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Research Papers: Hydrodynamic Lubrication

Numerical Study on Static and Dynamic Performances of a Double-Pad Annular Inherently Compensated Aerostatic Thrust Bearing

[+] Author and Article Information
Hui Zhuang

School of Science,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: zhuangh92@163.com

Jianguo Ding

School of Science,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: nustdjg@163.com

Peng Chen

School of Science,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: 693811579@qq.com

Yu Chang

School of Science,
Nanjing University of Science and Technology,
Nanjing 210094, China
e-mail: 2691200356@qq.com

Xiaoyun Zeng

Institute of Machinery Manufacturing Technology,
China Academy of Engineering Physics,
Mianyang 621900, China
e-mail: 96-zxy@caep.cn

Hong Yang

Institute of Machinery Manufacturing Technology,
China Academy of Engineering Physics,
Mianyang 621900, China
e-mail: oyanghongscu@163.com

Xingbao Liu

Institute of Machinery Manufacturing Technology,
China Academy of Engineering Physics,
Mianyang 621900, China
e-mail: liuxingbao@caep.cn

Wei Wei

Institute of Machinery Manufacturing Technology,
China Academy of Engineering Physics,
Mianyang 621900, China
e-mail: 418159170@qq.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received August 30, 2018; final manuscript received January 5, 2019; published online March 4, 2019. Assoc. Editor: Stephen Boedo.

J. Tribol 141(5), 051701 (Mar 04, 2019) (14 pages) Paper No: TRIB-18-1357; doi: 10.1115/1.4042657 History: Received August 30, 2018; Accepted January 06, 2019

The performances of aerostatic bearings have an important impact on machining accuracy in the ultraprecision machine tools. In this paper, numerical simulation is performed to calculate the static and dynamic performances of a double-pad annular inherently compensated aerostatic thrust bearing, while considering the effects of the upper bearing and lower bearing. The static results calculated by the computational fluid dynamics (CFD) method are compared with the finite difference method (FDM) for the specific model. By using polynomial fitting, the load-carrying capacity (LCC) of the bearing is calculated and the relationship between eccentricity ratio, design parameters, and static stiffness is analyzed. The active dynamic mesh method (ADMM) is applied to obtain the dynamic performance of the double-pad aerostatic thrust bearing based on the perturbation theory. Meanwhile, the effects of supply pressure, orifice diameter, squeeze number, and eccentricity ratio are comprehensively considered. Moreover, the step response of the double-pad thrust bearing is analyzed by using the passive dynamic mesh method (PDMM) based on dynamic equation. Related dynamic parameters including natural frequency are obtained through a system identification toolbox with Matlab, which can be used to avoid resonance. It is found that the dynamic calculation results computed by the ADMM and the PDMM are very close. The proposed method can be used to provide guidance for the design and optimization of the double-pad aerostatic thrust bearings.

