Dynamic Force and Moment Characteristics of Annular Gaps—Simulation Results and Evaluation of the Relevance of the Tilt and Moment Coefficients

Abstract

Nowadays, most studies of the dynamic characteristics of annular gaps focus only on the force characteristics due to translational motions, while the tilt and moment coefficients are less well studied. To expand the knowledge of the additional coefficients, we investigate both the dynamic force and the dynamic and moment characteristics of annular gaps. First, the rotordynamic influence of annular gaps is recapitulated. Second, a new simulation method is presented, using a perturbed integro-differential approach in combination with a Hirs' model and power-law ansatz functions for the velocity profiles to calculate the dynamic force and moment characteristics. Subsequently, an extensive parameter study is carried out. To evaluate whether the hydraulic tilt and moment coefficients need to be considered, an effective stiffness is defined and the influence of the annulus length, an eccentrically operated shaft, the centre of rotation, a modified Reynolds number, the flow number and the pre-swirl is investigated. It is shown that despite the annulus length, the flow number as well a modified Reynolds number are crucial for the relevance of the additional coefficients. This leads to a simple three-dimensional diagram, which makes it possible to assess the necessity of including the additional coefficients on the basis of the three variables.

Prediction of the static force characteristic of annular gaps using neural networks

“…Figure 1: Generic annular gap with an axial flow component, cf. Kuhr, Nordmann and Pelz (2022) To design a neural network for use with narrow annular gaps, the descriptive quantities of the annulus need to be known. In the following, only fluid lubricated narrow annuli without cavitation, i.e.…”

“…The number of inputs into the network can be reduced by conducting a dimensional analysis. Therefore and on dimensional grounds, the induced dimensionless force components F X := 2 FX /(ρ Ω2 R3 L) and F Y := 2 FY /(ρ Ω2 R3 L) as well as the pressure difference across the annulus ∆p := 2∆p/(ρ Ω2 R2 ) are only a function of five dimensionless measures: (i) the dimensionless annulus length L := L/ R, (ii) the relative eccentricity ε := ẽ/ h, (iii) the modified Reynolds number in circumferential direction ψRe * Kuhr, Nordmann and Pelz (2022). Here, ψ := h/ R is the gap clearance and n f is an empirical constant describing an arbitrary line within the double logarithmic Moody diagram…”

“…the left-hand side of equation 1, is developed and implemented using Matlab's Deep Learning Toolbox. To be more precise, the neural network will be used to approximate the Clearance-Averaged Pressure Model (CAPM) by Lang and Pelz (2016); Lang (2018); Kuhr, Nordmann and Pelz (2022). Within the CAPM, it is assumed that the radial velocity component as well as the pressure gradient over the gap height are negligible.…”

“…The integrals in the equations are solved analytically by using power-law ansatz functions to describe the velocity profiles in circumferential and axial direction, cf. Lang and Pelz (2016); Lang (2018); Kuhr, Nordmann and Pelz (2022). Due to the modular integration of the velocity profiles, the ansatz functions can be adapted to gap flows at arbitrary Reynolds numbers.…”

“…In particular, the power-law ansatz functions can be used to treat laminar, transitional and turbulent gap flows in a unified model framework. For further information about the Clearance-Averaged Pressure Model and the solver used for calculation, please refer to the work of Lang and Pelz (2016); Lang (2018); Kuhr, Nordmann and Pelz (2022); Kuhr (2022); Kuhr, Lang and Pelz (2022)…”