APM-56-10

O il-Film W h ir l— A N on-W h irlin g B earingB y B U R T L. N E W K IR K 1 a n d LL O YD

T h e s h a ft s o f tu r b in e s , g e n e r a to r s a n d o th e r h ig h -sp e e d m a c h in e s ru n in jo u r n a l b ea r in g s o n film s o f o i l so th a t th e r e is n o m e t a l - to -m e ta l c o n ta c t b e tw e e n th e jo u r n a l a n d th e b ea rin g . A lth o u g h th e b ore o f th e b ea r in g is o n ly a few th o u s a n d th s o f a n in c h la rg er t h a n th e d ia m e te r o f th e jo u r n a l th e o il film su p p o r ts th e r a p id ly r o ta t in g jo u r n a l a n d h o ld s i t s te a d ily in a very d e f in ite p o s it io n w ith in th e b ea r in g c lea ra n ce .

T h e p o s it io n w h ic h th e jo u r n a l ta k e s w ith in th e b ea r in g clea ra n ce d ep en d s o n th e v isc o s ity o f th e o il, t h e lo a d o n th e jo u r n a l, th e sp eed o f r o ta t io n , a n d t h e d im e n s io n s o f jo u r n a l a n d b ea r in g . F or ex a m p le , i f t h e r o ta t io n sp eed is o n ly a few rp m th e jo u r n a l r u n s n ea r t h e b o t to m o f i t s clea ra n ce . A t h ig h e r sp e ed s th e jo u r n a l r u n s so th a t i t s c lo se s t a p p r o a ch to th e b ea r in g is a t s o m e p o in t o n th e sid e o p p o site t o th a t w h ic h i t c l im b e d a t s ta r t in g . F or

P. G R O B E L ,2 S C H E N E C T A D Y , N . Y.

very h ig h sp e e d s th e s a m e jo u r n a l r u n s n ea r ly c e n te r e d in th e b e a r in g c le a r a n c e .

O b se r v a tio n a n d e x p er ie n c e te a c h t h a t in g e n e r a l th e o il fi lm fo r m s a very s te a d y s u p p o r t fo r th e jo u r n a l a n d th a t i t e v e n ex e r ts a d a s h p o t a c t io n o p p o s in g o u t s id e d is ­tu r b a n c e s t h a t w o u ld c a u s e t h e s h a f t t o v ib r a te . T h is re m a r k a b le s ta b i l ity , h o w ever , h a s b e e n fo u n d t o be s u b ­je c t t o a n o ta b le e x c e p tio n . W h en a s h a f t r u n s a t tw ic e i t s c r it ic a l sp eed or a t a n y h ig h e r sp eed th e e q u il ib r iu m b e tw e e n t h e lo a d a n d t h e l i f t o f t h e o il f i lm b e c o m e s u n ­s ta b le , th e jo u r n a l m o v e s in a m in u t e sp ira l o f in c r e a s in g ra d iu s , a n d t h e w h o le s h a f t p ic k s u p a w h ir l in g m o t io n . T h e w h ir l h a s t h e n a tu r a l fr e q u e n c y o f th e s h a f t a n d th e m o t io n i s o n e o f r e so n a n c e .

T h is p a p e r d e a ls w ith a la b o r a to r y s tu d y o f o i l- f i lm w h ir l p h e n o m e n o n a n d d e sc r ib e s a m e a n s fo r c o m b a t t in g i t .

TH E phenomenon of what has been termed shaft whipping due to oil action in journal bearings3 is a whirling or vibra­tion which develops when a rotor on journal bearings runs at approximately twice the critical speed of the shaft or a t any

higher speed. The whirl or vibration occurs a t the resonant frequency which, in cycles per minute, is equal to the revolutions per minute a t the critical speed. Thus the shaft builds up a resonant vibration or whirl when running a t a num ber of revolu­tions per minute equal to, or greater than twice the resonant frequency. The stimulus which builds up and m aintains the vibration lies in the oil film in the bearings. This was proved by shutting off the oil supply. As the oil ran out of the bearing the whirling ceased and it built up again when the oil supply was restored.

I t was found th a t rotors did not develop this whirl when run on friction damped spring bearings and th a t increasing the unit loading of the bearing prevented the whirl up to speeds somewhat above twice the critical speed. An obvious means to escape the difficulty in commercial design is to make the rotor of such stiff­ness th a t the critical speed is more than half of the running speed.

The phenomenon has since been observed in commercial ma­chines and all three of the expedients above mentioned have been used successfully at one time or another to combat it. W ith higher journal peripheral speeds the action of the oil film seemed

1 Research Laboratory, General E lectric Com pany. Mem.A.S.M .E. D r. Newkirk was g raduated from the U niversity of M inne­sota in the classical course. After some graduate work there in physics and m athem atics he studied a t th e Universities of M unich and Gottingen, Germ any, and la te r became associate professor of m athem atics and mechanics in the College of Engineering of the University of M innesota. He entered the Research L aboratory of the General Electric Com pany in 1920.2 Research Laboratory, General Electric Com pany. M r. Grobel was graduated from the U niversity of M innesota in 1924 w ith the degree of B.S. in Mechanical Engineering. Since g raduation he has been w ith the General Electric Com pany, from 1925 to the present tim e in their Research Laboratory.3 “Shaft W hipping Due to Oil Action in Journal B earings,” byB. L. Newkirk and H. D. Taylor, General Electric Review, Aug., 1925, p. 559.

C ontributed by the Applied M echanics Division and presented a t th e Annual M eeting, New York, N. Y., D ecem ber 4 to 8, 1933, of T h e A m e r i c a n S o c i e t y o f M e c h a n i c a l E n g i n e e r s .

