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# MECHANICAL DESIGN APPLICATIONS MECH 401

Rice University

GPA 3.92

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This 68 page Class Notes was uploaded by Shaina Lowe Jr. on Monday October 19, 2015. The Class Notes belongs to MECH 401 at Rice University taught by David McStravick in Fall. Since its upload, it has received 29 views. For similar materials see /class/224970/mech-401-rice-university in Mechanical Engineering at Rice University.

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Date Created: 10/19/15

MECH 401 Mechanical Design Applications Master Notes of Dr Marcia K O Malley Spring 2008 Dr D M McStravick Rice University Course Information 39 eillnhggfgy g5 D M McStravick a DH1064 PhD P E Prerequisites 39 39 MEB 224 a MECH 311 or CIVI 300 a Texts a Mechanical Engineering Design D Phone39 eSt39 2427 a by Budynas amp Nisbett 8th edition D dmcs riceedu Goals a Provide design skills to support MECH 407408 CI O lCe hOUFSI projects 0 Understand the application of engineering I wedneSday 1030 analysis to common machine elements 1 1 30 PM a Enhance your ability to solve practical design 39 problems using free body diagrams Mohr s I Monday 1030 circle beam analysis etc I 1130AM Syllabus General policies I 25 Homework a Late homework is not accepted a Neatness counts 5 lnclass Quiz on Stress Analysis I 25 lnclass Fundamentals Test 25 lnclass Applications Test 20 Project Background Comments I My Background Practical experience in design MECH 401 Defining course for Mech Major u Tools to make your dreams into a reality EXPERT WITNESSING All from this course TEXT Ifl could have only one reference book I Overview and introduction of design of machine elements Two primary phases of design Inventive phase creative aspect Engineering phase understanding of physical reality aspect I D makes a design unique or clever MECH 407408 n makes a design work This course will focus on 2nol aspect making our designs work Understanding of physical reality Theoretical results Empirical results Theory helps us understand physical phenomena so that we can address design at a fundamental level Theory often falls short however in describing complex phenomena so we must use empirical results Methodology Solving machine component problems a Step1 Defineunderstand a Step 2 Definesynthesize the structure ID interactions Draw diagrams as a sketch a Step 3 Analyzesolve using a Appropriate assumptions a Physical laws u Relationships u Rules u Step4 Check is the answer reasonable Homework format I Start each problem on a new page One side of sheet only I Use straightedge work neatly Known a Problem statement Schematic Given data Material properties nd a Conciser state what is to be determined Solution 1 Assumptions El El El NUDE Design decisions Equations make number substitutions last Comments when appropriate Video ENGINEERING DISASTERS a Modern Marvels Program Systems of Units Appendix lists units English SI conversion factors and abbreviations I Unit a A specified amount of a physical quantity by which through comparison another quantity of the same kind is measured a Examples Length time temperature I 2 basic systems of units a US customary footpoundsecond system fps u International System of Units SI Primary Quantities Sufficient to conceive of and measure other dimensions Examples 1 Mass 1 Length El Time El a whatwhere are the touchstones Secondary dimensions l Measured in terms of primary dimensions Examples 1 Area 1 Density 1 Velocity a Viscosity CI SI System of Units mLt Mass length and time I m kg I L m I t S F is secondaryderived unit I F is in Newtons 1 N 1 apple n F is defined a la Newton s 3rOI law I F ma 1N 1 kgms2 I US Customary Footpound fsecond fps Inchpoundsecond ips Not a consistent system of units Why fps 1 Force poundforce Derived from a pound mass m 1000 bf 1 kilopound 1 kip a For a consistent US customary system use 3rOI law a Derived unit of mass is Ibfszlft slug Statistical Considerations Dealing with uncertainty In engineering nothing is exact tolerances Introduction to reliability engineering We cannot assume that all the quantities that we utilize in failure analysis are deterministic quantities a We know their values absolutely In many cases especially in manufacturing this is NOT the case a A part dimension that is supposed to be 1 in diameter might vary between 095 and 105 inches due to variation in machining process tool wear Statistics and random variable methods enable designers to deal with variable quantities a Reliability Engineering l De nitions l Random stochastic Sample H height in inches