![Marcelo Gustavo Coelho Resende1
, Leandro José da Silva1
, Cláudio de Castro Pellegrini2
and Túlio Hallak Panzera1
*
1
Centre for Innovation and Technology in Composite Materials (CITeC), Federal University of São João del-Rei (UFSJ), Brazil
2
Department of Thermal and Fluid Sciences (DCTEF), Federal University of São João del-Rei (UFSJ), Brazil
*Corresponding author: Túlio Hallak Panzera, Centre for Innovation and Technology in Composite Materials (CITeC), Federal University of São João
del-Rei (UFSJ), Praca Frei Orlando 170, São João del-Rei, Brazil
Submission: September 12, 2018; Published: October 24, 2018
Evaluation of Air Flow Characteristics of Aerostatic
Thrust Porous Bearings: A Numerical Approach
Introduction
Aerostatic bearings have a gas flow restrictor that creates
a thin film between two surfaces in relative movement, thus
promoting near zero-friction. They are classified as “orifice”
or “porous” medium types. The porous medium type has the
potential to generate a more uniform pressure distribution in
the bearing gap, relative to the orifice aerostatic bearing. In this
manner, the porous bearing may provide enhanced stiffness and
damping characteristics [1-3]. The most widespread application
of aerostatic bearings is in the ultra-precision transformation
industry, in which rigidity and stability play a key role in achieving
movement accuracy. High precision milling machines require
rigidity and low vibration for high speed jobs. The vibration of the
tool has a significant influence on the machining accuracy. In these
applications, the use of aerostatic bearings with porous restrictors
is most advisable [4-8].
The effects of the geometry and operational parameters of
aerostatic bearings on their performance can be evaluated using
numerical simulation, such as Computational Fluid Dynamics
(CFD). Important parameters include the physical and mechanical
properties of the porous medium, such as porous pad geometry,
diffuser angle, loading, pressure and gas flow rate, among others.
Approximate solutions produced by CFD are obtained by solving
iteratively a set of conservative equations applied to defined
elementary volumes, that is, the control volumes [9]. The use
of computational analysis and approximate methods to predict
the behaviour of complex systems is important because of the
difficulties involved in obtaining closed analytical solutions and
conducting reliable experiments. This can considerably reduce the
project costs [10].
Mini Review
Evolutions in Mechanical
EngineeringC CRIMSON PUBLISHERS
Wings to the Research
1/5Copyright © All rights are reserved by Túlio Hallak Panzera.
Volume 1 - Issue - 4
Abstract
Aerostatic porous bearings have been investigated in the last decades for precision engineering designs, since these bearings offer zero-friction and
highoperatingspeeds,aswellasprovidingaveryprecisepositioningsystemwithoutexternalinfluence.NumericalmethodssuchasCFD(Computational
Fluid Dynamics) play an important role in the design and behaviour analysis of porous aerostatic bearings, being possible to adjust the geometry and
characteristics of the porous restrictor even before its manufacture. In the present work, the behaviour of the gas at the inlet and outlet of a porous
thrust bearing made of cementitious composites is analysed by numerical simulation using CFD method. The results reveal a stable behaviour of the
cementitious porous bearing and a good correlation between numerical and experimental load capacities.
Keywords: Aerostatic thrust bearing; Porous restrictor; CFD; numerical simulation; Cementitious composites
Figure 1: Aerostatic thrust bearing with cementitious porous medium.
ISSN: 2640-9690](https://image.slidesharecdn.com/eme-190410075132/85/Evaluation-of-Air-Flow-Characteristics-of-Aerostatic-Thrust-Porous-Bearings-A-Numerical-Approach-Crimson-Publishers-1-320.jpg)
![Evolutions Mech Eng Copyright © Túlio Hallak Panzera
2/5
How to cite this article: Marcelo G C R, Leandro J d S, Cláudio d C P, Túlio H P. Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings:
A Numerical Approach. Evolutions Mech Eng . 1(4). EME.000520.2018. DOI: 10.31031/EME.2018.01.000520
Volume 1 - Issue - 4
In this work, a new model of aerostatic bearing (Figure 1) is
studied through numerical simulation. The boundary conditions
are considered to analyse the air flow characteristics at the inlet
and outlet of the porous cementitious thrust bearing. In addition,
a comparison between the bearing load capacity obtained through
numerical simulation and experimentally is presented.
