Influence of roundness error screw on running characteristics of sliding bearing based on SDT

In order to study the influence of roundness error on the oil film characteristics of journal bearing rotor system, a dynamic model of journal bearing rotor system with roundness error was established, and a new generalized roundness error equation is derived based on the small displacement screw (SDT) theory. And the influence of roundness error screw parameter dx represented by SDT on critical speed and stability of sliding bearing is analyzed emphatically. The results show that the existence of journal roundness error is beneficial to the bearing capacity and stability of sliding bearing rotor system to a certain extent, and with the increase of roundness error screw parameter, its promoting effect is more obvious; At the same time, the critical speed of the system will increase with the increase of screw parameter, especially when eccentricity ε>0.6; And when Sommerfeld number S>0.6, the roundness error of journal has little influence on stability.

ROUNDNESS PROPERTIES OF ULTRAMETRIC SPACES

Motivated by a classical theorem of Schoenberg, we prove that an n + 1 point finite metric space has strict 2-negative type if and only if it can be isometrically embedded in the Euclidean space $\mathbb{R}^{n}$ of dimension n but it cannot be isometrically embedded in any Euclidean space $\mathbb{R}^{r}$ of dimension r < n. We use this result as a technical tool to study ‘roundness’ properties of additive metrics with a particular focus on ultrametrics and leaf metrics. The following conditions are shown to be equivalent for a metric space (X,d): (1) X is ultrametric, (2) X has infinite roundness, (3) X has infinite generalized roundness, (4) X has strict p-negative type for all p ≥ 0 and (5) X admits no p-polygonal equality for any p ≥ 0. As all ultrametric spaces have strict 2-negative type by (4) we thus obtain a short new proof of Lemin's theorem: Every finite ultrametric space is isometrically embeddable into some Euclidean space as an affinely independent set. Motivated by a question of Lemin, Shkarin introduced the class $\mathcal{M}$ of all finite metric spaces that may be isometrically embedded into ℓ2 as an affinely independent set. The results of this paper show that Shkarin's class $\mathcal{M}$ consists of all finite metric spaces of strict 2-negative type. We also note that it is possible to construct an additive metric space whose generalized roundness is exactly ℘ for each ℘ ∈ [1, ∞].