Seongwoo Woo Reliability Design of Mechanical Systems A Guide for Mechanical and Civil Engineers Reliability Design of Mechanical Systems Seongwoo Woo Reliability Design of Mechanical Systems A Guide for Mechanical and Civil Engineers 123 SeongwooWoo Reliability Association of Korea Seoul Korea (Republicof) ISBN978-3-319-50828-3 ISBN978-3-319-50829-0 (eBook) DOI 10.1007/978-3-319-50829-0 LibraryofCongressControlNumber:2016960023 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface In the beginning of the twentieth century, new sophisticated mechanical systems such as bridges, rockets, automobiles, airplanes, and space shuttles were designed and built for people to live comfortable lives through the engineering design pro- cesses. Typical design process can be broadly summarized as (1) define the prob- lems,(2)developtheproduct–prototype,designandtesting,(3)production.Dueto thefrequentoccurrenceofdisastersfornewproducts,productreliabilityhasbecome one of increasingly important factors (to consider) because of cost, competition, publicdemand,andadaptationofnewtechnology.Themosteffectivewaytoprotect the reliability disaster is to develop the reliability-embedded design process includingitsmethodologyinparallelwiththeestablisheddesignprocess. Asproductswithmultiplemodulesrequirehigherperformanceandmaterialcost reduction,thereliabilitydesignofproducthasbecomemorecomplexandincreases the risk of product failure. The studies of reliability engineering have been deep- enedtopreventthereliabilitydisastersofthepastcentury.Eventhoughtherearea large number of concepts, theory, and texts on reliability, an up-to-date book for emphasizing the new methodology of reliability design is still required to prevent the reliability disasters of the mechanical/civil system. From the standpoint of economics, company will decrease the operation profit forafailureinitsexpectedproduct lifetimebecauseofProductLiabilityLawinthe global market. All products from tires to electric components are fabricated from the structure (or materials) that will tend to degrade or break down abruptly by randomloads.Themechanicalsystemcaneventuallyfractureduetofatiguewhich canresultfromcyclicalstresses(orloads).Whenproductsaresubjectedtorandom loads,theystartthevoidinmaterial(ordesigndefects),propagate,andruptureit.If failure for a new product happens, theproduct may nolonger meet theestablished specificationsforproperproductfunctionality.Toavoidproductfailureinlifetime, product should be designed to robustly withstand a variety of loads. The main objectives of writing this book are focused on explaining the devel- opment necessity of the reliability-embedded design process and its methodology. v vi Preface As reliability methodology, we will suggest the new parametric accelerated life testing(ALT)thatmeetsthosemarketrequirements—higherperformance,material cost reduction, and higher reliability in field. The reliability-embedded design process consists of parametric ALT plan, failure mechanism and design, acceler- ation factor, sample size equation, and the parametric ALT. It produces the relia- bility quantitative test specifications (RQ) in accordance with the reliability target. Aparametric ALT method therefore will assessthereliabilityof product subjected to repetitive stresses. Based on the market data, parametric ALT plan will set up the reliability target ofproductanditsmodules.Mechanicalsysteminfieldsubjectedtoloadsarisehow to design product for the failure mechanisms—fatigue and fracture. The accumu- lated damage in system like palmer miner rule can be represented at the time-to-failure model. The acceleration factor with a new effort concept (or loads) was derived from a generalized life-stress failure model. So the new sample size equation with the acceleration factor enabled the parametric ALT to quickly evaluate the expected lifetime of product. This parametric ALT should help an engineer to uncover the missing design parameters affecting reliability during the design process of new product. Consequently,ifappliedinthe establisheddesignprocess,newparametricALT helpscompaniestoimprovenewproductreliabilityandavoidtherecallsofproduct failures in field. As the improper design parameters in the design phase are iden- tifiedbythisreliabilitydesignmethod,theproductwill improve thereliabilitythat willbe measuredbytheincreaseinlifetime,LB,andthereductioninfailurerate,k. Product will meet the reliability target in industry. This book will help to prevent the reliability disaster through the parametric ALT. We also provide a lot of parametricALTexamplesthatareeffectivetobeunderstoodinthemechanical/civil field. This book is