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Analysis and Optimization of an Internal Feedback Hydrostatic Turntable Oil Pad Power Consumption Based on Finite Difference Method

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Abstract

The hydrostatic turntable is a critical component of numerous CNC machine tools, as it performs a supporting function and enables precise rotary motion. To ensure that high-precision CNC machines can operate under heavy loads, it is imperative to minimize power consumption. The power consumption of a hydrostatic turntable is affected by various factors, such as oil viscosity, initial oil film thickness, and oil pad structure. This study focuses on investigating a hydrostatic turntable with internal feedback. The Reynolds equation of the sector oil pad is solved using the finite difference method to establish the pressure distribution model. Subsequently, the study examines the power consumed by the axial oil pad at different initial oil film thickness, lubricating oil viscosity, and sealing edge width. To minimize power consumption caused by the axial oil pad, this paper employs the genetic algorithm to identify optimal design parameters within specified constraints. Additionally, the load-bearing performance of the optimized axial oil pad is checked to ensure that the load-bearing capacity and stiffness meet the requirements. Finally, the use of simulation software for oil pads in finite element simulation can preliminarily demonstrate the reliability of the proposed method.

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Abbreviations

A s :

Area of the oil sealing edge and throttle (m−2)

A r :

Area of the oil pocket (m−2)

b :

Width of gap throttle edge (m)

B :

Width of oil pad sealing edge (m)

f r :

Friction in the radial direction (N)

f θ :

Friction in the circumferential direction (N)

F f :

Total friction (N)

h :

Film thickness (m)

h 0 :

Initial oil film thickness (m)

h 1 :

Oil film thickness of upper oil pad (m)

h 2 :

Oil film thickness of lower oil pad (m)

H :

Depth of the oil pocket (m)

i :

Numerical counters of the elements of r

j :

Numerical counters of the elements of θ

k :

Numerical counters of the elements of z

K :

Mean stiffness (N m−1)

l :

Length of gap throttle edge (m)

L :

Width of oil pad sealing edge (m)

N f :

Total friction power (W)

N P :

Support power (W)

N t :

Total power (W)

\(\overline{{\text{N}}} _{{{\text{fr}}}}\) :

Dimensionless friction power in radial direction

p :

Pressure (MPa)

p 0 :

Oil pocket pressure (MPa)

p s :

Inlet pressure (MPa)

p 1 :

Upper oil pocket pressure (MPa)

p 2 :

Lower oil pocket pressure (MPa)

Q :

Oil supply flow rate (m3  s−1)

\(\overline{{\text{q}}} _{{\text{r}}}\) :

Dimensionless flow rate in radial direction

r :

Radial coordinate

R 0 :

Outside diametesr of fan oil pad (m)

R 1 :

Inside diameter of fan oil pad (m)

R c 1 :

Oil inlet resistance in upper oil pocket (N s m−5)

R h1 :

Oil outlet resistance in upper oil pocket (N s m−5)

R c 2 :

Oil inlet resistance in lower oil pocket (N s m−5)

R h2 :

Oil outlet resistance in lower oil pocket (N s m−5)

U :

Radial velocity (m s−1)

\(\overline{{\text{U}}} _{{\text{Z}}}\) :

Dimensionless damping

V :

Circumferential velocity (rad s−1)

W :

External load on a pair of oil pads (N)

W 0 :

Oil pad thrust at no load (N)

W 1 :

Upper oil pad thrust (N)

W 2 :

Lower oil pad thrust (N)

z :

Film thickness coordinate

β 0 :

Initial throttling ratio

Δh :

Oil film thickness variation (m)

θ :

Circumferential coordinate

ρ :

Density (kg m−3)

ω :

Rotational angular velocity (rad s−1)

ω SOR :

SOR weight in successive Over Relaxation method

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Funding

This project is supported by National Natural Science Foundation of China (No. 52175447, No. 51975019), Natural Science Foundation of Beijing Municipality (No. 3232002) and Ministry of Industry and Information Technology's special project for high-quality development of manufacturing industry (No. TC210H039).

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Authors and Affiliations

  1. Institute of Advanced Manufacturing and Intelligent Technology, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Congbin Yang, Shuaihua Shao, Yanhong Cheng, Zhifeng Liu & Yongsheng Zhao

  2. Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Congbin Yang, Shuaihua Shao, Yanhong Cheng & Yongsheng Zhao

  3. School of Mechanical and Aerospace Engineering, Key Laboratory of CNC Equipment Reliability, Ministry of Education, Jilin University, Changchun, 130012, People’s Republic of China

    Zhifeng Liu

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  1. Congbin Yang
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Correspondence to Yanhong Cheng.

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Yang, C., Shao, S., Cheng, Y. et al. Analysis and Optimization of an Internal Feedback Hydrostatic Turntable Oil Pad Power Consumption Based on Finite Difference Method. Int. J. Precis. Eng. Manuf. 24, 2211–2228 (2023). https://doi.org/10.1007/s12541-023-00894-5

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