N o t e : Statem ents and opinions advanced in papers are to be understood as individual expressions of th e ir authors, and n o t those of the Society.

to be less easily suppressed by increased unit loading or by spring- supported bearings.

Some tim e ago this study was taken up again w ith a new ap­paratus built for study of this phenomenon as it develops with higher journal speeds. The highest speed of the previous in­vestigation was th a t of a l 7/ 8-in. journal a t 5000 rpm. In the

new apparatus a 2-in. journal was run a t more than 30,000 rpm, giving a journal peripheral speed of 16,000 fpm.

An object of the study was to develop if possible a system of grooves in the bearing th a t would control the behavior of the oil film so as to prevent development of the whirling phenomenon. Figs. 1 and 2 show developed bearing surfaces with systems of grooves th a t proved most satisfactory. Oil enters a t the hori­zontal joint on the downgoing side of the journal. Some of the

607

608 TRA NSA CTION S OF T H E A M ER IC A N SO CIETY OF M ECH ANICAL E N G IN E E R S

oil is pum ped by action of the shaft through the central pe­ripheral groove to the dam a t the end of the groove where con­siderable hydrodynamic pressure builds up, especially if the pe­ripheral speed of the journal is high. The upper half of the bear­ing fills up w ith oil and the axial grooves in the upper half of the bearing (Fig. 1) distribute the pressure. If the load on the bear­ing is sufficient to insure downward pressure under all circum­stances the lands in the upper half m ay be om itted (Fig. 2). Thus the bearing is kept full of oil so th a t air is not drawn in at any point and a considerable downward pressure is exerted on the journal by the oil in the upper half of the bearing. The downward load on the journal due to the oil pressure developed in the upper half of the bearing is not sufficient to account for the nonwhirling characteristic of our bearing by the increased load­ing of the journal alone. In other words a bearing of conven­tional design w ith external loading on the shaft equal to the load produced by the oil pressure in the upper half of the new bearing will still whirl.

The weights of the rotors used in most of these tests imposed a load on the bearing of negligible am ount. The whirling char-

F i g . 3 O i l P r e s s u r e i n C i r c u m f e r e n t i a l G r o o v e f o r V a r i o u s D e p t h s o f G r o o v e

(Bearing, 2 in . X 2B/s in .; clearance, 2.75 p a rts per thousand; peripheral velocity of journal, 15,700 ft (4785 m) per min. Groove system in bearing surface developed is indicated in insert.)

F i g . 4 P r e s s u r e a t D a m V e r s u s R p m f o r V a r i o u s D e p t h s o f G r o o v e

(Bearing, 2 in. X 25/s in.; clearance 2.75 p a rts per thousand. Groove system in bearing surface developed is indicated in insert.)

acteristic is therefore avoided in bearings of this design w ith a shaft substantially w ithout external loading, and w ith a pe­ripheral journal speed of 16,000 fpm. Some hydrodynam ic pres­sure develops in the lower groove so th a t the oil pressure increases continuously from the point of entrance of the oil to the dam. This groove in the lower half serves also to reduce the lifting power of the oil film in the lower half of the bearing by dividing the bearing surface into two sections and doubling the to ta l effec­tive end-leakage area besides shortening the leakage path.

The bearing has been called “non-whirling.” This does not

imply resistance to vibration stimuli bu t simply th a t the stimulus to whirling does not develop because of the action of the oil film. In fact an exception m ust be made even to this narrowed claim, inasmuch as rotors w ith very heavy and relatively long over­hangs m ounted on bearings of this design do develop the whirl a t a somewhat increased speed. This exceptional case will be discussed later.

Fig. 3 shows the development of hydrodynamic pressure along the peripheral groove as a function of the angular distance from the point of entrance of the oil. Fig. 4 shows the variation in pressure developed a t the dam as a function of journal speed.

The oil is supplied to the bearing with a pressure of five or ten pounds per square inch to cause it to enter in sufficient quantity. There is no passage provided for oil exit, consequently end leak­age carries away all the oil th a t passes through the bearing. I t is essential th a t the bearing run full of oil. The am ount th a t m ust be supplied depends, therefore, on end leakage which in tu rn depends on bearing diameter, clearance, pressure developed by the pum ping action of the journal, and viscosity of the oil.

The bearing functions well throughout a range of clearance. Excessively small clearances result in overheating a t high speeds as would be the case w ith any bearing. A clearance of 2.5 parts per thousand proved satisfactory for the two-inch journal up to the highest speed a t which tests were usually run; 30,000 rpm, corresponding to 15,700 fpm. For journals of larger diameter and especially a t the much lower journal peripheral speeds in commercial operation the commonly used clearances of 1.25 to

F i g . 5 O i l P r e s s u r e a n d G p m o p O i l t o B e a r i n g V e r s u s G r o o v e D e p t h

(Shaft running at 30,000 rpm. Bearing 2 in. X 26/s in. Clearance 2.75 parts per thousand.)1.50 parts per thousand are presumably satisfactory. Larger clearances result in an excessive am ount of oil passing through the bearing. This oil is pum ped up to considerable pressure within the bearing and then discharged with correspondingly increased power consumption. Fig. 5 shows the am ount of oil supplied, together w ith the pressure developed a t the dam in tests of the 2-in. journal a t 30,000 rpm with a 5.5-mil diametral clearance.

The grooves m ust be of ample capacity to carry oil enough to supply the end leakage and cause the bearings to run full. The circumferential grooves should have a cross-section from 2 to 4 or more times the product of radial clearance and journal circumference. In the lower half the peripheral groove is narrow and deep. In the upper half operation has been satisfactory with depths from 20 mils to 70 mils. Depths of from 30 to 40 mils are satisfactory a t the higher speeds. If the lands are om itted in the upper half and a very wide groove used, the groove depth need not be decreased because of the greater width.

