L - 7 More Forces in Machining

L - 7 More Forces in Machining - More Forces in Machining...

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More Forces in Machining Lecture 7 ME1800
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objectives Derive direction cosine matrix for force transformation Review relations between machining forces
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Machining forces and Friction α sin cos c t F F F + = sin cos t c F F N - = φ sin cos t c s F F F - = 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 tan tan t c c t F F F F - + = Tool workpiece friction coefficient µ
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Force relationships Pythagorean (N 2 +F 2 ) ½ = (Fc 2 +Ft 2 ) ½ = (Fs 2 +Fn 2 ) ½ = P α α Fc Ft F N P tool Axes rotation – direction F = Fc cos(90-α) +Ft cos α N = Fc cos (α) + Ft cos(90+α) cos(90-α) = sin α cos(90+α) = -sin α F = Fc sin α +Ft cos α N = Fc cos (α)- Ft sin α
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Axes rotation α α Fc Ft F N tool α 90- α N = Fc cos α + Ft cos(90+α) F = Fc cos(90- α) +Ft cos α cos(90-α) = sin α cos(90+α) = -sin α N = Fc cos (α)- Ft sin α F = Fc sin α +Ft cos α Two orthogonal force systems Fc and Ft N and F
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Friction coefficient and friction angle Friction coefficient = tangential/normal = F/N = µ Friction angle = atan F/N = atan µ = τ α F N tool α τ
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Friction angle, τ, to shear angle, Ф Merchant Equation (in degrees)
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L - 7 More Forces in Machining - More Forces in Machining...

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