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problem in machining forces

# problem in machining forces - F t F n F c F s Shear angle...

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Dynamic Shear Stress Prof. Christopher Brown

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Analysis problem in machining Describe how to find the dynamic shear stress (Fs/As) from the power, cutting conditions and the chip thickness. Given or measured: t1 (feed), t2, power, speed, rake angle
Shear angle - orthogonal Shear angle φ From Geometry: tanφ = r t cos α / (1- r t sin α) Chip thickness ratio r t = t 1 /t 2 Uncut chip thickness t 1 or depth of cut in orthogonal machining Vc – cutting velocity α Rake angle t 1 t 2

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Angles Rake α Shear φ Friction τ friction angle F t F n F c F s Forces (total P) Cutting Fc Thrust Ft Shear Fs Normal Fn (to Shear Plane) Friction F Normal N (to Rake Face) Machining forces
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

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Friction to shear angle 2 / 2 / 4 / α τ π φ + - = d/dφ(Fc=f(φ)) = 0 Orient the shear angle to minimize the cutting force

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Unformatted text preview: F t F n F c F s Shear angle ) cos( sin / ) cos(-+-= bA F C solution • From t1 and t2 get the chip thickness ratio and calculate the shear angle φ tanφ = r t cos α / (1- r t sin α) r t = t1/t2 • From the power and the speed get the cutting force Fc Power = Fc speed • From the shear angle and the rake angle get the friction angle τ • From the friction angle calculate the friction coefficient µ 2 / 2 / 4 / α τ π φ +-= N F = = μ tan Cont. • From the friction coefficient and the cutting force calculate the trust force from: Ft = (µ Fc - Fc tanα) /(1+ µ tanα) α μ tan tan t c c t F F F F-+ = • Calculate Fs from: • Calculate the dynamic shear stress Sd from Sd = Fs/As As = w t1/sinφ φ sin cos t c s F F F-=...
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problem in machining forces - F t F n F c F s Shear angle...

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