Figs. 1 and 2 do not show the grooves a t the ends of the bear­ings th a t are required to carry away the end leakage oil. Con­ventional means for this purpose are satisfactory bu t more than the ordinary bearing end-leakage oil m ust be taken care of.

A P PL IE D M ECH ANICS APM-56-10 609

Some measurements of the power loss in the bearing were made. W ith a 2-in. diam eter journal and a bearing 25/s in. long, having a clearance of 2.75 parts per thousand and using oil of 155 sec Saybolt viscosity (27 centipoises) a t 40 C, the following values of power consumption in the bearing were observed.

Oil feed, Oil,Rpm deg C Kw loss gpm15,000 35 2 .320,000 35 3 .925,000 35 6 . 230,000 35 9 .620,000 50 3.1 i ! 525,000 50 5 .4 2.130,000 50 8 .7 3 .220,000 60 2 .925,000 60 5.130,000 60 8 .3

T h e E x p e r i m e n t a l A p p a r a t u s

The apparatus was housed to confine the oil. No effort was made, however, to confine the oil w ithin the bearing housings. Oil was supplied by a gear pump. A cooling coil and a heating coil were used to control the tem perature of oil entering the bear­ing. Fig. 7 shows the apparatus w ith the longer shaft in place and the upper p a rt of the housing removed.

To observe accurately the behavior of the journal under the action of the oil film the short shaft, No. 1, was provided w ith a stiff projection, the end of which was observed w ith a microscope while the shaft was running. M ovements of the journal were amplified by the shaft extension 1.7 times a t the pointer tip. To increase the refinement of observation the tips of the points were provided w ith recesses into which ‘/is in-

The apparatus developed for this study has some points of interest. A fundam ental requirem ent was th a t the peripheral speed of the journal should be a t least as high as th a t of a 12-in. journal a t 3600 rpm. I t was necessary also th a t the mounting be so rigid th a t resonant vibration would not develop in any of its parts a t speeds within the range to be studied. One shaft, No. 1, had its critical speed above the range to be studied and another shaft, No. 2, had its critical speed considerably less than half the maximum speed to be studied. Most of the work was done with these two rotors. At a later date No. 2 was modified by adding a bell-shaped mass to the overhanging end and a third rotor was made with a long, heavy overhang.

The journal diameters were 2 in. (51 mm) and a speed of30.000 rpm gave a journal peripheral speed of 15,700 ft (4785 m) per minute. The journal lengths were 26/s in.(66 mm) for rotors Nos. 1 and 2, and 6 in. for No. 3.A 25-hp, 3600-rpm, d-c motor shunt wound, with a 10 to 1 spur-gear train was used for driving and the speed was controlled by varying the arm ature voltage. Shafts Nos. 1 and 2 are shown in Fig. 6. The longer one has a critical speed a t 8500 rpm, and no other critical speed below30.000 rpm. Both shafts have assemblies of punchings near the 2-in. bearing. These were used with a pair of electromagnets to load the shafts. Loads up to 400 lb (180 kg) could be applied. At the flanged end of each shaft a small plain journal bearing (7/s in. X 1 Va in.) and a ball bearing were used interchangeably. The coupling with the driving shaft was accomplished by lacing a light linen cord through holes in the two adjacent flanges on the driving spindle and the driven shaft, respectively.

The bearing standards were made of steel plates 23/s in. thick and the main standard was approximately 14 in. wide. The standards were set on a heavy steel plate which was solidly grouted in on a concrete base on the concrete floor of the labora­tory.

F i g . 6 S h a f t s f o r H i g h - S p e e d B e a r i n g T e s t s

F i g . 7 A p p a r a t u s f o r H i g h - S p e e d B e a r i n g T e s t s

F i g . 8 S h a f t f o r H i g h - S p e e d B e a r i n g T e s t s (Enlarged view of Vie-in. ball holder.)

(1.6 mm) steel balls were set and centered with small screws. Fig. 8 shows this considerably magnified. These balls acted as convex mirrors of small radius to give a virtual image of the cra­te r of a small direct-current arc lam p placed about 10 f t (3 m) away. This image was only about one-ten-thousandth inch (0.0025 mm) in diameter. Since the diameter of the ball is small compared w ith the distance from the light source the position of the v irtual image relative to the ball center changes very little

610 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERSwith small movements of the ball and the observed movements of the image represent w ith great fidelity the movements of the shaft tip and of the journal in the bearing.

A combined microscope and camera was used to observe and record the m otion of the pointers. The magnification on the photographic film was 18 diameters. Applied to movements of the journal when the shorter shaft was used the power would be 30 diameters. One division of the scale which shows in some of the photographs represents 1.8 mils (0.045 mm) a t the ball and1 mil (0.025 mm) a t the journal.

When the shaft is whirling or vibrating the image of the light source moves and leaves a track on the photographic film. On account of the retention of the image by the eye a track of light is observed visually also through the microscope. The arrange­m ent of shutters is such th a t the image m ay be focused and cen-

F i g . 9 C a m e r a - M i c r o s c o p e S e t - U p f o r O b s e r v i n g a n d P h o t o ­g r a p h i n g C o m p r e s s o r - I m p e l l e r - S h a f t V i b r a t i o n

tered in the field visually and photographed im mediately by operating two shutters. Fig. 9 shows the microscope and camera set up before a small compressor. The microscope was set with its axis in line with the shaft axis and the beam of light from the arc lamp made a small angle w ith this axis.

The shortest exposure obtainable with the shu tter was Veo sec. This corresponds to a complete revolution of the shaft a t 3600 rpm. At 30,000 rpm the shaft makes 500 revolutions in a second. Shorter exposures corresponding to less than a revolution a t the highest speed were obtained by using a revolving disk 1 1 3/4 in. in diam eter with a notch of definite length in its periphery. The disk was so placed and ro tated th a t it cut off the light beam ex­cept when the beam was passing through the notch. The shu tter was then set for an exposure shorter than the period of one revolution of the disk. In th is way the image recorded on

the film represented the movement of the pointer while the notch in the disk perm itted the beam of light to pass.

