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MAE486_Fall11_L20_S - MAE 486 Design of Mechanical Systems...

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Unformatted text preview: MAE 486 Design of Mechanical Systems Lecture 20 Fall 2011 Today s topics: Manufacturing consideration of design; Review Finite Element Analysis •  What are the limits of finite difference method (FDM)? •  SoluAon: Finite element method –  What is the main idea? •  Solid/Fluid: Divided into small finite segments/elements •  Cons6tu6ve Equa6ons: •  •  •  What are F_1 and F_2 in the above 1 ­node model? Rewrite in matrix form: SAffness matrix, and relaAon to elasAc modulus: Example Review Types of Elements •  Plane elements •  Curved edge •  Isoparame.c elements (the boundaries are curved in 3D) –  triangle –  tetrahedron (tet), –  hexahedron (hex) •  Structural elements: –  Beam element, –  Plate element, –  Shell element. FEM Errors •  For a linear axial element with displacements u=u1 at x=0 and u=u2 at x=L, how the displacement is varying along the element? u(x) = N(x)u(x) Shape factor: •  How about two ­ and three ­dimensional elements with more nodes and displacements at a node? –  Much more complex shape factor. –  Example: Consider a 2D triangular element with three nodes and two displacements per node, the components of displacement u (along x ­axis) and v (along y ­axis) are •  What is the strain in x ­axis? FEM Errors (cont’d) •  Discre.za.on errors: •  Formula.on errors: (LinearizaAon error) •  Convergence error: percent difference between the results of one run and the next iteraAon FEM Errors (cont’d) h ­element method p ­element method Steps in FEA Process •  Perform a preliminary analysis to define the problem •  Pre ­processing phase –  Geometry: The geometry of the part is imported from the CAD model –  Meshing: Make decisions concerning the division of the geometry into elements –  Boundary condi6ons: Determine how the structure is loaded and supported, or determine the iniAal condiAon (e.g., temp. in thermal problem) –  Cons6tu6ve equa6ons: for describing the material that relates displacement to strain and then to stress •  ComputaAon (FEA soWware) –  Numbering: The FEA program renumbers the nodes in the mesh to minimize comp. resources by minimizing the size of global K –  S6ffness matrix: It generates a sAffness matrix k for each element and assembles the elements together to maintain a conAnuity in K. Apply boundary condiAons –  Solve F ­D Matrix equa6on: Solve the massive matrix equaAon for the displacement vector and determine the constrain forces. •  Post processing (FEA soWware) –  Stress ­Strain mapping: Generate stress and strain field values –  Interpreta6on: Interpret data, generate visual displacement of data etc. –  Op6miza6on: Increasingly, FEA soWware is being combined with an opAmizaAon package and used for iteraAve opAmizaAon design Manufacturing FuncAons What are the different aspects involved in manufacturing? –  Process engineering –  Tool engineering –  Work standards –  Plant engineering –  Administra.on and control Manufacturing AcAviAes Types of Manufacturing Processes •  A natural division •  A different division Classes of Manufacturing Processes •  Cas.ng (solidifica.on) process •  Polymer processing (molding) •  Deforma.on processes •  Powder processing Classes of Manufacturing Processes (cont’d) •  Material removal or cuHng (machining) processes •  Joining processing •  Heat treatment and surface treatment •  Assembly processes Types of Manufacturing Systems •  Job shop •  Batch flow •  Assembly ­line produc.on: •  Con.nuous ­flow process Types of Manufacturing Systems (cont’d) Manufacturing Process SelecAon •  What are the factors that influence the selecAon of which process for making a part? Manufacturing Process SelecAon (cont’d) •  What are the steps involved in selecAng a manufacturing process? QuanAty of Parts Required •  How to determine the quanAty? What are the economic batch sizes for sand cas6ng and die cas6ng? QuanAty of Parts Required (cont’d) Economic batch sizes for typical manufacturing processes Example 1 •  Problem statement: Automobile plasAc bumpers –  What are the requirements for a good bumper? –  Four polymeric materials were chosen: •  Polyester reinforced with chopped ­glass fiber to improve toughness •  Polyurethane with glass ­flake filler to increase sAffness •  Rubber ­modified polypropylene to decrease the ducAle ­ bri^le transiAon to below 30C •  A polymer blend of polyester and polycarbornate to combine the excellent solvent resistance of the former with the high toughness of the la^er. Example 1 (cont’d) •  Tooling and labor costs •  Cost per part Shape and Feature Complexity •  The complexity of a part refers to its shape and type and number of features that it contains. Size •  Process versus range of size (mass) Size (cont’d) •  Range of available secAon thickness by different processes Required Quality of the Part •  How to characterize the quality of the part? •  Defects Required Quality of the Part (cont’d) •  Surface finish •  Surface roughness: •  Parameters to describe the state of surface roughness. Required Quality of the Part (cont’d) –  Rq is the root ­mean square of the deviaAon from the mean surface. –  Rq is someAmes given as an alternaAve to Ra because it gives more weight to the higher peaks in the surface roughness. –  Lay: direcAonal scratches –  Waviness: long range distance than the peaks and valleys of roughness Required Quality of the Part (cont’d) The surface are defined in words and by the preferred values, N, given by ISO surface roughness standard. Dimensional Accuracy and Tolerances Approximate values of surface roughness and tolerance on dimensions typically obtained with different manufacturing processes. Cost to Manufacturing What should be included in the manufacturing cost? Cost to Manufacturing (cont’d) •  How to determine unit cost CU, of a part with weight m? –  Material cost (f is a fracAon of material scrap) –  Labor cost: labor cost per unit Ame (  ­ ­ producAon rate) –  Tool cost: (  ­ ­ number of Ames the tooling must be replaced) Cost to Manufacturing (cont’d) –  Capital cost of equipment: (  ­  ­ ­ capital write ­off Ame; L – load factor, fracAon Ame the equipment is producAve; q – appreciaAon factor due to producAon share with mulAple products) –  Overhead cost: •  Tool unit cost: Example •  Problem Statements: –  Cost for making 500000 units of the fan. –  SpecificaAons: •  Radius of the blade: 9 in.; •  Hub: 0.5 in thick; Diameter of 4 in. •  12 blades, each with 1 in. wide at the root and 2.3 in. wide at the Ap. •  Each blade is 0.4 in. thick. Example (cont’d) •  The volume of the casAng is about 89 cu. In. If casAng in aluminum, it weighs 8.6 lb (3.9 kg) •  Only casAng or molding processes are considered (For an integral hub and blade process). Any disadvantages? –  Low ­pressure permanent mold cas.ng –  Squeeze cas.ng is a combinaAon Example •  Could be achieved by several casAng processes •  Die casAng •  Investment casAng – Lost ­wax casAng •  InjecAon molding •  Squeeze fasAng Example (cont’d) •  The surface finish on the blades must be at least N8 to minimize faAgue failure. Tolerance must be +/ ­0.020 in. Example (cont’d) Investment cas6ng is eliminated due to the small economic batch size Example (cont’d) ...
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