Mobility

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Mobility Mobility... ... A New Approach A pproach to Measuring Actual Forces Forces in Machinery  Machiner y  By A l an F ri edman dman & Gl Gl enn Whi te, te, When most of us began learning about vibration analysis in the context of machinery fault diagnosis, we l earned arned about how the vari vari ous faul ts appea appeared red i n the vi brati bration on spectra. spectra. Perha P erhaps ps we we w ere g gii ven som some e guidelines on what vibration amplitudes were acceptable and which were excessive for certain types of  machines. We most likely were left with the impression that when it comes to vibration in machinery, l ess is bette better and more is w orse. orse. U nfor nfortunate tunatell y, it i s not as si si mpl mple e as as it i t se seem ems. s. For example, in Figure 1 are two identical vertical machines wi th an equal equal am amount ount of i mbal mbal ance on the fans at the top. top. L ooking at at just the horizontal horizontal di re rection, ction, w e would expect xpect to see the same vibration levels at 1x, or the running speed of the machine. Now, if we take one of these machines and firmly attach it to a wall as shown at the left in the figure, what happens to its vibration levels at 1x (the shaft rate)? The assumption would be that it woul wou l d go down. A s the machi machi ne is now l ess ess free to vibrate one would expect it would vibrate less. Then let’s say that the machine that is not attached to the wall has vibration levels at 1x that exceed an “industry standard” and the one atta attached ched to the wall now has level level s l ow enough to not exceed xceed thatt al tha al arm level level . Whi ch one wi l l we bal bal ance? nce? Well, obviously the one that exceeds the alarm. But realistical cal l y, whi ch machi machi ne is going going to fai fai l fi rst? We know from f rom the way we set up this scenario that both machines contain the same amount of imbalance even though we can’t tell that now from the vibration data! You see; it’s not as simple as it seems!

Fi gure 1 - Two identical vertical machines with wi th an equal equal amount of i mbalance mbalance on on the  fans at the top. T he ri right ght one i s mounted  mounted  to a wall.

Lets think about it. In the machine not attached to the wall, the forces of imbalance are causing it to vibrate – generating motion. The machine that is attached to the wall is now less free to vibrate; in other words, it is less flexible or stiffer. So where are those forces of imbalance going? The force from the i mba mball ance must must be b born orne e by by the bea beari ri ngs on its i ts way to the wal l . Because there a are re more for forces ces on th the e be bea ari ng ngs s i n the atta attache ched d machi machi ne ne,, thi s one wi l l fail fi rst. Our i nstinct to repa repaii r the ma machi chi ne wi th hi gher her vibration levels would have been misguided! I n a second second exampl xampl e, w e have have a horizontal hori zontal machi machi ne wi th an i mb mbalance alance and and we take vibration mea measurements in the vertical and horizontal directions. You might think that we should have the same amplitude i n both ve v erti cal and h hori ori zontal axes axes at at 1x si nce the imba imball ance force shoul should d be the s sam ame e in thes these e two axes. axes. In re rea al i ty, ty, the two pe pea aks wi l l most most l i ke kell y not  be  be of the same amplitude! Which peak do we cite when we want to tell someone the machine needs to be balanced; the bigger one? Do we tell them it is onl y i mba mbal ance nced d i n the horizontal di re rection? ction? T he rea real question question i s why w i l l we se see e differe different nt vi bra bration tion l evels i n the th ese two axes? axes?

 The Concept of Mobility  If a machine is less free to vibrate, this would increase the force in the bearings. When we are talking about “freedom to vibrate” what we are really talking about is “stiffness”... a way of describing a structure’s structure’ s free freedom dom to vi brate brate or freedom freedom to move. move. What W hat I woul d l i ke to sug sugg gest iis s that if we do n not ot know a machine’s stiffness, we don’t know all the forces it is experiencing... and we don’t have informati on about the damage damage bei bei ng done. If I f w e don’t k know now anythi ng about about the dama damage ge bei bei ng done to the machine, why are we bothering to collect vibration data? Isn’t that the whole purpose of vibration analysis? Mobility is defined as the inverse of stiffness. If stiffness is the reluctance of a structure to respond to a force, mobility is the ease with which a structure responds to a force. High mobility means easy to move, and high stiffness means hard to move. I like to use mobility because it turns out that it is easier to measure in practice.

