the study of rotating units in turbochargers, the influence of...

The study of rotating units in turbochargers, the influence of relative clearance… 19

SCIENTIFIC PROBLEMS OF MACHINES OPERATION AND MAINTENANCE

1 (157) 2009

ALEKSANDER MAZURKOW*

The study of rotating units in turbochargers, the influence of relative clearance in sliding bearings with a floating ring on static and dynamic properties

K e y w o r d s

Turbocharger, rotating unit, sliding bearing with a floating ring, rigidity and damping factor.

S ł o w a k l u c z o w e

Turbosprężarka, zespół wirujący, łożysko ślizgowe z panewką pływającą, współczynniki sztywności i tłumienia.

S u m m a r y

This work is the continuation of the research concerning the dynamic model of a rotating unit in a turbocharger. In this model, masses of rotors and a shaft have been modelled as combined masses. The rotating unit has been propped on two supports forming lateral sliding bearings with a floating ring bearing. Each bearing is designed including the floating ring bearing mass. The shaft of a rotating unit rotates at angular velocity ω1; whereas, a floating ring bearing rotates at angular speed ω2.

A mathematical model constitutes a system of differential equations, mutually coupled. The mathematical model has been solved by determining the following: acceleration, velocity, and displacement in each knot. The paper shows the crucial influence of a bearing relative clearance on static and dynamic properties of a rotating unit in a turbocharger. The author suggests that the rotating unit will work in a stable state only in those cases where for given parameters the geometry of oil films is appropriately chosen. In conclusion, the author formulates suggestion that might be useful for the designers who work with these types of bearings.

* Rzeszów Uniwersity of Technology, Faculty of Mechanical Engineering and Aeronautics, Powstańców

Warszawy Ave. 8, 35-959 Rzeszów, tel.: (17) 865-16-40, e-mail: [email protected]

TRIBOLOGY •

A. Mazurkow

20

1. Introduction

Taking into account oscillations generation, a turbocharger (Fig. 1) is an independent system. The essential source of oscillations is the rotating unit [3], [5], [8], [9] with bearings. Because of the simple structure, appropriate dynamic properties and a adequate heat transmission in these types of structures, we often use sliding bearings with a floating ring [1], [4], [10]. In the paper, the author describes the influence of relative clearance of a bearing on static and dynamic properties of a rotating unit in a turbocharger.

The discussed model of the rotating unit has been described in the Fig. 1. In this model, each bearing is modelled in such a way that it takes into account the mass of a floating ring. Moreover, we pay attention to rigidity and damping factors as well as damping in oil films. The motion of the model is examined in the two planes: 0XZ and 0YZ. The rigidity factors (cx, cy) and damping factors (dx, dy) are treated as coupled values. The complete description of the dynamic model is presented in works [6], [7].

2. Mathematical model of a turbocharger rotating unit

The equations of motion for the discrete model are presented in Figure 1 and written in the form of matrix in planes 0XZ and 0YZ:

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ],(t)FxxxM xxyxxxyxxx =⋅+⋅+⋅+⋅+⋅ xCCxDD &&&&

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ],(t)FyyyM yyxyyyxyyy =⋅+⋅+⋅+⋅+⋅ yCCyDD &&&& (1)

The depiction of the above matrix elements is presented in the work [6].

Fig. 1. Model of a rotating unit Rys. 1. Model zespołu wirującego


3. Operational parameters of bearing knots

As mentioned, the shaft of a rotating unit is propped on sliding bearings with a floating ring bearing. The constructional elements of a bearing are (Fig. 2): the fixed bearing bush (2), and the loosely fixed floating ring (1) separating the journal and the fixed bearing bush- known as the floating ring bearing. The oil is supplied into the outer and the inner bearing under the pressure through the holes (3), which are in the fixed bearing bush and the floating ring. The circumferential lubricant grooves (4) in the fixed bearing bush and the floating ring bearing provide regular oil feed to the lubricant gaps. The directions of oil flow in a bearing (5) are shown in Fig. 2. The isothermal model of a short bearing has been adopted for calculations of parameters [2]. Operational parameters are expressed by the following:

– Sommerfeld Number which for inner oil film equals:

( ) 2

1

11211

⋅+=

Ro C

R

F

BDS

ωωη (2)

– Sommerfeld Number which for outer oil film equals:

2

2

3222

=

Ro C

R

F

BDS

ηω (3)

– Relative eccentricities ε1, ε2,

– Angular velocity of a floating ring ω2 and the quotient 1

2

ωων = (4)

– Dimensionless stiffness and damping factors for bearing supports:

ci

yyxx

ci

yxxx

ci

xyxx

ci

xxxx

cc

cc

cc

cc

αααα==== **** ,,, , where:

20

2 i

ici

B

ψωηα⋅

⋅⋅= (5)

di

yyxx

di

yxxx

di

xyxx

di

xxxx

dd

dd

dd

dd

αααα==== **** ,,, , where:

2

20

2 i

ici

B

ψωηα⋅

⋅⋅=

– Displacement amplitudes in bearing supports: x5, x6, y5, y6.

