ENME I. The rotating system tested in this experiment can cause SERIOUS HARM if not properly operated. Therefore:
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- Barnard Garrison
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1 ENME599 LAB #5: Dynamics f a Single Rtr System!"#$%&"'()#'"(*%+$(",%(-+./*+"/*0(&'"*#2"/&()+&#+-(3*/*("/(",%(-+.('%''/&4((5,%(-+.(*%3/*"(',/#-$(.%(%",%*("03%$(/*( 2-%+*-0(6*""%&(+&$('#.)""%$(&(",%(7/--/6&8(-+.('%''/&4(9:&%(*%3/*"(3%*(8*/#3;4(5,%(2/)3#"%*(2/$%'(',/#-$(.%( +33%&$%$(&(",%(*%3/*"4( OBJECTIVES. Familiarizing with the experimental setup fr investigating Rtr Dynamics, 2. Evaluatin f the errr mtin f the shaft, 3. Develping better analytical and intuitive understanding f the rtr dynamics, SAFETY and instrument prtectin: I. The rtating system tested in this experiment can cause SERIOUS HARM if nt prperly perated. Therefre: Befre turning the system n fr the first time WAIT FOR the FINAL INSPECTION f the setup by the instructr, Keep the GUARDS LOWERED AT ALL TIMES when the mtr is rtating, DO NOT TOUCH any rtating parts, STOP the rtatin IMMEDIATELY after finishing each partial test, If excessive vibratins ccur during the test, STOP the rtatin IMMEDIATELY by putting the MODE switch (bttm right) n the cntrl unit t the STOPPED psitin, Tuck in shirts and tie back lng hair II. Setting the ESSENTIAL CONTROLS t SAFE psitins: Bently-Nevada (B-N) Rtr Cntrller :. Set the MODE 3-psitin tggle switch (bttm right) t STOPPED, 2. Turn the MAX SPEED SETPOINT knb (tp middle) t 000 rev/min (max CCW), 3. Set the Ramp Switch (bttm middle) t DOWN, 4. Turn the RPM RATE knb (tp right) t 5,000 REV/MIN, i.e., the maximum clckwise, AGENDA. Familiarizatin with critical speed and single rtr balancing (TA will g ver the fllwing vectr analysis) 2. Familiarizatin with vectr analysis (bring a calculatr t analyze magnitudes and phases) U Unbalanced mass O C r O+C U* C 3. Demnstratin / Setup Instructins 4. Balancing f the Bently-Nevada experimental rtr kit, Calibratin mass Intrductin and Setup Part : Recrding infrmatin abut the physical prperties f the tested system:
2 ENME599 2 Measure:. The span f the shaft between the bearings (psitin the rtr in the midspan), < ' = 2. The disk diameter, 2= $ = 4. The disk thickness, 5 $ = 5. The diameter f the hles fr balancing screws ; the number f these hles ; the angular spacing f these hles 6. The distance f balancing hles frm the center f the rtr Part 2: Preparing instruments fr the test: The rtr. Remve balancing masses (if any left) in the threaded hles parallel t the axis f rtatin, near the rtr s periphery Tektrnix scpe: Nte: When yu use the scillscpe fr measurements, yu need t cmpensate the DC ffset! Bently-Nevada (B-N) Rtr Cntrller :. Make sure the cntrls are set as shwn in the sectin Setting the ESSENTIAL CONTROLS t SAFE psitins (SAFETY II - previus page), NOTE: The Cartesian crdinate system XYZ is defined by psitins f the prximity sensrs. The axes are hrizntal (X) and vertical (Y) in the plane perpendicular t the axis f the shaft. The Z axis is the same as the shaft axis, directed frm the disk(s) tward the mtr. Psitive angular rtatin is CCW. In the fllwing step yu will be asked t sketch a diagram f the setup. Bently-Nevada (B-N) Rtr Kit :. The fllwing picture shws the entire experimental setup - mre pictures are dwnladable frm the web-page f this Lab include them in future reprts, if apprpriate, and discuss relevant details. Figure The experimental setup in Vibratins Lab.
