Experimental investigation of self-excited vibrations of rotors due to the action of lubricating oil film in journal bearings

EXPERIMENTAL INVESTIGATION OF SELF-EXCITED VIBRATIONS

OF ROTORS DUE TO THE ACTION OF LUBRICATING OIL FILM IN

JOURNAL BEARINGS*

A. TONDI,

The ATational Research Institute of Heat Engineering, Prague (Czechoslovakia)

INTRODUCTION

The paper contains some of the results of an experimental investigation of self- excited vibrations of rotors caused by the action of lubricating oil film in journal bearings. The investigation was carried out partly to continue and supplement theoretical work293, partly to study certain effects of various parameters and compare the resistance of various types of bearings to the initiation of self-excited vibration. In addition to conventional cylindrical and elliptical bearings, tests were also conducted with CKD-type4 multi-lobe bearings, flexible-element bearings according to author’s designs, and with two versions of the loose-bushing bearings, one with cylindrical, the other with flexible-element loose bushing.

NOTATION

bearing length (cm) bearing diameter (cm) rotor weight (kg) specific load (kg/cmz) journal diameter (cm)

2d=D-

280

e

bearing clearance (cm) loose-bushing clearance (cm) eccentricity of the journal motion trajectory from the

bearing centre (cm) a = e/d

n0

n

ns

relative eccentricity of the journal motion trajectory rotor critical speed (minr) rotor speed (min-1) rotor speed at which self-excited vibrations are initi-

ated (min-1) w WE

angular velocity of rotor rotation (set-l) angular velocity of rotor rotation at which self-excited

vibrations are initiated (set-1) WO rotor natural angular frequency (set-r) q8 = n&0 = C&JO limit ratio of the initiation of self-excited vibrations

* Condensed from a monograph published by the National Research Institute of Heat Engineer- ing, Prague, Czechoslovakia, under the same titlcl.

Wear, 5 (1962) 136-147

SELF-EXCITED VIBRATIONS OF ROTORS I37

cf,

t V

h

V

H

f

outside diameter of the flexible-element bearing measured over the flexible elements (mm)

lubricating oil outlet temperature (“C) double amplitude of the journal motion in vertical

direction (mm) double amplitude of the journal motion in horizontal

direction (mm) double amplitude of the disk motion in vertical direc-

tion (mm) double amplitude of the disk motion in horizontal

direction (mm) frequency of measured vibrations (min-1)

TEST EQUIPMENT, METHOD OF MEASUREMENT AND TYPES OF INVESTIGATED BEARINGS

The test rotor with a single disk located mid-shaft was mounted in two bearings (see overall view of test equipment in Fig. I). Three test rotors were used, all with a jour-

Fig. I. View of the test and measuring equipment. (Capacitive Tesla indicator on the right-hand side of the bench.)

nal diameter of 40 mm and equal length (40 mm) of all test bearings. The first two rotors used in the majority of tests had a critical speed rzo of about IOOO rev./min. The specific loads of the bearings were 1.65 kg/cm2 (the heavier rotor) and 1.18 kg/cm2 (the lighter rotor). The third rotor giving a specific load of 1.11 kg/cm2 was slightly bent and had a critical speed of 730 rev./min. It was used in the study of the effect of bent shaft upon the limit of the initiation of self-excited vibrations.

Wear, 5 (1962) 136-147

138 A. TONDL

The rotor was driven by a Ward-Leonard set with a maximum speed of 8000 rev.; min. Turbine oil with a viscosity of 22.39 CP at 50°C was used for lubrication in most tests.

Five types of bearings were investigated. Four pairs of cylindrical bearings had a clearance 28 = 0.2; 0.4; 0.8 and 0.3 mm, respectively. The first three pairs were split, bronze bearings; the fourth was a steel, babitted bearing.

Fig. 2. Schematic diagram of the CKD multi-lobe bearings.

40 /

I I Aj Bi

Fig. 3. Flexible-element bearing.

