How does the cutting force changes with rake

# How does the cutting force changes with rake - eliminate...

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How does the cutting force changes with rake angle? Applications: Machining Grinding Friction Wear Prof. Christopher Brown WPI

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Machining forces and Friction α α sin cos c t F F F + = α α sin cos t c F F N - = φ φ sin cos t c s F F F - = φ φ cos sin t c n F F F + = Rake face Frictional force and normal force Shear plane forces F t F n F c F s N F = = τ μ tan α α μ tan tan t c c t F F F F - + = Tool workpiece friction coefficient µ 90-(τ-α+φ)
Fc=Fs cos φ + Fn cos (90- φ) Use Trig identity Fc=Fs cos φ + Fn sin (φ) 1. Write Fc in terms of Fs and Fn

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Eliminate Fn From the geometry of Merchant’s circle Fn=Fs/tan(90- (τ-α+φ)) =Fs tan(τ-α+φ) Fc=Fs cos φ + Fs tan(τ-α+φ)sin (φ) Fc=Fs (cos φ + tan(τ-α+φ)sin (φ))
Fs=S w doc/sin φ (shear stress * area) Fc=Sw doc/sin φ (cos φ + tan(τ-α+φ)sin (φ)) Fc=S w doc (cot φ + tan(τ-α+φ)) Write Fs in terms of shear stress and cutting geometry

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φ = 45-τ/2+α/2 (Merchant) Fc=S w doc (cot (45-τ/2+α/2) + tan(τ-α+ 45- τ/2+α/2)) Fc=S w doc (cot (45-τ/2+α/2) + tan(45+τ/2-α/2) Use Merchant’s equation to

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