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- Title
Stability and infinite static stiffness of hydrostatic lead screw compensated with a single-action membrane restrictor.
- Authors
Sha, Yuanpeng; Lu, Changhou; Pan, Wei; Chen, Shujiang
- Abstract
The single-action membrane restrictor affords better performance to hydrostatic leadscrew compared to fixed restrictors. A typical example is the static oil film stiffness of the hydrostatic lead screw being infinite, and the static oil film thickness of the hydrostatic leadscrew being independent of the external load. Although these features are quite appealing for industrial applications, using a single-action membrane restrictor leads to instability of the hydrostatic leadscrew. However, for this instability introduced by the membrane restrictor, the available conclusions are based on engineering experiences and lack in-depth investigation. Besides, current research relies on a linearized model near the system's equilibrium point to study its dynamic performance, constraining the analysis to the local stability. Hence, this paper analyzes the system's nonlinear dynamics and concludes that the source of global instability is the coupling of two nonlinear systems. Moreover, we define three factors that determine the magnitude of the external load and affect the system's stability: the membrane stiffness, the size of the membrane restrictor, and the hydrostatic lead screw. Spurred by these findings, we develop a nonlinear control law to control the membrane stiffness and maintain the infinite static stiffness of the oil film over a wide range of loads. Extensive simulations verify the effectiveness of the proposed nonlinear control law, demonstrating that overall, our theoretical work can influence practical applications improving machining accuracy, safety, and vibration resistance of hydrostatic leadscrews.
- Subjects
SCREWS; NONLINEAR systems; HYDROSTATIC extrusion
- Publication
Nonlinear Dynamics, 2023, Vol 111, Issue 11, p9971
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-023-08379-w