variable a A realvalued set of numbers that result from a random process or are descriptive of a random relationship For example if I were to construct a list of everybody s height in this class n Then height H would be considered a random variable i Height example Let s say there are 25 people in this Class Construct a histogram to represent the data If we divide the of people axis by the total number of people sampled then we have u Probability density function PFD a PDF gives the probability that a random variable will have a certain value a Same shape as the histogram a it s been normalized wrt N of people Probability flil ALJIDJLU l 5125 4125 325 225 1 if 5 5 Height in ullii ill 0 60 YD ED Height in Height example If we integrate this function we get the cumulative distribution function coir Fxi u Gives the probability likelihood that a random variable will be less than or equal to a given value a For a random variable X 1 xgt00 Probability le a For a discrete random variable FXi Height in xJSxi Characterizing random variables I A random variable is not a scalar but rather a vector I In this deterministic case we can say El x 635 inches This is a scalar since it has only a single value n In the stochastic case we know that the variable x can take on many values El X 635 687 621 etc I We define the discrete random variable x to be a vector of the samples x1 x2 El x We refer to x as the variate Note in this sense a vector can be considered a collection of numbers not a quantity with direction and magnitude It is helpful to have some scalar quantities that characterize the random variable vector Direction and magnitude won t do the trick Scalar quantities to characterize X Mean N Ax1x2x 1 y nzxi N Nzl u A measure ofthe central value of a distribution Standard deviation y A 1 Nlt Ar 2 0392 x N1 1 A measure of the dispersion or distribution ofdata a Note this is most useful as a comparative measure I By itself it s not particularly useful a Somlehpeople use 1N instead of 1N1 but 1N1 typically gives better results for sma The notation for mean and standard deviation of a variate are as follows x x Example of Mean and Standard Deviation Example 201 p 963 Example 202 p 964 Reliability Engineering Cont Terminology a Population I The total set of elements in which we are interested a Sample I A randomly selected subset of the total population on which measurements are taken class vs US Population Describing the shape of a distribution Uniform a Normal 1 Log Normal u Weibull U We ll look at these Uniform distribution Simplest All elements have the same value Area equal to 1 implies fix that all samples in the given range ofx have the same value of fx where fx describes the distribution Area i Normal distribution Also called Gaussian distribution 39 M fx A 039 Rama 1 I it in A l1 M Small standard deviation 3 Large standard deviation 6 Notation Normal distribution with mean and standard deviation This IS a complete characterization x Nzc9 CDF of Normal Gaussian Distribution cannot be found in closed form Use table A 10 Example 203 p966 Generalized description of normal CDF a Note x Z P Fx Jfudu Linear Regression Obtaining a bestfit to a set of data points Linear regression when best fit is a straight line Correlation coefficient tells you how good the b fit is yl m9q b l Linear Regression Equations Equation of a line a y mx b Error equation for a point yi mi b ei Solving for eiquot2 and minimizing eiquot2 gives eqns in m amp b Allows solving for m and b of the linear regression line How good is the fit to the data Use a correlation coefficient r rmquot sxlsy r is between 11 1 or 1 is perfect correlation mquot is the linear regression slope Sx is the standard deviation of the x coordinates Sy is the standard deviation of the y coordinates Materials Must always make things out of materials Must be able to manufacture this thing Topics first introduced in Materials Science course MSCI 301 I How do we determine the properties of a material 1 Tables I How were these values determined 1 Generally via destructive testing i Material properties Listed in tables Statistical variation Values listed are minimums Best data from testinq of prototypes under intended loadinq conditions i Material parameters Parameters of interest in material selection for design 1 Strength u Stiffness PRIMARY CONCERNS a Weight 1 Toughness a Conductivity 1 Thermal o Corrosion resistance Primary parameters of interest in material selection Strength u Amount of load or weight or force a part can take before breaking or bending Stiffness u Amount of deflection or deformation for a given load Weight I All of