Methodology
Figure 2 shows the bearing prototype proposed in this work. It
consistsofacylindricalinlet(4.2mmindiameter),adiffuserandthe
porous restrictor (50mm in diameter and 8 mm thick). The porous
restrictor was proposed by Panzera et al. [11], being designed based
on a cementitious composite reinforced with silica microparticles
via cold uniaxial pressing. This composite reaches 30% of porosity
and 1.14x10-15
m² of viscous permeability coefficient.
In most precision engineering applications, the bearing gaps
(air film thickness) range from 5 to 20μm. It is well known that
lower values of thickness provide lower gas consumption and
higher stiffness [1-3]. However, in the simulation process, a smaller
region of analysis requires a refined mesh. In order to reduce
computer time a thicker bearing gap of 20μm was considered. The
flow rate used in the numerical experiment was 2.104 ml.s-1
. This
value was determined experimentally using the bearing shown in
Figure 1.
Figure 2: Aerostatic bearing design, dimensions in mm.
TheCFDanalysiswasperformedbasedonastaticmodel(Figure
2), i.e., the bearing is not able to rotate and translate in radial and
axial directions. In addition, the inlet gas velocity (axial direction),
the outlet gas pressure (radial direction of the restrictor), the input
data and the bearing geometry were maintained constant.
Table 1: Contour conditions and domain data.
Material Model
Ideal gas-Air
Heat transfer model=Thermal energy
Turbulence model=SST (Shear Stress Transport)
Turbulent wall functions=automatic
Buoyancy model=non-buoyant
Domain motion=stationary
Reference pressure=1atm
Table 1 exhibits the mathematical models and conditions
imposed to solve the problem. For the simulation, the air was
considered an ideal gas. The effects of gravitational force on the gas
flow were disregarded and the domain was stablished as stationary.
The SST (Shear Stress Transport) two-equation turbulence model
was used in this work. This model is considered robust and is
widely used in aerodynamic applications [12]. It uses the K-omega
model in the inner boundary layer and K-epsilon in the free-flow
shear (Table 2).](https://image.slidesharecdn.com/eme-190410075132/85/Evaluation-of-Air-Flow-Characteristics-of-Aerostatic-Thrust-Porous-Bearings-A-Numerical-Approach-Crimson-Publishers-2-320.jpg)
![Evolutions Mech Eng Copyright © Túlio Hallak Panzera
3/5
How to cite this article: Marcelo G C R, Leandro J d S, Cláudio d C P, Túlio H P. Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings:
A Numerical Approach. Evolutions Mech Eng . 1(4). EME.000520.2018. DOI: 10.31031/EME.2018.01.000520
Volume 1 - Issue - 4
Table 2: Contour conditions and data of surfaces and boundaries.
Local Type Configuration
Input Inlet
Flow regime=Subsonic
Mass and momentum=Normal speed; 2.1m/s
Turbulence=Medium (Intensity=5%)
Heat transfer=Static temperature; 293K
Output Opening
Flow regime=Subsonic
Mass and momentum=Opening pressure: 0atm
Flow direction=Normal to boundary condition
Turbulence=Medium (Intensity=5%)
Heat transfer=Opening temperature; 293K
Wall Wall
Mass and momentum=No slip wall
Wall roughness=Smooth wall
Heat transfer=Adiabatic
Table 3 shows the characteristics used for the domain of the
porous restrictor. The properties of the porous pad were obtained
from Panzera et al. [11]. The interface regions that characterise the
air flow and the relationship between the fluid and porous domains
have been established for the contacts between the diffuser and the
restrictor, and between the restrictor and the bearing gap.
