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In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and thickness 8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is
  • a)
    0.006
  • b)
    0.031
  • c)
    0.062
  • d)
    0.600
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a single pass rolling process using 410 mm diameter steel rollers, ...
Calculation of Angle of Bite in Single Pass Rolling Process

Given:
Diameter of rollers (D) = 410 mm
Width of strip (W) = 140 mm
Initial thickness of strip (t1) = 8 mm
Reduction in thickness (Δt) = 10%

We know that the angle of bite (α) in radians is given by:
α = (π/2) x (D - t1 - Δt)/(W + Δt)

Substituting the given values, we get:
α = (π/2) x (410 - 8 - 0.1x8)/(140 + 0.1x8)
α = 0.062 radians

Therefore, the correct answer is option C.

Explanation:
The angle of bite is a crucial parameter in determining the deformation and force requirements in the rolling process. It refers to the angle subtended by the arc of contact between the rollers and the strip at the center of the roll. The larger the angle of bite, the greater is the contact length and the deformation of the strip.

In the given problem, we are given the dimensions of the rollers and the strip, as well as the reduction in thickness. We can use the formula for the angle of bite to calculate the required value. The formula takes into account the diameter of the rollers, the initial thickness of the strip, and the reduction in thickness due to rolling.

Substituting the given values in the formula, we get the value of the angle of bite as 0.062 radians. This means that the arc of contact between the rollers and the strip subtends an angle of 0.062 radians at the center of the roll. This value can be used to calculate other parameters such as the contact length, the rolling force, and the torque.
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