Turbocharger bearing support and rotor dynamics · PDF fileTurbocharger bearing support and rotor dynamics Bearing support and dynamics of turbocharger rotors ... K yx in Fig. 4)

Turbocharger bearing support and rotor dynamics

Bearing support and dynamics of turbocharger rotors Most of turbocharger (TCH) rotors are supported in floating-ring bearings (Fig. 1, item 4). These bearings are undemanding from manufacturing point of view and at the same time have good dynamic properties, resulting from high damping of the two oil films arranged in series. Renowned producers of TCH use 2 types of floating rings, i.e. rotating and non-rotating (stalled/semifloating) ones. Non-rotating bushings are sometimes arranged in one common casing called one-piece bushing or bushing “two in one”.

Fig. 1 Turbocharger rotor supported in two rotating bushings (left) and non-rotating double

bushing (right)

TCH rotors are specific by having journal bearings relatively close one to the other and heavy compressor and turbine impellers mounted at both overhang ends of rotor. Rotor dynamics is therefore to a great extent influenced by gyroscopic moments of impellers. Due to gyroscopic moments critical speeds of the rotor split to branches with co-rotating and counter-rotating precession, as can be seen from Campbell diagram in Fig. 2.

Fig. 2 Campbell diagram; without gyroscopic moment – left, with gyroscopic moments - right

Critical speeds of counter-rotating precession, which are lower than co-rotating ones, are not excited by unbalance and therefore they need not be considered in dynamic analysis. On the other hand branches of critical speeds with co-rotating precession are shifted due to gyroscopic moments to higher frequencies (curves 6 and 8), so that often they do not cross speed axes. In


such a case there is no bending critical speed in overall operating speed range. It is evident, that influence of gyroscopic moments to dynamics of TCH rotors is favourable, because TCH operate in broad speed range and due to gyroscopic effects it is possible to achieve whole operating speed range without resonance phenomena.

Problems of small and big TCH are somewhat different; in further text they will be therefore divided into two groups:

a) medium + big (for big trucks, stationary engines and ships) ,

b) small (for passenger vehicles and small trucks). 1.0 Turbochargers for medium and big engines

1.1 Rotating bushings

Rotating floating bushings exhibit speed equal to 0,15 to 0,35 of rotor speed; rotating speed depends on the bushing geometry, namely on ratio of inner to outer clearance, but partly also on bearing load (bushing speed of more loaded bearing at the turbine side used to be somewhat lower). Computer program for thermo-hydrodynamic calculation (considering viscosity changes due to temperature) should solve also equilibrium of moments at inner and outer bushing surface. As can be seen from Fig. 3, which present results of measurement and calculation of bushing speed of two different TCH types, the agreement between experimental and theoretical values is quite satisfactory.

Fig. 3 Measured and calculated bushing speed of two different types of TCH

TCH bearings are relatively lightly loaded – specific load varies in tenths of MPa and at compressor side it can be still lower. Lightly loaded bearings of circular cross section tend to instability of „oil whirl“ type, called also „half-speed-whirl“, because journal revolves around bearing centre with approximately one half of rotor rotation speed. Instability, or self-excited vibration, is invoked by destabilizing forces, which are generated in oil film due to high cross-coupling terms of stiffness matrix of a cylindrical bearing (elements Kxy, Kyx in Fig. 4).

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Fig. 4 Stiffness and damping elements of a bearing with rotating bushing

Instability of TCH rotor takes place mostly in outer oil film, which has lower specific load due to bigger dimensions. Tendency to instability of outer oil film, which is manifested by vibration with frequency equal to one half of bushing speed, can be found out by measurement of rotor relative vibrations (by relative vibrations we mean rotor excursions relative to TCH casing). Potential instability of outer film can be seen in frequency spectra of the rotor and bushing in Fig. 5, where quite dominating frequency component is that of about 110 Hz, which is one half of bushing speed.

Fig. 5 Frequency spectra of the rotor (up) and floating bushing (down)

Speeds of both bushings can be recognized in frequency spectra, which somewhat differ at compressor and turbine side. In most cases the instability is not fully developed, because this instability is not supported by exciting frequency of the rotor and also due to already mentioned high damping. However, some rotors with rotating bushings exhibit fully developed instability and the rotor vibrates within the whole bearing clearance, as can be seen from recorded signals in Fig. 6 and 7. Immediate failure does not occur only due to strongly nonlinear properties of the oil film, the stiffness of which significantly grows at high eccentricities of the rotor and bushing. Permanent TCH operation with these vibration levels is very dangerous, because relatively small change of operating conditions or penetrating of some solid particle into the bearing clearance may results in heavy damage of bearings and rotor.

