GATE

Minimum shear strain condition
Machining

Machining, Numerical

Question: A single point cutting tool with 12° orthogonal rake angle is used for orthogonal machining of a ductile material. Calculate the shear plane angle for the theoretically minimum possible shear strain. [GATE 1990] Solution: During machining, a layer of uncut workpiece material gets converted into chips by shearing. Chip thickness also increases substantially compared to the same before cut. The strain that is induced because of increment in dimension

Shear angle using rake angle, uncut chip thickness and nominal chip thickness
Machining

Machining, Numerical

Question: Following data correspond to an orthogonal turning of a 100mm diameter rod on a lathe. The orthogonal rake angle is +15°; the uncut chip thickness is 0.5mm, the nominal chip thickness after the cut 1.25mm. What is the shear angle for this? [GATE 2018] Solution: Shear angle (βo) indicates the direction of shear plane with respect to cutting velocity (Vc) vector. During any conventional machining process, the cutting tool

Calculate shear angle using orthogonal rake angle, uncut and cut chip thickness
Machining

Machining, Numerical

Question: A single point cutting tool with 12° orthogonal rake angle is used to machine a steel workpiece. The uncut chip thickness is 0.81mm. The chip thickness under orthogonal machining condition is 1.8mm. What is the shear angle? [GATE 2011] Solution: Machining is one subtractive manufacturing process where layers of material is gradually removed from workpiece by shearing in the form of chips. Shearing actually occurs throughout a 3-D region;

Schematic representation of shear angle in machining
Machining

Machining, Numerical

Question: During orthogonal machining of mild steel with a 10° orthogonal rake angle tool, the chip thickness ratio was found to be 0.4. Determine the shear angle. [GATE 2001] Solution: In conventional metal cutting processes, chip gets thickened after machining, and thus chip thickness (a2) becomes larger than uncut chip thickness (a1). The ratio between uncut chip thickness and chip thickness is termed as Chip Thickness Ratio (CTR). Its value