Table 3: Properties of the porous restrictor used.
Material Model
Cementitious com-
posite reinforced with
silica microparticles
Area porosity=Isotropic
Volume porosity=0.3
Loss model=Isotropic loss
Loss velocity type=Superficial
Isotropic loss=Permeability and loss coefficient
Permeability=1.14e-15 [m2
]
Fluid solid area density=Interfacial area
density
Interfacial area Den.=0.001[ m-1
]
Fluid solid heat transfer=Heat transfer coeffi-
cient
Heat transf. coeff. 1[Wm-2
K-1
]
Reference pressure=1atm
A three-dimensional mesh containing tetrahedral and prismatic
elements was used. A convergence test was performed for the mesh
configuration, attempting successive reductions in element size
until no significant difference in results is achieved.
Results
Figure 3 shows the streamlines configuration of the airflow
through the diffuser and the porous medium. A toroidal vortex can
be observed in the diffuser, alongside a main jet. It appears due to
the rapid increase in the area of the diffuser that causes a decrease
in velocity and therefore an increase in pressure. On the other hand,
the porous restrictor presents laminar flow, exhibiting a nearly
uniform distribution of airflow in the bearing gap.
Figure 3: Velocity result with the streamline.
Figure 4 shows the pressure distribution in the air gap. The
pressure profile is important because it allows the occurrence of
pneumatic instability (due to the asymmetry and magnitude of the
pressure distribution) to be observed. It can be seen in Fig. 4 that
the pressure distribution is symmetric and uniform, with a smooth
decay at the ends, indicating a stable behaviour for the bearing
studied.](https://image.slidesharecdn.com/eme-190410075132/85/Evaluation-of-Air-Flow-Characteristics-of-Aerostatic-Thrust-Porous-Bearings-A-Numerical-Approach-Crimson-Publishers-3-320.jpg)
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Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings: A Numerical Approach: Crimson Publishers
- 1. Marcelo Gustavo Coelho Resende1 , Leandro José da Silva1 , Cláudio de Castro Pellegrini2 and Túlio Hallak Panzera1 * 1 Centre for Innovation and Technology in Composite Materials (CITeC), Federal University of São João del-Rei (UFSJ), Brazil 2 Department of Thermal and Fluid Sciences (DCTEF), Federal University of São João del-Rei (UFSJ), Brazil *Corresponding author: Túlio Hallak Panzera, Centre for Innovation and Technology in Composite Materials (CITeC), Federal University of São João del-Rei (UFSJ), Praca Frei Orlando 170, São João del-Rei, Brazil Submission: September 12, 2018; Published: October 24, 2018 Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings: A Numerical Approach Introduction Aerostatic bearings have a gas flow restrictor that creates a thin film between two surfaces in relative movement, thus promoting near zero-friction. They are classified as “orifice” or “porous” medium types. The porous medium type has the potential to generate a more uniform pressure distribution in the bearing gap, relative to the orifice aerostatic bearing. In this manner, the porous bearing may provide enhanced stiffness and damping characteristics [1-3]. The most widespread application of aerostatic bearings is in the ultra-precision transformation industry, in which rigidity and stability play a key role in achieving movement accuracy. High precision milling machines require rigidity and low vibration for high speed jobs. The vibration of the tool has a significant influence on the machining accuracy. In these applications, the use of aerostatic bearings with porous restrictors is most advisable [4-8]. The effects of the geometry and operational parameters of aerostatic bearings on their performance can be evaluated using numerical simulation, such as Computational Fluid Dynamics (CFD). Important parameters include the physical and mechanical properties of the porous medium, such as porous pad geometry, diffuser angle, loading, pressure and gas flow rate, among others. Approximate solutions produced by CFD are obtained by solving iteratively a set of conservative equations applied to defined elementary volumes, that is, the control volumes [9]. The use of computational analysis and approximate methods to predict the behaviour