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# Instrumentation, Measurements, and Statistics M E 345

Penn State

GPA 3.79

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This 0 page Class Notes was uploaded by Chester Goldner III on Sunday November 1, 2015. The Class Notes belongs to M E 345 at Pennsylvania State University taught by John Cimbala in Fall. Since its upload, it has received 22 views. For similar materials see /class/233070/m-e-345-pennsylvania-state-university in Mechanical Engineering at Pennsylvania State University.

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Date Created: 11/01/15

M E 345 Fall 2009 Professor John M Cimbala Today we will Do some review example problems 7 RSM Review the pdf module Hypothesis Testjn Do some example problems 7 hypothesis testing Example Experimental design using RSM Given Cory uses RSM to increase the performance speed of a photocopier machine He changes three parameters simultaneously but in no particular pattern He takes enough data to determine the direction of steepest ascent Here are the variables a the tension on a belt drive 7 varied from 400 to 550 N b the volume ow rate of cooling air supplm from 18 to 45 Lmin c the voltage supplied to a component 7 varied from 20 to 35 V To do Calculate the range of coded variable x2 N 4 corresponding to physical variable b Solution uh x w M 39 TquotL 1 19 Example Response surface methodology Given ant to optimize the performance maximum power P in units of horsepower of a gasoline engine for a car We vary three parameters simultaneously and measure the engine s output power for each run with a dynamometer a spark plug gap inches b spark timing degrees before TDC 7 top dead center c fuelair mixture of turns of the set screw that controls fuelair mixture a To do Calculate the coded variable x for the second row of data Solution Jim 9 I h m l E b 9 c 1 Lit9 lJ 7 LAD la Ql Tt39 1 116 b To do Determine the direction of steepest ascent Solution Solution done in Excel 7 see file on course website Example Response surface methodology Given We want to optimize the efficiency 77 of a machine where 7 depends on three parameters a b and c We run several cases varying a b and 0 simultaneously around the current operating point a b c 77 15 4 02 715 16 6 05 806 a 1 15 5 03 744 W 14 6 04 677 6 qu 16 5 02 803 14 4 05 646 a To do Some questions to be asked in class My 6 cold vaL o u39 u u n 9 Iquot b To do Determine the direction of steepest ascent I used Excel for convenience Solution 0 Convert to coded variables x1 x2 and x3 0 Use regression analysis to determine the direction of steepest ascent I get 222 6604 1576 0505 1m 114 W m ow M mama 0x1 0x2 0x3 0 Pick one of the increments Axl sz or Ax3 and then calculate39t39he other two I picked Ax 05 Mukr 2 5 5X1 0 LLO 10 a 39h nn lq 1y Ax 1m x 39 x 1 33A 0 Convert these coded variable increments back to physical variables Aa Ab and Ac 4L o a 501 AX itquot 2 165 3 Les 7 7 Ac ool 1 Round off for convenience and march in the direction of steepest ascent varying a b and 0 simultaneously 0 II reach a maximum 77 of 920 at a 21 b 55 and c 0125 Example Hypothesis testing Given A manufacturer claims that a strut can hold at least 100 kg before failing We perform 10 tests to failure and record the load THIS wokmwc Tenn 05 n 10 number of data points in the sample f 21014 kg sample mean 1h J A Vi59 0quot S 23 kg sample standard deviation WE39TNW Mfume TEST To do Determine if we should accept or reject the manufacturer s claim Solution 0 This isa twosided t test The null hypothesis M39 le 61439quot K L3 SW v The si dte of the null hypothesis Luv Md mmo l d 914110 Mu xgtjlo h I The alternatlve hypothe51s 3M gt1 NW A our J The critical t statistic 1474 t 17 mvr t W X m The pValue Q kc P l33 c hhut kw J H m 5 0439 644 TNT mull 3 has 1 061315 Interpretatron and conclu51on FR Tu n