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Unformatted text preview: eliminate the shear angle Normalize and simplify Fc/Swdoc = (cot (45τ/2+α/2) + tan(45+τ/2α/2) Use trig identity Fc/Swdoc = 2tan(45+τ/2α/2) Fc=Fs cos φ + Fn cos (90 φ) 1. Fc=Fs cos φ + Fn sin (φ) 2. Fn=Fs/tan(90 (τα+φ))=Fs tan(τα+φ) Fc=Fs cos φ + Fs tan(τα+φ)sin (φ) 3. Fc=Fs (cos φ + tan(τα+φ)sin (φ)) 4. Fs=S w doc/sin φ (shear stress * area) Fc=Sw doc/sin φ (cos φ + tan(τα+φ)sin (φ)) 5. Fc=S w doc (cot φ + tan(τα+φ)) 6. φ = 45τ/2+α/2 (Merchant) Fc=S w doc (cot (45τ/2+α/2) + tan(τα+ 45τ/2+α/2)) 7. Fc=S w doc (cot (45τ/2+α/2) + tan(45+τ/2α/2) Fc/Swdoc = (cot (45τ/2+α/2) + tan(45+τ/2α/2) 8. Fc/Swdoc = 2tan(45+τ/2α/2) Normalized cutting force versus rake angle 2 4 6 8 10 12 14 16 18 20604020 20 40 60 rake angle degrees normalized cutting force µ=0.8 µ=0.6 µ=0.4...
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 Winter '08
 Brown
 Force, Cos, Fc Ft Fn, Fc=Fs cos

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