A. Mazurkow

22

Fig. 2. The sliding bearing with the floating ring: 1 – the fixed bearing bush, 2 – the floating ring, 3 – the holes in the fixed bearing bush and the floating ring,

4 – circumferential lubricant grooves in the fixed bearing bush and the floating ring, 5 – directions of oil flow in a bearing

Rys. 2. Łożysko ślizgowe z panewką pływającą: 1 – panewka stała, 2 – panewka pływająca, 3 – otwory w panewce stałej oraz pływającej, 4 – obwodowe kanaliki w panewce stałej oraz

pływającej, 5 – kierunki przepływu oleju w łożysku

4. Research of static and dynamic properties

The analysis of static and dynamic properties of the rotating unit in Fig. 1 has been carried out for two groups of structural cases described in (Table 1): − 1st group, constant values of geometric parameters and variable values of

load in bearings knots (Table 1), − 2nd group, the constant value of load and variable values of geometric

parameters of geometric knots (Table 2), geometric values are chosen in such a way that we can maintain the constant value of the parameter:

2

2

⋅

Ri

ii C

RR (6)


Table 1. Given parameters from calculations of the rotating unit Tabela 1. Parametry zadane od obliczeń zespołu wirującego

Lumped masses in particular knots [N·s2/m] m1 m2 m3 m4 m5 m6 5.0 0.3 0.25 2.0 0.055 0.055

Bearing loads in knots: (Fw2, Fw3) [N] I group: (150, 100), (200, 100), (300, 200), (3500, 300), (400, 350), (500, 400), (600, 450), (700, 500),

II group: (400, 600),

Radial clearances in bearings, in knots: (CR1, CR2 ) w2, (CR1, CR2 ) w3 [m]

I group: (CR1)w2,w3 = (CR2)w2,w3 = 0.05·10-3,

II group: (CR1)w2,w3 = (CR2)w2,w3 = 0.02·10-3; 0.03·10-3 ; 0.04·10-3; 0.05·10-3; 0.06·10-3; 0.07·10-3;

0.07·10-3; 0.09·10-3

Journal radiuses for inner and outer bearings in knots: (RJ1, RJ2 ) w2, (RJ1, RJ2 ) w3 [m]

I group: (RJ1)w2,w3 =15.82·10-3 I group: (RJ2)w2,w3 =19.03·10-3

II group: (RJ1, RJ2)w2,w3 ·10-3 = (12.254;14.741); (14.15;17.021); (15.82;19.03); (17.33;20.846); (18.718;22.517); (20.211;24.071); (21.225;25.531);

Bearing bushes widths in knots: (B ) w2, (B ) w3 [m]

(B)w2=0.17 (B)w3=0.17

Geometric parameters of rotating unit

a=0.055 [m] b=0.075 [m] c=0.045 [m] Ix=0.15·10-6 [m4]

Material constants

E=1.915·1011[N/m2] η=0,028 [Pa·s] Rotational speed of a shaft [rps]

Ν1=500, Unbalance of rotating masses [N·s2]

Nw1=0.18·10-4 Nw4=0.5·10-5

For given parameters which are described above in Table 1, we have

determined the following: Sommerfeld Number (S1, S2 ), relative eccentricities (ε1, ε2) rigidity and damping factors in bearings supports, (cxx , cxy , cyx, cyy, dxx, dxy = dyx, dyy ), we checked stability as well as calculated amplitudes of displacements in bearing knots: (x5, x6, y5, y6) for stable structural cases. The results of this study are given in Fig. (3–9).

Structural cases (Fig. 3, 4) whose load was variable, the rotating unit was working in a stable way, and Sommerfeld Number was higher than the value (S2)w2 > 0.6. In other cases, the rotating unit worked in a non-stable state. However, in the second group of structural cases when geometry of a bearing was variable, instability occurred in the case whilst the bearing clearance was the smallest CR = 0.02 ⋅ 10-3 [m]. Remaining cases worked in the stable area.

