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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

Engineering 11. ParaMetric Design. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. OutLine  ParaMetric Design. Design phase info flow Parametric design of a bolt Parametric design of belt & pulley Systematic parametric design Summary.

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

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  1. Engineering 11 ParaMetricDesign Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. OutLine  ParaMetric Design • Design phase info flow • Parametric design of a bolt • Parametric design of belt & pulley • Systematic parametric design • Summary

  3. Abstract embodiment Physical principles Material Geometry Special Purpose Parts: Features Arrangements Relative dimensions Attribute list (variables) Standard Parts: Type Attribute list (variables) Architecture Configuration Design Configuration Design

  4. ConFig Design Information Flow Special Purpose Parts: Features Arrangements Relative dimensions Variable list Standard Parts: Type Variable list Design variable values e.g. Sizes, dimensions Materials Mfg. processes Performance predictions Overall satisfaction Prototype test results Parametric Design Detail Design Product specifications Production drawings Performance Tests Bills of materials Mfg. specifications

  5. Engineering 11 Real LifeApplication Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  6. 3x00 S2-§19Seismic Protection Bruce Mayer, PEDir. System Engineering19Feb02 • EarthQuake • Magnitude 8.0 • Kurile Islands • 03Dec1995

  7. 3x00 Seismic Protection Analysis Plan • Measure/Calc Weight and Center of Gravity • Consult S2/§19 for Lateral Loading Criteria (0.63g) • Consult Mechanical Design Drawing for Seismic Structural-Element Location & Configuration • Use Newtonian Vector Mechanics to Determine Force & Moment Loads • Use Solid-Mechanics Analysis to Determine Fastener (Bolt) Stresses • Use Mechanical-Engineering & Materials Properties to determine Factors of Safety

  8. BMayer

  9. S2-0200 Test SystemAL3120F, s/n 111001 3x00 S2Testing: Tatsuno Japan, Dec01 3x00_S2S8_Tatsuno_PhotoDoc_0112.ppt

  10. 3x00 Seismic Loading & Geometry BMayer

  11. Loading Geometry Detail

  12. OverTurning Analysis • Analysis Parameters: • Worst Case → SHORTEST Restoring-Moment Lever-Arm • Lever Arms= 582mm, 710mm, 776mm (see slides 4&5) • Vertical (resisting/restoring) Acceleration of 0.85gper SEMI S2 §19.2.4 • Horizontal (overturning) Acceleration for non-HPM equipment of 0.63g per §19.2.2 • Results → Safe From Overturning WithOUT Restraints (but not by much!) 3x00_Seismic_Analysis_0202.xls

  13. Bracket Stress Analysis • Analysis Parameters • Assume Failure Pointat M6 or M10 Bolts • FOUR (4) Angle Brackets With a total of 8 Connecting & Anchor Bolts, Resist Shear • Two Bolts Per Point, Each Bolt Bears 50% of Load • Bolt Axial-PreLoad is negligible (Snug-Fit) • Shear Load Per Restraint Point = 500lb/2.22kN • Use Von Mises Yield Criteria: Ssy = 0.577Sy • Results 3x00_Seismic_Analysis_0202.xls

  14. ParaMetric Bolt Design • From Analysis Determine Failure Mode as AXIAL TENSILE YIELDING (E45) • The Configuration Design Sketch head Load Load shank threads

  15. Use Engineering Analysis • Force Load, Fp, That Causes a “Permanent Set” in a specific-sized Bolt is Called the “Proof Load” (N or lbs) • The “Proof Stress”, Sp, is the Proof-Load divided by the supporting Material Area, A (Pa or psi) • Mathematically the Axial Stress Eqn

  16. Use Engineering Analysis • Using ENGR36 Methods Determine the Bolt Load as 4000 lb (4 kip) • Thus the “Functional Requirement” for the Bolt • To Actually Purchase a Bolt we need to Spec a DIAMETER, d, and a length, L • Find d Using the FR & Stress-Eqn

  17. Design DECISION • We Now need to make a Design Decision – We get to CHOOSE • Bolt MATERIAL  Gives Proof Stress • Bolt DIAMETER  Gives Supporting Area • In this Case Choose FIRST a Grade-5, Carbon-Steel Boltwith Sp = 85 000 psi(85 ksi)