these depend on geometry a EXTENSIVE values We would like to derive results that are independent of size geometry a INTENSIVE values Extensive vs Intensive values Extensive Intensive a Weight kg m Density kgm3 u Strength N u Yield strength or Ultimate u Stiffness Nm Strength Nmz u Modulus of Elasticity Nm2 How do we determine these values Types of quasistatic material testing a Tension o Compression 1 Bending a Torsion Tensile tests specimens What is the difference between these specimens Mild ductile steel tensile test specimen Brittle cast iron tensile test specimen Tensile testing I Best for general case I Why a Uniform loading and uniform crosssection generate uniform stress a Compression poses stability problems buckling u Torsion and bending impose nonuniform stress Other test specimens Ductile and Brittle Compression Bending Torsion Stress Strain 6 8 Curves PointA Proportional limit Point B Elastic limit Point C Yield point 1 Usually defined by permanent set of e 0002 02 offset For purposes of design we often assume ABC and call this the yield point I Slope Of OA E 6 G true accounting for AA 1 Young s Modulus u Modulus of elasticity F 1 Like stiffness B C Point F Onset of failure A G39measured FVS AX Point G G Fracture Important design considerations Sy Yield strength a It is the stress level I That will result in permanent set I At which material undergoes marked decrease in stiffness At which Hooke s Law is no longer valid E Su Ultimate strength Su 3y A BC u Stress level that will result in fracture Ductile VS Brittle Material Behavior Remember the Titanic video Temperature issue Ductile material Brittle material a Sustains significant a No significant plastic plastic deformation prior deformation before to fracture fracture su su 3y sy quot E E Ductile vs Brittle Material Behavior The only true means of determining if a material is ductile or brittle is by testing it tensile test Note The same alloy can be either ductile or brittle depending upon temperature andor how it was formed Some general indications of brittle behavior a Glass ceramic and wood a Cast ferrous alloys u Materials in extreme cold temperatures 1 Also if you can t find Sy in a handbook only Su given Fatigue testing measuring endurance Most machines are loaded cyclically a Any piece of rotating machinery Strength decreases over time u Fatigue strength depends on number of cycles and the material I How to test a Use a rotating beam 1 More often vary axial loading over time Common metals in machine design Magnesium a Specific stiffness 25 MPakgm3 u Extremely light 15 steel u Extremely flammable Aluminum very common a Specific stiffness 26 u Stiffnesstoweight and strengthtoweight comparable to steel a 13 stiffness of steel a 13 density of steel More metals Gray cast iron a Specific stiffness 15 u Decent strength a Used where casting makes sense and weight doesn t matter Gears engine blocks brake disks and drums Brass bronze u Generally soft a Good for bearings bronze More metals Titanium a Specific stiffness 26 Excellent strengthtoweight Nonmagnetic Noncorrosive implants Can be cast a Expensive Ductile cast iron u Stronger than gray cast iron u Heavyduty gears automobile door hinges U U U U More metals Stainless steel u Nonmagnetic u Much less corrosive than steel u Difficult to machine Steel a Specific stiffness 27 u Excellent fatigue properties a Good stiffnesstoweight a Better alloys have excellent strengthtoweight Chromon bicycle frames Comparison of Young s Modulus for various metals magnesium 55 448 aluminum 104 713 gray cast iron I 5 m4 brass 11mm 2 16 110 titanium 165 114 ductile cast iron 24 1 st aimless stcel 275 i190 steel 30 I n m 2o 30 D 70 X40 210 Young39s Modulus E Mpsi GPa I Alloying and Crystal Structure Question Does all steel have the same strength Does all steel have the same stiffness Strength Sy 3 depends on alloy and state I Stiffness E depends only on metal type a ie E is a property of the metal and does not change with alloy or state So What affects the strength of a metal Two primary forms u Alloying 1 Crystal state I Metal alloys 1 Adding certain elements in trace amounts to a metal can significantly change its strength 1 Since the alloying elements are present in trace amounts they don t significantly alter modulus stiffness or density Alloying Steel Primary alloying elements a Manganese Nickel Chromium Molybdenum Vanadium DUDE The alloy is identified by AISISAE or ASTM numbering system a AlSl American Iron and Steel Institute a SAE Society of Automotive Engineering u ASTM American Society for Testing and Materials Altering crystal state Crystal state of steel