3 ENME599 3 Part 3: Identifying the reference marker signal n the scpe and setting the angular psitin f the rtr: Bently-Nevada (B-N) Rtr Cntrller :. Turn pwer ON (the rcker switch is n the back f the B-N cntrl unit). Make sure that the shaft des nt rtate (3-psitin tggle switch MODE is in STOPPED psitin), 2. Cnnect utput marked K OUT f the B-N Sensr Amplifiers t Ch3 input n the scpe. Use a BNC-BNC cable. 3. Lcate the reference slt n the flexible cupling between the mtr and rtr shaft (rtate the shaft manually until yu see the slt; hld the shaft ONLY at the smth end OPPOSITE t the mtr), 4. Psitin the shaft manually such that the reference slt faces the crrespnding hrizntal prximity sensr lcated clse t the mtr-shaft cupling (there are tw prximity sensrs near the cupling; ne f them is psitined against the sltted disc, the ther against the cylindrical prtin f the cupling with the reference slt). 5. Rtate the shaft and inspect the vltage level in Ch3. Observe that as the reference slt passes in frnt f the sensr, this level shifts dwn. Find the accurate angular shaft psitin that crrespnds t this transitin, which will cincide with the falling edge f the marker signal n the scpe. This psitin has t be determined fr the cunterclckwise (CCW) directin f the shaft rtatin (lking frm the mtr twards the free end f the shaft). 6. After lsening setscrews f the rtr (disk), rtate the disk, while hlding the shaft statinary, t such angular psitin n the shaft that the falling edge f the marker signal cincides with the 0 engraved line n the disk passing thrugh the X axis (hrizntal) f the assumed crdinate system. Evenly tightened bth setscrews in this new rtr rientatin. 7. Make sure that the guards are lwered. 8. Set the MODE tggle switch (bttm right) t SLOW ROLL. The disk will rtate. 9. Recrd the rtatinal speed (in rpm) f the shaft at Slw rll displayed n the B-N Rtr Cntrller &!= = rpm 0. Cmpute the crrespnding perid f rtatin: 5!= = ms Desktp cmputer: Cmputer Channels Spreadsheet File Oscillscpe Channels Descriptin Clumn Time 0 Clumn 2 Displacement Sensr (X) Clumn 3 2 Displacement Sensr (Y) 2 Clumn 4 3 Reference. Labview prgrams will be used: a. mnitring and data acquisitin sftware; b. balancing sftware prgram; and ptinal c. mass splitting prgram is als available 2. Fllw the technician s instructins. Experimental Tasks (Steps fr a single rtr balancing) A. Identifying shaft run-ut vectr (R) at lw rpm (centrifugal frces are negligible). Discuss surces f run-ut n the rtr Cnversin factr (sensitivity f sensrs): 2. Cpy the sensitivity cefficients f the Bently-Nevada prximity sensrs in SI units. The catalgue value is 200 mv/mil ; mil = 0.00 inch, a. in SI units this crrespnds t: ' 3 =... m/mv In this lab we are nt interested what the abslute distance frm this reference psitin is, but nly what the variatins f this distance are. 3. Set slw rll mde. Recrd the rpm. &!= =... rpm. Inspect the wavefrm in Ch (X axis). Recall that at this lw rpm the centrifugal frce is negligible. The wavefrm represents the shaft runut (errr mtin). 4. Estimate an amplitude f the runut (wavefrm in Ch), = /, and phase shift f the runut, r (see Nte belw)
4 ENME599 4 Nte: When yu use the scillscpe fr measurements, yu need t cmpensate the DC ffset! Nte: On the scpe... = / [mv] = / [m] 5!= [ms]!= [ms] r [rad] Amplitude Phase shift... use Cursrs -> Vltage mde... use Cursrs -> Time mde Recall that r = SR T SR 360 = SR T SR 2[rad] 5. Express the runut, *9";, as a vectr numerical values r = =.. rad r r ( t) R e i( ) n the cmplex plane, using the btained experimental r (t). Nte: use r in radians 6. Enable Channel 2 (push respective buttn Menu ), set sensitivity t the same level as in Ch. Display the signals in Ch2 vs Ch (select the X-Y display frm) t btain the rbit f the shaft s center. 7. Estimate the sampling frequency (sample rate) t be used fr capturing the signal. Assume that 360 samples per ne revlutin f the disk will be sufficient t apprximate the measured wavefrm. 7 ' &!