Y Vbu u TL am 0 the hit iV39Vh ut Kl m l ha 1 IN hgfo39YNN I 4mg Y H 93 o L 395 quotl339lo fwdAM hna l Tlne MM wf mun u w hm In LN l W 39 am H370 Halal lu r hl mtn r 44w 39J wt an 0 4m 3537 wn lqi l lm39 11 man39 AM U Sum 3amp7 gt35 wt auqk lnc mon d5 9 M m 35339 Filok lM u Min clad J he M E 345 Fall 2009 Professor John M Cimbala Today we will Do some review example problems 7 RSM Review the pdf module Hypothesis Testjn Do some example problems 7 hypothesis testing Example Experimental design using RSM Given Cory uses RSM to increase the performance speed of a photocopier machine He changes three parameters simultaneously but in no particular pattern He takes enough data to determine the direction of steepest ascent Here are the variables a the tension on a belt drive 7 varied from 400 to 550 N b the volume ow rate of cooling air supplm from 18 to 45 Lmin c the voltage supplied to a component 7 varied from 20 to 35 V To do Calculate the range of coded variable x2 N 4 corresponding to physical variable b Solution uh x w M 39 TquotL 1 19 Example Response surface methodology Given ant to optimize the performance maximum power P in units of horsepower of a gasoline engine for a car We vary three parameters simultaneously and measure the engine s output power for each run with a dynamometer a spark plug gap inches b spark timing degrees before TDC 7 top dead center c fuelair mixture of turns of the set screw that controls fuelair mixture a To do Calculate the coded variable x for the second row of data Solution Jim 9 I h m l E b 9 c 1 Lit9 lJ 7 LAD la Ql Tt39 1 116 b To do Determine the direction of steepest ascent Solution Solution done in Excel 7 see file on course website Example Response surface methodology Given We want to optimize the efficiency 77 of a machine where 7 depends on three parameters a b and c We run several cases varying a b and 0 simultaneously around the current operating point a b c 77 15 4 02 715 16 6 05 806 a 1 15 5 03 744 W 14 6 04 677 6 qu 16 5 02 803 14 4 05 646 a To do Some questions to be asked in class My 6 cold vaL o u39 u u n 9 Iquot b To do Determine the direction of steepest ascent I used Excel for convenience Solution 0 Convert to coded variables x1 x2 and x3 0 Use regression analysis to determine the direction of steepest ascent I get 222 6604 1576 0505 1m 114 W m ow M mama 0x1 0x2 0x3 0 Pick one of the increments Axl sz or Ax3 and then calculate39t39he other two I picked Ax 05 Mukr 2 5 5X1 0 LLO 10 a 39h nn lq 1y Ax 1m x 39 x 1 33A 0 Convert these coded variable increments back to physical variables Aa Ab and Ac 4L o a 501 AX itquot 2 165 3 Les 7 7 Ac ool 1 Round off for convenience and march in the direction of steepest ascent varying a b and 0 simultaneously 0 II reach a maximum 77 of 920 at a 21 b 55 and c 0125 Example Hypothesis testing Given A manufacturer claims that a strut can hold at least 100 kg before failing We perform 10 tests to failure and record the load THIS wokmwc Tenn 05 n 10 number of data points in the sample f 21014 kg sample mean 1h J A Vi59 0quot S 23 kg sample standard deviation WE39TNW Mfume TEST To do Determine if we should accept or reject the manufacturer s claim Solution 0 This isa twosided t test The null hypothesis M39 le 61439quot K L3 SW v The si dte of the null hypothesis Luv Md mmo l d 914110 Mu xgtjlo h I The alternatlve hypothe51s 3M gt1 NW A our J The critical t statistic 1474 t 17 mvr t W X m The pValue Q kc P l33 c hhut kw J H m 5 0439 644 TNT mull 3 has 1 061315 Interpretatron and conclu51on FR Tu n Y Vbu u TL am 0 the hit iV39Vh ut Kl m l ha 1 IN hgfo39YNN I 4mg Y H 93 o L 395 quotl339lo fwdAM hna l Tlne MM wf mun u w hm In LN l W 39 am H370 Halal lu r hl mtn r 44w 39J wt an 0 4m 3537 wn lqi l lm39 11 man39 AM U Sum 3amp7 gt35 wt auqk lnc mon d5 9 M m 35339 Filok lM u Min clad J he

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