Fig. 6 and 7 present relative vibrations of the rotor and bushings of a big TCH, specified for motors with the output of 1200 to 1700 kW [1]. Top down are given following signals:

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rotor –compressor side (RC) rotor – turbine side (RT) bushing - compressor side (BC) bushing - turbine side (BT)

Fig. 6 Fully developed instability of outer oil film at 40.000 rpm [1] (maximum vibration amplitude 45 µm)

Fig. 7 Fully developed instability of outer oil film in bearings with bigger clearance at 42.000 rpm [1] (maximum vibration amplitude 140 µm)

From signal in time domain and frequency spectra of both above examples it is apparent that both rotor ends and both floating bushings vibrate in-phase with subharmonic frequency equal to one half of bushing speed (about 56 and 59 Hz respectively) and with amplitude achieving practically the whole bearing clearance. Frequency of rotor speed (667 and 700 Hz, respectively) is hardly discernable at frequency spectra.

1.2 Stalled (semi-floating) bushings

To eliminate danger of instability non-rotating – stalled/semi-floating bushings were designed, which utilize only damping effect of outer oil film, generated by squeezing the oil out of bearing gap (so called „squeeze film“ effect) when the rotor vibrates due to residual unbalance. If the bushing does not rotate, no instability of outer oil film can occur, because there are no destabilizing forces. However, cylindrical inner geometry in most cases cannot ensure rotor stability, and it should be designed as a lobbed bearing with certain preload of sliding surfaces. Often used two-lobbed (lemon) geometry is not suitable due to strong anisotropy (different stiffness and damping in two perpendicular directions). With regard to manufacturing technology it is not possible to use offset-halves bearing geometry, which is applicable only with split bearings. As relatively the most simple therefore appears three-lobbed bearing, which could be


designed as bidirectional or unidirectional (see Fig. 8). Three-lobbed geometry is seldom used for bearings of bigger machines, because it is practically impossible to accomplish such a bearing as split. With floating bushings, which on the contrary cannot be split, it is a possibility how to achieve good dynamic properties with relatively simple geometry.

Fig. 8 Three-lobbed bearing with load on pad (LOP); left - bidirectional, right – unidirectional

As is evident from diagrams in Fig. 9, displaying stiffness and damping elements of both three-lobbed bearing types, bearing properties are isotropic – elements Kxx and Kyy, Bxx and Byy are the same.

Fig. 9 Comparison of stiffness and damping of bidirectional and unidirectinal three-lobbed bearing

It can be seen from Fig. 9 that unidirectional bearing has higher direct stiffness elements Kxx, Kyy and lesser difference between both cross-coupling (destabilizing) elements Kxy, Kyx, which is favourable from the standpoint of stability. Also direct damping elements Bxx, Byy of unidirectional bearing are higher than those of bidirectional one. These relations are valid for the case of static load orientation according to Fig. 8, i.e. load oriented „on pad“, (designated as LOP - load on pad). In case that static load is oriented „between pads“, according to Fig. 10 (designated as LBP – load between pads), the situation is somewhat changed. The influence of load direction in bidirectional bearing is documented by stiffness and damping diagram in Fig. 11. The difference between direct stiffness and damping elements is relatively great, while higher values are provided with load direction LBP. With LBP load orientation the difference between cross-coupling stiffness terms increases, which aggravates resistance to instability; as

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generally more favourable can be considered load orientation LOP. However, in TCH with low static bearing load dynamic load component from residual unbalance prevails, which will be manifested by certain change of bearing dynamic properties during one revolution.

Fig. 10 Three-lobbed bearing with load between pads (LBP); left - bidirectional, right – unidirectional

Fig. 11 Load direction influence on stiffness and damping elements of a bidirectional bearing

Influence of static load orientation on stiffness and damping of a unidirectional bearing is demonstrated in diagrams in Fig. 12. Situation is similar to that of bidirectional bearing, influence of load direction on direct stiffness elements is weaker, than in bidirectional one, however influence on direct damping elements is substantially stronger. Weaker is also influence of static load orientation on difference between cross-coupled stiffness elements. As well as in bidirectional bearing, more favourable is load direction LOP, what should be respected at TCH assembly. As was stated above, due to prevailing dynamic load component during TCH operation, the real bearing orientation has no fundamental significance.

