Parametric Design of Mechanical Systems: A Case Study on Bolt and Belt Pulley Design, Slides of Computer-Aided Design for Engineers

Download Parametric Design of Mechanical Systems: A Case Study on Bolt and Belt Pulley Design and more Slides Computer-Aided Design for Engineers in PDF only on Docsity! ParaMetric Design Docsity.com OutLine  ParaMetric Design • Design phase info flow • Parametric design of a bolt • Parametric design of belt & pulley • Systematic parametric design • Summary Docsity.com Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 11 Real Life Application Docsity.com Bruce Mayer, PE Dir. System Engineering 19Feb02 3x00 S2-§19 Seismic Protection EarthQuake – Magnitude 8.0 – Kurile Islands – 03Dec1995 Docsity.com 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 Docsity.com 8 7 | 6 5 4 3 2 | 1 a Ea = SEISMIC_RESTRAINT a yy ca NS irection. R prot ANCHOR \— Mia FLOOR M6_ FRAME ANCHOR’ BRAKET DETAIL 3x00 Seismic Loading & Geometry /\ ALL DIVERSIONS MILLIMETERS ZX cuwertne muras W ovneus w IE $x00_Seismie_Analysi_0202.8le BMayer | TBiMAvER| 3x00 SEISMIC PROTECTION Fa |! = MAYER] 1972802 APPLICATION, NOT_ScALE DRAWN 8 7 4 3 Docsity.com Loading Geometry Detail SEISMIC RESTRAIN BRACKET, 8 PLCS a a ON M R y— Direction p ——— Pivot Lines | ie SE ~. WR & Por) 9 ee) AQK k ‘|| -) 14 “3 KG il J \ > van _—— CG PIN )\ Negen N ; \— 10 FLOOR LEI —_ TT ANCHOR LIE J \— rN | ey) ) \ \— M6_FRAME oe « O)* \ ANCHOR - ei <| \ J o|S Es J : = ®= Level+-Leg Location - o cue . = BRAKET DETAIL 949 710 —we ea a) O ® Docsity.com 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 §19.2.4 3. Horizontal (overturning) Acceleration for non-HPM equipment of 0.63g per §19.2.2 • Results → Safe From Overturning WithOUT Restraints (but not by much!) Pivot Axis OverTurning Restoring Factor of Line Direction Moment (N-m) Moment (N-m) Safety R-S Y 6884 6966 1.01 P-Q X 6884 8504 1.24 3x00_Seismic_Analysis_0202.xls Docsity.com 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 pppp ASFAFS =⇒= Docsity.com Use Engineering Analysis • Using ENGR36 Methods Determine the Bolt Load as 4000 lb (4 kip) • Thus the “Functional Requirement” for the Bolt lbs 4000≥pF  To Actually Purchase a Bolt we need to Spec a DIAMETER, d, and a length, L  Find d Using the FR & Stress-Eqn p pp S AFAS lbs 4000lbs 4000 ≥⇒≥= Docsity.com 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 Sp = 85 000 psi (85 ksi) Docsity.com 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 Sp 2. Inverse • Start with FR and Use Math & Science to effectively DETERMINE the ENGR-Spec Docsity.com 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 2 2 2 2 in kip866 44 dd SdSF ppp ⋅   =⋅      == . ππ  This ParaMetric Relationship can be displayed in a plot Docsity.com ParaMetric Design of a Bolted Joint 0 2 4 6 8 10 12 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Bold Diameter (in) P ro of L oa d (K ip ) Bolt_Design_Parametr_d-F_0907.xls PARAMETERS • Grade-5 Steel • Sp =85 ksidc NOT Feasible FEASIBLE Functional Requirement Docsity.com Reduction-Free Bolt Design Determine best alternative Predict Performance Check Feasibility: Functional? Manufacturable ? Generate Alternatives Formulate Problem Analyze Alternatives Evaluate Alternatives Re-Design Re-Specify Select Design Variables Determine constraints Select values for Design Variables all alternatives feasible alternatives best alternative Refine Optimize refined best alternative  The “FORWARD” process • Use “Guess & Check” diameter d proof load >4000 d =0.1 in area = 0.008 in2 load < 668 Need to change either SIZE or MATERIAL