Two pairs of elliptical bearings were made in the same way as the split bronze bearings. The first had a clearance 281 = 0.28 mm in the vertical direction, and 282 = 0.5

mm in the horizontal direction; the second, 2& = 0.18 mm, and 282 = 0.4 mm. TWO

W~ZI, _s (1962) 136-~47


versions (three- and four-lobe bearings - Fig. 2) of the first type of multi-lobe bearings (made in accordance with the CKD patent application4 were tested. The principal bearing diameter is the same in both versions, viz. D = 40.2 mm (6 + 2s). This basic form was further modified by generating additional cylindrical surfaces having a radius RI and by displacing the centre by A. Since RI < $0, it is not necessary to split the bearings. Both bearings were made entirely symmetrical, whole and babitted. In the first case RI = 19.93 mm, A = 0.29 mm, in the second case RI = 19.72 mm and A = 0.50 mm.

Three versions of flexible-element bearings were tested: one with three identical and identically oriented elements, the other with four, two shorter and two longer, identically oriented elements (Fig. 3), and the third with three differently oriented elements.

The last type of bearings were those with a loose bushing. The working bushing is inserted into the bearing with a clearance. The clearance between the bearing and the loose bushing is filled with pressure oil, which acts as a cushion damping the working bushing motion. The bushing was made in two versions, namely cylindrical, provided with three symmetrically arranged axial cuts to permit the influx of pressure oil, and bushing with flexible elements (Fig. 4).

Fig. 4. Loose-bushing bearing; loose bushing is of the flexible-element type.

In the measurements, in addition to an optical method, a capacitive Tesla indicator was used, which made it possible to pick up two motion components. It was also possible to compose the signals of pick-ups following the vertical and horizontal motions and photograph directly the trajectory of the journal or disk motion.

CHARACTERISTIC FEATURES OF SELF-EXCITED VIBRATIONS AND SUB-HARMONIC

RESONANCE

During the experimental investigations two distinct phenomena have been observed, namely self-excited vibrations and the subharmonic resonance. The basic difference between these phenomena is the fact that the rotor vibrations in subharmonic resonance possess a )resonance character, whereas the self-excited vibrations do not. Let us now review the basic characteristic features of both phenomena.

WeW, 5 (1962) 136-147

Self-excited vibrations of the rotor due to the actiota of lubricating oil film

The most important characteristics of self-excited vibrations can be summarized as follows :

I. Self-excited vibrations can occur only in the case when the speed of the rotor is higher than the rotor first critical speed.

2. The frequency of self-excited vibrations practically equals the frequency of the natural vibrations of the rotor.

3. Self-excited vibrations are not a resonance phenonlenon. They occur within a wide region of rotor speeds, and in the majority of cases this region has only the lower limit, i.e. self-excited vibrations are observed at speeds higher than that at which they are initiated.

4. The limit of initiation depends primarily upon the bearing design. For the least resistant types of bearings and most adverse conditions, the limit lies in the neigh- bourhood of double the critical speed of the rotor.

5. In most cases, self-excited vibrations are very intensive and in bearings having low resistance to these vibrations their amplitude is larger than that corresponding to the critical speed of an unbalanced rotor.

6. The motion of the disk as well as of the journal is executed in synchronous pre- cession, i.e. the disk and the journal whirl in the same direction as the rotor.

7. The motion of the journal and that of the disk are in phase (this applies to the rotor mounted in two bearings).

8. At the onset of self-excited vibrations, there first occurs a change in the vibration frequency, namely a modulation of the vibrations due to the unbalance caused by self-excited vibrations, and then an apparent increase in the self-excited vibration amplitude.

9. When the speed is increased continually, the initiation of self-excited vibrations is almost always retarded (i.e. self-excited vibrations start at higher speeds), the more so the faster the rate of the increase of rotor speed.

IO. When the speed of the rotor is reduced after self-excited vibrations have been initiated, self-excited vibrations continue to exist even below the speed at which they were initiated (even if the speed is increased very slowly).

