Orthogonal Metal Cutting & Merchant Circle

Mechanical Engineering

How It Works

Orthogonal metal cutting on a lathe lathe shears material along a primary shear plane to generate a continuous curling chip. According to Merchant's circle theory, the shear plane angle (φ) maximizes cutting efficiency by minimizing the total work expended. The resultant cutting force resolves into cutting force (F_c), feed thrust force (F_t), normal force, and friction along the tool rake face.

Governing Equation
2 · φ + β - α = 90° (Merchant Law) , F_s = F_c · cos φ - F_t · sin φ , r_c = t₀ / t_c