Dynamic modeling of hydrostatic guideway considering compressibility and inertia effect

doi:10.1007/s11465-015-0331-4

Front. Mech. Eng.

2015, Vol. 10

Issue (1) : 78-88 https://doi.org/10.1007/s11465-015-0331-4

RESEARCH ARTICLE

Dynamic modeling of hydrostatic guideway considering compressibility and inertia effect

Yikang DU¹,Kuanmin MAO^1,^*(

),Yaming ZHU¹,Fengyun WANG¹,Xiaobo MAO¹,Bin LI^1,²

1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Download: PDF(1690 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Hydrostatic guideways are used as an alternative to contact bearings due to high stiffness and high damping in heavy machine tools. To improve the dynamic characteristic of bearing structure, the dynamic modeling of the hydrostatic guidway should be accurately known. This paper presents a “mass-spring-Maxwell” model considering the effects of inertia, squeeze, compressibility and static bearing. To determine the dynamic model coefficients, numerical simulation of different cases between displacement and dynamic force of oil film are performed with fluent code. Simulation results show that hydrostatic guidway can be taken as a linear system when it is subjected to a small oscillation amplitude. Based on a dynamic model and numerical simulation, every dynamic model’s parameters are calculated by the Levenberg-Marquardt algorithm. Identification results show that “mass-spring-damper” model is the most appropriate dynamic model of the hydrostatic guidway. This paper provides a reference and preparation for the analysis of the dynamic model of the similar hydrostatic bearings.

Keywords hydrostatic guidway dynamic model dynamic mesh technique Levenberg-Marquardt mass-spring-damper model

Corresponding Author(s): Kuanmin MAO

Online First Date: 09 March 2015 Issue Date: 01 April 2015

Cite this article:

Yikang DU,Kuanmin MAO,Yaming ZHU, et al. Dynamic modeling of hydrostatic guideway considering compressibility and inertia effect[J]. Front. Mech. Eng., 2015, 10(1): 78-88.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-015-0331-4
https://academic.hep.com.cn/fme/EN/Y2015/V10/I1/78

Fig.1 Oil film pad geometry

Fig.2 Hydrostatic guideway with single pad

Tab.1 Geometrical dimension of the bearing pad, lubricant properties

Fig.3 Massless spring-damper model

Fig.4 Mass-spring-damper model

Fig.5 Mass-spring-Maxwell of hydrostatic guidway

Fig.6 Pressure distribution of the pad at (a) t = 0 ; (b) t = 0.25 T ; (c) t = 0.5 T ; (d) t = 0.75 T

Fig.7 Variation of the dynamic force of bearing face vs excitation frequency of (a) 40 Hz; (b) 80 Hz

Fig.8 Amplitude-frequency curve of dynamic oil film force under the condition of h₀=95 μm, f=40 Hz and the oscillation amplitude of (a) 1 μm; (b) 2 μm; (c) 3 μm

Fig.9 Comparison of hysteresis loop for h₀=95 μm, A=1 μm and the oscillation frequency of 40, 60 and 80 Hz

Fig.10 Comparison of hysteresis loop for h₀=95, 85 and 80 μm, A=1 μm and f = 40 Hz

