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<p>This article presents the results of a theoretical study of the static and dynamic characteristics of an axial hydrostatic bearing with an elastic lubricant flow orifice. A nonlinear mathematical model of its dynamic motion is developed. Analysis of the linearized model demonstrates that the structure’s dynamics cannot be described via a harmonic oscillator. A small-scale study of the bearing’s dynamic characteristics revealed that the characteristic polynomial of its linear dynamic system has third order, demonstrating the inadequacy of the harmonic oscillator model for describing bearing dynamics and suggesting the possibility of its stable operation under low compliance conditions. The study demonstrated that the bearing is stable with zero and negative compliance under both light and heavy loads. The dimensionless parameters «compression number» σ and pocket volume <i>V</i> play crucial roles in ensuring stability. Analysis of the obtained calculated data revealed that the compression number σ can largely be considered a measure of the damping of the bearing lubrication system. There is exactly one set of values ​​for these parameters, for which the bearing exhibits ideal dynamics—a safety margin, aperiodic behavior, and the shortest transient damping time. Formulas have also been derived for calculating the optimal values ​​of these parameters. A formula was also derived for calculating the cylindrical compliance of the regulator, at which the bearing at the “calculation point” has zero static compliance of the supporting lubricant gap. An example of calculating the main dimensional values ​​of a bearing that correspond to the optimal dimensionless parameters σ and <i>V</i> is given.</p>

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Dynamic modeling of negative compliance hydrostatic thrust bearing with Laub’s elastic orifice

  • 期刊论文

  • 发表日期：

    2026年3月25日

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  • Vladimir Kodnyanko

摘要

This article presents the results of a theoretical study of the static and dynamic characteristics of an axial hydrostatic bearing with an elastic lubricant flow orifice. A nonlinear mathematical model of its dynamic motion is developed. Analysis of the linearized model demonstrates that the structure’s dynamics cannot be described via a harmonic oscillator. A small-scale study of the bearing’s dynamic characteristics revealed that the characteristic polynomial of its linear dynamic system has third order, demonstrating the inadequacy of the harmonic oscillator model for describing bearing dynamics and suggesting the possibility of its stable operation under low compliance conditions. The study demonstrated that the bearing is stable with zero and negative compliance under both light and heavy loads. The dimensionless parameters «compression number» σ and pocket volume V play crucial roles in ensuring stability. Analysis of the obtained calculated data revealed that the compression number σ can largely be considered a measure of the damping of the bearing lubrication system. There is exactly one set of values ​​for these parameters, for which the bearing exhibits ideal dynamics—a safety margin, aperiodic behavior, and the shortest transient damping time. Formulas have also been derived for calculating the optimal values ​​of these parameters. A formula was also derived for calculating the cylindrical compliance of the regulator, at which the bearing at the “calculation point” has zero static compliance of the supporting lubricant gap. An example of calculating the main dimensional values ​​of a bearing that correspond to the optimal dimensionless parameters σ and V is given.