 

How Machines Behave – Some Definitions M achines are are compl compl ex structures, structures, a and nd they do not behave beha ve li ke a si simpl mpl e mass mass when wh en exposed exposed to a force. M achi nes al al ways have na natural tural frequenci frequenci es, es, someti sometime mes s cal cal l ed resonance resonances, s, wh where ere di fferent parts of the structure structure are moving in different directions. These resonances occur at m many any frequenci es. es. IIn n ge general, neral, i t i s easy easy to set set a machi ma chi ne vibra vi brati ting ng is you force it i t at a resonance resonance frequency. This is analogous to pushing a child in a swing.  T he chi chill d-swi ng syste system m is i s in i n resonance resonance when you push p ush i t at the sa same me frequency frequency i s i ts naturall naturall y vi bra brate tes. s.  T he re resona sonance nce frequency frequency i s a all so where the mobil i ty i s relatively high... it is easy to move the machine with onl y a li ttle bit of force. From thi s, you ma may y have guesse uessed d that the mobi mobi l i ty of a m machine achine i s not constant when measured at different frequencies, and this is absolutely true! Figure 2 below shows a typical curve of  mobility versus frequency. Note that the curve is anything but uniform.

Fig ure 2 - A typical curve of of mo mobili bili ty versu versuss  fr  freq equency. uency. N ote that the curve cur ve i s anythi ng but  uniform.

Mobility and Force For those interested in the mathematics involved, mobility can be expressed as follows: M =V/ F (1) M obil i ty equal qual s Vi bration bration di vi ded ded by Force (M =V/ F). T he vi bra bration tion part part of the equa quation tion can be in either acceleration or velocity and it is frequency related. In other words, unless we are only interested in mobility (or force) at one frequency, we will need to enter the vibration levels at every frequency in a range and our mobility and force will look like spectra (see Figure 3). Phase information will be included in these calculations as well, but we can leave that for another paper. Let’s return to the first equation, M=V/F. Since the force is really what we are interested in, we should turn the th e eq equation uation around to be, F=V F=V / M . IIff I am not wri ti ng thi thi s just to was waste te your ti me, me, i t se seem ems s logical that there there must b be e a way to calcu calcull at ate e the mobil mobil i ty. Otherwi se, se, w we e re reall all y haven’t sa saii d much! L et ets s l ook at that now. We wi l l al so need need a cal cal i brate brated d hamme hammerr or a shake shakerr (F i gure 4). If we use the cal cal i bra brate ted d hamm hammer er to hi t the machi ma chi ne, we wi l l have a m mea easured sured inpu i nputt force and a mea measured output v vii bra brati ti on across a freque frequency ncy range. Our analyzer will be able to take care of the division and display the mobility spectrum.

cali brated brated hammer, hammer, we wi ll have h ave a Fig ure 3 - We will need to enter the vibration levels at every  Fig ure 4 - I f we use the cali measured me asured i nput force f orce and and a measur measured ed output output vi bration  fr  freq equency uency in a range and and our mobi mobi li ty and and force will look  across a fre fr equency quency range. Our Ou r analyze analyzerr wi will ll perf perform orm the the li ke spectra. spectra. divis di visii on and and di splay the mobili mobili ty spe spectrum. ctrum.

