Project ForgeManufacturing Engineering
Machining Processes
GATE 2012
Hard
In an orthogonal metal cutting process: chip thickness ratio=0.4, undeformed thickness=0.6 mm, rake angle=+10°, cutting speed=2.5 m/s, mean thickness of primary shear zone=25 microns. The shear strain rate in s⁻¹ during the process is
- A0.1781×10⁵
- B0.7754×10⁵
- 1.0104×10⁵
- D4.397×10⁵
Explanation
Shear angle: tanφ=r·cosα/(1−r·sinα)=0.4×cos10°/(1−0.4×sin10°)=0.3939/0.9305=0.4233, so φ≈22.93°. Shear velocity Vs=V·cosα/cos(φ−α)=2.5×cos10°/cos(12.93°)=2.462/0.9747≈2.526 m/s. Shear strain rate=Vs/Δy=2.526/0.000025≈1.0104×10⁵ s⁻¹.
Source: GATE ME 2012 (Booklet Code A) (2012)
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