W ith this equipment the behavior of both shafts in many bearings was observed and photographed. I t is understood of course th a t shaft No. 2 would not behave as a rigid body when whirling or vibrating a t a frequency near 8500 per m inute (its natura l frequency) or higher, and consequently would not indi­cate movement of the journal in its bearing while running at these high speeds. However, the ball a t the end of shaft No. 2 gives a sensitive indication of the whirling movement of the rotor when it occurs. Numerous photographs show movement a t the tip of shaft No. 2 of less than one scale division to ta l displacement (1 division = 1.8 mils a t the ball) a t speeds up to 30,000 rpm, w ith no load on the shaft except its own small weight. Fig. 10 shows an example of these photographs made with shaft No. 2. W ith bearings of ordinary design this rotor breaks into violent whirling a t speeds over 17,000 rpm. The numbers in Fig. 10 represent the following conditions:

Exposure Shaft speed, M agnetic load,num ber rpm lb

31/s 1 5 ,0 0 0 04 2 0 ,0 0 0 041/2 2 5 ,0 0 0 05 3 0 ,0 0 0 00 V 2 2 0 ,0 0 0 4 0 06 2 5 ,0 0 0 4 0 06 V2 3 0 ,0 0 0 4 0 07 (Shows bearing clearance)

No. 7 was made by taking six separate exposures with shaft sta­tionary and the journal pulled by hand against the bearing in different directions. This gives a chart of the bearing clearance. Exposures Nos. 3 ‘A to 6V2, inclusive, all show images less than one-scale division in diam eter and indicate very steady running of the rotor.

Photographs of the vibrations and whirls are difficult to re­produce and discussion in detail of their features is not necessary for present purposes. M ost runs were made with bearings of unusual proportions or grooves. W ith a conventional overshot bearing the stiff shaft, No. 1, ran true and in the center of its clearance up to 13,000 rpm with no load.

W ith the non-whirling bearings the journal ran a t a lower posi­tion in the bearing clearance a t speeds above 15,000 rpm than it did a t lower speeds.

H e a v il y O v e r h u n g R o t o r s

A subsequent study was made to throw more light on therna- ture of the oil-film whirl, especially its early stages when a rotor running in equilibrium begins to build up the whirl. Experience with two rotors having relatively long and heavy overhangs de­serves mention because of its bearing on both design and theory.

A bell-shaped p a rt was shrunk on shaft No. 2. This mass w7as so designed th a t the center of gravity of the overhanging end of the shaft was a t the Vie-in. ball which serves to reflect the image of the arc. The motion of the image, therefore, indicated the motion of the center of gravity of the mass. Fig. 11 shows a com­

A P PLIE D M ECH ANICS APM-56-10 611

bination microscope and motion-picture camera in position for observation and shaft No. 2 with its bell-shaped attachm ent.

The critical speed of this rotor was 2030 rpm. The load a t the main bearing was 59 lb. The distance from the center of gravity of the overhanging end to the bearing center was 1.2 times the distance between bearing centers. This was run in a bearing of conventional overshot design l 3/ 8 in. long with a clear­ance of 3 parts per thousand and with the oil mentioned previ­ously. I t ran somewhat unsteadily from 4000 rpm up to 4500 rpm. I t began to whirl a t 4500 rpm. The whirl built up slowly around the equilibrium position of the center of gravity of the overhung mass, in the natural frequency of the rotor. The rate of increase in the energy of whirling was approximately 0.005 w att in the early stages of development when the am­plitude of movement was only two or three mils.

I t was found th a t this rotor whirled feebly a t speeds above 5000 rpm with bearings of the non-whirling design, the instability increasing very gradually with increasing speed. For further study of this m atter a th ird shaft was made with a 6-in.-long bearing and a greater overhang. This is shown in Fig. 12.

This rotor had a critical speed of 1025 rpm. The load a t the main bearing was 115 lb and the overhang, measured from the center of the bearing to the center of gravity of the overhung mass was 1.3 times the distance between bearing centers. I t whirled a t 2600 rpm in a conventional bearing and with non-whirling bearings the whirling developed a t 3000 rpm. The behavior was similar to th a t of the rotor with bell-shaped overhang in th a t the whirling built up gradually about the equilibrium position. In this case the overhang was greater, compared to the dis­tance between bearings, and the overhung mass was much heavier, thereby giving a lower critical speed.

critical speed range but having their mass between the bearings do not whirl w ith these non-whirling bearings.

T h e o r i e s o f W h i r l i n g D u e t o O il-F ilm A c t io n

The phenomena of shaft vibration or whirling due to oil-film action have been discussed recently on the basis of hydrodynam ic theory.

Stodola4 discovered indications in theory th a t “critical speeds” m ay result from behavior of the oil film. The m atter was ampli-

F i g . 11 P h o t o g r a p h i c M i c r o - M o t i o n - P i c t u r e A p p a r a t u s S e t - U p t o O b s e r v e S h a f t V i b r a t i o n s

I t appears th a t rotors with relatively long, heavy overhangs show a very positive development of the oil-film whirl which is somewhat reduced but not obviated by the bearing design de­scribed above. From the point of view of theory it appears also th a t rotors having the same critical speed are not necessarily equivalent in their whirling tendencies since rotors in the same

F i g . 12 S h a f t No. 3 f o r H i g h - S p e e d B e a r i n g T e s t s W i t h 4 2 - L b W e i g h t S h r u n k O n

fied and an experimental study was m ade by Charles Hum m el,5 a pupil of Stodola’s.