It follows from the foregoing that in general the ratio of the frequency of the self- excited vibrations and the frequency of vibrations initiated due to the rotor unbalance is not an integer; this is a typical feature very helpful in the identification of self- excited vibrations.

There is one exception with regard to point 9. When the transition through the critical speed was very rapid, then in certain cases, following the transition, the vibration of the journal and the disk contained a motion component having the frequency of the rotor natural vibrations. After the limit of the initiation of self-excited vibrations had been passed the amplitude of this component grew rapidly.

Subharmonic Yesonance

The cause of the origin of the subharmonic resonance is the nonlinear character of the restoring force of the oil film (for theoretical justification see ref. 8). The characteristic features of the subharmonic resonance of this kind can be summarized as follows:

I. The subharmonic resonance is a resonance phenomenon occurring only within a narrow region of the rotor speed.

SELF-EXCITED VIBRATIONS OF ROTORS 141

2. The subharmonic resonance occurs predominantly in the vicinity of double, or

exceptionally, triple the critical speed of the rotor.

3. The vibration frequency equals one half (or one third) of the rotor rotational

frequency.

In the majority of cases the region of the subharmonic resonance occurrence was

narrow and the vibration intensity low, so that during the investigation the rotor speed

had to be carefully adjusted. The vibration amplitude relative to that at the critical

speed was many times smaller particularly in the case of the disk motion. Figure 5

Fig. 5. Diagram plotting the double amplitude of the vertical component of the journal motion in bearing relative to rotor speed; the case of the occurrence of sub-harmonic resonance.

shows the double amplitude of the vertical component of the journal motion relative

to the speed of the rotor mounted in cylindrical bearings. In this case the amplitude

of the vibrations in subharmonic resonance does not exceed double the vibrations in

its immediate vicinity. On the sides of the diagram there are records of the vertical

and horizontal components of the journal motion corresponding to the points marked

on the diagram. Below are the examples of the journal motion trajectories photo-

graphed with a camera.

THE RESULTS OF MEASUREMENT OF THE INDIVIDUAL TYPES OF BEARINGS

In the measurements, appart from the evaluation of the resistance of the individual

types of bearings to the initiation of self-excited vibrations, attention has been directed

to the study of certain effects such as rotor unbalance, shaft deflection, specific

load, oil viscosity, external impulse, effect of the driving motor, etc.

It was found that for all types of bearings the eccentricity of the rotor centre of

gravity exercises practically no effect upon the limit of self-excited vibration initia-

tion and upon its intensity. Similarly, minor changes in the lubricating oil pressure

(as mentioned before, the maximum attainable pressure was within the range of

1.0-1.6 kg/cmz, according to the value of the clearance and the speed of the rotor) had neither qualitative nor quantitative effect upon the initiation and the intensity of

self-excited vibrations.

For evaluating the various tested bearing types and their arrangements, the follow-

ing indices are the most important: the rotor speed at which self-excited vibrations

are initiated, and the intensity of the vibrations in the region of the initiation of self-

excited vibrations. The limit of initiation can best be characterized by the ratio of the

Wear, 5 (1962) 136-147

speed at which self-excited vibrations are initiated ns and the critical speed no or b!. the ratio of angular frequencies qS = ~U,/OO = n&o.

Cylindrical bearings

Self-excited vibrations were always very intensive in cylindrical bearings. As soon as the limit of their initiation had been passed, the amplitudes of vibrations grew ver! rapidly so that it was always necessary to reduce the speed of the rotor considerably, below the initial limit of initiation.

Long-term operation above the limit of initiation of self-excited vibrations was ab- solutely not possible. In practice, there was no interval of speed in which there existed the transition between intensive self-excited vibrations of the rotor and vibrations not containing the component with the frequency of self-excited vibrations.

Only the lower limit of the self-excited vibrations has always been observed for the cylindrical bearings. An attempt has been made to establish the existence of the upper limit of the region of self-excited vibrations, above which they would not occur. With the central split bearing fully clamped, the rotor speed was increased above the limit of the initiation of self-excited vibrations, and at various speeds (up to its maximum value) this auxiliary bearing was partially opened with care. In every case intensive self-excited vibrations occurred so that it was necessary to re-clamp the auxiliary bearing immediately.