A. Mazurkow

24

a)

b)

Fig. 3. Dimensionless rigidity and damping factors of oil films for structural cases, where CR1,2 = const, a) in knot w = 2, b) in knot w = 3

Rys. 3. Bezwymiarowe współczynniki sztywności i tłumienia filmów olejowych dla przypadków konstrukcyjnych, gdzie CR = const, a) strona turbiny (J = 1), b) strona sprężarki (J = 2)


Fig. 4. The influence of relative eccentricities on Sommerfeld Numbers Rys. 4. Wpływ mimośrodowości względnych na liczby Sommerfelda

Fig. 5. The influence of the velocity quotient (ν) of a bearing journal and a floating ring on Sommerfeld Numbers

Rys. 5. Wpływ ilorazu prędkości (ν) czopa łożyskowego i panewki pływającej na liczby Sommerfelda

A. Mazurkow

26

a)

b)

Fig. 6a) amplitudes of displacements in bearing knots in a radial clearances function, b) amplitudes of displacements in bearing knots in a Sommerfeld Numbers function

Rys. 6a) amplitudy przemieszczeń w węzłach łożyskowych w funkcji luzów promieniowych, b) amplitudy przemieszczeń w węzłach łożyskowych w funkcji liczb Sommerfelda


5. Conclusions

According to the results reported in this study, we can see the significant influence of Sommerfeld Number on work stability of the rotating unit. The stability of the rotating unit has been achieved due to the boost in bearings load (I group of structural cases), and the change of geometry of a bearing (II group of structural cases). The rotating unit works stably only in these cases when we choose properly a geometry of oil films for a given load and angular velocity of a journal. We can achieve the lowest oscillations level of the rotating unit provided that we make the compromise on the choice of radial clearances because values of displacements amplitude (x6, y5, y6) grow up while the amplitude of displacements x5 decreases with the growth of radial clearances. For the case which is considered here the clearance should equal about CR1 = CR2= 0,06·10-3 [m]. The bearing which we analyze here the relative clearances equal: for inner oil film ψ1 = 3,8 ‰, and outer oil film ψ2 = 3,1‰.

References

[1] Domes B.: Amplituden der Unwucht – und Selbsterregen Schwingungen Hochtouriger mit Rotierenden und nichtrotierenden Schwimmenden Büchsen. Diss. Universität Karlsruhe 1980.

[2] Kaniewski W.: Warunki diatermicznego filmu smarnego. Zeszyty naukowe Politechniki Łódzkiej. Zeszyt specjalny, z. 14, 1977.

[3] Kiciński J.: Dynamika wirników i łożysk ślizgowych. Instytut Maszyn Przepływowych im. R. Szewalskiego PAN, tom 28. Gdańsk 2005.

[4] Krause R.: Experimentelle Untersuchung eines dynamisch beanspruchten Schwimmbüchsenlagers. ETH, Zürich, 1987.

[5] Łączkowski R.: Wibroakustyka maszyn i urządzeń WNT, Warszawa 1983. [6] Mazurkow A.: Niepublikowane materiały Katedry Konstrukcji Maszyn Politechniki

Rzeszowskiej, Rzeszów 2007. [7] Mazurkow A.: The research of dynamic properties of rotating units in turbochargers.

Scientific Problems of Machines Operation and Maintenance, 2(154) Vol. 43 2008. Radom [8] Muszyńska A.: „Modelowanie wirników”. IV kurs szkoleniowy z cyklu Dynamika Maszyn.

Jabłonna 5–10 listopada 1979. [9] Parszewski Z.: Drgania i dynamika Maszyn. WNT, Warszawa 1982. [10] Spiegel K., Fricke J.: Bemessungs -und Gestaltungsregeln für Gleitlager: Anlagewinkel, An-

und Auslauf, Beanspruchung der Gleitflächen. Gesellschaft für Tribologie e.V., Reibung, Schmierung und Verschleiß. Göttingen, 2006.

Manuscript received by Editorial Board, January 15th, 2009

A. Mazurkow

28

Badanie właściwości dynamicznych zespołów wirujących turbosprężarek

S t r e s z c z e n i e

Praca stanowi kontynuację badań modelu dynamicznego zespołu wirującego turbosprężarki. W modelu tym masę wirników i wału zamodelowano jako masy skupione. Zespół wirujący został podparty na dwóch podporach stanowiących poprzeczne łożyska ślizgowe z panewką pływającą. Każde łożysko zamodelowano uwzględniając masę panewki pływającej. Wał zespołu wirującego obraca się z prędkością kątową ω1, natomiast panewka pływająca z prędkością kątową ω2. Model matematyczny stanowi układ równań różniczkowych, wzajemnie sprzężonych. Rozwiązania równań modelu matematycznego dokonano wyznaczając w każdym węźle: przyśpieszenia, prędkości i przemieszczenia. W pracy wykazano istotny wpływ względnego luzu łożyskowego na właściwości statyczne i dynamiczne zespołu wirującego turbosprężarki. Stwierdzono, że zespół wirujący będzie pracował stabilnie jedynie w przypadkach, gdy dla parametrów zadanych właściwie zostanie dobrana geometria filmów olejowych. We wnioskach przedstawiono zalecenia dla projektantów tego typu łożysk.

the study of rotating units in turbochargers, the influence of...

Documents