David Robertson of the University of Bristol has published a valuable paper on the phenomena of whirling.6

The Stodola theory expressly excluded any effect of shaft elasticity. The shaft of Hum m el’s experimental apparatus was short and very stiff and operation was undoubtedly well below the critical speed.

The theory is based on the equations for the half bearing. The conclusion is reached th a t below a certain speed limit of shaft rotation the journal is supported by the oil film in stable equilib­rium. When the shaft is running a t any speed below th a t at which equilibrium becomes unstable, resonant vibration should build up due to the quasi-elastic behavior of the oil film if a peri­odic disturbance acts with the appropriate frequency. A t two definite speeds the appropriate frequency is equal to the rotation frequency and consequently unbalance of the rotor acts to build up resonant vibration. Such speeds are therefore critical speeds due to oil film behavior. When the speed is increased above the critical value the vibration am plitude decreases.

According to the theory, the position of equilibrium of the journal in the bearing approaches the bearing center as speed increases, and the equilibrium becomes unstable if the distance between bearing center and journal center becomes less than about two-thirds of the radial bearing clearance. Hummel re­ports th a t his shaft did not run smoothly above the calculated limit of stability of the oil film.

The speed a t which theoretical instability sets in depends on unit load, bearing clearance, peripheral speed of the journal, andoil viscosity. For our experimental shafts of very small weight, Nos. 1 and 2, the calculated limit of stable running is only a few revolutions per minute. Even when the bearing was loaded by the attrac tion of the electromagnets acting on the punchings which were mounted on the shaft (a non-massive load) the jour­nal ran nearly central in the bearing a t the higher speeds. Con­sequently our experiments have been made in a field where theory

4 “K ritische W ellenstorung Infolge der Nachgiebigkeit des Oel- polsters im L ager,” by A. Stodola, Schweizerische Bauzeitung, vol. 85, p. 265.5 “K ritische D rehzahlen als Folge der N achgiebigkeit des Schmier- m ittels im L ager,” by Charles Hum m el, Forschungsarbeiten, V .D .I. H eft 287, 1926.6 “W hirling of a Journal in a Sleeve Bearing,” by D avid Eobertson, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, ser. 7, vol. XV, Jan ., 1933, p. 113.

612 TRANSACTIONS OF THE AM ERICAN SOCIETY OF MECHANICAL ENGINEERS

indicates instability. The earlier studies were made with heavier shafts but in those cases also the speeds at which whirling de­veloped were well above the limits of stable operation indicated by the Stodola theory.

Stodola points out4 also that the theory of a full circular bear­ing indicates that whirling would build up if the conditions of clearance, load, speed, and oil viscosity are such that the journal center approaches the bearing center. This does not explain our oil-film whirl, however, since our journals run steadily at definite locations near the bearing center up to the speeds at which reso­nant whirling starts.

It is interesting to note that in both of the theories cited, in­stability is indicated when, as in the case of light unit loading, the equilibrium position of the journal approaches the bearing cen­ter. We have found that with heavy unit loading, which causes the journal to run in a lower position in the bearing, the lowest speed at which whirling develops may be considerably more than twice the critical speed of the shaft. In other words, heavy unit loading which acts against development of the oil-film whirl ap­pears also in bearing theory as a factor making for stability.

The oil-film critical speeds of the Stodola theory are apparently not related to our oil-film whirl since our whirl occurs only with an elastic shaft, the frequency is determined by the shaft rather than the oil film, and for other obvious reasons. The instability of the oil film indicated by theory may however have a bearing on the matter inasmuch as the conditions for theoretical insta­bility are satisfied when the oil-film whirl builds up.

Dr. Robertson’s discussion is based on the theory of the full bearing. It is assumed that the journal is rotating about its own axis and whirling about the center line of the bearing. His theory explains the whirling of a vertical rigid rotor at a whirl frequency equal to half the running speed.

The conclusions regarding the horizontal rotor throw light on the force which maintains the whirl after it has developed to such an extent that the journal whirls substantially about the center line of the bearing. With horizontal (loaded) journal bearings, the whirl starts very gradually about the equilibrium position of the journal and in the natural frequency of the rotor. Dr. Robertson’s theory does not account for the early stages of the whirl. After the whirl has built up to a large magnitude so that the, journal whirls about the bearing center, the stimulus is represented, qualitatively at least, by the force Fnp of Dr. Robertson’s equation 4.25.

Dr. Robertson’s theory does not account for the start of the oil-film whirl when a shaft is restrained from whirling while it is brought up to a speed more than twice critical speed and then released.

O r i g i n a n d D e v e l o p m e n t o f t h e W h ir l

Since the whirl is a resonant movement having the frequency of the rotor, the elastic properties of the rotor must be a major factor from the beginning. The whirl must start with a dis­turbance of the rotor and build up by energy fed back by the oil film. The action in detail must be as follows:

The beginning must be a disturbance of the rotor causing it to vibrate in its natural frequencies. Disturbances are caused by building tremors, neighboring machines running out of bal­ance and by the unbalance of the rotor itself. It is not necessary to assume that such disturbances have the frequency of natural vibration of the rotor. Any shock or distortion sets up tremors in the natural frequencies of the distorted body.

Any plane vibration of the rotor in its natural frequency is quickly converted into a whirl of the same frequency by the ac­tion of the oil film. This occurs as follows:

The vibrating rotor causes corresponding movements of the journal. Movements of the journal change the bearing reaction

Where ft represents the tangential component of the resultant force acting on the journal, w represents the speed of rotation of the shaft, represents the whirling speed, and a represents some number, approximately equal to 2 in the cases studied and covered in this paper.