Viscosity and specific load exercise a direct effect upon the relative eccentricity of the mean position of the journal centre in the bearing. The question arises whether the limit ratio of the initiation of self-excited vibrations qS can be expressed as a func- tion of the relative eccentricity a = e/d the central position of the journal, or possibly by the equilibrium position of the journal. The limit of initiation of self-excited vibrations in relation to this relative quantity has been expressed by several authors (e.g.2). This mode of expression is, however, criticized by 0. PINK&, who states that the initiation of self-excited vibrations depends in a much more complex manner upon .

‘ . . : .

. m . .

2 . --

0 02 0.4 * 06 o1

Fig. 6. Diagram plotting the relation between the limit ratio q II = n&o of the initiation of self- excited vibration and the relative eccentricity of the journal centre a = e/6. (---, results of experi-

ments, - - -, calculated relation for a half-bearing.)

various factors, such as the temperature, oil viscosity, load, bearing clearance, etc. He explains the various reported discrepancies by experimental results of his own as well as of other authors. Although the deductions of this author are generally quite justified, the above-mentioned method can be employed for a rough evaluation of cylindrical bearings.

Figure 6 shows the results of measurements, viz. the limit ratio qs in relation to the

WEUY, 5 (1962) 136-147


relative eccentricity a. The theoretically calculated relationship for a half-bearing (see ref. 2) is cross-hatched. Although the quantitative difference is considerable, the qualitative character of both curves is in good agreement.

Elliptical bearings

These bearings exhibited better resistance to the initiation of self-excited vibrations than cylindrical bearings. The limit of initiation of self-excited vibrations was the higher the greater the ratio &/8i. The intensity of self-excited vibrations was lower than in the case of cylindrical bearings. The limit ratio q8 ranged over the limits of 2.7 and 4.9. The intensity of the self-excited vibrations was lower; the increase in the vibration amplitude above the limit of initiation was slighter. At a rapid increase in speed, this limit could be exceeded quite considerably. However, the vibration amplitude continued to increase even after the speed had been reduced and the self-excited vibrations persisted almost to double the critical speed.

This type of bearing bushing exhibited a more pronounced dependence upon the coupling of the driving motor, the effect on both the intensity of the self-excited vibrations and the limit of their initiation being quite significant. In one case, and for one direction of rotation only, the misalignment resulted in the occurrence of self- excited vibrations within a definite, bounded region, i.e. there existed also the upper limit to this region. Otherwise the upper limit of the region of self-excited vibration occurrence was not determined.

For the rotor with bent shaft the limit ratio q8 decreased, in particular for the bearing with larger &/& (q8 = 2.7 - 2.8).

In the region between the critical speed and the limit of initiation of intensive self-excited vibrations, particularly when passing rapidly through the critical speed, one could observe a motion component having the frequency of the rotor natural vibrations, similarly as in the case of a cylindrical bearing with a small clearance.

Multi-lobe bearings

The results of tests showed large differences in both the magnitude of the limit ratio q8 and the intensity of self-excited vibrations. These differences were caused partly by the effect of the driving motor mounting and the misalignment between the rotor and the driving motor axes, partly by a change in the direction of rotation of the rotor. The first effect was much more pronounced in this case than in the remaining four basic types of bearings under test. The second, in view of the assumed plane of symmetry of the bearings, was a proof of unsatisfactory manufacturing accuracy and of high sensitivity of these bearings to manufacturing inaccuracies.

In these bearings direct contact between the journal and the bushing surface is possible only in small areas left after subsequent machining in the original bushing. The question arises whether these parts of the bushing are not subject to a greater wear. Increased wear was actually observed in both bushings following a short period of operation.

Of all bearings under test, these bushings exhibited relatively most intensive subharmonic resonance. But even in this case the amplitude in subharmonic resonance was substantially lower than that of self-excited vibration (see Fig. 7; the lower record of the disk motion contains the speed marks).