 

Using Mobility to Calculate Force Let’s assume at this point that we have calculated the mobility of the machine (in all three axis if possible) at every test position and have saved this information. Now when we go to collect vibration on thi s ma machi ne, we simpl y ask ask the anal anal yzer to di vi de the the vibration by the mobil i ty spe spectrum ctrum (F= (F=V V / M ). What we wi l l now have i s a force spectrum. spectrum. A nd, even even thoug thou gh there a are re a as s yet yet no i ndustry standa standards rds that tel tel l us wha wh at forces are are al al l owable, we have a much much better better i dea of the l evel of dam dama agi ng forces in the machine. If we make the assumption that the mobility of the machine will not change dramatically over time (unless the mounting is changed or the machine is overhauled), we should only have to calculate the mobility once and simply store this information in our analyzer or analysis software for future use.

Some Data   T he ta table ble bel bel ow conta con taii ns som some e experi experime ments nts we di d to calcul calcu l ate m mobil obil i ty and force i n a ma machi chi ne at at two running speeds and in two axes. The configuration was similar to that shown in Figure 1 except the machine was horizontally oriented. The machine was tested normally for the first set of data and was then ri gi dl y cl amped mped to a tabl tabl e to coll ec ectt the second second set of data. data. One On e ca can n see that in the clampe clamped d cond condii tion, the forces in the bearings are nearly doubled in both tests while the vibration levels are only about 1/8 the level level i n the vertical vertical di re rection ction and 1/5 1/ 5 in the horizontal horizontal di rec rection. tion. T he run spe spee eds se sell ecte cted d for these tests coincide with resonant frequencies to further dramatize the results. It is apparent in this example that force and vibration have an inverse relationship. The test with higher vibration levels has l ower dama damag gi ng forces and and vi se versa versa.. A gain, i t i s the force that is r el at ated ed to the l i fe spa span n of thes these e be bea arings, not the vibration!

Table 1 - Mobili ty and Force Ex peri peri ments ments

OK, Vibration Can Still Be Useful! If we assume that what I have written above is true and we really cannot know the condition of the machine on the first test by looking at its vibration alone, it doesn’t mean we cannot see how it is changing changin g over ti me me.. I f we w e assume assume that the machi machi ne’s mobil mobi l i ty do does es not ch chang ange e from test to test, test, we can sa say y that i f the 1x peak peak rrii se ses, s, the ma machi chi ne is i s “more out of balance balance” ” than before before;; eve even n i f w e did not kn know ow its original state of imbalance.  T hat m may ay be be e enough nough – es especiall peciall y i f the goa goall i s to avoi avoi d cata catastrophi strophi c fail ure. We wi will l certainl certainl y see see the vibration spectrum change as the machine deteriorates. In the context of a predictive maintenance program, this is really the information we are interested in anyway. A better better approach appr oach takes takes thi s idea i dea a step step further fur ther by averag averagii ng data from fro m machi machi nes that app appea earr to be heall thy. A standard deviation hea devi ation i s add added ed onto the averag average e and new data i s compa compared red to thi s ba base sell i ne. Statistically speaking, when you get above this one deviation level (and two deviations especially) one can say the machine is deteriorating. I believe this method is valid, but again, it does not address the issue of the machine’s condition the first time you test it. A fi nal approach tha thatt is i s often often useful i s to compa compare re the spectra spectra from two i dentical ma machi chi nes (i f possibl e) e).. I f the ma machi chi nes are are trul y i dentical dentical,, i ncl udi ng how they th ey are are mounted, mounted, w e may may be able bl e to ma make ke the asassumption that sumption that their mobil i ties are are s sii mil ar and there therefore fore thei thei r vi bration bration l evel vel s should be simil ar. If one of  the machines displays higher vibration levels than the other we may be able to assume it is in worse condition.

