Mechanics

Shear strain from feed, chip thickness and rake angle
Machining

Machining, Numerical

Question: During orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produced is 0.5mm. The feed given to the zero degree rake angle tool is 0.2mm/rev. Calculate the shear strain produced during the operation? [GATE 2014] Solution: Cutting stain indicates the shear strain developed during any conventional machining operation due to the shearing of one thin layer of workpiece material over another

Shear strain formula from chip thickness ratio and rake angle
Machining

Machining, Numerical

Question: In a machining operation, the chip thickness ratio is 0.3 and the rake angle of the tool is 10°. What is the value of the shear strain? [ESE 2004] Solution: In any conventional machining process when sample material is ductile, material removal takes place due to shearing under the action of compressive force exerted by the cutting tool. The assumed 2-D plane along which shearing takes place is termed

Schematic representation of chip reduction coefficient and shear angle
Machining

Machining, Numerical

Question: In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is 0.2mm. The chip thickness fluctuates between 0.25mm and 0.4mm. Determine the ratio between the maximum shear angle to the minimum shear angle in this case. [GATE 2017] Solution: Machining is one subtractive manufacturing process where material is gradually removed from the workpiece by shearing under the presence of compressive force exerted by

Minimum shear strain in turning with a zero rake angle cutter
Machining

Machining, Numerical

Question: Determine the theoretically minimum possible shear strain in orthogonal turning with a cutting tool of zero orthogonal rake angle. [ESE 2009] Solution: Metal cutting processes are employed to remove excess material from workpiece to impart desired shape and finish. This material removal takes place by shearing when a wedge shaped cutting tool compresses a layer of workpiece material. The cutting strain developed due to shearing is termed as shear

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 velocity triangle in machining
Machining

Machining

In orthogonal machining, cutting velocity (VC) , chip flow velocity (Vf) and shear velocity (VS) are interrelated. These three velocity vectors together form a triangle, which is called velocity triangle in machining. A typical velocity triangle is depicted below. Here length of the sides of the triangle indicates the magnitude of corresponding velocity. The triangle is based on the assumptions of orthogonal machining (chip is flowing in orthogonal direction) and

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