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References

Zhang, S. J., To, S., and Wang, H. T., 2013, “A Theoretical and Experimental Investigation into Five-DOF Dynamic Characteristics of an Aerostatic Bearing Spindle in Ultra-Precision Diamond Turning,” Int. J, Mach. Tool Manuf., 71, pp. 1–10. [CrossRef]
An, C. H., Zhang, Y., Xu, Q., Zhang, F. H., Zhang, J. F., Zhang, L. J., and Wang, J. H., 2010, “Modeling of Dynamic Characteristic of the Aerostatic Bearing Spindle in an Ultra-Precision Fly Cutting Machine,” Int. J. Mach. Tool Manuf., 50(4), pp. 374–385. [CrossRef]
Kassab, S. Z., Noureldeen, E. M., and Shawky, M. A., 1997, “Effects of Operating Conditions and Supply Hole Diameter on the Performance of a Rectangular Aerostatic Bearing,” Tribol. Int., 30(7), pp. 533–545. [CrossRef]
Li, Y. T., and Ding, H., 2012, “A Simplified Calculation Method on the Performance Analysis of Aerostatic Thrust Bearing With Multiple Pocketed Orifice-Type Restrictors,” Tribol. Int., 56, pp. 66–71. [CrossRef]
Lu, L. H., Chen, W. Q., Wu, B., Gao, Q., and Wu, Q. H., 2016, “Optimal Design of an Aerostatic Spindle Based on Fluid-Structure Interaction Method and Its Verification,” P. I. Mech. Eng. J.-J. Eng., 230(6), pp. 690–696.
Nakamura, T., and Yoshimoto, S., 1997, “Static Tilt Characteristics of Aerostatic Rectangular Double-Pad Thrust Bearings With Double Row Admissions,” Tribol. Int., 30(8), pp. 605–611. [CrossRef]
Jeng, Y. R., and Chang, S. H., 2013, “Comparison Between the Effects of Single-Pad and Double-Pad Aerostatic Bearings With Pocketed Orifices on Bearing Stiffness,” Tribol. Int., 66, pp. 12–18. [CrossRef]
Nakamura, T., and Yoshimoto, S., 1996, “Static Tilt Characteristics of Aerostatic Rectangular Double-Pad Thrust Bearings With Compound Restrictors,” Tribol. Int., 29(2), pp. 145–152. [CrossRef]
Yoshimoto, S., Suganuma, N., Yagi, K., Toda, K., and Yamamoto, M., 2007, “Numerical Calculations of Pressure Distribution in the Bearing Clearance of Circular Aerostatic Thrust Bearing With a Single Air Supply Inlet,” ASME J. Tribol., 129(2), pp. 384–390. [CrossRef]
Talukder, H. M., and Stowell, T. B., 2003, “Pneumatic Hammer in an Externally Pressurized Orifice Compensated Air Journal Bearing,” Tribol. Int., 36(8), pp. 585–591. [CrossRef]
Bhat, N., Kumar, S., Tan, W., Narasimhan, R., and Low, T. C., 2012, “Performance of Inherently Compensated Flat Pad Aerostatic Bearing Subject to Dynamic Perturbation Forces,” Precis. Eng., 36(3), pp. 399–407. [CrossRef]
Yu, P. L., Chen, X. D., Wang, X. L., and Jiang, W., 2015, “Frequency-Dependent Nonlinear Dynamic Stiffness of Aerostatic Bearing Subjected to External Perturbations,” Int. J. Precis. Eng. Man., 16(8), pp. 1771–1777. [CrossRef]
Hassini, M. A., Arghir, M., and Frocot, M., 2012, “Comparison Between Numerical and Experimental Dynamic Coefficients of a Hybrid Aerostatic Bearing,” ASME J. Eng. Gas. Turb. Power, 134(12), 122506. [CrossRef]
Zhang, G., and Ehmann, K. F., 2015, “Dynamic Design Methodology of High Speed Micro-Spindles for Micro/Meso-Scale Machine Tools,” Int. J. Adv. Manuf. Tech., 76, pp. 229–246. [CrossRef]
Ye, Y. X., Chen, X. D., Hu, Y. T., and Luo, X., 2010, “Effects of Recess Shapes on Pneumatic Hammering in Aerostatic Bearing,” P. I. Mech. Eng. J.-J. Eng., 224(3), pp. 231–237.
Belforte, G., Colombo, F., Raparelli, T., Trivella, A., and Viktorov, V., 2010, “Perfo-Rmance of Externally Pressurized Grooved Thrust Bearing,” Tribol. Lett., 37(3), pp. 553–562. [CrossRef]
Charki, A., Diop, K., Champmartin, S., and Ambari, A., 2013, “Numerical Simulation and Experimental Study of Thrust Air Bearing With Multiple Orifices,” Int. J. Mech. Sci., 72, pp. 28–38. [CrossRef]
Ma, W., Cui, J. W., Liu, Y. M., and Tan, J. B., 2016, “Improving the Pneumatic Hammer Stability of Aerostatic Thrust Bearing With Recess Using Damping Orifices,” Tribol. Int., 103, pp. 281–288. [CrossRef]
Nishio, U., Somaya, K., and Yoshimoto, S., 2011, “Numerical Calculation and Experimental Verification of Static and Dynamic Characteristics of Aerostatic Thrust Bearing With Small Feedholes,” Tribol. Int., 44(12), pp. 1790–1795. [CrossRef]
