railway wagons.

Q.2 Explain effect of keyway on shaft strength. Give equation for ‘Shaft Strength factor’.

Ans :-

1. The keyway is required on the shaft as a functional requirement so as to mount the transmission elements like ; Gears, Pulleys, Sprockets, couplings, etc.

2. The keyway on the shaft reduces the strength of the shaft. This is due to the stress- concentration near the corness of the keyway and reduction in the cross-sectional area of the shaft.

3. The weakening effect of the keyway is normally accounted by the multiplying factor known as shaft strength factor.

4. The shaft strength factor is defined as the ratio of the strength of the shaft with keyway to the strength of the shaft without keyway.

5. The empirical relation for the shaft strength factor is,

$e= 1 – 0.2 [\frac{W}{d}] – 1.1[\frac{h_K}{d}$]

$e= 1 – 0.2 [\frac{W}{d}] – 0.55[\frac{h }{d}]$

where, e= Shaft strength factor,

w= width of the keyway, mm;

d = Diameter of the shaft, mm;

$h_K$ = Depth of the keyway, mm=h/2;

H = Height of the key,mm

1. It is usually assumed that the strength of a shaft with keyway is 75% of the strength of a shaft without keyway.

Q.3 Explain in detail different types of keys :-

Ans:- The keys are broadly classified into following five types:-

1] Sunk Keys

3] Tangent keys

4] Round keys and Taper pins

5] Splines

1] Sunk Keys :- The sunk keys are provided half in the keyways of the shaft and half in the keyway of the hub or boss of the rotating element.

The different types of sunk keys are as follows:-

I] Rectangular Key:-

• The rectangular key has a rectangular cross section.

• Widht of key, W=$\frac{d}{4}$,

• Height of key, h= $\frac{d}{6}$

where, d = shaft diameter

• The key has the toper of 1 in 100 on the top side only.

II] Square key :- The square key is similar to rectangular key, except it is square in cross section i.e. Its width and height are equal.

Therefore, $W=h=d/4$

III] Parallel Key:- This may be rectangular or square in cross-section uniform in width and thickness throughout, gear or other mating part is required to slide along the shaft.

• It is a rectangular key with a head at one end known as gib-head.

• It is usually provided to facilitate the removal of key

• $W=h=d/4 \ and \ h=d/6$

V] Feather key :- A Key attached to one member of a pair and which permits relative axial movement is known as feather key. It transmits torque as well as permits axial movement.

VI] Woodruff Key:-

-> It is a segment from cylindrical disc. It fits in a recess milled in the shaft.

• Due to its peculiar geometric shape, it can align itself in the seat.

• It is used in machine tool and automobile construction.

a) It accommodates itself to any taper in the hub.

b) It is useful on taper shafts, its extra depth in the shaft prevents any tendency to overturn.

c) It facilitates easy removal of hub from the shaft.

a) The depth of keyway is more and hence, it weakness the shaft.

b) It cannot be used to transmit high torque.

A) Flat- saddle key :- It is a taper key which fits in a keyway in the hub and is flat on the shaft.

B) Hollow – saddle key: It 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’.

• Applications :- Temporary fastening in firing and setting eccentrics , cams etc.

Note :- Saddle keys fit in the keyway of hub only i.e. there is no keyway in the shaft.

i) Flat saddle key:- Has flat surface at the bottom.

ii) Hollow saddle key:- has a concave surface at the bottom.

3] Tangent Keys :-

These are fitted in pair at right angles to each other. Each key is to withstand torsion in one direction only.

• Applications :- Large heavy duty shafts.

4] Round Keys :-

These are circular in section and fits into holes drilled partly in the shaft and partly in hub.

• Applications :- Low power drives.

5] Splines :-

In this case keys are made integral with the shaft which fits in the keyways branched in the hub. They have usually four, six, ten or sixteen splines. These are relatively stronger than single keyways.

Q.4 Explain the design procedure of sunk key :-

Ans :-

Note:-

I] A localized compressive stress at the area of contact between two components having relative motion between them known as Bearing Pressure.

II] If there is no relative motion between the stress is known as Crushing Stress.

The design procedure for the commonly used keys is given below:

1) Shear Failure of Key:- Direct Shear stress induced in the key

$t= \frac {\text{shear area}}{\text{resisting area}}$

= $\frac{F}{w.t}$

2) Crushing failure of key:- The crushing stress induced in the key.

$\sigma_{cr}$ = $\frac{\text{Compressive or crushing force}}{\text{Resisting Area}}$

= $\frac{F}{\frac{h}{2}.L}$

Q. 5 Classify coupling in detail

Ans:- Coupling is the mechanical element used to connect two shafts of a transmission system.

Couplings:

1. Rigid Coupling
2. Flexible Coupling

1. Rigid Coupling:

(i) Sleeve or muff coupling (ii) Clamp or split-muff or compression coupling (iii) Flange coupling

2. Flexible Coupling:

(i) Bushed Pin type (ii) Universal coupling (iii) Oldham coupling

• Rigid couplings are used to connect two shafts which are perfectly aligned.

• Flexible coupling are used to connect two shafts which has lateral and angular misalignment.

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