Miks Robust Design? 1: Firms aim for Six Sigma efficiency; [FIRST Edition] Del Jones. USA TODAY. McLean, Va.: Jul 21, pg. 01.

Transcription

1 Robust Design

2 Miks Robust Design? Lockheed Martin used to spend an average of 200 work-hours trying to get a part that covers the landing gear to fit. For years employees had brainstorming sessions, which resulted in seemingly logical solutions. None worked. The statistical discipline of Six Sigma discovered a part that deviated by one-thousandth of an inch. Now corrected, the company saves $14,000 a jet. 1 1: Firms aim for Six Sigma efficiency; [FIRST Edition] Del Jones. USA TODAY. McLean, Va.: Jul 21, pg. 01.B

3 Miks Robust Design? It will keep the company (Allied Signal) from having to build an $85 million plant to fill increasing demand for caprolactam used to make nylon, a total savings of $30 - $40 million a year. 1 Raytheon figures it spends 25% of each sales dollar fixing problems when it operates at four sigma, a lower level of efficiency. But if it raises its quality and efficiency to Six Sigma, it would reduce spending on fixes to 1%. 1 1: Firms aim for Six Sigma efficiency; [FIRST Edition] Del Jones. USA TODAY. McLean, Va.: Jul 21, pg. 01.B

4 Miks Robust Design? The reason to do DFSS is ultimately financial. It generates shareholder value based on delivering customer value in the marketplace. Products developed under the discipline and rigor of a DFSSenabled product development process will generate measurable value against quantitative business goals and customer requirements. DFSS helps fulfill the voice of the business by fulfilling the voice of the customer. 2 2: Design for Six Sigma in Technology and Product Development, C.M. Creveling, J. L. Slutsky, and D. Antis, Jr.

5 Robust Design Ülevaade Robust Design i taust Mis on Robust Design, DFSS,? Design for Quality Robust Design inseneriarvutustes Näited Ebatäpsuse allikad Ebatäpsuse efektid Deterministliku ja tõenäosusliku lähenemise võrdlus Tehnoloogiad

6 Küsimused Is your company interested in lower its warranty costs and increasing customer satisfaction? Are you having infield failures that you do not understand given your current analysis and you wish to understand and prevent these in the future? Is your company interested in the lowest total cost of producing a product? Do feel that you are currently over designing, but don t have an idea by how much? Are you currently holding all dimensions to the same tolerance just because this is what you have always done? Are you constantly testing new lots of material and having to reject some suppliers or shipments? Are you paying a premium to get material that meets or exceeds your exacting specifications? Are you rejecting too many parts during the final Product Inspection checks? Are you spending too much money on Product Inspection? When you come to a financial commitment gate in your development process, would you feel more secure making a decision if you had data from many design alternatives?"

7 Robust Design i taust Mis on Robust Design, DFSS, jne? Robust Design on sageli sünonüümks terminile Design for Six Sigma või Reliability-based Optimization Uncertainty Analysis Määratakse muutuvate suuruste mõju toote toimimisele (keskväärtused, standard hälve, jne) Reliability Analysis Määratakse arvuliselt usaldusväärsus (tõrke tõenäosus, defekte miljoni kohta) Robust Design or Design For Six Sigma (DFSS) Optimeeritakse toodet selliselt, et ta ei oleks tundlik muutuvate parameetrite suhtes (N. materjal, koormused, ) Reliability-based Optimization Toodet optimeeritakse selliselt, et usaldusväärsus oleks maksimaalne või siis tõrke tõenäosus oleks minimaalne (defektide arv miljoni toote kohta)

8 Robust Design i taust Design for Quality Six Sigma Quality = ainult 3.4 detaili ei vasta nõuetele Gaussian Distribution Area = Failure Probability Product is... Bad Good Product is... Good Bad LSL = Lower Specification Limit USL = Upper Specification Limit LSL USL Sigma-Value Six Sigma Quality on oma olemuselt tõenäosuslik meetod P.S.: Gaussi jaotus ei ole realistlik, kuid annab ideed edasi korrektselt

9 Six Sigma = Optimeerib tootmis protsessi selliselt, et toodetakse automaatselt tooteid mis täidavad six sigma quality nõudeid Design For Six Sigma = Optimeeritakse toodet selliselt, et toode täidaks six sigma quality nõudeid, s.t. kvaliteet and usaldusväärsus on kaasatud optimeerimis protsessi Rel. Cost of Design Change Robust Design i taust Design For Six Sigma Research Design Development PrototypeTests Production Product Development Phases Design for Quality Six Sigma 100% 80% 60% 40% 20% 0% Degree of Fredom to affect the Product Lifetime Costs Design for Six Sigma: Achieve Designed-In quality as opposed to letting customers find out about quality problems Make informed decision that are critical to quality early in the development process