Arghir, M., Hassini, M. A., Balducchi, F., and Gauthier, R., 2015, “Synthesis of Experimental and Theoretical Analysis of Pneumatic Hammer Instability in an Aerostatic Bearing,” ASME J. Eng. Gas. Turb. Power, 138(2), 021602. [CrossRef]
Akhondzadeh, M., and Vahdati, M., 2014, “Study of Variable Depth Air Pockets on Air Spindle Vibrations in Ultra-Precision Machine Tools,” Int. J. Adv. Manuf. Tech., 73, pp. 681–686. [CrossRef]
Sternlicht, B., and Maginniss, F. J., 1957, “Application of Digital Computers to Bearing Design,” Trans. ASME, 79, pp. 1483–1493.
Belforte, G., Colombo, F., Raparelli, T., Trivella, A., and Viktorov, V., 2011, “Comparison Between Grooved and Plane Aerostatic Thrust Bearing: Static Performance,” Meccanica, 46(3), pp. 547–555. [CrossRef]
Miyatake, M., and Yoshimoto, S., 2010, “Numerical Investigation of Static and Dynamic Characteristics of Aerostatic Thrust Bearing With Small Feed Holes,” Tribol. Int., 43(8), pp. 1353–1359. [CrossRef]
Chang, S. H., Chan, C. W., and Jeng, Y. R., 2015, “Discharge Coefficients in Aerostatic Bearing With Inherent Orifice-Type Restrictors,” ASME J. Tribol., 137(1), 011705. [CrossRef]
Chang, S. H., Chan, C. W., and Jeng, Y. R., 2015, “Numerical Analysis of Discharge Coefficients in Aerostatic Bearing With Orifice-Type Restrictors,” Tribol. Int., 90, pp. 157–163. [CrossRef]
Belforte, G., Raparelli, T., Viktorov, V., and Trivella, A., 2007, “Discharge Coefficients of Orifice-Type Restrictor for Aerostatic Bearings,” Tribol. Int., 40(3), pp. 512–521. [CrossRef]
Belforte, G., Raparelli, T., Trivella, A., Viktorov, V., and Visconte, C., 2015, “CFD Analysis of a Simple Orifice - Type Feeding System for Aerostatic Bearing,” Tribol. Lett., 58(2), pp. 1–8. [CrossRef]
Li, W., Zhou, Z. X., Xiao, H., and Zhang, B., 2015, “Design and Evaluation of a High-Speed and Precision Microspindle,” Int. J. Adv. Manuf. Tech., 78, pp. 997–1004. [CrossRef]
Eleshaky, M. E., 2009, “CFD Investigation of Pressure Depressions in Aerostatic Circular Thrust Bearing,” Tribol. Int., 42(7), pp. 1108–1117. [CrossRef]
Khan, Z., and Joshi, J. B., 2015, “Comparison of k-ε , RSM and LES Models for the Prediction of Flow Pattern in Jet Loop Reactor,” Chem. Eng. Sci., 127, pp. 323–333. [CrossRef]
Li, Y. F., Yin, Y. H., Yang, H., Liu, X. N., Mo, J., and Cui, H. L., 2017, “Modeling for Optimization of Circular Flat Pad Aerostatic Bearing With a Single Central Orifice-Type Restrictor Based on CFD Simulation,” Tribol. Int., 109, pp. 206–216. [CrossRef]
Lai, T. W., Fu, B., Chen, S. T., Zhang, Q. Y., and Hou, Y., 2017, “Numerical Analysis of the Static Performance of an Annular Aerostatic Gas Thrust Bearing Applied in the Cryogenic Turbo-Expander of the EAST Subsystem,” Plasma Sci. Technol., 19(2), pp. 115–122.
Chen, X. D., Zhu, J. C., and Chen, H., 2013, “Dynamic Characteristics of Ultra-Precision Aerostatic Bearing,” Adv. Manuf., 1(1), pp. 82–86. [CrossRef]
Gao, Q., Lu, L. H., Chen, W. Q., Chen, G. D., and Wang, G. L., 2017, “A Novel Modeling Method to Investigate THE Performance of Aerostatic Spindle Considering the Fluid-Structure Interaction,” Tribol. Int., 115, pp. 461–469. [CrossRef]
Cui, H. L., Wang, Y., Yue, X. B., Li, Y. F., and Jiang, Z. Y., 2018, “Numerical Analysis of the Dynamic Performance of Aerostatic Thrust Bearing With Different Restrictors,” P. I. Mech. Eng. J.-J. Eng., pp. 1–18.
Meruane, V., and Pascual, R., 2008, “Identification of Nonlinear Dynamic Coefficients in Plain Journal Bearing,” Tribol. Int., 41(8), pp. 743–754. [CrossRef]
Li, M. X., Gu, C. H., Pan, X. H., Zheng, S. Y., and Li, Q., 2016, “A New Dynamic Mesh Algorithm for Studying the 3D Transient Flow Field Of Tilting Pad Journal Bearing,” P. I. Mech. Eng. J.-J. Eng., 230(12), pp. 1470–1482.
ANSYS FLUENT 16.2 User’s Guide, 2015.
Eshghy, S., 1975, “Optimum Design of Multiple-Hole Inherently Compensated Air Bearings- Part 1: Circular Thrust Bearings,” ASME J. Lubr. Tech., 97(2), pp. 221–227. [CrossRef]