Since the incipient vibration of the rotor mass is of very small amplitude, and since an elastic shaft intervenes between the mass and the journal, the first movements of the journal out of its equilibrium position must be very minute but even these minute displacements arouse the component of the restoring force of the oil film that builds up the whirling.

While the journal whirls very near its equilibrium position in the early stages of the development, the whirl of the rotor mass may later build up to large amplitude so that the reaction at the bearing due to the centrifugal tendency of the- whirling mass exceeds that due to the weight of the rotor. In this stage the tangential component of the oil film reaction is considerable since it supplies all the energy consumed in the whirl, which in­volves energy-consuming deformations of the entire structure.

For shaft speeds only slightly above twice the shaft critical speed the oil film stimulus is small and variable in sense, becom­ing larger and more positive at higher speeds. With a heavy- unit bearing loading the whirl does not build up unless the shaft speed is considerably higher than twice the critical speed of the shaft. In a speed range slightly above twice the critical speed of the shaft the whirl sometimes builds up somewhat and then dies out.

It is well known that critical speeds, that is, speeds at which resonant vibrations of rotating shafts develop, are affected by elasticity of the bearing supports, such elasticity reducing the shaft critical speeds. We have made tests to determine whether or not such elasticity of bearing supports affects the whirling of the shaft due to oil film action. It appears, as would be expected, that such whirling starts at reduced speeds corresponding to the reduced critical speeds and that the frequency of the whirl is that of the reduced critical speed.

of the oil film. When the journal is displaced from its equilibrium position and moving, the resultant of load and bearing reaction is not zero and undoubtedly it is not directed exactly toward the equilibrium position of the journal. Consequently the journal does not return to its equilibrium position, and a plane vibration of the rotor is thus converted into a journal whirl in the natural frequency of the rotor.

When the journal is whirling in a minute spiral about its equi­librium position, the resultant of load and oil-film reaction un­doubtedly has at any instant a component tangential to the di­rection of motion. When such a component is in the direction of motion the whirl builds up and the journal center spirals outward. When the tangential component is in the opposite direction the journal spirals inward and the whirl dies out. Such a tangential component must vary from point to point of the path of the journal whirl and it may change sign in the course of one whirl. However, if the integrated effect of the tangential com­ponents of the bearing reaction adds energy to the whirling mo­tion of the rotor, the whirl of the journal builds up. This whirl in turn, since it has the shaft frequency, builds up the whirl of the shaft. We have therefore a sensitive feed-back system when­ever the integrated effect mentioned above is in the right sense.

It appears that this integrated effect increases the energy of the whirling motion provided the speed of rotation is, in general, twice or more than twice the whirling speed, otherwise such in­tegrated effect is in the opposite sense. This condition may be expressed in the following form:

APPLIED MECHANICS APM-56-10 613Finally, further tests showed that the feed-back effect is greater

when the overhanging mass is relatively heavy and the overhang great.

These remarks apply to all of the rotors used in our labora­tory study and to larger machines in the field. Critical speeds have ranged from 600 rpm to 8500 rpm. Bearing pressures have ranged from 1 lb per sq in. to over 200, and speeds have been run up to 30,000 rpm, and 16,000 fpm. Shaft diameters have varied from one inch to twelve inches; bearing supports have been very rigid and again intentionally flexible. Bearing clear­ances have varied widely. Throughout this entire range of con­ditions a feed-back characteristic of the oil film has developed in general when the shaft speed has exceeded twice the speed of its whirling in the natural frequency.

Studies based on hydrodynamic theory have not yet accounted for the early stage of the oil-film whirl. An explanation is needed of the energy input from the oil film to a minute whirling motion of the journal about its equilibrium position, when the rotation speed is approximately twice the whirling speed or greater.

Another shaft-whirling phenomenon was reported7 a few years ago. This is maintained by a different feed-back mechanism, namely, internal friction of the rotor, due to working of shrunk- on members. In such cases the whirl undoubtedly originates from shaft vibration. After the whirl is started the restoring force, due to shaft elasticity and cramping action of the shrunk- on member, has a tangential component which is in the direction of whirl if the speed of rotation exceeds the critical speed of the shaft. The whirl builds up, therefore, until the energy con­sumed in working of non-rotating parts of the structure and in increased bearing friction equals the energy fed back to the whirl by working at the fits on the rotor.

The expression “shaft whirling due to action of the oil film” is cumbersome and unsatisfactory in other respects. The ex­pression “shaft whipping” is unsatisfactory also since the word “whip” is frequently and properly used to designate motion of an overhung shaft. The name “oil-film whirl” seemed more appropriate. If this is acceptable the whirling described in the 1924 paper7 and called “shaft whipping” might be called the “cramped shaft whirl.”

A c k n o w l e d g m e n t

The experimental work has required good technique in bal­ancing the rotors and great accuracy in adjusting the steel ball reflector, etc. In this work our assistant Mr. F. B. Quinlan has shown remarkable skill and enthusiasm.

DiscussionR. P. K r o o n .5 It has been brought out that the downward

load on the journal due to the oil pressure developed in the upper half of the new bearing is not sufficient to account for the non­whirling characteristic. If this is the case, would the authors be able to tell what particular change in the oil flow affects the ten­dency of the journal to whirl. It seems to be a fact that quite a few bearings in the field have been made “non-whirling” by our service department simply by scraping away part of the bearing area. A hydrodynamic theory, if adequate, would probably explain quite a few practical points in the behavior of the whirl which, until now, appear mysterious.