= 360 =... samples per secnd (check with the instructr) Set the fllwing data acquisitin parameters in the Labview data acquisitin prgram: a. sample rate: fund in step 7 b. sample size: 3600 (i.e., 0 revlutins) 9. Save sample signals fr the reprt. Open the saved data with Excel (if available n the lab cmputer) and validate that they are nt crrupted. Nte that the signal acquisitin prgram used saves the time reference signal in secnds, and the wavefrms (X and Y shaft displacements, and the reference marker) in vlts. When prcessing the data fr the reprt, cnvert the recrded signals X and Y t micrmeters (the units f the marker signal are nt imprtant in this experiment). 0. Stp the shaft rtatin: put the MODE switch (bttm right) n the cntrl unit t the STOPPED psitin.. Use the Balancing Calculatr Labview prgram t estimate the magnitude and phase. r (t). B. Identifying the riginal unbalance vectr (O) at 75% f the critical speed Nte : Mst f rtrs, as manufactured, shw sme unbalance. Our test rtrs are n exceptin. Nte 2: Yu will spin the rtrs at high speeds. Please be VERY CAREFUL, FULLY CONCENTRATE n the experiment and ASK the instructr t verify the setup at this stage.. Set the Ramp Switch n B-N Cntrller t Up, set the MODE switch t RAMP 2. Increase the mtr rpm with the MAX SPEED SETPOINT knb until yu reach the critical speed (strng vibratins). Recrd this value and next reduce the rtatinal speed t 75% f the critical speed (this will assure that we d nt attempt balancing at the resnance f the system) & 2*( = rpm ; & >( = 0.75 & 2*( = rpm 3. After reaching the desirable speed, inspect the wavefrm in Ch. It represents the shaft displacement in the X directin. Adjust the sensitivity in Ch. What basic math functin describes best this wavefrm? Answer here:.. 4. Estimate an amplitude f the wavefrm in Ch,? /, and its phase shift, > (see Nte belw)
5 ENME599 5 Nte: On the scpe...? / [mv]? / [m] 5 / [ms] / [ms] / [rad] Amplitude Phase shift... use Cursrs -> Vltage mde... use Cursrs -> Time mde 5. Express the U, in the vectr frm (t). O ( ) ( t i ) X e 6. Estimate the sampling frequency (sample rate) t be used fr capturing the signal with 0_userStatin_Rtr.vi virtual LabView virtual instrument. Assume that 360 samples per ne revlutin f the disk will be sufficient t apprximate the measured wavefrm. n n =... rpm ; 7 ' =... samples per secnd (check with the instructr) 7. Set the fllwing data acquisitin parameters: a. sample rate: fund in step 6 b. sample size: 3600 (i.e., 0 revlutins) 8. Save sample signals fr the reprt. Open the saved data with Excel and validate that they are nt crrupted. 9. Stp the shaft rtatin: put the MODE switch (bttm right) n the cntrl unit t the STOPPED psitin. D nt change the MAX SPEED SETPOINT knb setting. 0. Use the Balancing Calculatr Labview prgram t estimate the magnitude and phase. (t). C. Calculating the actual unbalance vectr (U). Express the runut and x-displacement vectrs in the crdinates rtating with the disk (i.e., with the rtatinal speed > ; assume that the runut des nt change with this speed). Intrduce psitin vectrs R = / % ( * ) and O i( ) ( t ) X e ; R... and O =... ; 2. Find the true unbalance vectr as U = O - R. Find the directinal angle f this vectr (use vectr algebra and a calculatr); the unbalance is smewhere n a line with this angle that passes thrugh the center f the disk. U = O - R = D. Getting the unbalance psitin vectr with a calibratin mass at 75% f the critical speed. Make sure the rtr is fully stpped, 2. Place the calibratin mass (C-mass) g at a lcatin apprximately +90 r 90 degrees (whichever clser t 0 ) frm the identified unbalance psitin vectr. Since we have aligned the disk with the psitin marker (Ch3) and we cmputed the x-displacement with reference t this marker, we knw at which angle n the disk t place the C- mass. Nte the with CCW rtatin f the mtr the angular psitins engraved n the disk crrespnd t NEGATIVE angles (d nt hesitate t ask if yu have any questin regarding these angles). 3. Ask the instructr t validate yur selectin fr the C-mass psitin, 4. Set rpm t & /( = 0.75 & 2*( = rpm 5. Repeat steps 3-0 in Part B (n need t answer any questins) ; enter results int the fllwing table (Step 7). 6. After cllecting needed data stp the mtr by setting the MODE switch t STOPPED ; d nt change the MAX SPEED SETPOINT knb setting.
