2024Homework231ASolutions

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School

University of Maryland, College Park *

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Course

427

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by BrigadierRiver8411

Homework # 1 Name ________ Answer Key ____________________ ENME 427 Due: Friday, February 9, 2024 Problem 1: Identify the failure site, failure mode, and failure mechanism for the potential failures cited in the recall notices below. Recall # 1 (9 pts) Piaggio Group Americas. Inc. (Piaggio) is recalling certain 2020 Moto Guzzi V 85 TT motorcycles. The footrest mounting pin retaining clip may break, allowing the pin to disconnect and the footrest to fall off the motorcycle. A footrest that falls off while the motorcycle is in motion may become a road hazard, increasing the risk of a crash. Piaggio will notify owners, and dealers will inspect the retaining rings on all four footrests. If any of the clips are found to be defective, the dealer will replace the retaining clips on all four footrest pins, free of charge. Failure Site _ Footrest Mounting Pin Retaining Clip_ Failure Mode _ Footrest Falls Off _ Failure Mechanism _Fatigue and/or Fracture__ Recall # 2 (9 pts) Fujian Wanda Automobile Glass Industry (Wanda) is recalling certain aftermarket Replacement Windshields sold for use in 2014-2018 Toyota Highlander vehicles. The windshields have an attached wire harness that water may leak into, possibly causing damage to the vehicle’s Engine Control Module (ECM). The ECM damage may result in the engine stalling, increasing the risk of a crash. Wanda will notify owners and service centers will replace the windshields, and inspect the ECM for damage, having it replaced, if necessary, free of charge. Failure Site ___Engine Control Module____ Failure Mode ___Engine Stalling_______ Failure Mechanism ___Corrosion/Moisture Induced Failure_____

Recall # 3 (9 pts) Subaru of America, Inc (Subaru) is recalling certain 2018 Subara Legacy and Outback vehicles. Due to a software error, the low fuel warning light may not illuminate at the intended remaining fuel level and the miles-to-empty display may incorrectly indicate a positive number despite the tank being empty. The inaccurate fuel display may cause a driver to unexpectedly run out of fuel and the vehicle to stall, increasing the risk of a crash. Subaru will notify owners, and dealers will reprogram the combination meter software, free of charge. Failure Site ___(Software) Fuel Warning Light, Miles to Empty Display___ Failure Mode ___(Fuel Warning Light, Miles to Empty Display) Run out of Fuel_____ Failure Mechanism ___Software Error____ Recall # 4 (9 pts) Volkswagen Group of America, Inc. (Volkswagen) is recalling certain 2012-2015 Passat, 2011-2014 Golf A6, and 2011-2013 Audi A3 diesel vehicles, thought to have been previously repaired under one of the Takata air bag recalls. The driver's side air bag inflator may explode due to propellant degradation occurring after longterm exposure to high absolute humidity, high temperatures, and high temperature cycling. An inflator explosion may result in sharp metal fragments striking the driver or other occupants resulting in serious injury or death. Volkswagen will notify owners, and dealers will replace the driver's side air bag inflators, free of charge. Failure Site ___ The driver's side air bag inflator ___ Failure Mode __Explosion/Release of Metal Fragments_ Failure Mechanism ____Propellant Degradation in High Temperature,Humidity___

Problem 2: The hazard rate function for a product is given by h(t) = 0.01t for t ≥ 0. The failure rate is in failures per year. a) Find an expression for the reliability function for the time to failure of the product. (4 pts) R(t) = exp -(0.005t 2 ) b) Find the MTTF or expected value for the life of the product. (4 pts) exp -(0.005 t 2 )dt =0.5(  /0.005) 0.5 = 12.53 years

