Influences of Randomly Uncertain Factors on Dynamic Coefficients of an Interlocking Labyrinth Seal-Rotor System

Many randomly uncertain factors inevitably arise when gas flows through a labyrinth seal, and the orbit of the rotor center will not rotate along a steady trajectory, as previously studied. Here, random uncertainty is considered in an interlocking labyrinth seal-rotor system to investigate the fluctuations of dynamic coefficients. The bounded noise excitation is introduced into the momentum equation of the gas flow, and as a result, the orbit of the rotor center is expressed as the combination of an elliptic trajectory with the bounded noise perturbation. Simulation results of the coefficients under randomly uncertain perturbations with various strengths are comparatively investigated with the traditional predictions under ideal conditions, from which the influences of random uncertain factors on dynamic coefficients are analyzed in terms of the rotor speed, pressure difference, and inlet whirl velocity. It is shown that the deviation levels of the dynamic coefficients are directly related to the random perturbations and routinely increase with such perturbation strengths, and the coefficients themselves may exhibit distinct variation patterns against the rotor speed, pressure difference, and inlet whirl velocity.

Prediction of nonlinear dynamic coefficients of tilting-pad journal bearings with pad perturbation

In this paper, a modified partial derivative method is developed to predict the linear and nonlinear dynamic coefficients of tilting-pad journal bearings with journal and pad perturbation. To this end, Reynolds equation and its boundary conditions along with equilibrium equations of the pad are used. Finite difference, partial derivative method, and perturbation technique have been employed simultaneously for solving these equations. The accuracy of the results is investigated by comparing the linear dynamic coefficients of three types of tilting-pad journal bearings with those published the literature. It is shown that the nonlinear dynamic coefficients depend on Sommerfeld number, eccentricity ratio, and length to diameter ratio. Similar to the case of linear dynamic coefficients of TPJB, it is observed that the eccentricity ratio effects on nonlinear dynamic coefficients are more notable when the eccentricity ratio is higher than 0.8 or less than 0.2.

Parameter Sensitivity Analysis on Dynamic Coefficients of Partial Arc Annular-Thrust Aerostatic Porous Journal Bearings

Aerostatic bearings are widely used in high-precision devices. Partial arc annular-thrust aerostatic porous journal bearings are a prominent type of aerostatic bearings, which carry both radial and axial loads and provide high load-carrying capacity, low air consumption, and relatively low cost. Spindle shaft tilting is a resource-demanding challenge in numerical modeling because it involves a 3D air flow. In this study, the air flow problem was solved using a COMSOL software, and the dynamic coefficients for tilting degrees of freedom were obtained using finite differences. The obtained results exhibit significant coupling between the tilting motion in the x-and y-directions: cross-coupled coefficients can achieve 20% of the direct coefficient for stiffness and 50% for damping. In addition, a nonlinear behavior can be expected, because the tilting motion within 3°, tilting velocities within 0.0012°/s, and relative eccentricity of 0.2 have effects as large as 20% for direct stiffness and 100% for cross-coupled stiffness and damping. All dynamic coefficients were fitted with a polynomial of eccentricity, tilting, and tilting velocities in two directions, with a total of six parameters. The resulting fitting coefficient tables can be employed for the fast dynamic simulation of the rotor shaft carried on the proposed bearing type.

A novel signal processing method for friction and sliding wear

This current study proposed a new computationally efficient and comparatively accurate algorithm for calculating both static and dynamic coefficients of friction from high-frequency data. Its scope embraced an application in a real-time friction-based system, such as active braking safety systems in automobile industries. The signal sources were from a heavy duty reciprocating dry sliding wear test platform, focused on experimental data related to friction induced by stick-slip phenomena. The test specimen was a polytetrafluoroethylene (PTFE) coated basalt/vinyl ester composite material, tested at a large scale. The algorithm was primarily aimed to provide scalability for processing a significantly large tribological data in a real-time. Beside a computational efficiency, the proposed method adopted to evaluate both static and dynamic coefficients of friction using the statistical approach exhibited a greater accuracy and reliability when compared with the extant models. The result showed that the proposed method reduced the computation time of processing, and reduced the variation of the absolute values of both static and dynamic frictions. Although, the variation of dynamic friction was later increased at a particular threshold, based on the test duration.

Determination of stresses and dynamic coefficients when testing railway overpasses

This paper presents some results of instrumental measurements of dynamic coefficients and fiber stresses of reinforced concrete girder spans of railway overpasses under mobile load. The results obtained can be used for further monitoring of similar structures on the main railway lines of the Republic of Kazakhstan, to identify damage in the structures of bridges.

A method for the experimental estimation of direct and cross-coupled dynamic coefficients of tilting-pad journal bearings of vertical hydro-generators

This article presents a method to experimentally estimate the direct and cross-coupled dynamic coefficients of tilting-pad journal bearings of vertical hydro-generators and other similar rotating machinery for damage detection purposes. Based on a simplified second-order model of a journal bearing in the state-space, the method employs only the usually monitored vibrations, the shaft radial relative, and the bearing radial absolute vibrations originated by the hydro-generator residual unbalance or by hydraulic excitations in the turbine rotor. This article shows that the method was successfully tested using the shaft and bearing vibration signals synthesized by a mathematical model of a 700 MW hydro-generator, even when these signals are contaminated with random noise. This article also shows the method’s performance when applied to real vibration signals acquired from the modeled hydro-generator. Finally, it discusses the possible measures to improve the method’s efficiency.

Numerical Evaluation and High-Speed Rotating Test on Circular Arc Spring Dampers for Centrifugal Compressors

A circular arc spring damper (CASD) is a recently proposed fluid-film damper that has two or more arc-shaped centering springs and dual radial clearances formed by wire electric discharge machining. CASD requires less space and weight than a conventional cage-centered squeeze film damper (SFD). It provides linear stiffness and stable damping force in rotor-bearing systems to attenuate vibration due to imbalance or to improve rotordynamic stability. The authors have been investigated the dynamic characteristics of CASD in component-level experiments. However, their performance and applicability to real machines have not been confirmed in system-level experiments. Additionally, a theoretical means of evaluation for CASD should be established to predict its dynamic coefficients, and to understand the mechanism of dynamic force generation. In the first part of this study, a numerical evaluation method using two-way fluid-structure interaction analysis and its theoretical background is presented. Transient structural analysis and fluid-film flow analysis with a simple homogeneous cavitation model are coupled in the commercial multi-physics platform ANSYS. The accuracy of the method was validated by comparing the damping and added-mass coefficients with results from previous experiments. Furthermore, several aspects of the force generation mechanism, and the difference from conventional SFD were studied numerically. The second part of the study addresses the application of CASD in a multi-stage centrifugal compressor. A combined 4-inch diameter, 5-Pad tilting pad journal bearing (TPJB) with 4-arc type CASD was newly designed and manufactured. To prove the applicability of the developed damper bearing, a series of rotating tests was conducted at a high-speed balancing facility with a full-scale dummy rotor with a critical speed ratio of approximately 3.1. The measured unbalance response showed a much lower amplification factor than that of the conventional TPJB without the damper, which infers a significant improvement in the stability. The measured responses agreed with the rotordynamic analysis, which uses the dynamic coefficients of CASD derived from the proposed numerical evaluation method.