Value of the maximum shear stress , Mechanical Engineering

Value of the maximum shear stress:

Illustrates that for a given maximum shear stress the minimum diameter needed for a solid circular shaft to transmit P kW at N rpm may be expressed as

d = Constant × ( P/ N )3

What value of the maximum shear stress has been used if the constant equals 84.71, being in millimetre - N units?

Solution

 We know,

P × 103  = 2πNT /60 watts      

T =60 ×103/2πN

= (60 ×103 P /2πN )×1000 N mm

= 3 ×107 (P /πN )  N mm

2307_Value of the maximum shear stress.png

 T =  (π/16) d3 τm

d 3  = 16T /π τm

d 3  = (16T /π τm )× 3 × 107 ×   P = (48 × 107 / π2 τm  ). (P/ N)

∴ d = K ×(  P /N)(1/3)

where,

1324_Value of the maximum shear stress1.png

While   K = 84.71, we get,

84.71 = 368 / (τm )(1/ 3)

∴          (τm)(1/ 3)  = 368 /84.71 = 4.344

∴ τm = 82 N/mm2

Posted Date: 1/21/2013 2:49:57 AM | Location : United States







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