Question $1$

$[50$ Marks$]$

A flange coupling between two solid shafts each with a diameter of $60$ mm and $1$ m length,

transmits $2$ kNm of torque. Shear modulus for the shaft is $80$ GPa $.$ The flange coupling is held

together with $8$ bolts on a PCD of $300$ mm $.$ The flange coupling rotates at $250re\frac{v}{m}in.$ A

rectangular key is used in the coupling. The shear stress in each bolt may not exceed $30$ MPa

and the shear stress in the key may not exceed $50$ MPa $.$ Maximum allowable compressive

stress in the key is $80$ MPa $.$

Calculate the following:

a$)$ the width, thickness and the length of the key $($Round up the key length for easy

manufacturing. For example, if the calculated length is $149\mathrm{.}86$ mm $,$ then take the

length to be $150$ mm $).$

b$)$ the diameter of the bolts $($use the next bolt size above the calculated one. For

example, if the calculated one is $6\mathrm{.}69$ mm $,$ then use $8$ mm according to the catalogue$).$

c$)$ the shear stress and angle of twist in the shaft.

d$)$ Draw the configuration of the assembly and the manufacturing drawings of the two

shafts joint with flange coupling and two keys as described. The dimensions of the

configuration must conform with the SANS $10111$ standard.

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