~tW, 5 (1962) 136-147

Flexible-element bearings

As mentioned, three types of these bearings were tested, namely bearings with three and four identically oriented elements and one bearing with three differently oriented elements.

Fig. 7. Diagram plotting the double amplitude of the vertical component of disk motion relative to rotor speed (upper figure) and diagram plotting the frequency of vibration relative to rotor

speed (lower figure) ; examples of records of measurement.

Tests were conducted with flexible elements of various thicknesses and for various angular displacements of the bearing bushings, and for both directions of rotation. Considerably more complex conditions were encountered with these bearings than, for instance, with the cylindrical bearings, owing particularly to the fact that the flexible element bearings possess more variable parameters than the cylindrical bearings.

The results obtained showed a large scatter of data for the various arrangements; thus in the design special attention must be given to the proper selection of the bearing parameters and the bearing arrangement. With this type of bearings complete suppression of self-excited vibrations was successfully accomplished, with certain bearings within the whole range of the test speeds, i.e. up to eight times the critical speed.

The bushings were originally designed for one direction of rotation, namely for the rotation of the journal in the direction against the free ends of the flexible elements. But tests were also conducted for the opposite direction of rotation, and rather star- tling results were obtained. The measurements showed that for the latter direction not

Wear, .; (1962) 136-117

SELF-EXCITED VIBRATIONS OF ROTORS 145

only the motion of the journal in the bearing,was smoother and the limit of initiation of self-excited vibrations higher, but also that no significant increase in the temperature of the outlet oil was experienced.

But the capacity of the bearing particularly at higher specific load was reduced. For the rotation against the free ends of the flexible elements the rate of the increase

in the self-excited vibration amplitude was in the majority of cases much higher than for the opposite direction.

In this type of bearings the effect of the viscosity, or of the temperature of the lubricating oil, as well as of the specific load was much more pronounced than in the pre- vious types. In certain arrangements the self-excited vibrations occurred only within a narrow range of the lubricating oil temperatures. Outside this interval no self-

Fig. 8. Diagram plotting the limit speed of the initiation of the rotor self-excited vibration oevs’sus the temperature of outlet oil. 0, self-excited vibrations initiated without external impulse; A, self-

excited vibrations induced by tapping.

excited vibrations could be initiated within the available range of speeds, not even under the action of an external impulse, viz. tapping. Figure 8 shows plots of the limit speed n, of the initiation of self-excited vibration relative to the temperature in “C of the outlet oil.

The circles denote the values associated with the initiation of the self-excited vibrations (without external impulse), and triangles those for self-excited vibrations induced by tapping. In these regions no self-excited vibrations were observed within the given range of speeds. We can further state that the three-element bearings were more advantageous than the four-element ones.

Tests performed with the rotor with bent shaft showed that the limit ratio was practically not reduced even in the case of the four-element bearing.

Since in the case of the journal rotation in the direction of the free ends of the flexible elements better results were on average obtained as regards the resistance against the initiation of self-excited vibration although the bearing capacity was reduced in particular at higher specific loads, an attempt was made to combine both versions in order to exploit the merits of both arrangements and thus obtain sufficient resistance against the initiation of self-excited vibrations and good carrying capacity

as well. A three-element bearing was therefore tested, with two elements in the lower half of the bearing oriented against each other. The upper element is so oriented that the journal rotates against its free end.

Tests have proved that the load-carrying capacity was as good as assumed. Self- excited vibrations of relatively low intensity appeared within a limited interval of the rotor speed, the limits (both the upper and the lower) of which depended slightly upon the temperature of the outlet oil. Outside this interval self-excited vibrations could not be induced even by tapping the rotor.

Bearings with a loose bushing

These bearings were tested in two basic versions differing in the design of the working bushing. In the first case the bushing wascylindrical, in the second it was a flexible- element bushing. It was expected from this design that by loosening the working bushing and placing it into a cushion of pressure oil one would obtain both increased damping of self-excited vibrations and thus an increase in the limit ratio (as compared with the corresponding type of fixed bushing) and improved cooling of the working bushing with streaming oil.