In this respect the article,6 “Whirling of a Journal in a Sleeve Bearing,” by Dr. Robertson which is mentioned in the paper is interesting. Dr. Robertson has attempted to attack the prob-

7 “Shaft Whipping,” by B. L. Newkirk, G. E. Review, Mar., 1924, p. 169.* Experimental Division, Westinghouse Electric and Manufactur­

ing Company, South Philadelphia, Pa. Jun. A.S.M.E.

lem by a straightforward theoretical analysis but fails to come to conclusions which explain the physical facts. He is able to find, for speeds exceeding twice the critical speed, a force on the journal normal to the eccentricity, in other words pushing the journal around, but states that the oil force along the eccen­tricity is zero when there is no radial movement of the journal center. This is obviously not in line with what experience has shown about any horizontal non-whirling bearing. After equat­ing the elastic force of the flexible rotor to the oil-whirl driving force, Dr. Robertson states that as the shaft speed is raised above twice its critical value, the eccentricity should decrease, and, at a certain limiting speed, the whirl should disappear. This is not what happens in the actual case, where the relations between the oil-whirl driving force and the damping are apparently such that the eccentricity usually increases with increasing speed. It seems, therefore, that a theoretical solution still has to be de­veloped.

D a v i d R o b e r t s o n . 9 The authors are to be congratulated on finding a form of bearing which in most cases eliminates whirling at high speeds caused by the action of the oil in the bearings. It would add to the interest of their paper if they would reveal the process by which they arrived at the design shown. Were they guided by some sort of theory or did they merely make a lucky shot in a series of trials?

They have certainly set some new problems to those who deal with the theory of lubrication because the ordinary statement of that theory will not account for the building up of the pressure all round a groove of constant depth, and will find some difficulty in explaining the stability .which the new bearing gives.

The two outer portions of this bearing completely surround the journal. Without allowing for the end leakage which, how­ever, is a very important factor with this bearing, we should have a maximum pressure in these rims at about 135 deg and a mini­mum at about 225 deg. I t is probable that these rims re­ceive their oil by endwise flow from the groove between 180 deg and 300 deg and that the pressure inside the groove is sufficient to prevent the ingress of air to that low-pressure region from the ends of the bearing.

Endwise flow evidently plays a very important part in the action of these bearings and it is doubtful whether any satis­factory quantitative theory can be built up for them.

The force and couple transmitted by the shaft to each bearing must be balanced by the oil forces on the journal. Since the directions of the latter forces, and of the couple which they pro­duce, have some definite relation to the distribution of the journal eccentricity along its length, both in direction and amount, a steady whirl must correspond to some journal position in which this relation is stably satisfied.

Working on these lines, the writer has studied several cases in which forces only, and no couples, act on the journals, and has made model experiments which give a general confirmation of the theoretical results arrived at. A paper on the subject is now in preparation but as it will not be ready for publication for some time a summary of the results may be given here.

With very little or no lubrication, the friction between the journal and the bearing drives the journal center backward, and can maintain, and even start, a backward whirl which runs just below the critical speed, provided the shaft speed exceeds a certain limit which is only a fraction of the whirl speed.

The whirl speed remains practically constant at all shaft speeds above that which corresponds to that of the journal when rolling around inside the bearing without slipping.

• Professor, Electrical Engineering Dept., Merchant Venturers’ Technical College, Faculty of Engineering, University of Bristol, England.

614 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERSWith lower shaft speeds, the whirl speed adjusts itself to the

rolling condition and, at a particular speed, it suddenly stops.As expected from the theory, the backward whirl ceases as soon

as the bearings are filled with oil and cannot be restarted until most of the oil has run out. There was, however, one notable exception to this statement.

With the model running vertically, hung from a ball bearing at its upper end and the bottom of the 1/ 4-in. shaft in a 6/ s-in. diameter bearing immersed in a pool of oil, the journal would not stay in the central position but would whirl forward in the man­ner already described from theory6 by Dr. Robertson and men­tioned by the authors. This whirl was a very slow one, probably because the ball bearing offered a lot of resistance to that kind of motion and the oil forces would be quite small with such ab­normal bearing clearance.

But to our surprise, a stable high-speed backward whirl could be started by plucking the shaft and occasionally it would arise spontaneously. Most unexpectedly, it was found to run at pre­cisely the same speed as it did when the bearing was dry, thus indicating that the angle of friction was the same in both cases.

It still remains a puzzle how the forward or the backward whirl can be equally well maintained by the same bearing under the same conditions with no change whatsoever beyond the mere starting of the backward whirl. The one whirl requires a for­ward component and the other a backward component of the force acting on the journal center.

In connection with this work, the writer has been making a fresh study of Newkirk and Taylor’s paper on shaft whirling3 with the object of finding the cause of the whirling at high shaft speeds.

He has come to the conclusion that the oil has two distinct actions, the first depending on the force exerted on the journal when it is eccentric but substantially parallel to the bearing, and the second arising from the couple tending to tilt the journal when it does not lie in that direction.

In the paper already mentioned, it is shown that the first action of the oil completely explains the “oil resonance whirl” found by Newkirk and Taylor when the shaft runs just a little faster than twice its critical speed. It accounts for the whirl running at the critical speed and for its disappearance when the shaft runs too fast.

The authors seem uncertain about the way in which this theory explains how the whirl restarts after the shaft has been steadied at the center of the bearing. Since the central position is un­stable, the least error in centering the journal or the slightest tremor from some external source is sufficient to start the journal on its outward journey.

The second action of the oil probably accounts for the whirling at shaft speeds above the limit at which the first action ceases to be effective but the theory is still only in a nebulous state.

When the journal moves away from its unstable central posi­tion, its two ends may move in opposite directions so that the journal assumes a tilted position and performs a conical whirl. Newkirk and Taylor observed this sort of motion in the bearing when it was free to move.

The tilting of the journal throws the rotor out of balance but the unbalance rotates with the journal whirl, not with the shaft. Consequently, the rotor whirl it induces must also go at the same speed as the journal whirl. We may easily suppose that the mini­mum speed, at which the oil-pressure forces are sufficient to produce enough tilt, is often above that at which the first oil- induced whirl dies away.

