Applications of force vibration. Rotating unbalance Base excitation Vibration measurement devices

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1 Applicaios of foce viaio Roaig ualace Base exciaio Viaio easuee devices

2 Roaig ualace 1 Roaig ualace: Viaio caused y iegulaiies i he disiuio of he ass i he oaig copoe.

3 Roaig ualace 0 FBD 1 FBD x x 0 e 0 F x F kx c x FBD 1 FBD x x F 0 0 x F cx kx x 0 x cx kx 0 x x esi e si x cx kx e si 0

4 Roaig ualace 3 x cx kx e si 0 0e x x x si z, Ze x I[ z ] z z z 0e e Z 0e 0e 1 H 0e x H si θ ; θ a 1 1

5 Roaig ualace 4 0e x H si θ X si θ H X e 0

6 Exaple: washig achie A odel of a washig achie is illusaed i he figue. A udle of we clohes fo a ass of 10 kg 0 ad causes a oaig ualace. The oaig ass id 0 kg icludig 0 ad he diaee of he washe aske e is 50 c. Assue ha he spi cycle oaes a 300 p. Le k e 1000 N/ ad a Calculae he foce asied o he sides of he washig achie. The quaiies, 0 e ad ae all fixed y he pevious desig. Desig he isolaio syse so ha he foce asied o he side of he washig achie is less ha 100 N.

7 Exaple: Ualace oo A elecic oo has a ecceic ass of 1 kg 10% of he oal ass ad is se o wo ideical spigs k 3. N/. The oo us a 1750 p, ad he ass ecceiciy is 100 fo he cee. The spigs ae oued 50 apa wih he oo shaf i he cee. Neglec dapig ad deeie he apliude of veical viaio.

8 Base exciaio io Exaples Sesiive equipe placed o viaig foudaio A auooive suspesio syse Buildigs sueced o eahquakes

9 Base exciaio 1 EOM x c x y k x y 0 Assupio: y he ase oves haoically cos FBD 1s ehod: supeposiio x cx kx c si k cos 1s haoic ipu d haoic ipu x p x p 1 x p

10 Base exciaio d ehod: Fequecy espose ehod x cx kx cy ky x x x y y y cos z, Ze Re[ e ] x Re[ z ] Su. io EOM o chage o coplex fo Coplex EOM z z z e e Ze e Z 1 1 ;

11 Base exciaio 3 ] Re[ z x Ze z H Z 1 1 e H Z θ θ θ e H e e H z H 1 1 cos θ H x cos θ X x H X ;

12 Displacee asissiiliy 1 Disp. asissiiliy Oupu disp. Ipu disp. X H 1 1 Disp. Tasissiiy specifies how oio is asied fo he ase o he ass a vaious divig fequecy.

13 Displacee asissiiliy Icease Icease 1. 0 D.T D.T. lage 3. < D.T. > 1 Lage, sall D.T. D.T. 1 > D.T. < 1 Lage, lage D.T. X H 1 1

14 Foce asissiiliy 1 The foce asied o he ass is doe hough he spig ad dape. 0 y x k y x c x y x c y x k F Fo EOM x y x k y x c F cos θ H x Fo cos θ H x cos cos θ θ F H F T

15 Foce asissiiliy cos cos θ θ F H F T H F T 1 1 k F T F T k F T F.T. ells how uch foce is asied fo he ase o he ass a vaious divig fequecies

16 Foce asissiiliy 3 F T k 1 1

17 Exaple Base exciaio y 0.01si v v k/h ad/s Deeie he effec of speed o he apliude of displacee of he auooile as well as he effec of he value of he ca s ass. Assue ha he suspesio syse povides a equivale siffess of N/ ad dapig of N.s/.

18 Exaple Base exciaio Deeie he apliude of veical viaio of he spig-oued aile as i avels a a velociy of 5 k/h ove he oad whose coou ay e expessed y a siusoid. The ass of he aile is 500 kg ad ha of he wheels aloe ay e egleced. Duig loadig, each 75 kg added o he load caused he aile o sag 3 o is spigs. Assue ha he wheels ae i coac wih he oad a all ies ad eglec dapig. A wha ciical speed v c is he viaio of he aile geaes? [J. L. Meia & L. G. Kaige 8/71]

19 Measuee devices 1 y : Acual viaio of he ieesed oec x : Viaio of he ass iside a easuee device Measued value : w x y FBD EOM x c x y k x y 0 w cw kw y Assupio: he ase oves haoically y cos

20 Measuee devices w cw kw y w w w y y cos z Ze, Re[ e ] w Re[ z ] Su. io EOM o chage o coplex fo Coplex EOM z z z e Ze e Z 1 Fequecy espose H o T

21 Measuee devices 3 θ θ e T e e T Ze z cos cos ] Re[ θ θ W T z w 1 T W e T T Z θ 1 Acual viaio Measued viaio Displacee Tasissiiliy Diffe fo Displacee asissiiliy of ase exciaio

22 Seisoee Is used o easue displacee of viaio The value of T appoaches uiy whe is lage Seisoee egio > 3 Low aual fequecy lage ass o sall k Ca easue i a age fo 10 o 500 Hz wih is aual fequecy of 1 o 5 Hz T W Iceasig Rage fo seisoee

23 Acceleoee 1 Is used o easue acceleaio of viaio Use piezoelecic effec: Foce acceleaio Volage Quaz o ceaic cysals 1 T W 1 1 A W y 1 A W y

24 Acceleoee T appoaches uiy whe is sall acceleoee egio Acceleoee age is wides whe dapig aio < < 0.6 High aual fequecy sall ass ad lage k Ca easue i a age fo 0 o ove 10 khz wih is aual fequecy of 30 o 50 khz ad weigh less ha 0 g. Iceasig W A 1 y

25 Exaple : Acceleoee A acceleoee has a suspeded ass of 0.01 kg wih a daped aual fequecy of viaio of 150 Hz. Whe oued o a egie udegoig a acceleaio of 1 g a a opeaig speed of 6000 p, he acceleaio is ecoded as 9.5 /s y he isue. Fid he dapig cosa ad he spig siffess of he acceleoee. [Sigiesu S. Rao, Ex 10.3]

FBD of SDOF Base Excitation. 2.4 Base Excitation. Particular Solution (sine term) SDOF Base Excitation (cont) F=-(-)-(-)= 2ζω ωf

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