  18. Bolt Grade DEFINES Bolt Size • Use Sp and the FR to find the Bolt Area • Relate A to dusing Geometry • Since Bolts Have Circular X-Sections

  19. Spec Bolt • We can PICK any Grade-5 Bolt with a Diameter >0.245” • To Keep down the Bulkiness of the Hardware choose d = ¼” (0.25”) • Thus We Can Specify the Bolt as • Grade-5 • ¼-20 x 6” • CHOOSE Coarse Thread (the “20”) • CHOOSE a Bolt Length of 6” based on sizeof Parts Connected

  20. Forward & Inverse Analysis • As Design Engineers we Can approach the quantitative Functional Requriments (FR’s) in Two Ways • Forward ≡ Guess & Check • Set the ENGR-Spec and then Check if the FR is Satisfied (The Seismic Case) • e.g; Guess a ½-12 Grade-2 bolt & chkSp • Inverse • Start with FR and Use Math & Science to effectively DETERMINE the ENGR-Spec

  21. ParaMeterization • The Bolt Design Problem, After Selecting Grade-5 Material, depends on the Bolt DiaMeter as a PARAMETER • The Bolt Proof Load as a Fcn of d • This ParaMetric Relationship can be displayed in a plot

  22. NOT Feasible FEASIBLE Functional Requirement

  23. Inverse Analysis ReCap • The Steps used to Find Bolt Diameter • Reviewed concept and configuration details • Read situation details • Examined a sketch of the part  2D side view • Identified a mode of failure to examine tensile (stretching) yield • Determined that a variable (proof load) was “constrained” to a Maximum value by its Function • Obtained analytical relationships for Fp and A • “Reduced” those equations to “find” a value d

  24. Reduction Limitations • Many times such an Orderly Physical Reduction is NOT Possible • Science & Math may not provide clear guidance; e.g., • There is NO Theory for Turbulent Flow • Many Times Design-Engineering is AHEAD of the Science; e.g., the First Planar Transistor • We have 10000+ possible Decisions • Not Sufficient time to do ALL of them

  25. Reduction-FreeBolt Design diameter d proof load >4000 d =0.1 in area = 0.008 in2 load < 668 • The “FORWARD” process • Use “Guess & Check” Need to change either SIZE or MATERIAL

  26. Before Next Example… • Take a Short BREAK

  27. Example  Flat-Belt Drive Sys • Functional Requirements for Buffing Wheel Machine • 1800 rpm, ½ HP Motor • 600 rpm Buff Wheel Speed • Constraints • Belt/Pulley CoEfficient of Friction = 30% • Max Belt Tension = 35 lb

  28. Example  Flat-Belt Drive Sys • Goals • Slip-before-Tear for Belt (FailSafe) • DRIVE Pulley (motor side) to Slip Before Driven Pulley • High Power Efficiency • Compact System

  29. Motor Pulley (driver) Grinding Wheel Pulley (driven) System Diagram NOTE:n→ Spin Speed (RPM) NOTE:d = 2r

  30. FreeBody Diagram of Drive Pulley • Some Physics

  31. Solution Evaluation Parameters • The SEP’s are those Quantities that we can Measure or Calculate to Asses How well the Design meets the System CONSTRAINTS and GOALs • In This case • Tb Check for Belt SLIPPING (ENGR36) • F1 Check for Belt BREAKING • Manufacturer’s Data • c  Check for COMPACT System • Our (or Customer) Judgement

  32. Summarize SEPs • If Belt SLIPS then Tb < Tmotor • If Belt BREAKS then F1 > 35 lbs • If System is compact then c ≈ “small” • Summarize SEPs in Table

  33. Design ParaMeters (Variables) • Design ParaMeters, or Variables, are those quantities that are under the CONTROL of the DESIGN ENGINEER • In This Case there are Two DPs; the Center-Distance & Driven-Pulley Dia. • Summarize DPs in Table

  34. Problem Definition ParaMeters • PDP’s are those quantities that are Fixed, or “Given” by the Laws of Physics or UnChangeable System Constraints. In this Case the “Givens”

  35. Analysis/Solution Game Plan • Calc Buffing Wheel Diameter, d2 • Calc Motor Torque, Tm • Calc (F1 – F2) • DECIDE Best Estimate for Ctr-Dist, c1 • Calc Angles of Wrap, φ1 & φ2 • Calc F1 by Friction Reln (c.f. ENGR36) • Calc F2 • Calc The Initial belt Tension, Fi

