Question? Leave a message!




Computer Aided Design (CAD)

Computer Aided Design (CAD)
16.810 16.810 Engineering Design and Rapid Prototyping Engineering Design and Rapid Prototyping Lecture 4 Computer Aided Design (CAD) Instructor(s) Prof. Olivier de Weck January 6, 2005 Plan for Today „ CAD Lecture (ca. 50 min) „ CAD History, Background „ Some theory of geometrical representation „ SolidWorks Introduction (ca. 40 min) „ Led by TA „ Follow along stepbystep „ Start creating your own CAD model of your part (ca. 30 min) „ Work in teams of two „ Use hand sketch as starting point 16.810 2 Course Concept today 16.810 3 Course Flow Diagram (2005) Learning/Review Deliverables Problem statement Design Intro / Sketch (A) Hand Sketch Hand sketching (B) Initial Airfoil CAD design CAD Introduction FEM/Solid Mechanics FEM/Xfoil analysis (C) Initial Design Xfoil Airfoil Analysis optional Optimization Design Optimization Revise CAD design CAM Manufacturing (D) Final Design Training Parts Fabrication (E) Completed Wing Structural Wind Assembly Tunnel Testing Assembly (F) Test Data Test Cost Estimation Final Review (G) CDR Package 16.810 4 What is CAD „ Computer Aided Design (CAD) „ A set of methods and tools to assist product designers in „ Creating a geometrical representation of the artifacts they are designing „ Dimensioning, Tolerancing „ Configuration Management (Changes) „ Archiving „ Exchanging part and assembly information between teams, organizations „ Feeding subsequent design steps „ Analysis (CAE) „ Manufacturing (CAM) „ …by means of a computer system. 16.810 5 Basic Elements of a CAD System Main System Output Devices Input Devices Computer CAD Software Keyboard Hard Disk Database Mouse Network Ref: menzelus.com Printer CAD keyboard Plotter Templates Space Ball Human Designer 16.810 6 Brief History of CAD „ 1957 PRONTO (Dr. Hanratty) – first commercial numerical control programming system „ 1960 SKETCHPAD (MIT Lincoln Labs) „ Early 1960’s industrial developments „ General Motors – DAC (Design Automated by Computer) „ McDonnell Douglas – CADD „ Early technological developments „ Vectordisplay technology „ Lightpens for input „ Patterns of lines rendering (first 2D only) „ 1967 Dr. Jason R Lemon founds SDRC in Cincinnati „ 1979 Boeing, General Electric and NIST develop IGES (Initial Graphic Exchange Standards), e.g. for transfer of NURBS curves „ Since 1981: numerous commercial programs „ Source: http://mbinfo.mbdesign.net/CADHistory.htm 16.810 7 Major Benefits of CAD „ Productivity (=Speed) Increase „ Automation of repeated tasks „ Doesn’t necessarily increase creativity „ Insert standard parts (e.g. fasteners) from database „ Supports Changeability „ Don’t have to redo entire drawing with each change „ EO – “Engineering Orders” „ Keep track of previous design iterations „ Communication „ With other teams/engineers, e.g. manufacturing, suppliers „ With other applications (CAE/FEM, CAM) „ Marketing, realistic product rendering „ Accurate, high quality drawings „ Caution: CAD Systems produce errors with hidden lines etc… „ Some limited Analysis „ Mass Properties (Mass, Inertia) „ Collisions between parts, clearances 16.810 8 Generic CAD Process Start Engineering Sketch Settings Units, Grid (snap), … 3D 2D dim Construct Basic Create lines, radii, part Solids contours, chamfers = extrude, rotate Boolean Operations Add cutouts holes (add, subtract, …) Annotations Dimensioning CAD file Drawing (dxf) Verification Output x.x IGES file 16.810 9 Example CAD A/C Assembly Loft Nacelle „ Boeing (sample) parts „ A/C structural assembly „ 2 decks „ 3 frames FWD Decks „ Keel „ Loft included to show interface/stayout zone to Kee A/C l „ All Boeing parts in Catia file format „ Files imported into SolidWorks by converting to IGES format (Loft not shown) Frames Aft Decks 16.810 10 Vector versus Raster Graphics Raster Graphics .bmp raw data format „ Grid of pixels „ No relationships between pixels „ Resolution, e.g. 72 dpi (dots per inch) „ Each pixel has color, e.g. 8bit image has 256 colors 16.810 12 Vector Graphics .emf format CAD Systems use vector graphics Most common interface file: IGES „ Object