ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 1 Bruce Mayer, PE Engineering-11: Engineering Design Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 11 ParaMetric Design

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 2 Bruce Mayer, PE Engineering-11: Engineering Design OutLine  ParaMetric Design  Design phase info flow  Parametric design of a bolt  Parametric design of belt & pulley  Systematic parametric design  Summary

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 3 Bruce Mayer, PE Engineering-11: Engineering Design Configuration Design Configuration Design Configuration Design Special Purpose Parts: Features Arrangements Relative dimensions Attribute list (variables) Standard Parts: Type Attribute list (variables) Abstract embodiment Physical principles Material Geometry Architecture

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 4 Bruce Mayer, PE Engineering-11: Engineering Design Information Flow Special Purpose Parts: Features Arrangements Relative dimensions Variable list Standard Parts: Type Variable list Parametric Design Parametric Design Design variable values e.g. Sizes, dimensions Materials Mfg. processes Performance predictions Overall satisfaction Prototype test results Detail Design Detail Design Product specifications Production drawings Performance Tests Bills of materials Mfg. specifications ConFig Design

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 5 Bruce Mayer, PE Engineering-11: Engineering Design Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 11 Real Life Application

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 6 Bruce Mayer, PE Engineering-11: Engineering Design Bruce Mayer, PE Dir. System Engineering 19Feb02 3x00 S2-§19 Seismic Protection EarthQuake – Magnitude 8.0 – Kurile Islands – 03Dec1995

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 7 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 8 Bruce Mayer, PE Engineering-11: Engineering Design BMayer

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 9 Bruce Mayer, PE Engineering-11: Engineering Design 3x00 S2Testing: Tatsuno Japan, Dec01 S Test System AL3120F, s/n x00_S2S8_Tatsuno_PhotoDoc_0112.ppt

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 10 Bruce Mayer, PE Engineering-11: Engineering Design 3x00 Seismic Loading & Geometry BMayer

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 11 Bruce Mayer, PE Engineering-11: Engineering Design Loading Geometry Detail

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 12 Bruce Mayer, PE Engineering-11: Engineering Design OverTurning Analysis  Analysis Parameters: 1.Worst Case → SHORTEST Restoring-Moment Lever-Arm –Lever Arms= 582mm, 710mm, 776mm (see slides 4&5) 2.Vertical (resisting/restoring) Acceleration of 0.85g per SEMI S2 § Horizontal (overturning) Acceleration for non-HPM equipment of 0.63g per §  Results → Safe From Overturning WithOUT Restraints (but not by much!) 3x00_Seismic_Analysis_0202.xls

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 13 Bruce Mayer, PE Engineering-11: Engineering Design Bracket Stress Analysis  Analysis Parameters 1.Assume Failure Point at M6 or M10 Bolts 2.FOUR (4) Angle Brackets With a total of 8 Connecting & Anchor Bolts, Resist Shear 3.Two Bolts Per Point, Each Bolt Bears 50% of Load 4.Bolt Axial-PreLoad is negligible (Snug-Fit) 5.Shear Load Per Restraint Point = 500lb/2.22kN 6.Use Von Mises Yield Criteria: S sy = 0.577S y  Results 3x00_Seismic_Analysis_0202.xls

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 14 Bruce Mayer, PE Engineering-11: Engineering Design ParaMetric Bolt Design  From Analysis Determine Failure Mode as AXIAL TENSILE YIELDING (E45)  The Configuration Design Sketch shank head threads Load

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 15 Bruce Mayer, PE Engineering-11: Engineering Design Use Engineering Analysis  Force Load, F p, That Causes a “Permanent Set” in a specific-sized Bolt is Called the “Proof Load” (N or lbs)  The “Proof Stress”, S p, is the Proof- Load divided by the supporting Material Area, A (Pa or psi)  Mathematically the Axial Stress Eqn

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 16 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 17 Bruce Mayer, PE Engineering-11: Engineering Design 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 Bolt with S p = psi (85 ksi)

