3d numerical study on the aerostatic thrust bearing with ...3d numerical study on the aerostatic...

3D Numerical Study on The Aerostatic Thrust Bearing with Annular Gap Throttling Structure

1,2Wuxue Ma, 3Dongsheng Li

1, First Author and Corresponding Author College of Mechatronic Engineering, Northeast Forestry University, Harbin 150001, Heilongjiang, P.R. China, [email protected]

2, College of Mechatronic Engineering, Heilongjiang Institute of Technology 3 College of Metrology and Measurement Engineering, China Jiliang University,

Abstract

An aerostatic thrust bearing (ATB) with annular gap throttling structure and trapezoid air chamber was investatged using Computational fluid dynamic (CFD) method. The CFD software FLUENT was used for solveing NS equations. SST k-ω was used to serve as a turbulent flow model for the three dimensional periodic fluid field. The numerical results agree well with experiement dates. The ATB flow field was subsonec and the load capacity, air flow rate at different bearing clearance were obtained by numerical simulation. The flow details such as pressure and velocity at different bearing clearance were discussed. The results shows that CFD is a useful tool in the design of aerostatic thrust bearing.

Keywords: Aerostatic Thrust Bearing, Load Capacity, CFD, Pressue Field.

1. Introduction

Nowadays, air bearing is widely used in three-coordinate measuring machines, high-speed rotating machine tools, microelectronic machines and medical devices[1–5]. The computation of radial flow in aerostatic circular thrust bearing is usually carried out by solving the classical Reynolds equation for compressible isothermal flow, unfortunately, this computational approach fails to estimate the pressure distribution in the inlet region when negative pressures and flow discontinuities exist. The clearance of ATB is between several micron and hundred-micron, and when the clearance is too big, the air speed will reach supersonic and the load capacity decreases sharply, this is a current hotspot problem in ATB field.

As the ATB static performance is very important, many researchers have done a great deal work in this field. Yuntang Li [6] made a CFD study using FLUENT on the effects of orifice diameter, film thickness, and air chamber’s dimension on the performance of ATB with pocketed orifice-type restrictor, they found that the bearing has a good performance when orifice diameter and film thickness are small. Eleshaky [7] carried out the CFD investigation of the pressure and shock wave distribution in a circular ATB, the results show that the transition from supersonic to subsonic flow in aerostatic bearing occurs via a shock region (pseudo-shock) and the relaminarization of the flow occurs due to this process, due to the presence of upper and lower boundary layers of ATB walls, the compression shock in the bearing gap is far from a plane discontinuity, like Mohamed, many investigators reasoned the pressure depression to the occurrence of shock waves in the bearing clearance, but Yoshimoto [8] reasoned this phenomenon to the transition from laminar to turbulent flow and claimed that no shock wave is generated at the boundary between supersonic and subsonic flows. Jyh-Chyang Renn [9] described the experimental and CFD study on the mass flow-rate characteristic through an orifice-type restrictor in aerostatic bearings a series of simulations and experiments are carried out and the results show that the mass flow-rate characteristic through an orifice is di��erent from the tradition mathematical model which assumes the air through a ideal nozzle. Other types of ATB were also studied recent years except orifice-type, for example, Nishio [10] investigated the static and dynamic characteristics of an annular ATB with feedholes of less than 0.05mm in diameter using CFD software CFX, the results confirmed that aerostatic thrust bearings with small feedholes have a larger stiffness and a higher damping coefficient than bearings with compound restrictors.

. As the develop of CFD, solving NS equations directly using CFD software has gained more and more attention and has a lot of successful cases [11-12]. In this paper a new structure ATB is

3D Numerical Study on The Aerostatic Thrust Bearing with Annular Gap Throttling Structure Wuxue Ma, Dongsheng Li

Advances in information Sciences and Service Sciences(AISS) Volume4, Number20, Nov 2012 doi: 10.4156/AISS.vol4.issue20.11

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investigated using CFD software FLUENT. The static performance of new ATB is compared with traditional orifice circular type, Then the effects of ATB geometry on static performance has been done. The velocity and pressure distribution have been discussed and compared with orifice type. 2. Geometry and numerical details 2.1 Governing equations

The governing equations for two dimensional compressible and turbulence flow are given by the equation of continuity, the equation of motion and the energy equation, and are called the compressible Navier-Stokes equations (NS equations):

Continuity equation ( )

0i

i

u

x

Momentum equation ' '( ) 2

[ ( )] ( )3

i j ji iij i j

j i j j i i j

u u uu uP Pu u

x x x x x x x

iu is the time averaged Cartesian velocity components in the three coordinate directions. The

Reynolds stress tensor ' '

i ju u is written as:

' ' 2( ) ( )

3ji i

i j t ij t

i j i

uu uu u k

x x x

, where t is the turbulent eddy-viscosity, ij is the

Kronecker delta symbol which is equal to unity when i=j and zero when i≠j, and k is the turbenlent

kinetic energy ' '1

2 i ju u . In order to close the equations, two more equations are required to determine t

and k. In this paper the Stand k-ω turbulent model [13] is used.