of complex systems is important because of the difficulties involved in obtaining closed analytical solutions and conducting reliable experiments. This can considerably reduce the project costs [10]. Mini Review Evolutions in Mechanical EngineeringC CRIMSON PUBLISHERS Wings to the Research 1/5Copyright © All rights are reserved by Túlio Hallak Panzera. Volume 1 - Issue - 4 Abstract Aerostatic porous bearings have been investigated in the last decades for precision engineering designs, since these bearings offer zero-friction and highoperatingspeeds,aswellasprovidingaveryprecisepositioningsystemwithoutexternalinfluence.NumericalmethodssuchasCFD(Computational Fluid Dynamics) play an important role in the design and behaviour analysis of porous aerostatic bearings, being possible to adjust the geometry and characteristics of the porous restrictor even before its manufacture. In the present work, the behaviour of the gas at the inlet and outlet of a porous thrust bearing made of cementitious composites is analysed by numerical simulation using CFD method. The results reveal a stable behaviour of the cementitious porous bearing and a good correlation between numerical and experimental load capacities. Keywords: Aerostatic thrust bearing; Porous restrictor; CFD; numerical simulation; Cementitious composites Figure 1: Aerostatic thrust bearing with cementitious porous medium. ISSN: 2640-9690
- 2. Evolutions Mech Eng Copyright © Túlio Hallak Panzera 2/5 How to cite this article: Marcelo G C R, Leandro J d S, Cláudio d C P, Túlio H P. Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings: A Numerical Approach. Evolutions Mech Eng . 1(4). EME.000520.2018. DOI: 10.31031/EME.2018.01.000520 Volume 1 - Issue - 4 In this work, a new model of aerostatic bearing (Figure 1) is studied through numerical simulation. The boundary conditions are considered to analyse the air flow characteristics at the inlet and outlet of the porous cementitious thrust bearing. In addition, a comparison between the bearing load capacity obtained through numerical simulation and experimentally is presented. Methodology Figure 2 shows the bearing prototype proposed in this work. It consistsofacylindricalinlet(4.2mmindiameter),adiffuserandthe porous restrictor (50mm in diameter and 8 mm thick). The porous restrictor was proposed by Panzera et al. [11], being designed based on a cementitious composite reinforced with silica microparticles via cold uniaxial pressing. This composite reaches 30% of porosity and 1.14x10-15 m² of viscous permeability coefficient. In most precision engineering applications, the bearing gaps (air film thickness) range from 5 to 20μm. It is well known that lower values of thickness provide lower gas consumption and higher stiffness [1-3]. However, in the simulation process, a smaller region of analysis requires a refined mesh. In order to reduce computer time a thicker bearing gap of 20μm was considered. The flow rate used in the numerical experiment was 2.104 ml.s-1 . This value was determined experimentally using the bearing shown in Figure 1. Figure 2: Aerostatic bearing design, dimensions in mm. TheCFDanalysiswasperformedbasedonastaticmodel(Figure 2), i.e., the bearing is not able to rotate and translate in radial and axial directions. In addition, the inlet gas velocity (axial direction), the outlet gas pressure (radial direction of the restrictor), the input data and the bearing geometry were maintained constant. Table 1: Contour conditions and domain data. Material Model Ideal gas-Air Heat transfer model=Thermal energy Turbulence model=SST (Shear Stress Transport) Turbulent wall functions=automatic Buoyancy model=non-buoyant Domain motion=stationary Reference pressure=1atm Table 1 exhibits the mathematical models and conditions imposed to solve the problem. For the simulation, the air was considered an ideal gas. The effects of gravitational force on the gas flow were disregarded and the domain was stablished as stationary. The SST (Shear Stress Transport) two-equation turbulence model was used in this work. This model is considered robust and is widely used in aerodynamic applications [12]. It uses the K-omega model in the inner boundary layer and K-epsilon in the free-flow shear (Table 2).