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 18 Bruce Mayer, PE Engineering-11: Engineering Design Bolt Grade DEFINES Bolt Size  Use S p and the FR to find the Bolt Area  Relate A to d using Geometry  Since Bolts Have Circular X-Sections

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 19 Bruce Mayer, PE Engineering-11: Engineering Design 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 size of Parts Connected

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 20 Bruce Mayer, PE Engineering-11: Engineering Design Forward & Inverse Analysis  As Design Engineers we Can approach the quantitative Functional Requriments (FR’s) in Two Ways 1.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 & chk S p 2.Inverse –Start with FR and Use Math & Science to effectively DETERMINE the ENGR-Spec

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 21 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 22 Bruce Mayer, PE Engineering-11: Engineering Design NOT FeasibleFEASIBLE Functional Requirement

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 23 Bruce Mayer, PE Engineering-11: Engineering Design 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 F p and A “Reduced” those equations to “find” a value  d

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 24 Bruce Mayer, PE Engineering-11: Engineering Design 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 possible Decisions –Not Sufficient time to do ALL of them

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 25 Bruce Mayer, PE Engineering-11: Engineering Design Reduction-Free Bolt Design  The “FORWARD” process Use “Guess & Check” diameter d proof load >4000 d =0.1 in area = in 2 load < 668 Need to change either SIZE or MATERIAL

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 26 Bruce Mayer, PE Engineering-11: Engineering Design Before Next Example…  Take a Short BREAK

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 27 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 28 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 29 Bruce Mayer, PE Engineering-11: Engineering Design System Diagram Motor Pulley (driver) Grinding Wheel Pulley (driven ) NOTE: d = 2r NOTE: n → Spin Speed (RPM)

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 30 Bruce Mayer, PE Engineering-11: Engineering Design FreeBody Diagram of Drive Pulley  Some Physics

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 31 Bruce Mayer, PE Engineering-11: Engineering Design 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 T b  Check for Belt SLIPPING (ENGR36) F 1  Check for Belt BREAKING –Manufacturer’s Data c  Check for COMPACT System –Our (or Customer) Judgement

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 32 Bruce Mayer, PE Engineering-11: Engineering Design Summarize SEPs  If Belt SLIPS then T b < T motor  If Belt BREAKS then F 1 > 35 lbs  If System is compact then c ≈ “small”  Summarize SEPs in Table ItemParameterSymbolUnits Lower Limit Upper LImit 1Belt TorqueTbTb in-lb--TmTm 2Belt TensionF1F1 lbs--35 3Center Distancecin.small--

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 33 Bruce Mayer, PE Engineering-11: Engineering Design 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 ItemParameterSymbolUnits Lower Limit Upper LImit 1Center Distancecinsmall-- 2Driven Pulley Dia.d2d2 in--

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 34 Bruce Mayer, PE Engineering-11: Engineering Design 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” ItemParameterSymbolUnits Lower Limit Upper LImit 1Friction Coefficientf Belt StrengthF max lbs--35 3Motor PowerWHp½½ 4DRIVE Pulley Dia.d1d1 in.22 5Driven Pulley Spdn2n2 rpm600

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 35 Bruce Mayer, PE Engineering-11: Engineering Design Analysis/Solution Game Plan 1.Calc Buffing Wheel Diameter, d 2 2.Calc Motor Torque, T m 3.Calc (F 1 – F 2 ) 4.DECIDE Best Estimate for Ctr-Dist, c 1 5.Calc Angles of Wrap, φ 1 & φ 2 6.Calc F 1 by Friction Reln (c.f. ENGR36) 7.Calc F 2 8.Calc The Initial belt Tension, F i

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 36 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  Mechanically The SPEED RATIO Sets the DiaMeter Ratio - use to find d 2  Thus the MINIMUM Center Distance

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 37 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 38 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  With Consistent Units Calc T m  Now by PHYS4A or ENGR36  Next Find Reln between F 1 & F 2 by ENGR36 Pulley-Friction Analysis

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 39 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  In This Case We assume that ≈100% of the Motor Power is Transmitted to the DRIVE Pulley; Thus  Subbing for T m & F 2 in Torque Eqn

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 40 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  Now by GeoMetry & TrigonoMetry  We can now (finally) Construct an eqn to express F 1 as function of c

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 41 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  Now use the F 1 = 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 42 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  Increase c to 5¼ inches  Since lbs is LESS than the Rated Max for the belt, the 5.25” design works But is 5.25” the BEST?