( ) ( )i k k k

i j j

kku G Y

x x x

( ) ( )i

i j j

u G Yx x x

Where G represents the generation of turbulence kinetic energy due to mean velocity gradients.

G represents the generation of . k and represent the effective diffusivity of k and ,

respectively. Y and Y represent the dissipation of k and due to turbulence. All of the above terms

are calculated as described below.

Energy equation 2

( ( )) [ ( ( )]3

ji ij eff i t ij

j i j j i i

uu uTu e P u

x x x x x x

The total energy, e, and the effective thermal conductivity, eff , are written as: 2 2 2

1 2 3( + )

2p

u u uP Pe C

R

, p t

eff

t

C m

Pr .

Where is the thermal conductivity and tPr is the Prandtl number taken for air is 0.85.

The molecular viscosity of the air is calculated from the Surherland’s law given by: *

32

* *( )

T T S

T T S

, * =1.716×10-5Pa.s, S=110.55K, and T*=273.11K.


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2.2 Geometry and grid of the ATB

Figure 1. Geometry of the aerostatci thrust bearing

The ATB geometry used in this paper is shown in Fig.1, the thrust bearing is composed of

main thrust bearing and blocking, the throttling structure of the ATB is an annular gap type with bearing diameter 80mm, the annular gap size is 0.2mm, there is an air chamber with length 17.5mm, 12 trapezoid grooves are cut in main thrust bearing part. So the air thrust bearing is periodic and a 1/12 geometry is used in this paper.

The grid details are shown in Fig.2, prism and hexahedron mesh are used in this paper. The total elements number is about 850,000.

Figure 2. Numerical mesh of the aerostatic thrust bearing

2.3 Boundary condition

To solve the NS equations, the flowing boundary conditions are set in FLUENT: (1) Inflow boundary: the air flow direction is normal to the inflow surface. Total pressure

and temperature (300K) are set as a constant. The turbulence intensities in the inflow boundary have been set to 5%, the total pressure are from 0.3Mpa to 0.7Mpa.

(2) Outflow boundary: zero normal gradients for velocity and temperature T are prescribed at the outflow surface, a constant static pressure Pb 101325 is set for all cases in this paper. In


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case of supersonic outflow, the normal gradients for all variables ui, T, and P are set to zero. The turbulence intensities in the outflow boundary is as the same as inflow boundary.

(3) All the walls including bearing working surface are set to be no-slip and considered to be impermeable and adiabatic. In order to bridge and describe the flow between the fully turbulent region and the viscous boundary layer near the wall, a wall function has been used in this paper.

(4) Periodic boundary type has been used in order to save the simulation time.

Figure 3. Boundary condition of the aerostatic thrust bearing

3. Results and analysis

In order to investigate the accuracy of the utilized flow solver for ATB, two classical ATB experiment results have been compared with FLUENT simulation results carried out in this paper. The first bearing used in this selection has an air chamber used by Salem[7], the inlet pressure is 514.5kPa, and the back pressure is 101.3kPa. The second bearing is a single bearing with on inlet hole and no air chamber[8]. It can be seen from Fig.4 a~b that the FLUENT results agree well with those of experiments.

0.0 0.2 0.4 0.6 0.8 1.0-0.2

0.0

0.2

0.4

0.6

0.8

1.0 h=25.4μm FLUENT Experiment date h=50.8μm FLUENT Experiment date h=127μm FLUENT Experiment date

P/Ps

r/R a


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0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

P/Ps

r/R

80μm FLUENT 80μm Experiment date 100μm FLUENT 100μm Experiment date

b

Figure 4. Comparison between CFD and experimental pressure distribution: a. compared with Ref.[7], b. compared with Ref.[8]

Fig.5 shows the load capacity at different supply pressure, as the supply pressure increases

from 0.3Mpa to 0.7Mpa, the load capacity increases within 400N-2400N (bearing clearance 10μm to 50μm). Fig.6 gives the mass flow rate at different supply pressure, as the supply pressure increases, the air mass flow rate increases almost linearly, as there is no supersonic flow happens in ATB, so no chocking flow occurs in bearing chamber and the mass flow rate increases linearly. It can be seen that CFD tools could finish the static prediction of ATB.

10 20 30 40 500

400

800

1200

1600

2000

2400

Lo

ad

cap

aci

ty(N

)

Bearing clearance (m)

0.3Mpa 0.4Mpa 0.5Mpa 0.6Mpa 0.7Mpa

Figure 5. Load capacity results at different supply pressure


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10 20 30 40 500.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007 0.3Mpa 0.4Mpa 0.5Mpa 0.6Mpa 0.7Mpa

Ma

ss fl

ow

rat

e (

kg/s

)

Bearing clearance (m) Figure 6. Mass flow rate results at different bearing clearance

Fig.7 gives the pressure distribution at supply pressure 0.5Mpa and bearing clearance 40μm,

Fig.8 gives the pressure distribution along the radial direction from these two figures it can be seen that there are three typical parts of the aerostatic thrust bearing calculated in this paper. zone1 is a high pressure zone, its pressure field is very uniformity and its average static pressure is slightly less than supply total pressure, zone1 is a round chamber and the air flow over it to zone2, because of the special structure of zone1, the air supply pressure has little pressure drop in zone1 and it could provide high load capacity. When air flow into zone2 and zone3, the air speed is increased sharply as the flow surface is increased, and the static pressure will decrease sharply. So it can be conclude that zone1 is the mainly working zone which provides high pressure.