- 3. Evolutions Mech Eng Copyright © Túlio Hallak Panzera 3/5 How to cite this article: Marcelo G C R, Leandro J d S, Cláudio d C P, Túlio H P. Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings: A Numerical Approach. Evolutions Mech Eng . 1(4). EME.000520.2018. DOI: 10.31031/EME.2018.01.000520 Volume 1 - Issue - 4 Table 2: Contour conditions and data of surfaces and boundaries. Local Type Configuration Input Inlet Flow regime=Subsonic Mass and momentum=Normal speed; 2.1m/s Turbulence=Medium (Intensity=5%) Heat transfer=Static temperature; 293K Output Opening Flow regime=Subsonic Mass and momentum=Opening pressure: 0atm Flow direction=Normal to boundary condition Turbulence=Medium (Intensity=5%) Heat transfer=Opening temperature; 293K Wall Wall Mass and momentum=No slip wall Wall roughness=Smooth wall Heat transfer=Adiabatic Table 3 shows the characteristics used for the domain of the porous restrictor. The properties of the porous pad were obtained from Panzera et al. [11]. The interface regions that characterise the air flow and the relationship between the fluid and porous domains have been established for the contacts between the diffuser and the restrictor, and between the restrictor and the bearing gap. Table 3: Properties of the porous restrictor used. Material Model Cementitious com- posite reinforced with silica microparticles Area porosity=Isotropic Volume porosity=0.3 Loss model=Isotropic loss Loss velocity type=Superficial Isotropic loss=Permeability and loss coefficient Permeability=1.14e-15 [m2 ] Fluid solid area density=Interfacial area density Interfacial area Den.=0.001[ m-1 ] Fluid solid heat transfer=Heat transfer coeffi- cient Heat transf. coeff. 1[Wm-2 K-1 ] Reference pressure=1atm A three-dimensional mesh containing tetrahedral and prismatic elements was used. A convergence test was performed for the mesh configuration, attempting successive reductions in element size until no significant difference in results is achieved. Results Figure 3 shows the streamlines configuration of the airflow through the diffuser and the porous medium. A toroidal vortex can be observed in the diffuser, alongside a main jet. It appears due to the rapid increase in the area of the diffuser that causes a decrease in velocity and therefore an increase in pressure. On the other hand, the porous restrictor presents laminar flow, exhibiting a nearly uniform distribution of airflow in the bearing gap. Figure 3: Velocity result with the streamline. Figure 4 shows the pressure distribution in the air gap. The pressure profile is important because it allows the occurrence of pneumatic instability (due to the asymmetry and magnitude of the pressure distribution) to be observed. It can be seen in Fig. 4 that the pressure distribution is symmetric and uniform, with a smooth decay at the ends, indicating a stable behaviour for the bearing studied.
- 4. Evolutions Mech Eng Copyright © Túlio Hallak Panzera 4/5 How to cite this article: Marcelo G C R, Leandro J d S, Cláudio d C P, Túlio H P. Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings: A Numerical Approach. Evolutions Mech Eng . 1(4). EME.000520.2018. DOI: 10.31031/EME.2018.01.000520 Volume 1 - Issue - 4 Figure 4: Profile pressure in the air gap region. The load capacity of the air bearing can be obtained by integrating the simulated pressure along the surface area of the restrictor. Based on the pressure distribution shown in Figure 4, a load capacity of 7.23 N was calculated, fitting well with the bearing weight shown in Fig. 1, 7.46 N (a 3% difference). Figure 5: Distribution of the frequency of turbulence.
