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

Transkrypt

1 The study of rotating units in turbochargers, the influence of relative clearance 19 TRIBOLOGY SCIENTIFIC PROBLEMS OF MACHINES OPERATION AND MAINTENANCE 1 (157) 009 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 Key words Turbocharger, rotating unit, sliding bearing with a floating ring, rigidity and damping factor. Słowa kluczowe Turbosprężarka, zespół wirujący, łożysko ślizgowe z panewką pływającą, współczynniki sztywnoś i tłumienia. Summary 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 veloty ω 1; whereas, a floating ring bearing rotates at angular speed ω. A mathematical model constitutes a system of differential equations, mutually coupled. The mathematical model has been solved by determining the following: acceleration, veloty, and displacement in each knot. The paper shows the crual 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, Rzeszów, tel.: (17) , algarze@rz.onet.pl

2 0 A. Mazurkow 1. Introduction Taking into account osllations generation, a turbocharger (Fig. 1) is an independent system. The essential source of osllations 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 (c x, c y ) and damping factors (d x, d y ) are treated as coupled values. The complete description of the dynamic model is presented in works [6], [7].. 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: [ M x ] [ & x ] + [ D ] [ x& ] + [ Dxy ] [] x& + [ C ][] x + [ Cxy ] [] x = [ Fx (t)], [ M ] [ y& ] + [ D ] [ y& ] + [ D ] [ y& ] + [ C ] [ y] + [ C ] [ y] [ F (t)], & (1) y yy yx yy yx = The depiction of the above matrix elements is presented in the work [6]. y Fig. 1. Model of a rotating unit Rys. 1. Model zespołu wirującego

3 The study of rotating units in turbochargers, the influence of relative clearance 1 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. ): the fixed bearing bush (), 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 rcumferential 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.. The isothermal model of a short bearing has been adopted for calculations of parameters []. Operational parameters are expressed by the following: Sommerfeld Number which for inner oil film equals: S ( + ω ) η ω1 D 1 1B R1 o = F CR1 () Sommerfeld Number which for outer oil film equals: S ηω D B R3 o = F CR (3) Relative eccentrities ε 1, ε, ω Angular veloty of a floating ring ω and the quotient ν = (4) ω Dimensionless stiffness and damping factors for bearing supports: 1 c * c = c c * xy * yx * yy 0 i, c =, c =, c =, where: ψ i c η ω B = (5) d * d = d d * xy * yx * yy 0 i, d =, d =, d =, where: = di di di di ψ i d η ω B Displacement amplitudes in bearing supports: x 5, x 6, y 5, y 6.

4 A. Mazurkow Fig.. The sliding bearing with the floating ring: 1 the fixed bearing bush, the floating ring, 3 the holes in the fixed bearing bush and the floating ring, 4 rcumferential lubricant grooves in the fixed bearing bush and the floating ring, 5 directions of oil flow in a bearing Rys.. Łożysko ślizgowe z panewką pływającą: 1 panewka stała, 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), nd group, the constant value of load and variable values of geometric parameters of geometric knots (Table ), geometric values are chosen in such a way that we can maintain the constant value of the parameter: R i R i (6) CRi

5 The study of rotating units in turbochargers, the influence of relative clearance 3 Table 1. Given parameters from calculations of the rotating unit Tabela 1. Parametry zadane od obliczeń zespołu wirującego Lumped masses in particular knots [N s /m] m 1 m m 3 m 4 m 5 m Bearing loads in knots: (F w, F w3 ) [N] I group: (150, 100), (00, 100), (300, 00), (3500, 300), (400, 350), (500, 400), (600, 450), (700, 500), II group: (400, 600), Radial clearances in bearings, in knots: (C R1, C R ) w, (C R1, C R ) w3 [m] I group: (C R1 ) w,w3 = (C R ) w,w3 = , II group: (C R1 ) w,w3 = (C R ) w,w3 = ; ; ; ; ; ; ; Journal radiuses for inner and outer bearings in knots: (R J1, R J ) w, (R J1, R J ) w3 [m] I group: (R J1 ) w,w3 = I group: (R J ) w,w3 = II group: (R J1, R J ) w,w = (1.54;14.741); (14.15;17.01); (15.8;19.03); (17.33;0.846); (18.718;.517); (0.11;4.071); (1.5;5.531); Bearing bushes widths in knots: (B ) w, (B ) w3 [m] (B) w =0.17 (B) w3 =0.17 Geometric parameters of rotating unit a=0.055 [m] b=0.075 [m] c=0.045 [m] I x = [m 4 ] E= [N/m ] Material constants Rotational speed of a shaft [rps] Ν 1 =500, Unbalance of rotating masses [N s ] η=0,08 [Pa s] N w1 = N w4 = For given parameters which are described above in Table 1, we have determined the following: Sommerfeld Number (S 1, S ), relative eccentrities (ε 1, ε ) rigidity and damping factors in bearings supports, (c, c xy, c yx, c yy, d, d xy = d yx, d yy ), we checked stability as well as calculated amplitudes of displacements in bearing knots: (x 5, x 6, y 5, y 6 ) 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 (S ) w > 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 C R = [m]. Remaining cases worked in the stable area.