Figure 7. Pressure distribution of the bearing surface (0.5Mpa, 40μm)


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0.00 0.01 0.02 0.03 0.040.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

3.0x105

3.5x105

4.0x105

Sta

tic p

ress

ure

(P

a)

Bearing clearance (m)

zone1

zone2

zone3

Figure 8. Pressure distribution along the radial derction (0.5Mpa, 40μm)

Fig.9 shows the middle plan in the bearing clearance direction, it can be seen that in zone 1

the air speed is equal to zero which means that this zone has a very high pressure. When the air flow through the annular gap, the air speed is increases sharply compared with the air speed in zone1. In zone2, because of the trapezoid structure, the air speed keeps increasing which makes the pressure decreases very fast.

Figure 9. Velocity distribution of the bearing clearance middle plane (0.5Mpa, 40μm)

4. Conclusions

A comparison numerical study has been carried out in order to investigate a new aerostatic thrust bearing static performance. The 3D flow field has been built and NS equations have been solved for compressed flow field using CFD software FLUENT. The static performance and flow details have been discussed and compared. The numerical result shows that there is high pressure zone which makes the aerostatic thrust bearing work at a high load capacity. Other conclusion is as follows:

1 As the supply pressure increases, the load capacity and air mass flow rate increases. 2 There is high pressure zone which makes the aerostatic thrust bearing work at a high load

capacity, in this zone the air speed is nearly to zero.


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5. Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant No.51075378). 6. References [1] Kassab SZ. “Empirical correlations for the pressure depression in externally pressurized gas

bearings”. Tribology International, vol.30, no.1, pp.59-67, 1997. [2] Wen-Ming Zhang, Guang Meng, Hai Huang. “Characteristics analysis and dynamic responses of

micro-gas-lubricated journal bearings with a new slip model”. Journal of Physics D:Applied Physics. vol.41, no.15, pp.1-16, 2008.

[3] Kuang Chao Fan, Chi-Chung Ho, Jong-I Mou. “Development of a multiple-microhole aerostatic air bearing system”. J. Micromech Microeng, vol.12, no.5, pp.636–643, 2002.

[4] Kwan Y-BP, Post JB. “A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings”. Tribology International, vol.33, no.8, pp.581-586, 2000.

[5] Kassab SZ, Noureldeen EM, Shawky MA. “Effects of operating conditions and supply hole diameter on the performance of a rectangular aerostatic bearing”. Tribology International, vol.30, no. 7, pp.533-545, 1997.

[6] Yuntang Li, Han Ding. “Influences of the geometrical parameters of aerostatic thrust bearing with pocketed orifice-type restrictor on its performance”. Tribology International, vol.40, no.7, pp.1120–1126, 2007.

[7] Mohamed E. Eleshaky. “CFD investigation of pressure depressions in aerostatic circular thrust bearings”. Tribology International, vol.42, no.2, pp.1108-1117, 2009.

[8] Shigeka Yoshimoto, Makoto Yamamoto, Kazuyuki Toda. “Numerical Calculations of Pressure Distribution in the Bearing Clearance of Circular Aerostatic Thrust Bearings With a Single Air Supply Inlet”. Journal of Tribology ASME Transaction, vol. 129, no.5, pp.384-390, 2007.

[9] Jyh-Chyang Renn, Chih-Hung Hsiao. “Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings”, Tribology International, vol.37, no.4, pp.309–315, 2004.

[10] Uichiro Nishio, Kei Somaya, Shigeka Yoshimoto. “Numerical calculation and experimental verification of static and dynamic characteristics of aerostatic thrust bearings with small feedholes”. Tribology International, vol.44, no.12, pp.1790-1795, 2011.

[11] Lin Cai, Jinli Wang, Hongtao Zheng. “A Numerical Study on Oil-air Lubrication of Cooling a Hot Rotating Cylinder”. International Journal of Digital Content Technology and its Applications. vol.5, no.8, pp.332-339, 2011.

[12] Lin Cai, Jinli Wang, Hongtao Zheng. “A numerical study of circumferential groove effect on the thermohydrodynamic performance of a journal bearing”. International Journal of Advancements in Computing Technology. vol.3, no.10, pp.208-215, 2011.

[13] V. Yakhot and S. A. Orszag. “Renormalization Group Analysis of Turbulence: I. Basic Theory”. Journal of Scientific Computing, vol.1, no.1, pp.1-51, 1986.


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