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Study on the Influence of Dynamic Characteristics of Servo Valve on Coupling Vibration of Cold Rolling Mill

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Abstract

The cold rolling mills are complex electro-hydro-mechanical systems in which vibrations are usually detected as issues during production process. In the present work, the vibrations with frequencies of 80Hz were found at top of the rolling mill and the pressure behind servo valve during the production process. In order to understand the vibration mechanism and to explore the measurements for vibration suppression, the dynamic models were proposed to describe valve spool, 8-DOF cold rolling mill, and hydraulic system based on the dynamic characteristics of servo-valve. The analytical solutions and numerical solutions were obtained for the vibration rules for the valve spool displacement and the output flow rate under different working conditions. Moreover, the influence of dynamic characteristics of servo-valve on the vibrations and optimization of the servo-valve were discussed. The results suggest that the dynamic characteristics of servo-valve have a significant influence on the hydro-mechanical coupled vibration of rolling mill and the vibrations can be dampened by improving the dynamic characteristics of rolling mill. This work is expected to provide a new perspective to suppress the hydro-mechanical coupled vibrations.

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Abbreviations

\(A_{{\text{p}}}\) :

Hydraulic cylinder piston area

\(B\) :

Magnetic induction around energized coil

\(B_{{\text{v}}}\) :

Damping coefficient

\(c_{{\text{h}}}\) :

Total leakage coefficient of hydraulic cylinder

\(cc\) :

Conjugate of preceding terms

\(C_{{\text{d}}}\) :

Discharge coefficient

\(C_{{\text{v}}}\) :

Velocity coefficient

\(D\) :

Coil diameter

\(f_{1}\) :

Dimensionless amplitude of small excitation

\(f_{2}\) :

Dimensionless amplitude of large excitation

\(F\) :

Dynamic ampere force amplitude

\(F_{{\text{a}}}\) :

Ampere force on spool

\(\Delta F_{{\text{a}}}\) :

Dynamic ampere force

\(F_{{\text{k}}}\) :

Spring force

\(F_{{\text{f}}}\) :

Steady-state flow force

\(I\) :

Current intensity of energized coil

\(K\) :

Natural stiffness of rolling mill

\(K_{1}\) :

Coefficient of stiffness first-order term

\(K_{3}\) :

Coefficient of stiffness cubic term

\(K_{{\text{e}}}\) :

Equivalent stiffness of rolling mill

\(K_{{\text{f}}}\) :

Steady-state flow stiffness

\(\overline{K}_{{\text{f}}}\) :

Steady-state flow stiffness stability amplitude

\(K_{{{\text{f1}}}}\) :

Amplitude of steady-state flow stiffness fluctuation

\(L\) :

Length scale in dimensionless process

\(m_{{\text{v}}}\) :

Equivalent mass of valve spool and coil

\(N\) :

Coil turns

\(\Delta p\) :

Valve port differential pressure

\(t\) :

Dimensionless time

\(T\) :

Time scale in dimensionless process

\(T_{n}\) :

N-order time scale

\(V_{1}\) :

Volume of oil inlet chamber of hydraulic cylinder

\(W\) :

Valve port area gradient

\(x_{{\text{v}}}\) :

Spool displacement

\(x\) :

Dimensionless spool displacement

\(\alpha\) :

Vibration amplitude of dimensionless system

\(\alpha_{{\text{g}}}\) :

Gain of mill modulus control

\(\beta\) :

Vibration phase of dimensionless system

\(\beta_{{\text{e}}}\) :

Effective bulk modulus of elasticity

\(\varepsilon\) :

Small parameter

\(\zeta\) :

Damping ratio of dimensionless system

\(\theta\) :

Valve port jet angle

\(\sigma\) :

Tuning parameters

\(\omega\) :

Dimensionless disturbance frequency

\(\omega_{0}\) :

Natural frequency of dimensionless system

\(\Omega\) :

Dynamic ampere force frequency

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Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Yujie Liu, Jiebin Qi, Xuewei Wang & Xiaoqiang Yan

  2. Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, 18015, USA

    Shen Wang

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  1. Yujie Liu
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Yujie Liu, Shen Wang and Jiebin Qi. The typesetting and proofreading format were completed by Xuewei Wang. Supervision by Xiaoqiang Yan. The first draft of the manuscript was written by Yujie Liu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Xiaoqiang Yan.

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Liu, Y., Wang, S., Qi, J. et al. Study on the Influence of Dynamic Characteristics of Servo Valve on Coupling Vibration of Cold Rolling Mill. Int. J. Precis. Eng. Manuf. (2024). https://doi.org/10.1007/s12541-024-01017-4

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