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Problem 3: Using the data from the paper clip experiment for the 45 ⁰ bending (see Table I below), use Microsoft Excel to calculate the values and the plot the following (8 pts for each curve). Note group the data into groups of 5 cycles (e.g. 1-5, 6-10, 11-15, 16-20, etc.) before calculating. a. The life characteristic curve b. The reliability curve c. The unreliability curve d. The probability density function e. The hazard rate f. What type of failure (infant mortality, random, or wearout failure) is indicated by the hazard rate data for the paper clips and why. (4 pts)? Wearout failure because it shows increasing hazard rate with time. g. Plot the hazard rate curve for the samples that underwent 90 ⁰ bending and compare it to the hazard rate curve for those that underwent the 45 ⁰ bending. Describe the change in the shape and location of the curve. (4 pts) The hazard rate curve for the higher stress level (90 ⁰ bending) is higher and shorter in lifetime than the one for the lower stress level (45 ⁰ bending) h. If the paper clips were subjected to 3 cycles of 90 ⁰ bending before bending at 60 ⁰ , what is the average number of cycles of 60 ⁰ bending to be expected then before failure? (4 pts)? n 1 /N f1 + n 2 /N f2 = 1 n/38.3 + 3/19.5 = 1 n/38.3 = 0.846  n = 32.4 (or 32) i. Draw an S-N curve for the average time to failure for the 45 ⁰ , 60 ⁰ , and 90 ⁰ bending results. Using this curve, what would you estimate to be the average time to failure if the paper clips were subjected to 30 ⁰ bending? (4 pts) Using the trend line formula: Nf = 17,544 (bending angle) -1.507 N f for 30 ⁰ bending is 104 cycles

Table I: Paper Clip Bending Data from Class BEND ANGLE Cycles at 45 ⁰ Cycles at 90 ⁰ Cycles at 60 ⁰ 46 23 41 76 23 42 53 20 55 97 18 32 42 20 37 49 15 56 41 42 25 45 17 28 45 17 50 41 18 35 43 16 32 62 19 48 50 16 33 61 14 49 77 13 41 73 24 38 46 20 34 43 15 33 46 26 36 71 15 21 44 19 39 22 82 18 MEAN 55.30435 19.56522 38.3 STD DEV 15.90033 5.81472 9.274158 S-N Curve for Problem 3i. y = 17544x -1.507 R² = 0.9952 0 10 20 30 40 50 60 0 20 40 60 80 100 Cycles to Failure

Curves a. The life characteristic curve b. The reliability curve 0 1 2 3 4 5 6 7 8 9 1 to 5 6 to 10 11 to 15 16 to 20 21 to 25 26 to 30 31 to 35 36 to 40 41 to 45 46 to 50 51 to 55 56 to 60 61 to 65 66 to 70 71 to 75 76 to 80 81 to 85 86 to 90 91 to 95 96 to 100 Life Characteristic Curve 0 0.2 0.4 0.6 0.8 1 1.2 1 to 5 6 to 10 11 to 15 16 to 20 21 to 25 26 to 30 31 to 35 36 to 40 41 to 45 46 to 50 51 to 55 56 to 60 61 to 65 66 to 70 71 to 75 76 to 80 81 to 85 86 to 90 91 to 95 96 to 100 Reliability

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c. The unreliability curve d. The probability density function 0 0.2 0.4 0.6 0.8 1 1.2 1 to 5 6 to 10 11 to 15 16 to 20 21 to 25 26 to 30 31 to 35 36 to 40 41 to 45 46 to 50 51 to 55 56 to 60 61 to 65 66 to 70 71 to 75 76 to 80 81 to 85 86 to 90 91 to 95 96 to 100 Unreliability 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 1 to 5 6 to 10 11 to 15 16 to 20 21 to 25 26 to 30 31 to 35 36 to 40 41 to 45 46 to 50 51 to 55 56 to 60 61 to 65 66 to 70 71 to 75 76 to 80 81 to 85 86 to 90 91 to 95 96 to 100 PDF

e. The hazard rate 0 0.05 0.1 0.15 0.2 0.25 1 to 5 6 to 10 11 to 15 16 to 20 21 to 25 26 to 30 31 to 35 36 to 40 41 to 45 46 to 50 51 to 55 56 to 60 61 to 65 66 to 70 71 to 75 76 to 80 81 to 85 86 to 90 91 to 95 96 to 100 Hazard Rate