The tests have proved that both goals were attained, particularly in the case of the loose flexible-element bushing, where self-excited vibrations occurred only exceptionally, and when they occurred their limit of initiation was sufficiently high. The working bushing was inserted into the fixed bearing without any protection against possible rotation. A pickup of special design installed directly in the bearing stand per- mitted indication of the loose bushing rotation. It was found during the measurements that at low clearances the bushing rotated very infrequently; only a significant re- duction in the specific load brought about regular rotation of the bushing.

As compared with cylindrical bearings, the limit of initiation of self-excited vibrations was a little higher as long as the rotor shaft was aligned with the driving motor; this held true for both directions of rotation. No difference was found to exist between the limit associated with the external impulse and that of the self-initiation. Misalign- ment of the centrelines of the two shafts (the rotor and the driving motor shafts) resulted in a considerable increase in the limit ratio.

In bearings with small clearances (28 = z& = 0.2 mm) rotation of the working bushing was sometimes experienced. In such cases the limit of initiation of self- excited vibrations was much higher or the self-excited vibrations were not initiated at all.

The flexible-element working bushing greatly raised the bearing resistance to self- excited vibrations. For the rotation in the direction of the free ends of the flexible elements, self-excited vibrations were not initiated and could not be induced even by tapping the rotor. In isolated cases there occurred insignificant disturbances exhibited in the vertical component of the journal motion.

For the opposite direction of the rotor rotation the self-excited vibrations were not initiated when both clearances (zS and 2&t) were large. When the clearances (particularly 6) were small, the self-excited vibrations were observed but the limit of their initiation was high and their intensity relatively low. In all cases the limit of initiation of self-excited vibrations greatly depended on the lubricating oil temperature. A more detailed investigation yielded the fact that self-excited vibrations occurred only within a certain interval of the oil temperatures. Outside this interval, self-excited vibra-

Wear, 5 (1962) 136-147


tions could not be initiated even by tapping the rotor. The intensity of self-excited vibrations also decreased toward the boundaries of this interval.

As we have mentioned before (see section on flexible-element bearings, p. 144)

for the rotation in the direction of the free ends of the flexible elements and at higher specific loads, the bearing load-carrying capacity decreased. With a loose bushing good capacity was obtained for both directions of rotation.

It can be stated that bearings with a flexible-element loose bushing are of all the bearings tested indisputably the most resistant to the initiation of self-excited vibrations and they maintain good load-carrying capacity.

REFERENCES

1 A. TONDL, Experimental investigation of self-excited vibrations of rotors due to the action of lubricating oil film in journal bearings, Monographs and Memoranda, No. I, The National Re- search Institute of Heat Engineering, Prague, 1961.

2 A. TONDL, Vliv nosne mazaci vrstvy na stabi& pohybu Eepu v lotisku a vznik samobuzenych kmitd rotorb, Rozpravy Ceskoslov. akad. vgd, Rada tech. v.?d, 66 (1956) I.

2 A. TONDL, The motion of a journal in a bearing in the unstable region of equilibrium position of the centre of the journal, IX. Congvbs international de mbcanique appliqub, 1957. Vol. 5.

4 J. BLASS, Czechloslovak Patent Application PV 1918. 5 A. TONDL, Czechoslovak Patent No. 87116. osterreichisches Patentschvift Nr. 196181. Deutsche

Patentschrift 1065672. 6 A. TONDL, Czechoslovak Patent Application PV 1968-60. 7 0. PINKUS, Experimental investigation of resonant whip, Trans. ASME, 78 (1956) 975. 8 i\. TONDL, Resonance subharmonique d’un rotor ayant une caracteristique non lineaire des

appuis de roulement, Rev. m&can. appl., Acad. r&b. populaire Roumaine. 2 (1957) 143.

Wear, 5 (1962) 136-147

Documents

Experimental investigation of self-excited vibrations of rotors due to the action of lubricating oil film in journal bearings