Comparison of bearing types from the point of dynamic properties therefore turns out somewhat more favourably for unidirectional bearing, namely as regards stability. It holds also with substantial increase of oil inlet temperature, which becomes more and more up-to-date with regard to still growing TCH parameters. Increasing the oil inlet temperature from 80 to 120°C brings lowering of direct stiffness and damping elements, which is somewhat more pronounced in unidirectional bearings. However, the difference between cross-coupling stiffness terms, which is decisive as regards stability, remains in unidirectional bearings substantially lesser than

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in bidirectional ones; with growing oil inlet temperature the difference changes still more in favour of unidirectional bearings.

Fig. 12 Load direction influence on stiffness and damping elements of unidirectional bearing

Most relative rotor vibrations were measured only on rotors supported in stalled bushings with bidirectional geometry. Fig. 13 presents signals in time domain and frequency spectra of the same rotor as in Figs. 6 and 7, this time supported in three-lobbed non-rotating bidirectional bushings.

Fig. 13 Stable operation of rotor in three-lobbed bidirectional stalled bushings at 42.000 rpm [1] (the same rotor as in Figs. 6. and 7, maximum vibration amplitude 25 µm)

In comparison with rotating bushings support vibration amplitudes of the rotor decreased from 45 µm, or 140 µm to about 25 µm and only rotational frequency of rotor was present at frequency spectra. With another variant of stalled bushings the vibration amplitude decreased even to 5 µm; subharmonic frequency of about 215 Hz appeared in frequency spectra of the rotor at turbine side with amplitude not exceeding 2 µm.

Comparative measurement of unidirectional and bidirectional bushings was carried out on smaller TCH (for motors with output about 500 kW) in 2010 [3]. As is proved by frequency spectra in Fig. 14, rotor vibration amplitude at speed in neighbourhood of 80.000 rpm in unidirectional bushings is less than half of that in bidirectional bearings. In region of lower speeds the difference between both bearing support variants is substantially lower. This is documented by diagram of RMS value of rotor vibration amplitude vers. speed, which is shown in Fig. 15. In frequency spectra of both bearing types there are only components with frequency of rotor speed, while amplitude of subharmonic frequency component is negligible.

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Fig. 14 Comparison of vibration amplitude of the rotor supported in bidirectional (left Aot≈15 µm) and unidirectional (right Aot≈6 µm) stalled bushings at about 80.000 rpm

Fig. 15 Comparison of RMS value of rotor vibration amplitude in unidirectional and bidirectional bushings

Theoretical assumption concerning better stability of unidirectional bushings in comparison with bidirectional ones could not be verified experimentally, because stability limit was not achieved even with bidirectional bushings. Better dynamic properties of unidirectional bushings were indirectly confirmed by measurement of lower rotor vibration amplitudes of the rotor.

1.3 Comparison of rotating and stalled bushings

For comparison of bearings with rotating and stalled bushing Figs. 16 and 17 present signals in time domain and frequency spectra of a smaller TCH rotor (for motors with the output of 350 to 1200 kW). Results for bi-directional bearings only are available [2]. Sequence of signals in Figs. 16 and 17 is the same as in Figs. 6, 7 and 13, i.e. RC, RT, BC, BT. Fully developed instability of the rotor supported in rotating bushings is shown in Fig. 16; quite dominant at the spectra is subharmonic frequency with one half of bushing speed about 110 Hz, rotor speed of 1200 Hz is hardly discernible.

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Fig. 16 Fully developed instability of smaller TCH with the rotor supported in rotating bushings at 72.000 rpm [2] (maximum vibration amplitude about 55 µm)

On the other hand the same rotor supported in stalled bidirectional bushings exhibits stable operation with vibration amplitude limited to about 10 µm, which is documented by Fig. 17.

Fig. 17 Stable operation of the same TCH as in Fig. 14 with the rotor supported in stalled bidirectional bushings at 72.000 rpm [2] (maximum vibration amplitude about 10 µm)

To asses vibration characteristics of high-speed rotors the most important quantity is RMS (root mean square) value of velocity or deviation. This quantity is determined statistically from the record containing great number of cycles. If the record is not distorted by strong electric disturbances, it very well represents intensity of vibration. RMS value of velocity is used in measurements of absolute vibrations at the machine casing or bearing pedestals, while RMS value of amplitude is used for relative vibration measurement.

