A cylindrical workpiece is turned at a feed of 0.1 mm/rev with a perfectly sharp tool. In the ASA system, the side and end cutting edge angles are 15° and 5°, respectively, as shown in the figure. The peak-to-valley roughness (in µm, up to one decimal place) of the machined surface is ________.

This question was previously asked in

GATE PI 2018 Official Paper

**Concept:**

Turning operation by a sharp tool

The peak-to-valley surface roughness (h) is given by

**h = \(\frac {f}{\cotϕ \ + \ \cotϕ_1 }\)**

Where, **f** = feed rate (mm/rev);** ϕ** = Principal cutting edge angle; **ϕ _{1}** = Auxiliary cutting edge angle;

Also, from the figure

**ϕ = 90° - ϕ _{s} **

**ϕs** = Side cutting angle in ASA system;

**Calculation:**

**Given:**

f = 0.1 mm/rev; ϕs = 15°; ϕ = 5°;

ϕ = 90° - ϕs = ϕ = 90° - 15°

**ϕ = 75° **

h = \(\frac {f}{\cotϕ \ + \ \cotϕ_1 }\) = \(\frac {0.1}{\cot75 \ + \ \cot5 }\)

h = 0.00868 mm

**h = 8.68 μm **

__Mistake Points__

Don't forget to convert the side cutting edge angle to the principal cutting edge angle.