10 FROM: Reactive Quality Management Robust Design i taust Design for Quality Robust Design is a Paradigm Shift TO: Predictive Quality Management Extensive Design Rework Assess Performance by build-test-build-test- Fix performance/quality problems after manufacturing Quality is Tested-In Controlled Design Parameters Estimate likelihood/rate of performance problems in design & development Address quality problems in design & development Designed for robust performance and quality Quality is Designed-In

11 Robust Design i taust Robust Design in Engineering Analysis Purpose of Robust Design Input ANALYSIS ALYSIS Output Material Properties Geometry Boundary Conditions Deformation Stresses / Strains Fatigue, Creep,... It s a reality that input parameters are subjected to scatter => automatically the output parameters are uncertain as well!!

12 Robust Design i taust Robust Design in Engineering Analysis Purpose of Robust Design ANALYSIS Questions answered with Robust Design: How large is the scatter of the output parameters? What is the probability that output parameters do not fulfill design criteria (failure probability defects per million)? How much does the scatter of the input parameters contribute to the scatter of the output (sensitivities critical-to-quality)?

13 Robust Design i taust Sources of Uncertainty Property Metallic materiales, yield Carbon fiber composites, rupture Metallic shells, buckling strength Junction by screws, rivet, welding Bond insert, axial load Honeycomb, tension Honeycomb, shear, compression Honeycomb, face wrinkling Launch vehicle, thrust Transient loads Thermal loads Deployment shock Acoustic loads Vibration loads SD/Mean % Source: Klein, Schueller et.al. Probabilistic Approach to Structural Factors of Safety in Aerospace. Proc. CNES Spacecraft Structures and Mechanical Testing Conf., Paris 1994

14 Robust Design i taust Effects of Uncertainty CAD ±5-100% Thermal Analysis Materials, Bound.- Cond., Loads,... FEM Geometry ± % CFD Materials, Bound.- Cond.,... ±5-50% Structural Analysis ±5-100% FEM Materials, Bound.- Cond., Loads,... LCF Materials ±30-60% ±??%

15 Robust Design i taust Effects of Uncertainty Elastsusmooduli ja termilise joonpaisumisteguri mõju termilistele pingetele: thermal = E T Deterministlik lähenemine: Mean = E Mean Mean T Mean = tavaliselt kasutatav lahend Tõenäosuslik lähenemine: Tõenäosus et ( thermal >= 105% Mean ) ( thermal >= 110% Mean ) E hajuvus ±5% 16% (~1 out of 6) 2.3% (~1 out of 40) E ja hajuvus ±5% 22% (~1 out of 4) 8% (~1 out of 12) E, & T hajuvus ±5% 28% (~1 out of 4) 13% (~1 out of 8)

16 Robust Design i taust Compare Deterministic/Probabilistic Turbiini What-If analüüsi seeria

17 Robust Design i taust Enabling tehnoloogia: Parametriseerimine Robust Design for all parameters including: APDL Parameters CAD Parameters (Workbench) APDL Parameters Paramesh db Initial mesh Parameter value /syp,parabatch.exe,'testpb.rsx','testpb.cdb','location',%value%,'testpb_mod.cdb' /inp,testpb_mod,cdb! Input the modified geometry Parameter name Output mesh Import Output mesh ParaMesh Parameters

18 Robust Design i taust Võimaldav tehnoloogia: DesignXplorer DesignXplorer manages the parameters and the uncertainties

19 Robust Design i näide CAD Geomeetria FEM Mesh FEM rajatingimused

20 Robust Design i näide Results for Maximum Principal Stress Pressure Side Suction Side Peak Value s Peak Value p Design Variables and Uncertainties Tang. Leaning Axial Leaning Material Density (Gaussian) Fillet Radius (Lognormal) Mass Dove Tail Width Imbalance: ( p s ) 2 Avg.Stress: 0.5( p + s )

21 Teooria Keskväärtus Standard hälve Asümeetria Kurtosis

22 Gaussian (Normal) Kõige tavalisem statistiline jaotus Kasutatakse paljude füüsikaliste parameetrite kirjeldamiseks. Truncated Gaussian Kõige Gaussi jaotuse puhul, kuid äärmised piirid lõigatakse, et elimineerida mõõtmisvigasid Kasutatakse näiteks materjali omaduste või geomeetria tolerantside kirjeldamiseks.