can be altered by heat treatment or cold working I Quenching u Heat to very high 1400 F temp and cool rather suddenly by immersion in water a Creates crystal structure called martensite which is extremely strong but brittle Ouerlched As formed More methods Tempering U u Reheat to moderate a Ouenched temperature and cool slowly u Adds ductility at the expense of Tempe ed decreased strength A5 formed Annealing u Resets the alloy to original low strength ductile state a Reheat alloy above critical temperature and allow to cool slowly More methods Normalizing u Between tempering and annealing r3 lncreasrngly I Cold working fr cold worked a Another means of increasing As formed strength at the expense of ductility Hot working u Reheating as the metal is deformed to maintain ductility Question lfyou re going to have a piece of metal machined would you rather use a cold worked or hot worked metal 0 Stress MPa 2500 2000 1 500 1000 500 AlSl 4142 as quenched AlSl 1095 hot rolled 1 AlSl 1020 hot rolled 39 01 02 03 e Strain Steel numbering systems Used to define alloying elements and carbon content 1St two digits 1 Indicate principal alloying elements I Last 2 digits 1 Indicate amount of carbon present a In 100ths of a percent Steel number systems Plain carbon steel El UUUUUU 1st digit 1 2nOI digit O No alloys other than carbon are present AISI 10051030 Lowcarbon steels AISI 10351055 Mediumcarbon steels AISI 10601085 Highcarbon steels AISI 11xx series adds sulfur Improves machinability Called freemachining steels Not considered alloys u Sulfur does not improve mechanical properties El Makes it brittle Titanic Steel number systems I Alloy steels El El Have various elements added in small quantities Improve material s Strength Hardenability Temperature resistance Corrosion resistance Other Nickel Improve strength without loss of ductility Enhances case hardenability Molybdenum In combination with nickel andor chromium Adds hardness Reduces brittleness Increases toughness Other alloys used to achieve specific properties Steel numbering systems Tool steels a Medium to high carbon alloy steels o Especially formulated to give Very high hardness Wear resistance Sufficient toughness to resist shock loads experienced in machining Stainless steels u Alloy steels with at least 10 chromium u Improved corrosion resistance over plain or alloy steels i Steel numbering systems Martensitic stainless steels El El El CI 115 to 15 Grand 015 to 12 C Magnetic Can be hardened by heat treatment Cutlery Ferritic stainless steel El DUDE El Over 16 Cr and low C content Magnetic Soft Ductile Not heat treatable Cookware Both martensitic and ferritic called 400 series i Steel numbering systems Austenitic stainless steel u 17 to 25 Cr and 10 to 20 nickel a Better corrosion resistance due to Ni 1 Nonmagnetic 1 Excellent ductility and toughness a Cannot be hardened except by cold working a 300 series 300 series very weldable 400 series less so Aluminum alloys Principal alloying elements 1 Copper 1 Manganese a Silicon El Zinc Alloys are designated by the Aluminum Association AA numbering system Aluminum alloys cont Aluminum alloys are also heattreatable as designated by the T Classification in the AA numbering system 0 Stress MPa l l I 7075 T6 2024T351 1100 x 010 e Slraln 1 005 015 Aluminum alloys Wroughtaluminum alloys u Available in wide variety of stock shapes Ibeams angles channels bars etc a 1St digit indicates principal alloying element a Hardness indicated by a suffix containing a letter and up to 3 numbers a Most commonly available and used in machine design applications I 2000 series I 6000 series i Aluminum alloys 2024 Oldest alloy 1 Among the most machinable a One of the strongest AI alloys 1 High fatigue strength a Poor weldability and formability 6061 u V dely used in structural applications 1 Excellent weldabilty a Lower fatigue strength than 2024 u Easily machined and popular for extrusion 7000 series 1 Aircraft aluminum 1 Strongest alloys I Tensile strengths of metals 4340 4140 Jawit 1 mvaTE 109s alloy 39ma mis 6150 Aluminum allo s 9255 t E mow m613T5 1050 556346 Steel alloys l E ne3 0 kpsi 50 100 0 MP5 345 690 Kpsi 0 100 20 Ch 0 700 140 mm strength tcnsnle strength Roz um mm mm 2 Ni 9 m tun 0L IEI 016 ELI O l 1 00 am 12 am 11 I 9L 981 03 91 08E EL 006 52 USSI LEE um 1 1 m L6 0L9 31 I rm m can 9i 1 OSZE LIZ OOCI 9G 0E9 Ga 968 12 091 56 859 m 0101 an 968 891 0601 9m 0m 81 09 15 99 1 I QLL 91 I 002 on 596 9E1 080i 6 9E9 301 m vol LIL 89 0an 91 0 l 90 615 98 065 911mm EZH rs om gu our 50 ERSI 9 now 018 001 59 moon or 0178 En m9 Slf ow so cool ms 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