Question

A strip with a cross section 150 mm x 4.5 mm is being rolled with 20% reduction of area using 450 mm diameter rolls. the angle subtended by the deformation zone at the roll center is (in radians)

0.02

0.03

0.01

0.06

Answer 1

• Given:- A strip with a cross section 150 mm x 4.5 mm is being rolled with 20% reduction of area using 450 mm diameter rolls.

• To find:- The angle subtended by the deformation zone at the roll center (in radians)

• Solution:- we know,

θ = tan^(-1) [√(R∆h) / { R- (∆h/2)}]

according to the question,as we have 20% reduction in cross sectional area

150×4.5× 0.8 = 150×h

or, h = 3.6 mm

∆h= 4.5-3.6 = 0.9 mm

θ = tan^(-1) [√(225×0.9) / { 225- (0.9/2)}]= 362° = 0.06 rad

so, the angle subtended by the deformation zone at the roll center is (in radians) 0.06