- 5. Evolutions Mech Eng Copyright © Túlio Hallak Panzera 5/5 How to cite this article: Marcelo G C R, Leandro J d S, Cláudio d C P, Túlio H P. Evaluation of Air Flow Characteristics of Aerostatic Thrust Porous Bearings: A Numerical Approach. Evolutions Mech Eng . 1(4). EME.000520.2018. DOI: 10.31031/EME.2018.01.000520 Volume 1 - Issue - 4 Figure 5 shows the simulated turbulence eddy frequency in the aerostatic bearing. This information is also important to verify the existence of resonance and consequently of pneumatic instability. Theresultsreveal ahigherfrequencyintheairgap region,especially in the central portion of the outlet surface of the porous restrictor. Conclusion The numerical simulation proposed in this work estimated the characteristics of the airflow within the aerostatic bearing, the distribution of the air pressure in the bearing gap, the stability and load capacity of the bearing. A toroidal vortex formation was observed in the diffuser; however, a laminar airflow through the porous restrictor was observed in the simulation, suggesting a stable behaviour for the cementitious bearing. These results corroborate the development of the design of the aerostatic thrust bearing, which will be the scope of future investigations. Acknowledgment The authors would like to thank CAPES, and CNPq (MCTI/CNPq no. 01/2016) for the financial support provided. References 1. Kwan YBP, Corbett J (1998) Porous aerostatic bearing-an updated review. Wear 222: 69-73. 2. Silva LJ, Panzera TH, Viera LMG, Bowen CR, Duduch JG, et al. (2018) Cementitious porous material applied to precision aerostatics bearings. International Journal of Precision Engineering and Manufacturing 19(2): 239-243. 3. Silva LJ, Panzera TH, Viera LMG, Bowen CR, Duduch JG, et al. (2017) Carbon nanotubes and superplasticizer reinforcing cementitious composite for aerostatic porous bearing. Proceedings of the Institution of Mechanical Engineers, Part J, Journal of Engineering Tribology 231(11): 1397-1407. 4. Huo D, Cheng K, Wardle F (2010) Design of a 5-axis ltraprecision micro milling machine–ultramill: part 1: holistic design approach, design considerations, and specifications. International Journal of Advanced Manufacturing Technology 47(9): 867-877. 5. Gao SY, Cheng K, Ding H (2016) Multiphyscials-based design and analysis of the high-speed aerostatic spindle with application to micro-milling. Proceedings of the IMechE, Part J: Journal of Engineering Tribology 230(7): 852-871. 6. Yuan JL, Zhang FH, Dai YF, Kang R, Yang H, et al. (2010) Development research of science and technologies in ultra-precision machining field. Chinese Journal of Mechanical Engineering 46(8): 161-177. 7. Wang W, Jiang Z, Tao W, Zhuang W (2015) A new test part to identify performance of five-axis machine tool–part I: geometrical and kinematic characteristics of S part. International Journal of Advanced Manufacturing Technology 79(5-8): 1-10. 8. An C, Zhang Y, Xu Q, Zhang FH, Zhang JF, et al. (2010) Modeling of dynamic characteristic of the aerostatic bearing spindle in an ultra- precision fly cutting machine. International Journal of Machine Tools and Manufacture 50(4): 374-385. 9. Cui H, Wang Y, Yue X, Huang M, Wang W (2017) Effects of manufacturing errors on the static characteristics of aerostatic journal bearing with porous restrictor. Tribology International 115: 246-260. 10. Pinto RN, Afzal A, D’souza LV, Ansari Z, Mohammed Samee AD (2017) Computational fluid dynamics in turbomachinery: a review of state of the art. Archives of Computational Methods in Engineering 24(3): 467- 479. 11. Panzera TH, Rubio JCC, Bowen C, Walker P (2008) Microstructural design of materials for aerostatic bearings. Cement & Concrete Composites 30(7): 649-660. 12. Neves MT, Schwarz VA, Menon GJ (2007) Analysis of externally pressurized gas journal bearing by using the finite element method. In: 19th International Congress of Mechanical Engineering, Brasília. Proceedings of COBEM2007 ID code: 2173. For possible submissions Click Here Submit Article Creative Commons Attribution 4.0 International License Evolutions in Mechanical Engineering Benefits of Publishing with us • High-level peer review and editorial services • Freely accessible online immediately upon publication • Authors retain the copyright to their work • Licensing it under a Creative Commons license • Visibility through different online platforms