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Machining of Curved Geometries and Parametric Surfaces Guide

Learn about CNC programming for curved shapes, surfaces, and curves. Understand tool selection and offset curves in machining. Explore free-form surfaces and bilinear surface creation.

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Machining of Curved Geometries and Parametric Surfaces Guide

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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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