1st Exam-Mechanical Engineering Design II PDF

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MAE$433$Mechanical$Engineering$Design$II$ 1st$Exam$ due$on$6/4/2019$ by$10:00pm$ (Total$Points:$35)$ $ $ $ Problem$1$(10$points)$ $ An$AISI$1050$cold-drawn$steel$shaft$with$the$geometry$shown$in$Fig.$1$transmits$40$hp$at$450$rpm$and$ carries$a$transverse$load$FC$=$3250$lbf$and$a$transverse$load$FD$=$4503$lbf,$with$the$corresponding$effective$ centers$ of$ the$ gears$ for$ force$ transmission$ at$ points$ C$ and$ D,$ respectively.$ The$ keyseats$ are$ cut$ with$ standard$endmills$(r/d$=$1/48).$$ $ a.$Determine$the$fatigue$factor$of$safety$at$the$keyway$at$point$ D.$Use$the$DE-Goodman$criterion.$You$may$ assume$that$the$torque$is$steady,$ and$the$bending$moment$ is$fully$reversed.$Use$a$strength$reliability$of$ 90%$(5$points)$ $ b.$The$shaft$is$simply$supported$in$cylindrical$roller$bearings$at$A'and$B.$If$the$largest$allowable$slope$at$ the$bearings$is$0.001$rad,$what$is$the$factor$of$safety$guarding$against$damaging$distortion?$(3$points)$ $ c.$Calculate$the$shaft's$first$critical$speed$assuming$that$the$shaft$is$simply$supported$and$has$a$uniform$ diameter$of$2.2$in.$(2$points)$ $

$ $$$Figure$1$(all$dimensions$shown$are$in$inches)$

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$ Problem$2$(15$points)$ $

A$double$reduction$helical$gearset$is$shown$in$Fig.$2.$Pinion$2$is$the$driver$and$receives$a$torque$of$1200$ lbf·in$from$its$shaft$in$the$direction$shown$in$Fig.$2.$Pinion$2$has$a$normal$pressure$angle$of$20°,$a$normal$ diametral$pitch$of$8$teeth/in,$14$teeth,$and$is$cut$right-handed$with$a$helix$angle$of$30°.$The$mating$gear$ 3$has$36$teeth.$Gear$4$has$a$normal$pressure$angle$of$20°,$15$teeth,$a$normal$diametral$pitch$of$5$teeth/in,$ and$is$cut$left-handed$with$a$helix$angle$of$15°.$Mating$gear$5$has$45$teeth.$The$teeth$are$standard$AGMA$ full-depth$profiles.$Find$the$magnitude$and$direction$of$the$reaction$forces$exerted$by$the$bearings$E'and$ F'on$shaft$c,$assuming$that$bearing$E'can$take$only$a$radial$load$while$bearing$F'is$mounted$to$take$both$ radial$and$thrust$loads.$

$ Figure$2$(all$dimensions$shown$are$in$inches)$

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Problem$3$(10$points)$ A$gear$reduction$unit$uses$the$countershaft$shown$in$Fig.$3.$Spur$gear$A$receives$power$from$another$gear$ with$the$transmitted$force$ FA'=$ 900$lbf$applied$at$a$20°$pressure$angle.$The$power$is$transmitted$on$the$ countershaft,$which$rotates$at$1000$rpm,$and$is$delivered$through$spur$gear$B$on$the$output$shaft.'' ' Use$a$gear$ratio$ mg'=$3,$a$quality$number$Qv'=$9$(commercial$unit),$a$diametral$pitch$Pd'='6$teeth/in,$a$face$ width$of$4$times$the$circular$pitch,$and$Grade$2$ steel$through-hardened$to$a$Brinell$hardness$of$350.$The$ desired$life$is$50000$hours$with$a$95$percent$reliability.$Calculate$the$AGMA$bending$and$contact$stresses$ and$the$corresponding$factors$of$safety$for$pinion$B.$ $ $

Figure$3$

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