composed of nine chapters. Chapter 1 presents the present aspect andneedofreliabilityengineeringintheadvanceofmoderntechnology.Chapter2 reviews the historical reliability disasters and their root cause within the past cen- tury. It will explain the significance of reliability assessment, and its methodology needtopreventreliabilitydisastersinthedesignprocess.Chapter3willexplainthe most important fundamental definitions of statistics and probability theory, the mathematical essentials of reliability engineering, and the most significant aspects of reliability engineering developed within the past century. It will help one to understandthebasicconceptsofreliabilitymethodologiesthatwillbediscussedin Chap.8.Chapter4throughChap.6presentloadanalysis,stressconcept,andabrief overview of the typical reliability failure mechanism of product—fatigues and fractures.Chapter7willpresentthe fundamentalconceptsoftheparametricALTin product that will be the core of this book. Chapter 8 will also present case studies that are useful in a variety of engineering areas. Chapter 9 will cover the future aspectsofparametric ALTinmechanicalproduct thatwillbedevelopedassystem engineering. Preface vii This book is intended to introduce the prerequisite concepts of the parametric ALT for senior level undergraduate and graduate students, professional engineers, college and university level lecturers, researchers, and design managers of the engineering system. We hope this noble methodology explained in this book will help to prevent the reliability disasters of new product in field. The authors would alsoliketothankSpringerforthepublishingofthiswork,especiallyMayraCastro, Springer DE. With their help, this book has been published. Seoul, Korea (Republic of) Seongwoo Woo Contents 1 Introduction to Reliability Design of Mechanical/Civil System . .... 1 1.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 1 2 Reliability Disasters and Its Assessment Significance.... ..... .... 7 2.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 7 2.2 Reliability Disasters . ..... .... .... .... .... .... ..... .... 10 2.2.1 Versailles Rail Accident in 1842... .... .... ..... .... 12 2.2.2 Tacoma Narrows Bridge in 1940 .. .... .... ..... .... 13 2.2.3 De Havilland DH 106 Comet in 1953... .... ..... .... 14 2.2.4 GCompanyandMCompanyRotaryCompressorRecall in 1981. .... ..... .... .... .... .... .... ..... .... 15 2.2.5 Firestone and Ford Tire in 2000... .... .... ..... .... 17 2.2.6 Toshiba Satellite Notebook and Battery Overheating Problem in 2007... .... .... .... .... .... ..... .... 18 2.2.7 Toyota Motor Recalls in 2009 .... .... .... ..... .... 19 2.3 Development of Reliability Methodologies in History ..... .... 20 2.3.1 In the Early of 20s Century—Starting Reliability Studies.. .... .... .... .... .... ..... .... 20 2.3.2 In the World War II—New Electronics Failure in Military... ..... .... .... .... .... .... ..... .... 24 2.3.3 In the End of World War II and 1950s—Starting the Reliability Engineering ... .... .... .... ..... .... 26 2.3.4 In the 1960s and Present: Mature of Reliability Methodology—Physics of Failure (PoF). .... ..... .... 30 References.. .... .... .... ..... .... .... .... .... .... ..... .... 34 3 Modern Definitions in Reliability Engineering . .... .... ..... .... 35 3.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 35 3.1.1 Bathtub Curve..... .... .... .... .... .... ..... .... 36 3.2 Fundamentals in Probability Theory.. .... .... .... ..... .... 37 3.2.1 Probability... ..... .... .... .... .... .... ..... .... 38 3.2.2 Probability Distributions . .... .... .... .... ..... .... 40 ix x Contents 3.3 Reliability Lifetime Metrics .... .... .... .... .... ..... .... 44 3.3.1 Mean Time to Failure (MTTF).... .... .... ..... .... 44 3.3.2 Mean Time Between Failure (MTBF)... .... ..... .... 45 3.3.3 Mean Time to Repair (MTTR) .... .... .... ..... .... 46 3.3.4 BX% Life... ..... .... .... .... .... .... ..... .... 46 3.3.5 The Inadequacy of the MTTF (or MTBF) and the Alternative Metric BX Life. .... .... ..... .... 47 3.4 Statistical Distributions.... .... .... .... .... .... ..... .... 49 3.4.1 Poisson Distributions.... .... .... .... .... ..... .... 49 3.4.2 Exponential Distributions .... .... .... .... ..... .... 51 3.5 Weibull Distributions and Its Applications. .... .... ..... .... 52 3.5.1 Introduction.. ..... .... .... .... .... .... ..... .... 52 3.5.2 Shape Parameters b. .... .... .... .... .... ..... .... 54 3.5.3 Confidence Interval. .... .... .... .... .... ..... .... 54 3.5.4 A Plotting Method on Weibull Probability Paper ... .... 55 3.5.5 Probability Plotting for the Weibull Distribution.... .... 