Examples on Merchant Circle Diagram Example 1: During turning a ductile alloy by a tool α=10°, it was found Ft=1000N, Px=400N , Py= 300N and β-α = 2.5. Evaluate , using MCD, the values of F, N and Φ as well as Fs & Fn for the above machining. Ans: Data Given: α=10° Ft=1000N Px=400N Py= 300N β-α = 2.5

Mechant Circle Diagram: Scale= 1cm = 100N

Data to find: F=? N= ? Fs = ? Fn = ? Φ=?

Calculations: 



Cutting force (Fc) 

𝐹𝑐 = √𝑃𝑥 2 + 𝑃𝑦 2

 

𝐹𝑐 = √4002 + 3002 𝑭𝒄 = 𝟓𝟎𝟎 𝑵

Shear Angle Φ 𝑐𝑜𝑠𝛼  tan ∅ = (𝛽−𝛼)−𝑠𝑖𝑛𝛼  

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Prepared by: Dishank Upadhyay Mechatronics Department

tan Φ = cos10 / 2.5-sin10 Φ = 23 ° = 24°

From Graph  R=1118 N  F = 667 N  N = 896 N  Fs= 711 N  Fn = 862 N

Example 2: During turning a ductile alloy by a tool α=20°, it was found Ft=1000N, Px=800N , Py= 600N and Φ=10°. Evaluate, using MCD, the values of F, N and βαas well as Fs & Fn for the above machining. Ans: Data Given: α=20° Ft=1000N Px=800N Py= 600N Φ = 10° Mechant Circle Diagram: Scale= 1cm = 100N

Data to find: F=? N= ? Fs = ? Fn = ? β=? Calculations: 

Cutting force (Fc)   



Shear Angle Φ 𝑐𝑜𝑠𝛼  tan ∅ = (𝛽−𝛼)−𝑠𝑖𝑛𝛼   



Prepared by: Dishank Upadhyay Mechatronics Department

𝐹𝑐 = √𝑃𝑥 2 + 𝑃𝑦 2 𝐹𝑐 = √8002 + 6002 𝑭𝒄 = 𝟏𝟎𝟎𝟎 𝑵

tan 10 = cos20 / (𝛽 − 𝛼 )-sin20 𝜷 − 𝜶 = 5.6715° 𝜷 = 25.6715°

From Graph  R= 1400 N  F = 1200 N  N = 600N  Fs= 8500N  Fn = 1200 N