If the rotor is supported in rolling bearings, it is possible to obtain representative values of vibration level by measurement of absolute vibrations. However, sliding bearings, due to their high damping, transfer to machine casing only minimum of rotor vibration. To get representative data it is therefore necessary to measure relative rotor vibration and evaluate RMS value of amplitude. Fig. 18 presents RMS values of vibration amplitude of two TCH, with rotors supported in rotating and stalled bushings, in dependence on speed. It concerns TCH of different dimensions, the vibration records in vicinity of maximum speed and pertinent frequency spectra of which were presented earlier (Figs. 6, 7, and 16 – rotating, Figs. 13 and 17 - stalled). In both cases there is very significant reduction of RMS value of vibration amplitude in the whole operating speed range with rotors supported in stalled bushings with three-lobed inner geometry.


Fig. 18 Comparison of RMS values of rotor vibration amplitude in rotating and stalled bearings; left – big TCH [1] (Figs. 6, 7 and 13), right – smaller TCH [2] (Figs. 16 and 17)

2.0 Turbochargers for automobile engines

Due to small bushing dimensions (inner diameter varies from 5 to 10 mm) and great number of manufactured pieces it is not viable to use lobbed inner geometry in small TCH. Rotor instability with rotating and stalled bushings is therefore prevented by simpler means, in most cases by interruption of continual cylindrical surface by axial grooves (Fig. 19).

Fig. 19 Floating rings with inner sliding surface interrupted by axial grooves

2.1 Rotating bushings

Extensive measurement of relative rotor vibrations of small TCH, carried out simultaneously with measurement of vibrations at bearing casing of several different types of TCH, enabled to investigate namely subharmonic frequencies, which could indicate rotor instability. Results of these tests enable to make some more general conclusions for dynamic behaviour of rotors supported in rotating bushings, because one rotor with three variants of bearing support, differing only by ratio of outer and inner clearance was used in one test [7]. Inner and outer bushing diameter was Di = 9 mm and Do = 13,5 mm. Dimensionless data of variants designated

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as V1 to V3 are, together with data of a smaller TCH [5, 6] (Di /Do = 6/9 mm, designated as V5), given in following table: V1 V2 V3 V5

inner relative clearance 4,2.10-3 3,1.10-3 4,1.10-3 3,7.10-3 outer relative clearance 6,5.10-3 4,3.10-3 3,2.10-3 7,1.10-3 co/ci ratio 2,35 2,15 1,19 3,09

The most important result of the test is the fact, that in frequency spectra of the rotor (and bushing) there was always subharmonic frequency linked to bushing speed. However, this frequency was equal neither to one half of bushing rotational frequency, which indicates instability of outer oil film (see chapter 1.1), nor to one half of sum of rotor and bushing frequencies, which should signalize instability of inner film.

Fig. 20 shows mutual dependency of subharmonic frequency and frequency of rotor or bushing rotation.

Fig. 20 Ratio of subharmonic frequency to frequency of rotor and bushing rotation

It can be seen from the left diagram, that ratio of subharmonic frequency to rotor rotational frequency varies from about 0,6 – at minimum speed, to about 0,2 – at maximum speed. As subharmonic frequency is linked to bushing speed, it is lowest for the bushing with small co/ci ratio of var. V 3. Subharmonic frequency follows also sharp changes of bushing speed caused by vacillation of inlet oil temperature (var. V2, V3), or by passage of bending critical speed of the rotor (var. V5 around 90.000 rpm). It can be seen from the right diagram of Fig. 20 that ratio of bushing speed to subharmonic frequency varies for one type of the rotor in relatively narrow range 0,3 to 0,5 (var. V1, V2, V3), while for smaller rotor with higher co/ci ratio it varied from 0,5 to 0,7.

Left diagram in Fig. 21 shows relative bushing speed in dependence on rotor speed. Ratio of fp/fot varies in the range 0,1 to 0,3 (var. V1-V3) or 0,2 to 0,35 (var. V5). It can be seen from the curves for variants V1, V2, V3, that co/ci ratio has relatively small effect on bushing speed; individual curves even intersect one another. Stronger influence has evidently bushing geometry; bushings of var. V1-V3 had peripheral groove for oil distribution at outer sliding surface, while var. V5 has outer surface without groove, but inner sliding surface has much narrower width than outer one.

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Fig. 21 Relative bushing speed, ratio of subharmonic frequency to rotor and bushing rotation frequency

Right diagram in Fig. 21 shows dependence of subharmonic frequency and rotational frequency of both bushings of V5 variant on rotor speed. Mutual relationship of subharmonic frequency and bushing rotational frequency is very well apparent, inclusive vacillation in region of 90.000 rpm, when rotor passed through the 1st bending critical speed. It is the one from very rare cases, when passage of bending critical speed in TCH was so distinct.