6 ENME Estimate an amplitude f the wavefrm in Ch,? 2, and its phase shift, 2 (ptinal) Nte: On the scpe...? /2 [mv]? /2 [m] 5 /2 [ms] /2 [ms] /2 [rad] Amplitude... use Cursrs -> Vltage mde Phase shift... use Cursrs -> Time mde i( ) 8. Express the C, in the vectr frm O C X c c e using the Labview prgram. O C. E. Calculating the calibratin vectr (C). Cmpute the psitin vectr f the change, C, caused by the C-mass; C = O C - O =.. Nte: We d nt subtract the shaft runut errr estimated at slw rll, since the vectrs O C and O are identically distrted by this errr. 2. Check if the directin f the cmputed vectr C is in gd agreement with the lcatin f the C-mass (errr n mre than ±5 degrees). F. Cmputing the Crrective mass (CR-mass) and its lcatin Nte: Please be VERY CAREFUL, since a severe unbalance may ccur if yu incrrectly cmpute and/r place the CRmass.. Remve the C-mass frm the rtr 2. Cmpute the CR-mass and its lcatin. Nte that the CR-mass has t generate the centrifugal frce equal in value t the frce caused by the riginal unbalance U. The directin f the crrective frce has t ppsite t the U vectr. Therefre the angular psitin f the crrective mass is A= = U -80 =.. (the sign f U is imprtant! Remember that the angle engraved n the rtr is negative. Fr example if U is 45, A= = U -80 => place the CR-mass at the 225 mark Since the C-mass f g generates a frce whse crrespnding x-displacement vectr C has knwn magnitude, we can calibrate the riginal unknwn unbalance mass (f the entire rtr) int an equivalent smaller mass lcated at the same radius as the C-mass. This equivalent mass is btained as m U U mcal g = C C u* 3. It is mst likely that the CR-mass can nt be placed at the required angular psitin (threaded hles are 22.5 spaced). Additinal cmputatins, referred t as the mass splitting are therefre necessary. Fr example, assume the required CR-mass is ) #B =.2g lcated at the angle 90. The nearest threaded hles are at 80 and As shwn in Fig. 2, the crrective masses ) C and ) D are such that m u * m m2. Expressing these vectrs in plar crdinates we btain m u* e i90 m e m i202.5 m e i80 cs m 2 2 m [cs i sin 202.5] m cs80 i[ m sin m 2 2 sin80] [cs80 i sin80] which in turn gives a system f tw simultaneus algebraic equatins t be slved fr ) C and ) D ) cs202.5) 2 cs 80 ) $ cs90 ) sin202.5) 2 sin80) $ sin90 Nte: It wuld be easy t generalize the abve equatins t be applicable t arbitrary angles f the invlved vectrs, but it is nt essential t perfrming this experiment. Als Nte: There is a mass splitting prgram available at yur lab statin
7 ENME Summarize the btained results in the fllwing table E #B =( ) C =( ) D =( #B =( C =( D =( Im{...} m Psitive angl md =.2 ei*90 [g] m Re{ Figure 2 Example f the mass splitting. G. Re-measure and cmpare the deflectin befre and after the balancing. Fllw the step B t remeasure the vectr O new with the balancing mass. 2. Cmpare between O and O new.
8 ENME599 8 Lab Assignment Due beginning f the next labratry. Lab Assignment must be TYPED. Append Matlab r Mathematica cdes (if used). Make sure yu put the crrect UNITS fr all yur analysis.. Sketch a simplified diagram f the investigated system; the fllwing figure prvides a framewrk fr this sketch. Y prximity sensr Rtr Y Bearing Shaft X prximit sensr Disc X Bearing Z Mtr The span f the shaft between the bearings (psitin the rtr in the midspan), < ' = The disk diameter, 2= $ = The disk thickness, 5 $ = The diameter f the hles fr balancing screws ; the number f these hles ; the angular spacing f these hles The distance f balancing hles frm the center f the rtr 2. Pltting in the rectangular crdinates X-Y the errr mtin (rbit) f the tested shaft (vectr R). Finding accurate values f its amplitude and phase shift. Discuss the results btained between using the scillscpe vs. the Labview prgram. 3. Pltting in the rectangular crdinates X-Y the errr mtin (rbit) f the tested shaft (vectr O). Finding accurate values f its amplitude and phase shift. Discuss the results btained between using the scillscpe vs. the Labview prgram. 4. Pltting in the rectangular crdinates X-Y the errr mtin (rbit) f the tested shaft (vectr O+C). Finding accurate values f its amplitude and phase shift. 5. Calculate the cunter balance mass, Mu*. 6. Plt the vectr diagrams based n the experimental prcedure (use the fllwing figure as the reference). 7. Discuss the results (/2 page) by cmparing the O and O new. Discuss surces f errrs. Axes are in mv Im{...} Psitive angl Re{
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