# Clamp or Compression Coupling

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## Clamp or CompressionÂ Coupling

It is also known as split muff coupling. InÂ this case, the muff or sleeve is made into two halvesÂ and are bolted together as shown in Fig. 1. TheÂ halves of the muff are made of cast iron. The shaftÂ ends are made to abutt each other and a single keyÂ is fitted directly in the keyways of both the shafts.Â One-half of the muff is fixed from below and theÂ other half is placed from above. Both the halves areÂ held together by means of mild steel studs or boltsÂ and nuts. The number of bolts may be two, four or six. The nuts are recessed into the bodies of theÂ muff castings. This coupling may be used for heavy duty and moderate speeds. The advantage of thisÂ coupling is that the position of the shafts need not be changed for assembling or disassembling of theÂ In the clamp or compression coupling, the power is transmitted from one shaft to the other byÂ means of key and the friction between the muff and shaft. In designing this type of coupling, theÂ following procedure may be adopted.

1. Design of muff and key

The muff and key are designed in the similar way as discussed in muff coupling (Art. 13.14).

2. Design of clamping bolts

Let T = Torque transmited by the shaft,

d = Diameter of shaft,

db = Root or effective diameter of bolt,

n = Number of bolts,

Ïƒt = Permissible tensile stress for bolt material,

Î¼ = Coefficient of friction between the muff and shaft, and

L = Length of muff.

We know that the force exerted by each bolt

=Â Ï€/4 (db)^2 Ã—Â Ïƒt

âˆ´ Force exerted by the bolts on each side of the shaft

=Â Ï€/4 (db)^2 Ã—Â ÏƒtÂ Ã— n/2

Let p be the pressure on the shaft and the muff surface due to the force, then for uniformÂ pressure distribution over the surface,

p = Force /Â Projected area = {Ï€/4 (db)^2 Ã—Â ÏƒtÂ Ã— n/2} / {1/2 Ã— L / d}

âˆ´ Frictional force between each shaft and muff,

F = Î¼ Ã— pressure Ã— area =Â Î¼ Ã— p Ã— (1/2) Ã— Ï€d Ã— L

Â =Â Î¼ Ã— {Ï€/4 (db)^2 Ã—Â ÏƒtÂ Ã— n/2} / {1/2 Ã— L / d} Ã— (1/2) Ã— Ï€d Ã— L

Â =Â Î¼ Ã— {Ï€/4 (db)^2 Ã—Â ÏƒtÂ Ã— n/2}Â Ã—Â Ï€

and the torque that can be transmitted by the coupling,
T = FÂ Ã— d / 2 =Â Î¼ Ã— {Ï€/4 (db)^2 Ã—Â ÏƒtÂ Ã— n/2}Â Ã—Â Ï€Â Ã— d / 2

Â =Â Ï€^2/ 16Â Ã— Î¼ (db)^2Â Ã—Â ÏƒtÂ Ã— nÂ Ã— d

From this relation, the root diameter of the bolt (db) may be evaluated.

Note: The value of Î¼ may be taken as 0.3.

Reference A Textbook of a Machine Design by R. S. Khurmi and J. K. Gupta

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