Material Selection for Design in Mechanical Engineering - Prof. David M. Mcstravick, Study notes of Mechanical Engineering

Download Material Selection for Design in Mechanical Engineering - Prof. David M. Mcstravick and more Study notes Mechanical Engineering in PDF only on Docsity! MECH 401 Mechanical Design Applications Master Notes of Dr. Marcia K. O’Malley Spring 2008 Dr. D. M. McStravick Rice University Course Information Meeting time T-Th 8:00 – 9:15 DH 1064 Prerequisites MECH 311 or CIVI 300 Texts Mechanical Engineering Design by Budynas & Nisbett (8th edition) Goals Provide design skills to support MECH 407/408 projects Understand the application of engineering analysis to common machine elements Enhance your ability to solve practical design problems using free body diagrams, Mohr’s circle, beam analysis, etc. D. M. McStravick, PhD, P.E. MEB 224 Phone: est. 2427 dmcs@rice.edu Office hours: Wednesday 10:30 -11:30 PM Monday 10:30 – 11:30 AM Overview and introduction of design of machine elements Two primary phases of design 1 Inventive phase – creative aspect 2 Engineering phase – understanding of physical reality aspect 1 makes a design unique or clever (MECH 407/408) 2 makes a design work This course will focus on 2nd 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 Step 1 Define/understand Step 2 Define/synthesize the structure ID interactions Draw diagrams (as a sketch) Step 3 Analyze/solve using: Appropriate assumptions Physical laws Relationships Rules Step 4 Check – is the answer reasonable? Homework format Start each problem on a new page One side of sheet only Use straight-edge, work neatly Known: Problem statement Schematic Given data Material properties Find: Concisely state what is to be determined Solution: Assumptions Design decisions Equations (make number substitutions last) Comments (when appropriate) Video -- a ENGINEERING DISASTERS a Modern Marvels Program Systems of Units Appendix lists units (English, SI), conversion factors, and abbreviations Unit A specified amount of a physical quantity by which through comparison another quantity of the same kind is measured Examples? Length, time, temperature 2 basic systems of units U.S. customary foot-pound-second system (fps) International System of Units (SI) SI System of Units (mLt) Mass, length, and time m – kg L – m t – s F is secondary/derived unit F is in Newtons: 1 N ~ 1 apple (**) F is defined a la Newton’s 3rd law F = ma 1 N = 1 kg·m/s2 U.S. Customary Foot-pound (f)-second (fps) Inch-pound-second (ips) Not a consistent system of units (Why?) fps: Force – pound-force (Derived from a pound mass) 1000 lbf = 1 kilopound = 1 kip For a consistent US customary system use 3rd law Derived unit of mass is lbf-s2/ft (slug) Statistical Considerations Dealing with uncertainty In engineering nothing is exact (tolerances) 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 Probability density function (PFD) PDF gives the probability that a random variable will have a certain value Same shape as the histogram (it’s been normalized w.r.t. N) Height example If we integrate this “function”, we get the cumulative distribution function (cdf) Gives the probability (likelihood) that a random variable will be less than or equal to a given value For a random variable x, For a discrete random variable, 1)(lim = ∞→ xF x ( ) ∑ ≤ = ij xx ji xfxF )( ( )ixF Characterizing random variables A random variable is not a scalar, but rather a vector In this deterministic case, we can say x = 63.5 inches This is a scalar, since it has only a single value In the stochastic case, we know that the variable x can take on many values x = 63.5, 68.7, 62.1, etc We define the discrete random variable x to be a vector of the samples x1, x2, … , xn 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! ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = nx x . . . 1 x Reliability Engineering, Cont. Terminology Population The total set of elements in which we are interested Sample A randomly selected subset of the total population on which measurements are taken (class vs. US Population) Describing the shape of a distribution Uniform Normal Log Normal Weibull We’ll look at these Uniform distribution Simplest All elements have the same value Area equal to 1 implies that all samples in the given range of x have the same value of f(x), where f(x) describes the distribution Normal distribution Also called Gaussian distribution Small standard deviation (σ)^ Large standard deviation (σ)^ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −− = 2 ˆ ˆ 2 1 2ˆ 1)( σ μ πσ x exf Linear Regression Equations Equation of a line y = mx + b Error equation for a point yi = mi + b + ei Solving for ei^2 and minimizing ei^2 gives eqns. in m & b Allows solving for m and b of the linear regression line iii bmxy ε++= How good is the fit to the data? Use a correlation coefficient r r=m^ sx/sy r is between -1-+1 +1 or -1 is perfect correlation m^ 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) How do we determine the properties of a material? Tables How were these values determined? Generally via destructive testing Material properties Listed in tables Statistical variation Values listed are minimums Best data from testing of prototypes under intended loading conditions