  36. Analysis  Check Ctr Dist • Mechanically The SPEED RATIO Sets the DiaMeter Ratio - use to find d2 • Thus the MINIMUM Center Distance

  37. Analysis  Check Ctr Dist • Since we do NOT want the Pulleys to RUB, Estimate c = 4.5 in. • Next Calc Motor Torque using Motor Power. From Dyamnics (PHYS 4A) • Need to take Care with Units • ½ hp = 373 W = 373 N·m/s • 1800 rpm = 60π rads/s • Note that radians are a PURE Number

  38. Analysis  Check Ctr Dist • With Consistent Units Calc Tm • Now by PHYS4A or ENGR36 • Next Find Reln between F1 & F2 by ENGR36 Pulley-Friction Analysis

  39. Analysis  Check Ctr Dist • In This Case We assume that ≈100% of the Motor Power is Transmitted to the DRIVE Pulley; Thus • Subbing for Tm & F2 in Torque Eqn

  40. Analysis  Check Ctr Dist • Now by GeoMetry & TrigonoMetry • We can now (finally) Construct an eqn to express F1 as function of c

  41. Analysis  Check Ctr Dist • Now use the F1 = u(c) Eqn to Check the 4.5 inch estimate • Since 36 lbs EXCEEDS the 35 lb Max Tension for the belt we must ITERATE

  42. Analysis  Check Ctr Dist • Increase c to 5¼ inches • Since 34.53 lbs is LESS than the Rated Max for the belt, the 5.25” design works • But is 5.25” the BEST?

  43. Analysis  Check Ctr Dist • Find the Best, or Minimum, Value of c using the MATH-Processor software MATLAB (c.f. ENGR25) • PLOT F1(c) to see how F1 varies with c • cmin at crossing pt for line F1 = 35 lbs • Use the fzero function to precisely determine cmin for F1 = 35 lbs • See MATLAB file Belt_Center_Distance_Chp8_Sp10.m

  44. FR = Fmax =35 lb cmin = 4.9757 in

  45. % Bruce Mayer, PE * ENGR11 * 03Jul09 % Plot & Solve for Belt Drive System Center Distance % file = Belt_Center_Distance_Chp8_Sp10.m % clear % clear out memory % c to range over 4-8 inches c = [4:.01:6]; % % F1 = f(c) by anonymous function F1 = @(z) 17.52./(1-1./(exp(0.3*(pi-2*asin(2./z))))) % % Make F1 Plotting Vector F1plot = F1(c); % % Make Horizontal line on (c, F1) plot Fmax =[35, 35]; cmax = [4,6] % % Plot F1 as a funcition of c plot(c,F1plot, cmax,Fmax) % %Make Function to ZERO to find Cmin F35 = @(z) 35-17.52./(1-1./(exp(0.3*(pi-2*asin(2./z))))) cmin = fzero(F35,5) The MATLAB Code

  46. Analysis  Check Ctr Dist • We “don’t want push it” by using a design the produces Belt Tension that is very close to 35 lbs. • Try c = 9” Check F1(9) by MATLAB >> F9 = F1(9) F9 = 31.6097 • Calc the “Factor of Safety” for Belt-Tearing

  47. Analysis  Check Ctr Dist • Finally for System SetUp Determine the No-Load Belt PreTension, Fi • First Find “Slack” Side Tension F2 from previous analysis AT LOAD • At Load F1 = (Fi + ΔF) & F2 = (Fi− ΔF) Thus theFi Calc

  48. Specify Design • The Center Distance of 9” meets all the Functional Requirements and the System Goals (if 9” is a “compact” size) • Thus Spec the Design • Flat-Belt Drive System • 2” DRIVE Pulley • 6” Driven Pulley • 9” Center Distance • 23 lb No-Load Belt PreTension

  49. TradeOffs • Note that we encountered a “Trade-Off” Between Compactness & Reliability • In this case as c INCREASES • Compactness DEGRADES • Drive System becomes Larger • Reliability IMPROVES • Tearing/Stretching Tension becomes Less • The “BEST” Value determined thru TradeOff Consultations w/ the Customer

  50. DPs NOT Always Continuous • DPs can be DISCRETE or BINARY

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