6 4 A. Mazurkow a) b) Fig. 3. Dimensionless rigidity and damping factors of oil films for structural cases, where C R1, = const, a) in knot w =, b) in knot w = 3 Rys. 3. Bezwymiarowe współczynniki sztywnoś i tłumienia filmów olejowych dla przypadków konstrukcyjnych, gdzie C R = const, a) strona turbiny (J = 1), b) strona sprężarki (J = )

7 The study of rotating units in turbochargers, the influence of relative clearance Fig. 4. The influence of relative eccentrities on Sommerfeld Numbers Rys. 4. Wpływ mimośrodowoś względnych na liczby Sommerfelda Fig. 5. The influence of the veloty quotient (ν) of a bearing journal and a floating ring on Sommerfeld Numbers Rys. 5. Wpływ ilorazu prędkoś (ν) czopa łożyskowego i panewki pływającej na liczby Sommerfelda 5

8 6 A. Mazurkow 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

9 The study of rotating units in turbochargers, the influence of relative clearance 7 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 veloty of a journal. We can achieve the lowest osllations level of the rotating unit provided that we make the compromise on the choice of radial clearances because values of displacements amplitude (x 6, y 5, y 6 ) grow up while the amplitude of displacements x 5 decreases with the growth of radial clearances. For the case which is considered here the clearance should equal about C R1 = C R = 0, [m]. The bearing which we analyze here the relative clearances equal: for inner oil film ψ 1 = 3,8, and outer oil film ψ = 3,1. References [1] Domes B.: Amplituden der Unwucht und Selbsterregen Schwingungen Hochtouriger mit Rotierenden und nichtrotierenden Schwimmenden Büchsen. Diss. Universität Karlsruhe [] Kaniewski W.: Warunki diatermicznego filmu smarnego. Zeszyty naukowe Politechniki Łódzkiej. Zeszyt specjalny, z. 14, [3] Kiński J.: Dynamika wirników i łożysk ślizgowych. Instytut Maszyn Przepływowych im. R. Szewalskiego PAN, tom 8. Gdańsk 005. [4] Krause R.: Experimentelle Untersuchung eines dynamisch beanspruchten Schwimmbüchsenlagers. ETH, Zürich, [5] Łączkowski R.: Wibroakustyka maszyn i urządzeń WNT, Warszawa [6] Mazurkow A.: Niepublikowane materiały Katedry Konstrukcji Maszyn Politechniki Rzeszowskiej, Rzeszów 007. [7] Mazurkow A.: The research of dynamic properties of rotating units in turbochargers. Sentific Problems of Machines Operation and Maintenance, (154) Vol Radom [8] Muszyńska A.: Modelowanie wirników. IV kurs szkoleniowy z cyklu Dynamika Maszyn. Jabłonna 5 10 listopada [9] Parszewski Z.: Drgania i dynamika Maszyn. WNT, Warszawa 198. [10] Spiegel K., Fricke J.: Bemessungs -und Gestaltungsregeln für Gleitlager: Anlagewinkel, Anund Auslauf, Beanspruchung der Gleitflächen. Gesellschaft für Tribologie e.v., Reibung, Schmierung und Verschleiß. Göttingen, 006. Manuscript received by Editorial Board, January 15 th, 009

10 8 A. Mazurkow Streszczenie Badanie właśwoś dynamicznych zespołów wirujących turbosprężarek 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 prędkośą kątową ω 1, natomiast panewka pływająca z prędkośą kątową ω. Model matematyczny stanowi układ równań różniczkowych, wzajemnie sprzężonych. Rozwiązania równań modelu matematycznego dokonano wyznaczając w każdym węźle: przyśpieszenia, prędkoś i przemieszczenia. W pracy wykazano istotny wpływ względnego luzu łożyskowego na właśwoś statyczne i dynamiczne zespołu wirującego turbosprężarki. Stwierdzono, że zespół wirujący będzie pracował stabilnie jedynie w przypadkach, gdy dla parametrów zadanych właświe zostanie dobrana geometria filmów olejowych. We wnioskach przedstawiono zalecenia dla projektantów tego typu łożysk.