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Dynamics of a rotor-aerostatic journal bearings system with asymmetric air feeding

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Abstract

In this study, the effect of the symmetric and asymmetric air feeding on the dynamics of a shaft-aerostatic journal bearing system is theoretically investigated. In this scope, the pressure distribution of the air in the clearance is modeled with Reynold's equation and the lubrication forces are calculated using this distribution. Then, equations of motion derived in four degrees of freedom are solved for different rotational speeds under symmetric and asymmetric air feeding conditions. To validate the simulation results, an experimental test rig comprised of a rotor, air bearings, and measurement equipment is set up and run for different rotational speeds. The nonlinear dynamic behavior of the imbalance responses of the bearing-shaft system is analyzed using bifurcation diagrams, Poincare map, waterfall, and orbit plots. The results of the presented study brought to light that the system has a nonlinear dynamic motion due to a pneumatic hammer. However, the pneumatic hammer frequency of an aerostatic bearing with asymmetric supply pressure condition is lower than an aerostatic bearing with the symmetric condition. And the results also showed that the bearing performance will be improved by asymmetric supply pressure conditions.

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Abbreviations

c :

Clearance between journal and shaft surface, μm

c d :

Coefficient of discharge at orifice

d o :

Diameter of orifice, mm

D :

Diameter of journal, mm

e :

Eccentricity

e u :

Unbalanced degree, μm

F :

Air film force, N

g :

Acceleration of gravity, m/s2

h :

Function of the film thickness

H :

Function of the dimensionless film thickness, h/c

I :

Transverse mass moment of inertia, kg m2

I zz :

Polar mass moment of inertia, kg m2

k xy :

Air film stiffness, N/m

k :

Parameter of differential transform method

L :

Journal length, mm

L r :

Shaft length, mm

m :

Shaft mass, kg

\(\dot{m}\) :

Mass flow rate, kg/s

\(\dot{M}\) :

Dimensionless mass flow rate

p :

Pressure, Pa

P :

Dimensionless pressure, p/pa

p a :

Atmospheric pressure

P d :

Dimensionless downward pressure

p s :

Supply pressure

R 0 :

Gas constant, J/kg °K

T 0 :

Reference temperature, °K

t :

Time, s

U :

Linear velocity of the shaft surface, m/s

W :

Air film force, N

x, y, z :

Coordinate axes

ε :

Eccentricity ratio

μ :

Air viscosity, Pa s

κ :

Specific heat ratio

θ :

Circumferential axis in dimensional form, x/R

ξ :

Axial axis in dimensionless form, z/R

τ u :

Unbalanced degree in rotational direction, rad

ω :

Rotational speed, rad/s

\(\phi ,\varphi\) :

Pitch and yaw axis, rad

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Funding

The present study was supported by Turkish Council of Research and Scientific Foundation under Grant No. 112M847.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Engineering Faculty, Adana Alparslan Türkeş Science and Technology University, 01250, Adana, Turkey

    Abdurrahim Dal

  2. Department of Mechanical Engineering, Engineering Faculty, Gazi University, 06570, Ankara, Turkey

    Tuncay Karaçay

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  1. Abdurrahim Dal
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Correspondence to Abdurrahim Dal.

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Technical Editor: Pedro Manuel Calas Lopes Pacheco.

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Dal, A., Karaçay, T. Dynamics of a rotor-aerostatic journal bearings system with asymmetric air feeding. J Braz. Soc. Mech. Sci. Eng. 44, 317 (2022). https://doi.org/10.1007/s40430-022-03601-z

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