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Question

# In turning trail using orthogonal cutting, a chip length of 84mm was obtained for uncut chip length of 200 mm. The cutting conditions were: Vc=30 m/min, uncut chip thickness is 0.5 mm, rake angle is 20∘, width of cut is 2 mm, cutting force is 900 N, and cutting tool is HSS. The shear stress induced in the layer of work material is

A
284 MPa
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B
267 MPa
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C
239 MPa
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D
None
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Solution

## The correct option is A 284 MPaShear stress, τ=FsSheared area =FsLs×b=Fst1×b×sinϕ =Fscos(β−α)×cos(ϕ+β−α) =900cos(40.26−20)×cos(24.74+40.26−20) Fs=678.36 N τ=678.36sin24.740.5×2=283.89=284 MPa

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