Passage of bending critical speed is very well noticeable also from records of run-up and run-down of var. V5 in Fig. 22.

Fig. 22 Run-up and run-down of TCH rotor variant V5

Up down are displayed signals from relative sensors of the rotor located 45º from vertical (up – sensor in upper part of casing, amid – sensor in lower part of casing) and from accelerometer fastened to bearing casing (lower signal). Rapid changes of vibration amplitude of the rotor, which are discernible also on casing vibrations, testify change of rotational axis. When passing through critical speed rotational axis changes from axis of symmetry to the main inertia axis, while the phase angle alters 180º. It is worth mentioning, that the 1st bending critical speed

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determined by calculation was around 83.000 rpm, which very well agrees with results of this test. Records of run-up and run-down show clearly also lift or drop of the rotor, caused by generation or squeeze out of hydrodynamic lubricating film.

Fig. 23 demonstrates agreement of measured and calculated bushing speed for variants V1, V2 (left diagram) and V5 (right diagram).

Fig. 23 Calculated and measured bushing speed variants V1, V2 and V5

Satisfactory qualitative agreement of theoretical and experimental values (corresponding slope of the curve as a function of speed) is evident, quantitative agreement can be considered as good for var. V1. Calculated bushing speed is universally lower than measured.

Accuracy of ascertaining rotor critical speed is dependent on used dynamic model. Following conclusions can be drawn from the example of var. V5 and other analyzed cases:

• The 1st bending critical speed, which is not much dependent on stiffening of the shaft by compressor impeller, could be determined with satisfactory precision,

• The 2nd bending critical speed, which is on the contrary strongly dependent on stiffening of the shaft by compressor impeller, cannot be calculated with sufficient accuracy; therefore it is necessary to carry out vibration measurement, preferably on the rotor and casing simultaneously.

Changes of the 1st and 2nd bending critical speed with consideration of shaft stiffening by compressor impeller are summarized in Table 1. PP or SP in table designates type of precession; critical speed of counter-rotating precession (backward) PP is not contrary to co-rotating precession (forward) SP excited by unbalance. It can be seen from the table that position of the 1st b.c.s. (bending critical speed) is minimally influenced by stiffening of the shaft, but position of the 2nd b.c.s. is influenced substantially. It is given by the shaft bending modes, which are different for individual rotors and that is why influence of shaft stiffening on position of the 2nd b.c.s. will be different. Rate of shaft stiffening is dependent on the shape of the impeller, its interference with the shaft and other factors, which can to some extent differ even in case of rotors of the same type. To estimate stiffening influence of compressor impeller on position of the 2nd b.c.s. is thus very difficult.

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Table 1 Critical speeds of rotor of V5 variant

Branch

No.

Vibration mode

Type of precession

Critical speed (rpm) and rate of damping (%)

without stiffening with stiffening

5 1st bending PP 34.116 31,6 % 36.355 40,0 %

6 1st bending SP 82.063 21,3 % 83.141 23,4%

7 2nd bending PP 104.649 28,0 % 134.759 16,2 %

8 2nd bending SP 169.326 3,8 % 241.293 2,0%

Improperly designed rotor can behave in a manner shown in left diagram of Fig. 24, which shows unacceptable increase of velocity in region of maximum speed at bearing casing, indicating proximity of the 2nd b.c.s.

Fig. 24 RMS values of velocity at TCH casing of improperly (left) and well (right) designed rotor

Improperly designed rotor exhibits in region around 200.000 rpm RMS value of velocity exceeding 10 mm/s in radial direction and even 20 mm/s in tangential direction. Increased unbalance at compressor impeller multiplies these values many times. On the other hand, rightly designed rotor (right diagram) exhibits only local increase of RMS value of velocity in region of passage of the 1st b.c.s. and mild grow in region of maximum speed. Increase of unbalance at compressor impeller does not change this character, which proves that the 2nd b.c.s. is in sufficient distance from maximum speed. 2.2 Stalled/semi-floating bushings

Instability of outer oil film, which was encountered in bigger TCH, was not observed on small TCH. Neither subharmonic frequencies, which are present in spectra of the rotor and bushings, nor magnitude of vibration amplitudes indicate potential instability of inner film. In spite of that, many renowned TCH manufacturers use stalled bushings, but practically only in the form of one-piece bushing. As was already suggested in introduction to this part, danger of instability occurrence is prevented by division of inner sliding surface by axial grooves to several parts, by which destabilizing effects of oil film are reduced. Breaking of continuous sliding surface by axial grooves is not so effective, as use of several sliding surfaces with preload, but in small

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TCH it used to be sufficient. In some cases it is possible to achieve stable operation of the rotor even without breaking of inner sliding surface due to high damping of one-piece bushing.