Extensive vs. Intensive values Extensive Weight (kg) Strength (N) Stiffness (N/m) Intensive Density (kg/m3) Yield strength or Ultimate Strength (N/m2) Modulus of Elasticity (N/m2) How do we determine these values? Types of quasistatic material testing Tension Compression Bending Torsion Tensile tests specimens Mild ductile steel tensile test specimen Brittle cast iron tensile test specimen What is the difference between these specimens? Stress-Strain (σ-ε) Curves Point A – Proportional limit Point B – Elastic limit Point C – Yield point Usually defined by permanent set of ε = 0.002 (0.2% offset) For purposes of design, we often assume A~B~C, and call this the yield point Slope of O-A = E Young’s Modulus Modulus of elasticity Like stiffness Point F – Onset of failure Point G, G’ - Fracture G – true (accounting for ΔA) εO A B C G’ – measured (F vs. Δx) F E σ Important design considerations Sy = Yield strength It is the stress level… That will result in permanent set At which material undergoes marked decrease in stiffness At which Hooke’s Law is no longer valid Su = Ultimate strength Stress level that will result in fracture εO A, B, C F E σ Sy Su Ductile vs. Brittle Material Behavior Ductile material Sustains significant plastic deformation prior to fracture Brittle material No significant plastic deformation before fracture ε O E σ Sy Su ε O E σ Sy Su Remember the Titanic video -- Temperature issue Common metals in machine design Magnesium Specific stiffness ~ 25 MPa/(kg/m3) Extremely light (~1/5 steel) Extremely flammable Aluminum (very common) Specific stiffness ~ 26 Stiffness-to-weight and strength-to-weight comparable to steel 1/3 stiffness of steel 1/3 density of steel More metals… Gray cast iron Specific stiffness ~ 15 Decent strength Used where casting makes sense and weight doesn’t matter Gears, engine blocks, brake disks and drums Brass, bronze Generally soft Good for bearings (bronze) More metals… Titanium Specific stiffness ~ 26 Excellent strength-to-weight Non-magnetic Non-corrosive (implants) Can be cast Expensive Ductile cast iron Stronger than gray cast iron Heavy-duty gears, automobile door hinges Alloying and Crystal Structure Question… Does all steel have the same strength? Does all steel have the same stiffness? Strength (Sy, Su) depends on alloy and state Stiffness (E) depends only on metal type i.e., 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 – Alloying Crystal state Metal alloys Adding certain elements in trace amounts to a metal can significantly change its strength Since the alloying elements are present in trace amounts, they don’t significantly alter modulus (stiffness) or density Alloying Steel – Primary alloying elements: Manganese Nickel Chromium Molybdenum Vanadium The alloy is identified by AISI/SAE or ASTM numbering system AISI – American Iron and Steel Institute SAE – Society of Automotive Engineering ASTM – American Society for Testing and Materials More methods… Normalizing Between tempering and annealing Cold working Another means of increasing strength at the expense of ductility Hot working Reheating as the metal is deformed to maintain ductility Question If you’re going to have a piece of metal machined, would you rather use a cold worked or hot worked metal? Steel numbering systems Used to define alloying elements and carbon content 1st two digits Indicate principal alloying elements Last 2 digits Indicate amount of carbon present In 100ths of a percent Steel numbering systems Tool steels Medium- to high- carbon alloy steels Especially formulated to give: Very high hardness Wear resistance Sufficient toughness to resist shock loads experienced in machining Stainless steels Alloy steels with at least 10% chromium Improved corrosion resistance over plain or alloy steels Steel numbering systems Martensitic stainless steels 11.5 to 15% Cr and 0.15 to 1.2% C Magnetic Can be hardened by heat treatment Cutlery Ferritic stainless steel Over 16% Cr and low C content Magnetic Soft Ductile Not heat treatable Cookware Both martensitic and ferritic called 400 series Steel numbering systems Austenitic stainless steel 17 to 25% Cr and 10 to 20% nickel Better corrosion resistance (due to Ni) Nonmagnetic Excellent ductility and toughness Cannot be hardened except by cold working 300 series 300 series very weldable 400 series less so Aluminum alloys Wrought-aluminum alloys Available in wide variety of stock shapes I-beams, angles, channels, bars, etc 1st digit indicates principal alloying element Hardness indicated by a suffix containing a letter and up to 3 numbers Most commonly available and used in machine design applications: 2000 series 6000 series Aluminum alloys 2024 Oldest alloy Among the most machinable One of the strongest Al alloys High fatigue strength Poor weldability and formability 6061 Widely used in structural applications Excellent weldabilty Lower fatigue strength than 2024 Easily machined and popular for extrusion 7000 series Aircraft aluminum Strongest alloys Tensile strengths of metals alloy sea SE ont za 6063-6 Ez 1OD-HI8 A] 1100-0 J ; ot Okpsi 50 100 OMPa 345 690 tensile strength Aluminum alloys Steel alloys ==> AISI # 4340 4140 1095 [= 6150 Fe 9255 [= 3140 1050 1040 1030 1118 1020 1015 Kpsi 0 100 = 20€ GPa 0 700 140¢ tensile strength