23 Lognormal (option 1) Samuti laialt levinud ja kasutatav jaotus. Kasutatakse füüsikaliste suuruste kirjeldamiseks, milliste teatud andmete logaritmid taanduvad normaaljaotusele. Kasutatav näiteks väsimuse kirjeldamisel. You provide values for the mean value µ and the standard deviation T of the random variable x. The PDS calculates the logarithmic mean U and the logarithmic deviation V:

24 Lognormal (option 2) You provide values for the logarithmic mean value U and the logarithmic deviation V. The parameters U and V are the mean value and standard deviation of ln(x)

25 Triangular Kasutatakse juhuslike suuruste kirjeldamiseks kui andmeid ei ole olemas. Väga tihti kasutatakse eksperthinnangute kirjeldamisel matemaatilises mudelis ja ka koormuste kirjeldamisel. Olenemata probleemist on ekspertidelt võimalik küsida näiteks "What is the one-ina-thousand minimum and maximum case for this random variable? Või sarnaseid küsimusi. Uniform Ühtlane jaotus on fundamentaalne jaotusfunktsioon sellistes olukkordades kus muud info ei ole kättesaadav kui alumine ja ülemine piir. Väga kasulik geomeetria tolerantside kirjeldamiseks. Kasutatakse ka sellistel juhtudel kui ei ole ühtegi tõendust juhuslike väärtuste jaotuse kohta kindlas intervalis. Võidakse kasutada ka juhtudel kui "lack of engineering knowledge mängib rolli.

26 Exponential The distribution is mostly used to describe timerelated effects; for example, it describes the time between independent events occurring at a constant rate. It is therefore very popular in the area of systems reliability and lifetime-related systems reliability, and it can be used for the life distribution of non-redundant systems. Typically, it is used if the lifetime is not subjected to wear-out and the failure rate is constant with time. Wear-out is usually a dominant life-limiting factor for mechanical components, which would preclude the use of the exponential distribution for mechanical parts. However in cases where preventive maintenance exchanges parts before wear-out can occur, then the exponential distribution is still useful to describe the distribution of the time until exchanging the part is necessary

27 Beta The Beta distribution is very useful for random variables that are bounded at both sides. If linear operations are performed on random variables that are all subjected to a uniform distribution then the results can usually be described by a Beta distribution. An example is if you are dealing with tolerances and assemblies, where the components are assembled and the individual tolerances of the components follow a uniform distribution. In this case the overall tolerances of the assembly are a function of adding or subtracting the geometrical extension of the individual components (a linear operation). Hence, the overall tolerances of the assembly can be described by a Beta distribution. Also, as previously mentioned, the Beta distribution can be useful for describing the scatter of individual geometrical extensions of components as well. The uniform distribution is a special case of the Beta distribution

28 Gamma The Gamma distribution is again a more time-related distribution function. For example it describes the distribution of the time required for exactly k events to occur under the assumption that the events take place at a constant rate. It is also used to describe the time to failure for a system with standby components. Weibull In engineering, the Weibull distribution is most often used for strength or strength-related lifetime parameters, and it is the standard distribution for material strength and lifetime parameters for very brittle materials (for these very brittle material the "weakest-link-theory" is applicable).

29 Monte Carlo simulatsioon Matemaatiline mudel sisaldab juhuslikke sündmusi, juhuslikke suurusi või nende arvkarakteristikuid (näiteks keskväärtust, dispersiooni). Sellise mudeli koostamist nimetatakse statistiliseks modelleerimisek laias tähenduses või Monte Carlo meetodi rakendamiseks laias tähenduses Direct Sampling Latin Hypercube Sampling

30 Monte Carlo simulatsioon The method is always applicable regardless of the physical effect modeled in a finite element analysis. It not based on assumptions related to the random output parameters that if satisfied would speed things up and if violated would invalidate the results of the probabilistic analysis. Assuming the deterministic model is correct and a very large number of simulation loops are performed, then Monte Carlo techniques always provide correct probabilistic results. Of course, it is not feasible to run an infinite number of simulation loops; therefore, the only assumption here is that the limited number of simulation loops is statistically representative and sufficient for the probabilistic results that are evaluated. This assumption can be verified using the confidence limits, which the PDS also provides. Because of the reason mentioned above, Monte Carlo Simulations are the only probabilistic methods suitable for benchmarking and validation purposes. The individual simulation loops are inherently independent; the individual simulation loops do not depend on the results of any other simulation loops. This makes Monte Carlo Simulation techniques ideal candidates for parallel processing. Direct Sampling Latin Hypercube Sampling

31 Monte Carlo simulatsioon Direct Sampling Latin Hypercube Sampling Meetodil ei ole mälu 20% kuni 40% vähem katseid