Oriented „ relationship between pixels captured „ describes both (anchor/control) points and lines between them „ Easier scaling editing 16.810 13 Major CAD Software Products „ AutoCAD (Autodesk) Æ mainly for PC „ Pro Engineer (PTC) „ SolidWorks (Dassault Systems) „ CATIA (IBM/Dassault Systems) „ Unigraphics (UGS) „ IDEAS (SDRC) 16.810 14 Some CADTheory Geometrical representation (1) Parametric Curve Equation vs. Nonparametric Curve Equation (2) Various curves (some mathematics ) Hermite Curve BezierCurve BSpline Curve NURBS (Nonuniform Rational BSpline) Curves Applications: CAD, FEM, Design Optimization 16.810 15 Curve Equations Two types of equations for curve representation (1) Parametric equation (u or θ ) x, y, z coordinates are related by a parametric variable (2) Nonparametric equation x, y, z coordinates are related by a function Example: Circle (2D) Parametric equation xR= cos θ, y= R sin θ (0 ≤θ≤ 2π ) Nonparametric equation 2 2 2 x + y − R = 0 (Implicit nonparametric form) 2 2 (Explicit nonparametric form) y =± R − x 16.810 16 Curve Equations Two types of curve equations (1) Parametric equation Point on 2D curve: p= () xu y() u Point on 3D surface: p= () xu y() uz() u u : parametric variable and independent variable yf= () x : 2D , z= f (x, y) : 3D (2) Nonparametric equation : Parametric equation Which is better for CAD/CAE It also is good for xR= cos θ , y= R sin θ (0 ≤θ≤ 2π ) calculating the points at a certain ∆θ interval along a curve 2 2 2 x +y− R = 0 2 2 y=± R− x 16.810 17 Parametric Equations – Advantages over nonparametric forms 1. Parametric equations usually offer more degrees of freedom for controlling the shape of curves and surfaces than do nonparametric forms. e.g. Cubic curve 3 2 Parametric curve: xa= u + bu + c+u d 3 2 ye= u + fu + g+x h 3 2 Nonparametric curve: ya= x + bx + c+x d 2. Parametric forms readily handle infinite slopes dy dy / du =⇒ dx / du=0 indicates dy/ dx =∞ dx dx / du 3. Transformation can be performed directly on parametric equations e.g. Translation in xdir. 3 2 Parametric curve: xa= u + bu + c+u+d x 0 3 2 ye= u + fu + g+x h 3 2 Nonparametric curve: y=a(xx− )+b(xx − ) +c(xx− ) +d 0 0 0 16.810 18 Hermite Curves Most of the equations for curves used in CAD software are of degree 3, because two curves of degree 3 guarantees 2nd derivative continuity at the connection point Æ The two curves appear to one. Use of a higher degree causes small oscillations in curve and requires heavy computation. u Simplest parametric equation of degree 3 P() u= () xuy(u)z(u) 2 3 END START = a+ a u+ a u+ a u (0≤ u≤ 1) 0 1 2 3 (u= 1) (u= 0) aa , , a , a : Algebraic vector coefficients 0 1 2 3 The curve’s shape change cannot be intuitively anticipated from changes in these values 16.810 19 Hermite Curves 2 3 P() u = a + au + au + au (0 ≤ u≤ 1) 0 1 2 3 Instead of algebraic coefficients, let’s use the position vectors and the tangent vectors at the two end points Position vector at starting point: P= P(0) = a 0 0 u Position vector at end point: P= P(1) = a+ a+ a+ a 1 0 1 2 3 ′ P ′ 0 P P 1 0 P ′ 1 ′ Tangent vector at starting point: P= P (0) = a 0 1 START END ′ (u= 0) ′ Tangent vector at end point: P= P (1) = a + 2a+ 3a 1 1 2 3 (u= 1) P ⎡ ⎤ 0 Blending functions ⎢⎥ P 1 ⎢⎥ 2 3 2 3 2 3 2 3 : Hermit curve P() u =− 1 3u + 2u 3 u − 2 u− u 2+uu − uu + ⎢⎥ ′ P 0 ⎢ ⎥ ⎢ ⎥ ′ P ⎣ 1 ⎦ No algebraic coefficients ′′ PP , , P , P : Geometric coefficients 0 0 1 1 The curve’s shape change can be intuitively anticipated from changes in these values 16.810 20 Effect of tangent vectors on the curve’s shape P ⎡ ⎤ P(0) ⎡⎤ 0 ⎢ ⎥ ⎢ ⎥ P P (1) 1 ⎢ ⎥ ⎢ ⎥ = : Geometric coefficient matrix 1 1 ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ Is this what you really wanted ′ ′ P P (0) 0 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 5 1 ⎢ ⎥ ⎢ ⎥ ′ ′ P (1) ⎢ ⎥ P ⎣ ⎦ ⎣ 1 ⎦ 11 ⎡ ⎤ ⎢ ⎥ 13 13 ⎢ ⎥ 51 ⎢ ⎥ Geometric coefficient matrix ⎢ ⎥ 13 13 ⎣ ⎦ controls the shape of the curve ⎢ ⎥ 55 11 ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ 55 ⎣ ⎦ 51 ⎢ ⎥ 11 ⎡ ⎤ ⎢ ⎥ 22 ⎢ ⎥ ⎢ ⎥ 51 22 ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ 11 11 ⎡⎤ ⎢ ⎥ ⎢⎥ 11 51 ⎣ ⎦ ⎢ ⎥ ⎢⎥ 40 ⎢⎥ 40 START (1, 1) END (5, 1) ⎣⎦ u ( u = 0) ( u = 1) dy dy / du 0 = == 0 dx dx / du 4 16.810 21 Bezier Curve In case of Hermite curve, it is not easy to predict curve shape according to ′′ changes in magnitude of the tangent vectors, P and P 0 1 Bezier Curve can control curve shape more easily using several control points (Bezier 1960) n n n ⎛⎞ ⎛⎞ n i n−i P() u= u (1−u) P , where = ∑⎜⎟ i ⎜⎟ i i in ( − )i i=0 ⎝⎠ ⎝⎠ P : Position vector of the i th vertex (control vertices) i Control vertices P 2 P 1 Number of vertices: n+1 Control polygon n=3 (No of control points) Number of segments: n Order of the curve: n P 0 P 3 The order of Bezier curve is determined by the number of control points. n control points Order of Bezier curve: n1 16.810 22 Bezier Curve Properties The curve passes through the first and last vertex of the polygon. The tangent vector at the starting point of the curve has the same direction as the first segment of the polygon. The nth derivative of the curve at the starting or ending point is determined by the first or last (n+1) vertices. 16.810 23 Two Drawbacks of Bezier curve (1) For complicated shape representation, higher degree Bezier curves are needed. Æ Oscillation in curve occurs, and computational burden increases. (2) Any one control point of the curve affects the shape of the entire curve. Æ Modifying the shape of a curve locally is difficult. (Global modification property) Desirable properties : 1. Ability to represent complicated shape with low order of the curve 2. Ability to modify a curve’s shape locally Bspline curve 16.810 24 BSpline Curve n Developed by Cox and Boor (1972) P () u= N ()u P ∑ ik , i i= 0 where 0 0 ≤ik ⎧ P : Position vector of the i th control point i ⎪ t= i−k + 1 k≤i≤n ⎨ i ( ut− ) N () u ( t − ) uN () u i ,1 ik − + ik + 1, i −1 k ⎪ Nu () = + ik , nk −+ 2 ni≤n +k ⎩ t − t t − t ik +−1 i ik + +i 1 (Nonperiodic knots) 1 t ≤≤u t ⎧ i +i 1 Nu ()= ⎨ i,1 0 otherwise ⎩ k: order of the Bspline curve The order of curve is independent of the number of control points n+1: number of control points 16.810 25 BSpline Curve Example Order (k) = 3 (first derivatives are continuous) No of control points (n+1) = 6 Advantages (1) The order of the curve is independent of the number of control points (contrary to Bezier curves) User can select the curve’s order and number of control points separately. It can represent very complicated shape with low order (2) Modifying the shape of a curve locally is easy. (contrary to Bezier curve) Each curve segment is affected by k (order) control points. (local modification property) 16.810 26NURBS (Nonuniform Rational BSpline) Curve n hN P () u n ∑ ii i, k ⎛⎞ i=0 Bspline : P(u) = P N (u) P() u = ∑ i i, k ⎜⎟ n ⎝ i=0 ⎠ hN () u ∑ i i, k i=0 P : Position vector of the ith control point i h : Homogeneous coordinate i If all the homogeneous coordinates (h ) are 1, the denominator becomes 1 i n If h=∀0 i, then hN ( u ) = 1. i ∑i i, k i=0 Bspline curve is a special case of NURBS. Bezier curve is a special case of Bspline curve. 16.810 27 Advantages of NURBS Curve over BSpline Curve (1) More versatile modification capacity Homogeneous coordinate h , which Bspline does not have, can change. i Increasing h of a control point Æ Drawing the curve toward the control point. i (2) NURBS can exactly represent the conic curves circles, ellipses, parabolas, and hyperbolas (Bspline can only approximate these curves) (3) Curves, such as conic curves, Bezier curves, and Bspline curves can be converted to their corresponding NURBS representations. 16.810 28 Summary (1) Parametric Equation vs. Nonparametric Equation (2) Various curves Hermite Curve BezierCurve BSpline Curve NURBS (Nonuniform Rational BSpline) Curve (3) Surfaces Bilinear surface Bicubic surface Bezier surface BSpline surface NURBS surface 16.810 29 SolidWorks Introduction „ SolidWorks „ Most popular CAD system in education „ Will be used for this project „ 40 Minute Introduction by TA „ http://www.solidworks.com (Student Section) 16.810 30
sharer
Presentations
Free
Document Information
Category:
Presentations
User Name:
Dr.TomHunt
User Type:
Teacher
Country:
United States
Uploaded Date:
23-07-2017