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Machining of Curved Geometries

Machining of Curved Geometries. Pelton cup. Impeller. Knee joint prothesis. Intake manifold. Forging die for Blade. Pinion. PARAMETRIC SURFACES. Surfaces of Known Form Plane surface Cylindrical surface Conical surface Spherical Surface Toroidal Surface . PARAMETRIC CURVES.

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Machining of Curved Geometries

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  1. Machining of Curved Geometries • Pelton cup • Impeller • Knee joint prothesis • Intake manifold • Forging die for Blade • Pinion

  2. PARAMETRIC SURFACES Surfaces of Known Form Plane surface Cylindrical surface Conical surface Spherical Surface Toroidal Surface

  3. PARAMETRIC CURVES Parametric Representation of Curve x = f ( u ); y = g( u ); z = 0; 0  u  1.0 u = 1 u = 0

  4. PARAMETRIC CURVES Parametric Representation of Curve x = f ( u ); y = g( u ); z = 0; 0  u  1.0 u = 1 u = 0

  5. CNC Programming

  6. CNC Programming

  7. OFFEST CURVE dx dy du du Parametric Representation of Curve x = f ( u ); y = g( u ); z = 0; 0  u  1.0 pn= - pu= dy dx du du 0 0

  8. OFFEST CURVE nx pn ny n= = Parametric Representation of Curve x = f ( u ); y = g( u ); z = 0; 0  u  1.0 pn 0 Parametric Representation of Offset Curve X = f ( u ) + nx r Y = g( u ) + ny r Z = 0

  9. Machining of Curved Geometries

  10. CNC Programming

  11. CNC Programming Gouging

  12. CNC Programming 1 kmax= rmin

  13. TOOL SELECTION dx (pu x puu ) . (pux puu) du k2= pu= dy (pu. pu)3 Parametric Representation of Curve x = f ( u ); y = g( u ); z = 0; 0  u  1.0 du d2x 0 du2 puu= d2y du2 0

  14. PARAMETRIC SURFACES Surfaces of Known Form Plane surface Cylindrical surface Conical surface Spherical Surface Toroidal Surface

  15. w u

  16. PARAMETRIC SURFACES Flat End Mill Ball End Mill

  17. FREE-FORM SURFACES Parametric Surface x = f (u, w); y = g (u, w); z = (u, w); 0  u  1.0; 0  w  1.0 Offset Surface X = f (u, w) + nx.r; Y = g(u, w) + ny.r; Z = (u, w) + nz.r; 0  u  1.0; 0  w  1.0 δx δx δu δw δy δy (pu x pw ) pu = pw = δu δw n= (pu x pw) δz δz δu δw

  18. FREE-FORM SURFACES Parametric Surface x = f (u, w); y = g (u, w); z = (u, w); 0  u  1.0; 0  w  1.0 E = (pu . pu ) F = (pu . pw ) G = (pw . pw ) L = (puu . n ) M = (puw . n ) N = (pww . n ) (LN – M2 ) = k1 k2 K = (EG – F2 ) (EN + GL -2FM) = 0.5(k1 + k2) H = 2 (EG – F2 ) (pu x pw ) n= (pu x pw)

  19. p(u, 1) RULED SURFACE p(u, 0) Input Two curves p(u, 0), p(u, 1) p(u, w) = (1-w) p(u, 0) + w p(u, 1)

  20. p(0, 1) BILINEAR SURFACE p(1, 0) p(1, 1) p(0, 0)

  21. BILINEAR SURFACE(HYPERBOLIC PARABOLOID) Four Corner Points p(0, 0), p(1, 0), p(0, 1), p(1, 1) p(u, w) = (1-u) (1-w) p(0, 0) + u (1-w) p(1, 0) + (1-u) w p(0, 1) + u w p(1, 1)

  22. BILINEAR SURFACE(HYPERBOLIC PARABOLOID)

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