 

Anecdotal Evidence A l arge gea earbox rbox i n a cool coolii ng tower was teste tested d by one of our engineers. engineers. Excess Excessii ve vi vibra brati ti on l evels of 132 V dB (a (appr pprox. ox. 1.6 i n/ s RM S) w were ere ci cite ted d at the shaft shaft rate frequency. frequency. T Thes hese ee exces xcessiv sive e leve levell s res resul ul te ted d in a strongly worded recommendation to overhaul the unit. One year later, the same engineer returned to the same same si site te to test the machi machi ne aga agaii n. A pp ppare arentl ntl y, the si site te had opted to conti nue nu e runni run ni ng the gearbox, gearbox, and i t had been been in i n conti nuous u use se since sin ce the pri or tes test. t. T he e enginee ngineerr recorded the e exact xact s sa ame vi bra brati tion on l eve evell s and was surprised that the machine had neither failed nor been overhauled. Intrigued by this seemingly inexplicable situation, the engineer investigated the possible explanations and noticed that the gearbox was mounted on a flimsy base of rotting wood.  T he non-sti non-stiff ff ba base se al l owed the g gea earbox rbox to vi brate brate,, or i n other words, wor ds, i t had a high deg degree ree of mobil i ty. Dividing high vibration levels by high mobility would result in low forces and this would serve as an explanation for the machine’s continued trouble free operation. Unfortunately, the engineer was not equipped to calculate the mobility of the machine at that time and therefore this evidence is merely anecdotal.

Conclusions M achi nes nes in the re rea al worl d are not i nfi ni tel tel y stiff and do not move as whol e b bodi odi es. They be bend, nd, fl ex and contain resonances. Thus, machines do not respond uniformly to an input force or vibration at every frequency. freque ncy. Because Because of thi s, whe wh en w e view a vibration spectrum spectrum i t i s di storte storted d at a all mos mostt every every ffreque requency ncy by the machi machi ne’s structure. structu re. Some peaks peaks may may be unu unusuall suall y hi gh beca because use they they fal l on or n nea earr resonant frequencies while others will be unusually low because the fall on or near anti-resonant frequencies.  T here wi l l be few peaks peaks wh whose ose ampl ampl i tudes are are not effecte effected d one way or the other by the ma machi chi ne’s ne’s structure (there (there are are very very few f ew freque frequenci nci es where wh ere the mobil mobil i ty i s e equa quall to one or the res response ponse is perfectly fl at (Figure 2)). What this i mpli es i s that that i f w e a are re just looki ng at at the vibration vibration spe spectra ctra,, wi th no know l edge dge of m mobil obil i ty, ty, we cannot really tell in which way or by how much the amplitudes of various peaks are effected. If we are usi ng the ampl ampl i tudes tud es of thes th ese e peaks peaks to di agnose agnose faults faul ts in i n the ma machi chi ne or make make repa repaii r recomme recommendandations, we may be missing the mark by a long shot! One solution to this dilemma is to calculate the mobility of the machine at the test locations by dividing the response vibration by a known input force using a dual channel analyzer and a calibrated hammer. me r. Di vi di ng future vi brati brati on spectra b by y these mobil i ty spectra tto o calcu calcull ate ate the force spe spectra, ctra, we es esse sennti al l y rre emove the effe effects cts of the machi machi ne’s ne’s structure from our readi readi ngs ngs.. A nother al al te ternative rnative i s to use vi brati brati on ana anall ysis i n a historical hi storical context, comparin comparing g new data as part of a trend plot, to mask alarms or to an average (plus 1 sigma) baseline all based on prior data from the machi ma chi ne. Thi T hi s soluti solu ti on make makes s the assum assumpti pti on that the machi machi ne’s ne’s mobil i ty w won’t on’t change and that a abso bso-lute vibration aresaying not asitimportant as changes in vibration levelsof atthe specific frequencies. is is simply anotherlevels way of is not necessary to know the condition machine on day 1,This what i mport mporta ant i s how i ts conditi on i s chang changii ng ove over ti me. me. For more information on vibration and mobility, please feel free to call PREDICT/DLI at 206-842-7656 or vi sit our w ebs bsii te at www.Pre ww w.Predi di ct-DLI .com. .com.

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