Docsity.com Before Next Example… • Take a Short BREAK Docsity.com 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 Docsity.com FreeBody Diagram of Drive Pulley 1r 2F 1F 1n T1φ yB xB x y  Some Physics ( )211 FFrT −= 1TnP = ( )       −°+= 2 90 121 φcosFFBx ( )       −°−= 2 90sin 121 φFFB y Docsity.com 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 Docsity.com 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 Item Parameter Symbol Units Lower Limit Upper LImit 1 Belt Torque Tb in-lb -- Tm 2 Belt Tension F1 lbs -- 35 3 Center Distance c in. small -- Docsity.com Analysis/Solution Game Plan 1. Calc Buffing Wheel Diameter, d2 2. Calc Motor Torque, Tm 3. Calc (F1 – F2) 4. DECIDE Best Estimate for Ctr-Dist, c1 5. Calc Angles of Wrap, φ1 & φ2 6. Calc F1 by Friction Reln (c.f. ENGR36) 7. Calc F2 8. Calc The Initial belt Tension, Fi Docsity.com Analysis  Check Ctr Dist • Mechanically The SPEED RATIO Sets the DiaMeter Ratio - use to find d2 ( ) in 6in 23 in 2600 1800 2 2 1 2 2 1 ==⇒=⇒= dd d d n n  Thus the MINIMUM Center Distance in 4in 3in 1 2 in 6 2 in 2 22 21 =+= +=+= ddcmin Docsity.com 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 nPTTnP m =⇒= Docsity.com Analysis  Check Ctr Dist • Now by GeoMetry & TrigonoMetry  We can now (finally) Construct an eqn to express F1 as function of c       −−°= c rr 12 1 arcsin2180φ ( )           − ⋅ =             −− ce F in 1in 3230 1 11in 1 lbin 5217 arcsin. . π Docsity.com 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 ( ) ( ) lbs 0336 11in 1 lbin 5217in 54 in .54 in 22 1 . .. arcsin =           − ⋅ =            −πf e F Docsity.com 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? ( ) ( ) lbs 5334 11in 1 lbin 5217in 54 in .255 in 22 1 . .. arcsin =           − ⋅ =            −πf e F Docsity.com The M ATLAB 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 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) Docsity.com 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 111 lbs 1.63 lbs 35 9 .== ⇒= n F Fn design allowable Docsity.com 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 the Fi Calc lbs 114 1 5217631 1 122 1 1 . .. =−=−=⇒+= r TFFF r TF mm lb 8522 2 114631 2 21 ... =+=+= FFF i Docsity.com DPs NOT Always Continuous • DPs can be DISCRETE or BINARY Type of value Example Variable Values numerical Length 3.45 in, 35.0 cm non-numerical material mfg. process Configuration aluminum machined left-handed threads continuous height 45 in, 2.4 m discrete tire size lumber size R75x15 2x4, 4x4 discrete (binary) zinc coating safety switch with/without yes/no, (1,0) Docsity.com ParaMetric Design Summary Determine best alternative Predict Performance Check Feasibility: Functional? Manufacturable ? Generate Alternatives Formulate Problem Analyze Alternatives Evaluate Alternatives Re-Design Re-Specify Select Design Variables Determine constraints Select values for Design Variables all alternatives feasible alternatives best alternative Refine Optimize refined best alternative 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 Docsity.com 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 Docsity.com Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege.edu Engineering 11 Appendix Docsity.com 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 Docsity.com The Taguchi Philosophy Taguchi definition of Quality: Quality is related to the total /oss to society due to functional and environmental variance of a given product Taguchi's method focuses on Robust Design through use of: * S/N Ratio to quantify quality * Orthogonal Arrays to investigate quality ® Docsity.com