Tab.2 Amplitude of the FRFs of different cases

Fig.11 FRF for h₀=95 μm, A=1, 2 and 3 μm

Fig.12 Frequency-response function for h₀=95, 85 and 80 μm, A=1 μm

Tab.3 Parameter identification of spring-damper model

Tab.4 Parameter identification of mass-spring-damper model

Tab.5 Parameter identification of mass-spring-Maxwell model

Fig.13 Comparison of simulation curve and model curve

1	Brown G. The dynamic characteristics of a hydrostatic thrust bearing. International Journal of Machine Tool Design and Research, 1961, 1(1-2): 157–171(J) https://doi.org/10.1016/0020-7357(61)90050-6
2	Dimond T W, Sheth P N, Allaire P E, Identification methods and test results for tilting pad and fixed geometry journal bearing dynamic coefficients-A review. Shock and vibration, 2009, 16(1): 13–43 https://doi.org/10.3233/SAV-2009-0452
3	Bouzidane A, Thomas M. Equivalent stiffness and damping investigation of a hydrostatic journal bearing. Tribology Transactions, 2007, 50(2): 257–267 https://doi.org/10.1080/10402000701309745
4	Jolly P, Hassini M A, Arghir M, . Identification of stiffness and damping coefficients of hydrostatic bearing with angled injection. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2013, 227(8): 905–911 https://doi.org/10.1177/1350650113482613
5	Jeon S Y, Kim K H. A fluid film model for finite element analysis of structures with linear hydrostatic bearings. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2004, 218(3): 309–316 https://doi.org/10.1243/095440604322900435
6	Wang Z W, Zhao W H, Lu B H. Influencing factors on dynamic response of hydrostatic guideways. Advanced Materials Research, 2011, 418-420: 2095–2101 https://doi.org/10.4028/www.scientific.net/AMR.418-420.2095
7	Gao D, Zheng D, Zhang Z. Theoretical analysis and numerical simulation of the static and dynamic characteristics of hydrostatic guides based on progressive mengen flow controller. Chinese Journal of Mechanical Engineering, 2010, 23(06): 709–716 https://doi.org/10.3901/CJME.2010.06.709
8	Zhao J H, gao D R. Dynamic characteristic comparison of open-type hydrostatic worktable both before and after linearization. Journal of Mechanical Engineering, 2012, 48(24): 158 (in Chinese) https://doi.org/10.3901/JME.2012.24.158
9	9.Lee W J, Kim S I. Joint stiffness identification of an ultra-precision machine for machining large-surface micro-features. International Journal of Precision Engineering and Manufacturing, 2009, 10(5): 115–121 https://doi.org/10.1007/s12541-009-0102-4
10	Huang S, Borca-Tasciuc D A, Tichy J A. A simple expression for fluid inertia force acting on micro-plates undergoing squeeze film damping. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2010, 467(2126): 522–536 https://doi.org/10.1098/rspa.2010.0216
11	Brecher C, Baum C, Winterschladen M, . Simulation of dynamic effects on hydrostatic bearings and membrane restrictors. Production Engineering, 2007, 1(4): 415–420 https://doi.org/10.1007/s11740-007-0051-7
12	Hashemi S, Roylance B. Analysis of an oscillatory oil squeeze film including effects of fluid inertia. Tribology Transactions, 1989, 32(4): 461–468 https://doi.org/10.1080/10402008908981914
13	Hashemi S, Roylance B. Steady-state behavior of squeeze film bearings subjected to harmonic excitation—Including fluid inertia and system effects. Tribology Transactions, 1989, 32(4): 431–438 https://doi.org/10.1080/10402008908981910
14	Tichy J A. Measurements of squeeze-film bearing forces and pressures, including the effect of fluid inertia. ASLE Transactions, 1985, 28(4): 520–526 https://doi.org/10.1080/05698198508981650
15	Andres S L. Transient response of externally pressurized fluid film bearings?. Tribology Transactions, 1997, 40(1): 147–155 https://doi.org/10.1080/10402009708983640
16	ANSYS-FLUENT. Documentations Solver Theory/Fluent [M/OL], 2013
17	Bevington P R, Robinson D K. Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill, 1991, 151–153
18	Wang G, Luo C. Data Processing of Engineering. <PublisherLocation>Cha<?Pub Caret?>ngchun</PublisherLocation>: Jilin University Press, 1990, 202–204

[1]	Gang HAN, Fugui XIE, Xin-Jun LIU. Evaluation of the power consumption of a high-speed parallel robot[J]. Front. Mech. Eng., 2018, 13(2): 167-178.
[2]	Shaodan ZHI,Jianyong LI,A. M. ZAREMBSKI. Modelling of dynamic contact length in rail grinding process[J]. Front. Mech. Eng., 2014, 9(3): 242-248.
[3]	Kejia LI, Xilun DING, Marco CECCARELL. A total torque index for dynamic performance evaluation of a radial symmetric six-legged robot[J]. Front Mech Eng, 2012, 7(2): 219-230.
[4]	DU Zhaocai, YU Yueqing, YANG Jianxin. Analysis of the dynamic stress of planar flexible-links parallel robots[J]. Front. Mech. Eng., 2007, 2(2): 152-158.

Viewed

Full text

Abstract

Cited

Shared

Discussed