56 Reference .. .... .... .... ..... .... .... .... .... .... ..... .... 59 4 Failure Mechanics, Design, and Reliability Testing . .... ..... .... 61 4.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 61 4.2 Failure Mechanics and Designs . .... .... .... .... ..... .... 63 4.2.1 Product Design––Intended Functions ... .... ..... .... 64 4.2.2 Specified Design Lifetime.... .... .... .... ..... .... 66 4.2.3 Dimensional Differences Between Quality Defects and Failures.. ..... .... .... .... .... .... ..... .... 67 4.2.4 Classification of Failures. .... .... .... .... ..... .... 68 4.3 Failure Mode and Effect Analysis (FMEA) .... .... ..... .... 70 4.3.1 Introduction.. ..... .... .... .... .... .... ..... .... 70 4.3.2 Types of FMEA ... .... .... .... .... .... ..... .... 72 4.3.3 System-Level FMEA.... .... .... .... .... ..... .... 72 4.3.4 Design-Level FMEA.... .... .... .... .... ..... .... 73 4.3.5 Process-Level FMEA ... .... .... .... .... ..... .... 73 4.3.6 Steps for Performing FMEA.. .... .... .... ..... .... 74 4.4 Fault Tree Analysis (FTA). .... .... .... .... .... ..... .... 79 4.4.1 Concept of FTA ... .... .... .... .... .... ..... .... 79 4.4.2 Reliability Evaluation of Standard Configuration ... .... 83 4.5 Robust Design (or Taguchi Methods). .... .... .... ..... .... 85 4.5.1 A Specific Loss Function .... .... .... .... ..... .... 86 4.5.2 Robust Design Process .. .... .... .... .... ..... .... 89 4.5.3 Parameter (Measure) Design.. .... .... .... ..... .... 90 4.5.4 Tolerance Design .. .... .... .... .... .... ..... .... 90 4.5.5 A Parameter Diagram (P-Diagram). .... .... ..... .... 91 4.5.6 Taguchi’s Design of Experiment (DOE). .... ..... .... 91 4.5.7 Inefficiencies of Taguchi’s Designs. .... .... ..... .... 93 Contents xi 4.6 Reliability Testing .. ..... .... .... .... .... .... ..... .... 94 4.6.1 Introduction.. ..... .... .... .... .... .... ..... .... 94 4.6.2 Maximum Likelihood Estimation .. .... .... ..... .... 95 4.6.3 Time-to-Failure Models.. .... .... .... .... ..... .... 97 4.6.4 Reliability Testing.. .... .... .... .... .... ..... .... 100 5 Load Analysis .. .... .... ..... .... .... .... .... .... ..... .... 107 5.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 107 5.2 Modeling of Mechanical System .... .... .... .... ..... .... 108 5.2.1 Introduction.. ..... .... .... .... .... .... ..... .... 108 5.2.2 D’Alembert’s Modeling for Automobile. .... ..... .... 109 5.3 Bond Graph Modeling .... .... .... .... .... .... ..... .... 112 5.3.1 Introduction.. ..... .... .... .... .... .... ..... .... 112 5.3.2 Basic Elements, Energy Relations, and Causality of Bond Graph . .... .... .... ..... .... 113 5.3.3 Case Study: Hydrostatic Transmission (HST) in Seaborne Winch . .... .... .... .... .... ..... .... 118 5.3.4 Case Study: Failure Analysis and Redesign of a Helix Upper Dispenser... .... .... .... ..... .... 124 5.4 Load Spectrum and Rain-Flow Counting .. .... .... ..... .... 127 5.4.1 Introduction.. ..... .... .... .... .... .... ..... .... 127 5.4.2 Rain-Flow Counting .... .... .... .... .... ..... .... 129 5.4.3 Goodman Relation . .... .... .... .... .... ..... .... 131 5.4.4 Palmgren-Miner’s Law for Cumulative Damage.... .... 132 References.. .... .... .... ..... .... .... .... .... .... ..... .... 137 6 Mechanical System Failures.... .... .... .... .... .... ..... .... 139 6.1 Introduction ... .... ..... .... .... .... .... .... ..... .... 139 6.2 Mechanism of Slip.. ..... .... .... .... .... .... ..... .... 142 6.3 Facture Failure . .... ..... .... .... .... .... .... ..... .... 144 6.4 Fatigue Failure . .... ..... .... .... .... .... .... ..... .... 146 6.4.1 Introduction.. ..... .... .... .... .... .... ..... .... 146 6.4.2 Type of Fatigue Loading. .... .... .... .... ..... .... 147 6.4.3 Stress Concentration at Crack Tip.. .... .... ..... .... 150 6.4.4 Crack Propagation and Fracture Toughness... ..... .... 152 6.4.5 Crack Growth Rates .... .... .... .... .... ..... .... 153 6.4.6 Ductile–Brittle Transition Temperature (DBTT) .... .... 155 6.4.7 Fatigue Analysis... .... .... .... .... .... ..... .... 157 6.5 Stress–Strength Analysis... .... .... .... .... .... ..... .... 159 6.6 Failure Analysis .... ..... .... .... .... .... .... ..... .... 160 6.6.1 Introduction.. ..... .... .... .... .... .... ..... .... 160 6.6.2 Procedure of Failure Analysis. .... .... .... ..... .... 162 6.6.3 Case Study: PAS (Photo Angle Sensor) in Automobile..... .... .... .... .... .... ..... .... 164 6.6.4 Fracture Faces of Product Subjected to a Variety of Loads in Fields.... .... .... ..... .... 167 References.. .... .... .... ..... .... .... .... .... .... ..... .... 169