Investigations of the static and dynamic characteristics of the precision hydrostatic spindle with mid-thrust bearing under different loads

Abstract

This paper investigates the static and dynamic characteristics of the precision hydrostatic spindle with a mid-thrust bearing under different working conditions. Firstly, the paper establishes the fluid governing equations of the coupled journal and thrust bearings based on orifice restrictors; and the dynamic and static Reynolds equations are solved using the perturbation and finite difference methods to obtain the steady and transient pressure distribution functions. Then the stiffness and damping characteristics of matrixes of the spindle are obtained by integrating the steady and transient pressure. Furthermore, by establishing the motion equation for the spindle rotor with five degrees of freedom, the quasi-static equilibrium position and stability criterion of the rotor under different working conditions are determined. Finally, the relationships between the dynamic and static characteristics of the spindle and cutting force, rotational speed, and cutting distance are simulated and analyzed. The simulation results show the patterns of variation in performance indices such as stiffness, damping, quasi-static position, and stability of the spindle under different working conditions, which provides important design information to be taken into consideration concerning the precision hydrostatic spindle.

Keywords

Precision hydrostatic spindle five degrees of freedom coupled journal and thrust bearings static and dynamic coefficients stability

Get full access to this article

View all access options for this article.

References

Przybyãl

. Some aspects of application of the hydrostatic bearings in machine tools. Mech Mech Eng 2008; 12: 243–253.

Cheng

. Simultaneous identification of bearing dynamic coefficients in a water-gas lubricated hydrostatic spindle with a big thrust disc. J Mech Sci Technol 2016; 30: 4095–4107.

Knapp

Arneson

Oss

. Ultra-precision, high speed micro-machining spindle. In: Proceedings of the 11th EUSPEN international conference, May 2011.

Kim

B-S

Bae

G-T

Kim

G-N

. A study on the thermal characteristics of the grinding machine applied hydrostatic bearing. Trans Can Soc Mech Eng 2015; 39: 717–728.

Fedorynenko

Kirigaya

Nakao

. Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultra-precision machine tools. Prec Eng 2020; 63: 187–196.

Nakao

Sagesaka

. Development of water drive spindle. In: Proceedings of the 6th JFPS international symposium on fluid power, Tsukuba, November 2005.

Jang

Kim

. Calculation of dynamic coefficients in a hydrodynamic bearing considering five degrees of freedom for a general rotor-bearing system. J Tribol 1999; 121: 499–505.

Lund

Thomsen

. A calculation method and data for the dynamic coefficients of oil-lubricated journal bearing. In: Proceedings of the ASME design and engineering conference, Minneapolis, 1978, pp.1.

Castelli

Shapiro

. Improved method for numerical solutions of the general incompressible fluid film lubrication problem. J Lubr Technol 1967; 89: 211–218.

10.

Liang

. Dynamic coefficients and stability analysis of a water-lubricated hydrostatic bearing by solving the uncoupled Reynolds equation. Chin J Aeronaut 2020; 33: 2110–2122.

11.

Liu

. Dynamic analysis of 5-DOFs aerostatic spindles considering tilting motion with varying stiffness and damping of thrust bearings. J Mech Sci Technol 2019; 33: 5199–5207.

12.

Shi

Cao

Chen

. Effect of angular misalignment on the dynamic characteristics of externally pressurized air journal bearing. Sci China Technol Sci 2019; 62: 1520–1533.

13.

Dal

Karaçay

. Effects of angular misalignment on the performance of rotor-bearing systems supported by externally pressurized air bearing. Tribol Int 2017; 111: 276–288.

14.

Kim

Jang

Kim

. Stability analysis of a disk-spindle system supported by coupled journal and thrust bearings considering five degrees of freedom. Tribol Int 2010; 43: 1479–1490.

15.

Kim

Jang

Lee

. Complete determination of the dynamic coefficients of coupled journal and thrust bearings considering five degrees of freedom for a general rotor-bearing system. Microsyst Technol 2011; 17: 749–759.

16.

Jang

Lee

. Determination of the dynamic coefficients of the coupled journal and thrust bearings by the perturbation method. Tribol Lett 2006; 22: 239–246.

17.

Kim

Jang

. A generalized Reynolds equation and its perturbation equations for fluid dynamic bearings with curved surfaces. Tribol Int 2010; 43: 1479–1490.

18.

Koutsovasilis

. Automotive turbocharger rotor dynamics: interaction of thrust and radial bearings in shaft motion simulation. J Sound Vib 2019; 455: 413–429.

19.

Jiang

Lin

. Static and dynamic characteristics of externally pressurized porous gas journal bearing with four degrees-of-freedom. J Tribol 2018; 140: 1–13.

20.

Zhang

. An improved lumped parameter method for calculating static characteristics of multi-recess hydrostatic journal bearings. Proc IMechE, Part J: J Engineering Tribology 2020; 234: 301–310.

21.

Zhou

Wei

Wang

. A superlinear iteration method for calculation of finite length journal bearing’s static equilibrium position. R. Soc. Open Sci 2017; 4: 1–19.

22.

Ito

Matsumura

. Theory and practice in machining systems. New York: Springer International Publishing, 2017.

23.

Bittencourt Visnadi

de Castro

. Influence of bearing clearance and oil temperature uncertainties on the stability threshold of cylindrical journal bearings. Mech Mach Theory 2019; 134: 57–73.

24.

Ren

Feng

. Stability analysis of water-lubricated journal bearings for fuel cell vehicle air compressor. Tribol Int 2016; 95: 342–348.

25.

Rowe

Chong

. Computation of dynamic force coefficients for hybrid hydrostatic/hydrodynamic journal bearings by the FD technique and by the perturbation technique. Tribol Int 1986; 19; 260–271.