Figures

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Fig. 1

Bearing configuration: (a) aerostatic thrust bearing gas film and (b) gas flow status

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Fig. 2

Mesh model and boundary conditions

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Fig. 3

Flowchart of the dynamic mesh calculation process: (a) the ADMM and (b) the PDMM

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Fig. 4

Mesh deformation at the axial direction

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Fig. 5

Diagram for the gas domain of the FDM

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Fig. 6

Flowchart of the FDM process

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Fig. 7

Convergence test of CFD simulation

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Fig. 8

Comparison between numerical values and experimental results. (a) Geometric model [28]. (b) The radial pressure distribution of a circular flat pad aerostatic bearing (R = 20 mm, ps = 0.5 MPa, Pout = 0 MPa, d = 0.23 mm. (c) Geometric model [40]. (d) The static and dynamic calculation results of an aerostatic thrust bearing. (R0 = 20.3 mm, R2 = 13.7 mm, ps = 4.403 atm, Pout = 0.968 atm, d = 0.74 mm, N0 = 6), and (e) Geometric model (case 3 in Ref. [17]) (R0 = 25.6 mm, R2 = 32 mm, ps = 0.5 MPa, Pout = 0.1 MPa, d = 0.6 mm, N0 = 8).

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Fig. 9

Pressure distribution of the gas film: (a) pressure of the lower gas film, (b) pressure of the upper gas film, (c) pressure distribution of line AB, and (d) one-twelfth of the computational model pressure

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Fig. 10

LCC of the single-pad thrust bearing versus gas film thickness under different supply pressures (comparison between the CFD and the FDM)

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Fig. 11

LCC of the single-pad thrust bearing versus gas film thickness under different orifice diameters (comparison between the CFD and the FDM)

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Fig. 12

Effects of supply pressure and eccentricity ratio on the LCC of the double-pad thrust bearing

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Fig. 13

Effects of orifice diameter and eccentricity ratio on the LCC of the double-pad thrust bearing

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Fig. 14

Effects of supply pressure and eccentricity ratio on the dimensionless static stiffness of the double-pad thrust bearing

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Fig. 15

Effects of orifice diameter and eccentricity ratio on the dimensionless static stiffness of the double-pad thrust bearing

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Fig. 16

Schematic diagram of external perturbation and the change in the gas film force

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Fig. 17

Effects of perturbation frequency and eccentricity ratio on the dynamic stiffness of the double-pad thrust bearing

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Fig. 18

Effects of perturbation frequency and eccentricity ratio on the damping coefficient of the double-pad thrust bearing

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Fig. 19

Effects of supply pressure and squeeze number on the dimensionless dynamic stiffness of the double-pad thrust bearing (eccentricity ratio ε = 0.2)

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Fig. 20

Effects of supply pressure and squeeze number on the dimensionless damping coefficient of the double-pad thrust bearing (eccentricity ratio ε = 0.2)

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Fig. 21

Effects of orifice diameter and squeeze number on the dimensionless dynamic stiffness of the double-pad thrust bearing (eccentricity ratio ε = 0.2)

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Fig. 22

Effects of orifice diameter and squeeze number on the dimensionless damping coefficient of the double-pad thrust bearing (eccentricity ratio ε = 0.2)

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Fig. 23

Effects of eccentricity ratio and squeeze number on the dimensionless dynamic stiffness of the double-pad thrust bearing (ps = 0.5 MPa, d = 0.2 mm)

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Fig. 24

Effects of eccentricity ratio and squeeze number on the dimensionless damping coefficient of the double-pad thrust bearing (ps = 0.5 MPa, d = 0.2 mm)

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Fig. 25

Dynamic model of the double-pad aerostatic thrust bearing

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Fig. 26

Numerical step response analysis of the double-pad thrust bearing: (a) eccentricity ratio ε = 0.07 (with mass of spindle 10 kg) and (b) eccentricity ratio ε = 0.14 (with mass of spindle 20 kg)

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Fig. 27

Natural frequency of the double-pad thrust bearing versus eccentricity ratio

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Fig. 28

Dynamic performance of the double-pad thrust bearing calculated by the ADMM and the PDMM at natural frequency: (a) dynamic stiffness and (b) damping coefficient

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