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 43 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  Find the Best, or Minimum, Value of c using the MATH-Processor software MATLAB (c.f. ENGR25) PLOT F 1 (c) to see how F 1 varies with c –c min at crossing pt for line F 1 = 35 lbs Use the fzero function to precisely determine c min for F 1 = 35 lbs –See MATLAB file Belt_Center_Distance_Chp8_Sp10.m

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 44 Bruce Mayer, PE Engineering-11: Engineering Design FR = F max =35 lb c min = in

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 45 Bruce Mayer, PE Engineering-11: Engineering Design The MATLAB Code % 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 F /(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 F /(1-1./(exp(0.3*(pi-2*asin(2./z))))) cmin = fzero(F35,5)

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 46 Bruce Mayer, PE Engineering-11: Engineering Design 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 F 1 (9) by MATLAB >> F9 = F1(9) F9 =  Calc the “Factor of Safety” for Belt-Tearing

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 47 Bruce Mayer, PE Engineering-11: Engineering Design Analysis  Check Ctr Dist  Finally for System SetUp Determine the No-Load Belt PreTension, F i  First Find “Slack” Side Tension F 2  from previous analysis AT LOAD  At Load F 1 = (F i + ΔF) & F 2 = (F i − ΔF) Thus the F i Calc

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 48 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 49 Bruce Mayer, PE Engineering-11: Engineering Design 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

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 50 Bruce Mayer, PE Engineering-11: Engineering Design DPs NOT Always Continuous  DPs can be DISCRETE or BINARY Type of valueExample VariableValues numericalLength3.45 in, 35.0 cm non-numerical material mfg. process Configuration aluminum machined left-handed threads continuousheight45 in, 2.4 m discrete tire size lumber size R75x15 2x4, 4x4 discrete (binary) zinc coating safety switch with/without yes/no, (1,0)

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 51 Bruce Mayer, PE Engineering-11: Engineering Design ParaMetric Design Summary read, interpret sketch restate constraints as eqns guess, ask someone, use experience, BrainStorm calculate Experiment (test) calculate/determine satisfaction Use Weighted Satisfaction Calc improve “best” candidate

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 52 Bruce Mayer, PE Engineering-11: Engineering Design Summary  ParaMetric Design  The Parametric Design phase involves decision making processes to determine the values of the design variables that: satisfy the constraints and maximize the customer’s satisfaction.  The five steps in parametric design are: formulate, generate, analyze, evaluate, refine/optimize

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 53 Bruce Mayer, PE Engineering-11: Engineering Design Summary  ParaMetric Design  During parametric design analysis we predict the performance of each alternative, reiterating (i.e., re-designing) when necessary to assure that all the candidates are feasible.  During parametric design evaluation we select the best alternative (i.e., assessing satisfaction)  Many design problems exhibit “trade-off" behavior, necessitating compromises among the design variable values.  Weighted rating methods, using customer satisfaction functions, can be used to determine the “best” candidate from among the feasible design candidates.

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 54 Bruce Mayer, PE Engineering-11: Engineering Design All Done for Today Engineering IS TradeOffs

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 55 Bruce Mayer, PE Engineering-11: Engineering Design Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 11 Appendix

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 56 Bruce Mayer, PE Engineering-11: Engineering Design Design for Robustness  A “Robust” Design results in a product whose (excellent) Function is INSENSITIVE to Variations in Manufacturing (materials & processes) “Alignment” Wear Operating Environment  Typically Uses Statistical Methods Monte Carlo, Taguchi, RSM, DoE, others

ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt 57 Bruce Mayer, PE Engineering-11: Engineering Design The Taguchi Philosophy