Chapter 16
Modeling and Parameter Identification
for Active Lubricated Hydrostatic
Bearing-Rotor System
Shuo Zhan, Wei Pan, Yixin Zhang, and Changhou Lu
Abstract Active lubricated hydrostatic bearing-rotor system can achieve large
bearing capacity, high motion accuracy, high anti vibration ability and long service
life. Models from first principles are often complex and inaccurate caused by the
discrepancy between the ideal hypothesis and the actual situation. And the multipleinput multiple-output (MIMO) characteristics of the system further increase the
complexity of modeling, but the system requires low complexity dynamic model
over its entire operating range. In order to solve the problem, this paper presents a
modeling and identification method. Firstly, a segmented linear model is established
in a small displacement of the shaft, and the parameters are solved by the prediction
error method. The parameter variation law of the system is obtained by fitting identified system parameters. Then, the dynamic equation of the system can be obtained.
Finally, the identified model is validated by impulse signals. The experimental results
demonstrate the validity and accuracy of the identified model.
Keywords Active lubricated bearings · Grey-box modelling · Linear
parameter-varying system · System identification
16.1 Introduction
Hydrostatic bearings have wide applications in precision and ultra-precision
machinery. Although systems composed of hydrostatic bearings and other functional
units have the self-adjusting abilities, they are usually “passive". It means that when
the external load changes, the equilibrium position of the rotor changes, resulting
in vortex trajectory and loss of mechanical accuracy. The traditional passive hydrostatic bearing-rotor system is relatively mature and has low potential for significant
improvements [1, 2]. The active lubricated bearing-rotor system, which combines
S. Zhan · W. Pan (B) · Y. Zhang · C. Lu
Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, National
Demonstration Center for Experimental Mechanical Engineering Education, School of
Mechanical Engineering, Shandong University, Jinan 250061, Shandong Province, China
e-mail: panw@sdu.edu.cn
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. Xu and K. M. Pandey (eds.), Mechanical Engineering and Materials,
Mechanisms and Machine Science 100,
https://doi.org/10.1007/978-3-030-68303-0_16
197
Modeling and Parameter Identification
for Active Lubricated Hydrostatic
Bearing-Rotor System
Shuo Zhan, Wei Pan, Yixin Zhang, and Changhou Lu
Abstract Active lubricated hydrostatic bearing-rotor system can achieve large
bearing capacity, high motion accuracy, high anti vibration ability and long service
life. Models from first principles are often complex and inaccurate caused by the
discrepancy between the ideal hypothesis and the actual situation. And the multipleinput multiple-output (MIMO) characteristics of the system further increase the
complexity of modeling, but the system requires low complexity dynamic model
over its entire operating range. In order to solve the problem, this paper presents a
modeling and identification method. Firstly, a segmented linear model is established
in a small displacement of the shaft, and the parameters are solved by the prediction
error method. The parameter variation law of the system is obtained by fitting identified system parameters. Then, the dynamic equation of the system can be obtained.
Finally, the identified model is validated by impulse signals. The experimental results
demonstrate the validity and accuracy of the identified model.
Keywords Active lubricated bearings · Grey-box modelling · Linear
parameter-varying system · System identification
16.1 Introduction
Hydrostatic bearings have wide applications in precision and ultra-precision
machinery. Although systems composed of hydrostatic bearings and other functional
units have the self-adjusting abilities, they are usually “passive". It means that when
the external load changes, the equilibrium position of the rotor changes, resulting
in vortex trajectory and loss of mechanical accuracy. The traditional passive hydrostatic bearing-rotor system is relatively mature and has low potential for significant
improvements [1, 2]. The active lubricated bearing-rotor system, which combines
S. Zhan · W. Pan (B) · Y. Zhang · C. Lu
Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, National
Demonstration Center for Experimental Mechanical Engineering Education, School of
Mechanical Engineering, Shandong University, Jinan 250061, Shandong Province, China
e-mail: panw@sdu.edu.cn
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
J. Xu and K. M. Pandey (eds.), Mechanical Engineering and Materials,
Mechanisms and Machine Science 100,
https://doi.org/10.1007/978-3-030-68303-0_16
197