The eccentricity of the center of gravity of rotor which can be produced by tilting the journal within the limits set by the bear­ing clearance is much greater than that clearance. Hence the second oil-induced whirl may have a larger amplitude than the

first and the amplitude may be expected to grow as the shaft speed increases for this causes the oil forces to increase.

Further, the journal of a horizontal rotor is already tilted by the deflection due to gravity and may, therefore, be expected to give the second oil-induced whirl at a lower speed than when it is vertical.

All these conclusions agree with Newkirk and Taylor’s experi­mental results and may also have some bearing on the present authors’ experience with rotors having a heavy overhang.

C. R i c h a r d S o d e r b e r g . 10 The phenomenon referred to as oil-film whirl appears to belong to an extensive group of vibra­tion phenomena, which may be called self-excited motions. It was covered by a separate paper11 contributed by the Applied Mechanics Division, A.S.M.E., sometime ago and has proved to be of real practical significance in high-speed machinery. All that is needed is a vibrating system with “negative damping forces,” that is, reaction forces which act in the direction of motion. Dur­ing a few years, we have encountered several obscure vibration phenomena which, upon closer examination, appeared to belong to this class. The most representative group is governor hunting phenomena.

In those instances when we have run into the oil-film whirl, we have succeeded in eliminating it by modifications of the oil flow to the bearing. Some years ago, we used to have a “round- hole” type of bearing in our turbo-generator test arrangement. They very frequently gave rise to oil-film whirl, which at one time presented a very baffling problem. It was eventually overcome by side relief of the bearings. Our standard bearing with a pronounced side relief and only 90- to 120-deg active support­ing arc has given rise to this problem in only a few rare cases which have been taken care of by detail modifications of the same nature.

The paper presents a welcome addition to this obscure subject and the authors are to be congratulated on their very complete results.

M. S t o n e . 12 The paper covers a very interesting and origi­nal research into a bearing problem that has had many exposi­tions during the past ten years or so. The authors’ experiments, leading to a practical method of reducing the whirling in bearings, form the type of investigation that is all too infrequent.

As to the theories of shaft vibration as affected by bearing oil films, there is much that remains controversial however. As a result of Stodola’s and Hummel’s work mentioned in the paper, this discussor undertook an investigation of such phenomena on large power machines. Very sensitive electromagnetic instru­ments, measuring the position of the shaft in its bearings to an accuracy of 10-5 in. were mounted on the 9 in. X 18 in. bearings of a 10,000-kw, 900-rpm synchronous condenser. In this way the motion of the shaft in the hydrodynamic-force field was ob­tained accurately. At the same time, pedestal vibrations were measured with a Geiger vibrograph. Tests were run at various speeds from zero to 900 rpm and for perfect and poor mechanical balance. The results were briefly: (1) No relation between shaft motion and pedestal motion. The latter showed a reso­nance condition, for example, where none was revealed in the former. (2) Motions of shaft in the bearing were so large (0.003 in.) that corresponding critical speeds should be very low, where-

10 Manager, Turbine Apparatus Division, Westinghouse Electric and Manufacturing Co., S. Philadelphia Works, Philadelphia, Pa. Mem. A.S.M .E.11 “Self-Induced Vibrations,” by J. G. Baker, A.S.M.E. Trans., 1933, paper APM-55-2.12 Mechanical Engineer, Westinghouse Electric and Manufacturing Company, East Pittsburgh, Pa.

APPLIED MECHANICS APM-56-10 615as the actual pedestal critical speeds were practically as calcu­lated, not including the apparently very great flexibility in the film itself. This work will be published later.

In Robertson’s paper, referred to by the authors, assumptions are made that far from represent the actual hydrodynamic con­ditions in bearings, such as, for example, that the equilibrium position of a shaft in a horizontal bearing is when the two center­lines are on the same level, etc. Admittedly, an accurate analy­sis of these phenomena is very complex—but there is much to be discarded and much more to be carefully 'scrutinized in the al­ready published works on the question.

A u t h o r s ’ C l o s u r e

In response to Mr. Kroon’s request for our views of the mechanism of oil-film behavior in our bearing we can only repeat the suggestions made in the paper that reduction of lifting power due to the central groove in the bottom, and downward pressure, increasing with increasing speed, due to oil pressure in the top seem to make for stability. A satisfying answer to this question must wait until the hydrodynamic equations are set up for this case and adequately discussed.

It was stated in the 1925 paper that increased unit loading, accomplished by removing some part of the bearing area raised the speed at which whirling would develop. This might well prove a valuable help in cases of trouble in the field.

Dr. Robertson inquires about the process by which we arrived

at the design shown. In the view that bearings of conventional design run with considerable air in the clearance in the upper half we thought a dashpot effect might develop if the upper half could be kept full of oil. The first forms of our bearing were designed to accomplish this. A reduction in the whirling ten­dency was noted and further modifications were made to perfect the performance of the bearing. Later a careful study was made with this bearing and with conventional bearings of the amplitude of critical speed whirling and of the rate at which vibrations die out. It did not show any marked advantage for our bearing in dashpot or damping action.

While the developments of Dr. Robertson’s theory are in­teresting and suggestive the conclusions must be accepted with reservation because the theory of the full circular bearing which Dr. Robertson has taken as his basis leads to conclusions known to be considerably at variances with observed behavior of journals and oil films in bearings.

The backward whirl has been observed in our work. A shaft may whirl at its resonant frequency in either direction if an appropriate tangential stimulus is present. Oil-film action and Coulomb friction act in opposite directions and either may maintain a whirl.

Mr. Soderberg reports that side relief of the bearings has proved effective in overcoming whirling tendencies. We have found this helpful but not so effective (for example in the case of light, high-speed shafts) as the bearing now proposed.