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Numerical analysis on the dynamic behavior of the water-lubricated bearing of the energy recovery turbocharger during start-up

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Abstract

The dynamic behavior of the water-lubricated bearing of the energy recovery turbocharger during start-up is investigated. Rough surfaces of the bearing are characterized by using the Weierstrass–Mandelbrot function. The hydrodynamic pressure is obtained by solving the average Reynolds equation with the finite difference method. Moreover, the asperity contact force is calculated by the Greenwood–Tripp contact model. The results show that the hydrodynamic force increases suddenly and the asperity contact force decreases sharply during the initial stage of the start-up process. The reduction in acceleration time leads to a decrease in the asperity contact force and time. Meanwhile, the increase in radius clearance leads to a sharp increase in the hydrodynamic force and a sharp decrease in the asperity contact force.

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Data availability

The datasets analyzed during the current study are available in the [Figures] Data compression package.

Abbreviations

c :

Radius clearance, c = Rb − Rs

d :

Standard separation

D 1, D 2 :

Fractal dimension

D sum :

Asperity density

e :

Eccentric distance

E 1, E 2 :

Equivalent modulus of shaft surface and bearing surface, respectively

E′:

Equivalent elasticity modulus, 1/E′ = (1 − υ12)/E1 + (1 − υ22)/E2

F h, F c :

Hydrodynamic force and asperity contact force, respectively

F r, F τ :

Radius force and tangential force of shaft center, respectively

G 1, G 2 :

Fractal roughness

h :

Water-film thickness

h T :

Real water-film thickness

H :

Normalized film thickness, H1 = h/c

H 1 :

Stribeck ratio, H1 = h/σ

L :

Bearing length

m :

Shaft mass

n :

Rotating speed

R s :

Shaft radius

R b :

Bearing radius

U :

Velocity of the shaft surface

V r, V τ :

Radius and tangential velocities of shaft center, respectively

u x, u y :

Displacements in the x and y directions.

υ 1, υ 2 :

Poisson’s ratio

W :

External load

z 1, z 2 :

Asperity height of shaft surface and bearing surface, respectively

z s * :

Asperity height

P i j :

Normalized hydrodynamic pressure at each node

P :

Normalized hydrodynamic pressure, P = p/p0

P asp :

Individual asperity contact force

γ :

Surface pattern parameter

β :

Asperity radius

ω s * :

Interference distance of asperities, ωs* = zs*-d

σ s :

Standard deviation of summit height

σ :

Standard deviation of roughness distribution

ε :

Eccentricity ratio, ε = e/c

θ :

Attitude angle

ϕ :

Circumferential angle

ρ :

Density of water

μ :

Water viscosity

f(z s * ) :

Gaussian distribution function of asperity height

ϕ x, ϕ y :

Pressure flow factors in x and y direction, respectively

ϕ s, ϕ c :

Shear flow factor and contact factor, respectively

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Funding

This work was supported by National Natural Science Foundation of China [Grant Numbers U2106225 and 52005224], Natural Science Foundation of Jiangsu Province for Distinguished Young Scholars [Grant Numbers BK20211547] and Program for Jiangsu Excellent Scientific and Technological Innovation Team [Grant Numbers SKJ (2021)-1].

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Authors and Affiliations

  1. National Research Center of Pumps, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Yan Li, Yanqiang Ning, Desheng Zhang, Xiaoyan Ye, Zhengsheng Li & Yinhe Zhi

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  1. Yan Li
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  2. Yanqiang Ning
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  3. Desheng Zhang
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  4. Xiaoyan Ye
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Contributions

LY was involved in conceptualization, methodology, validation, investigation. NY helped in software, data curation, numerical analysis, writing—original draft, writing—review and editing. ZD contributed to resources, supervision, project administration, funding acquisition. YX performed data curation, numerical analysis, writing—review and editing. LZ assisted in software, investigation. ZY contributed to data curation, formal analysis.

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Correspondence to Desheng Zhang.

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Li, Y., Ning, Y., Zhang, D. et al. Numerical analysis on the dynamic behavior of the water-lubricated bearing of the energy recovery turbocharger during start-up. Nonlinear Dyn 112, 5349–5364 (2024). https://doi.org/10.1007/s11071-023-09245-5

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