Example of two TCH of different manufacturers for the same motor demonstrates advantages of stalled double-bushing in comparison with classical rotating bushings. Fig. 25 shows dependence of relative rotor vibrations and acceleration at TCH casing for both upper mentioned types. With regard to rotor excursions and acceleration at TCH casing more favourable values exhibits bearing support with stalled double-bushing. Lower vibration level is apparent namely in region of higher speeds, which is important for especially for automobiles.

Fig. 25 Comparison of RMS values of relative rotor vibrations (left) and acceleration at TCH casing (right) with rotating bushings and stalled double bushing

With regard to Fig. 25 it is necessary to point out that also vibration level of TCH with rotating bushings is still acceptable. Comparison based on one example cannot be generalized, because vibration level is influenced not only by bearing support type, but by many other factors, namely by quality of balancing and distribution of residual unbalance along the rotor, by magnitude of clearances etc. Ratio of rotor vibration amplitudes or acceleration at bearing casing for rotating and stalled bushings can be therefore in case of another pair of TCH quite opposite. Final TCH vibration level is influenced namely by achieved precision of manufacture, balancing and assembly. Manufacturing technology of small TCH should be supplemented by in-situ balancing, i.e. balancing in assembled state, because small deformations occurring during assembly to some extent destroy very good level of balancing of individual parts. Conclusions Turbocharger rotors represent quite special group of rotors, the dynamics of which is substantially influenced by gyroscopic moments of heavy impellers, located at overhang ends of rotor. Due to gyroscopic effects the critical speeds split to branches with counter-rotating and co-rotating precession. Critical speeds with counter-rotating precession are not excited by unbalance and if the branch with co-rotating precession does not intersect speed axis, the whole operation speed range can be without resonance phenomena.

Frequency spectra of rotors with commonly used rotating bushings always include subharmonic frequency related to bushing speed. Subharmonic frequency usually indicates rotor instability, however, real instability in TCH is relatively scarce. In documented cases of bigger

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TCH instability occurred always in outer oil film, because it was characterized by frequency equal to one half of bushing speed. In smaller TCH no instability of either outer or inner oil film was encountered, although marked subharmonic frequency component was in vibration spectra always present.

By use of bearings with staled bushing and lobbed inner geometry was in all documented cases instability of inner oil film suppressed and was achieve stable operation with very low level of rotor vibration amplitude. Bearing design with bi-directional and unidirectional three-lobbed geometry was verified both theoretically and experimentally. Based on results of calculation it can be stated, that somewhat higher stability reserve have rotors supported in unidirectional stalled bushing. It was not possible to prove this fact by experiment, because instability was not encountered neither in unidirectional or in bi-directional bushings. However, results of measurement showed that vibration amplitudes in unidirectional bearings are lower than those in bi-directional ones, by which better dynamic properties of unidirectional bearings are indirectly confirmed.

Facts presented in this study are results of many measurements and calculations, carried out during a number of years. They were obtained on turbochargers of different types and sizes (motors from about 100 to 1700 kW).

References: [1] Šimek, J.: Measurement of rotor and bushing relative vibrations of NR20SJ turbocharger.

Technical report TECHLAB No. 06-413

[2] Šimek, J.: Verification of turbocharger journal bearing conception. Technical report TECHLAB No. 06-416

[3] Šimek, J.: Measurement of rotor and non-rotating bushing relative vibrations of TCR14 turbocharger. Technical report TECHLAB No. 06-410

[4] Šimek, J.: Verification of influence turbocharger journal bearing conception on behaviour of small turbocharger rotor. Technical report TECHLAB No. 07-403

[5] Šimek, J. - Svoboda, R.: Theoretical and experimental analysis of dynamic behaviour of KKK and Garrett turbochargers. Technical report TECHLAB No. 10-414

[6] Šimek, J. - Svoboda, R.: Theoretical and experimental analysis of dynamic behaviour of KKK and Garrett turbochargers. 2nd part. Technical report TECHLAB No. 11-402

[7] Šimek, J.: Analysis of C13 turbochargers vibration measurement. Technical report TECHLAB No. 11-404

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