Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy

The tidal perturbation of embedded protoplanets on their natal disks has been widely attributed to be the cause of gap-ring structures in submillimeter images of protoplanetary disks around T Tauri stars. Numerical simulations of this process have been used to propose scaling of characteristic dust-gap width/gap-ring distance with respect to planet mass. Applying such scaling to analyze observed gap samples yields a continuous mass distribution for a rich population of hypothetical planets in the range of several Earth to Jupiter masses. In contrast, the conventional core-accretion scenario of planet formation predicts a bimodal mass function due to (1) the onset of runaway gas accretion above ∼20 Earth masses and (2) suppression of accretion induced by gap opening. Here, we examine the dust disk response to the tidal perturbation of eccentric planets as a possible resolution of this paradox. Based on simulated gas and dust distributions, we show the gap-ring separation of Neptune-mass planets with small eccentricities might become comparable to that induced by Saturn-mass planets on circular orbits. This degeneracy may obliterate the discrepancy between the theoretical bimodal mass distribution and the observed continuous gap width distribution. Despite damping due to planet–disk interaction, modest eccentricity may be sustained either in the outer regions of relatively thick disks or through resonant excitation among multiple super Earths. Moreover, the ring-like dust distribution induced by planets with small eccentricities is axisymmetric even in low viscosity environments, consistent with the paucity of vortices in Atacama Large Millimeter/submillimeter Array images.

Generation and Evolution Conditions of Polygonal Wear of High-Speed Wheel

Wheel polygonal wear has long been a problem that confused the safety of railway operation which has important theoretical value and research significance. In this paper, the conditions of polygonal wear of high-speed wheel are analyzed based on the wear model and verified by the field measured data. Considering the wheel track interaction caused by rotation, a finite element model of wheelset rotor dynamics is established. The effects of rotor speed, mass eccentricity, wheelset, and track flexibility on the vibration characteristics of wheelset rotor system and wheel polygonal wear characteristics are analyzed by beam element and solid element, respectively. The results show that the wheel longitudinal vibration is the main reason of wheel polygonal wear, and the wheel polygonal wear follows the law of “constant frequency and divisible.” Its “constant frequency” comes from the wheel track contact vibration, which stimulates the third-order vertical bending vibration of wheelset and the eighth-order coupled bending vibration of track, and the order is equal to the ratio of “constant frequency” to the wheelset rotation frequency.

Establishment of Dynamic Model of axle Box Bearing of high-speed Train under Variable Speed Conditions

This paper establishes a dynamic model of the bearing rotor system of a high-speed train under variable speed conditions. Different from previous works, the proposed model simplifies the contact stress and considers the compensation balance excitation caused by the rotor mass eccentricity. The angle iteration method is used to solve the challenging problem that the roller space position cannot be determined in bearing rotation. The simulation results show that the model accurately describes the dynamics of bearing under varying speed profiles that contain acceleration, deceleration and speed oscillation stages. The order ratio spectrum of the bearing vibration signal indicates that both single frequency and multiple frequency in simulation results are consistent with that in theoretical results. Experiments of bearing with outer ring fault and inner ring fault under various operating conditions are presented to verify the developed model.

A Model To Estimate Synchronous Vibration Amplitude For Detection of Unbalance in Rotor-Bearing System

A numerical technique for detection of unbalance magnitude of a rotor-bearing system is proposed and verified by experimental analysis. Dimensional analysis is used for development of mathematical model of an unbalanced rotor-bearing system following rigid rotor approach. A developed mathematical model is solved by factorial regression analysis method using the experimental data obtained by a Box-Behnken design. The proposed approach integrates the rotor parameters, disc parameters, bearing parameters and operating conditions with the synchronous vibration amplitude. Confirmation experiments are conducted using Taguchi design methodology with unbalance mass, rotor speed, mass eccentricity and radial load as parameters with different levels assigned to them.

Dynamic modeling and vibration response analysis of a synchronous motorized spindle with inclined eccentricity

The air-gap eccentricity will produce unbalanced magnetic pull and cause vibrations and noises in a motor. In this study, the dynamic behavior of a synchronous motorized spindle with inclined eccentricity is investigated. A semi-analytical method is proposed to model the unbalanced magnetic pull and the electromagnetic torque of a rotor with inclined eccentricity, and the semi-analytical method is verified by the finite element method. The dynamic model of a spindle-bearing system is built by taking the centrifugal force and gyroscopic effects into account. Then, the vibration response of dynamic displacement eccentricity, inclined eccentricity including displacement eccentricity and angle eccentricity, rotating speed, and unbalanced mass eccentricity in both time domain and frequency domain are simulated and analyzed. The results show that the eccentricities can lead to fluctuations in amplitudes of the dynamic displacement response and the angle response. The frequency components of the dynamic responses are the combination of rotating frequency, VC frequency, and power frequency. It is indicated that the coupling interactions of bearing forces, unbalanced mass force, and unbalanced magnetic pull have an obvious effect on the spindle-bearing system.

Nonlinear Dynamic Analysis of Rotor-Bearing System with Cubic Nonlinearity

Nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity are investigated. The comprehensive effects of the unbalanced excitation, the internal clearance, the nonlinear Hertzian contact force, the varying compliance vibration, and the nonlinear stiffness of support material are considered. The expression with the linear and the cubic nonlinear terms is adopted to characterize the synthetical nonlinearity of the rotor-bearing system. The effects of nonlinear stiffness, rotating speed, and mass eccentricity on the dynamic behaviors of the system are studied using the rotor trajectory diagrams, bifurcation diagrams, and Poincaré map. The complicated dynamic behaviors and types of routes to chaos are found, including the periodic doubling bifurcation, sudden transition, and quasiperiodic from periodic motion to chaos. The research results show that the system has complex nonlinear dynamic behaviors such as multiple period, paroxysmal bifurcation, inverse bifurcation, jumping phenomena, and chaos; the nonlinear characteristics of the system are significantly enhanced with the increase of the nonlinear stiffness, and the material with lower nonlinear stiffness is more conducive to the stable operation of the system. The research will contribute to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system.

Stability analysis of rotating shaft under electromagnetic and bearing oil-film forces

The stability of the fixed pints of a flexible rotor supported by journal bearings is investigated through the Bifurcation diagrams. In this paper the effect of nonlinear electromagnetic harmonic force is added to the simultaneous consideration of the effects of the nonlinearity in curvature and inertia, mass eccentricity and hydrodynamic forces of the journal bearings. Solution of the Reynolds equation renders the pressure distribution in the bearings. The bearing forces are found from integrating the pressure distribution on the surface of bearings. Derivation of the equations is performed using the Hamilton's principle and the nonlinearity terms are related to the eccentricity and the curvature of shaft. Primary and combination resonances are imposed to the rotor-bearing system and steady state responses show the effects of magnetic and bearing forces on the stability of amplitudes. In combination resonance, frequency of the electromagnetic load is tuned as the average of the forward and backward natural frequencies of the rotor. Existence of unstable Hopf points demonstrates that periodic, quasi-periodic and chaotic motions may be arisen in the nonlinear behavior of rotor.

Nonlinear Dynamic Performance of a Bolt-Disc Rotor with the Position Error of Circumferential Bolt-Holes

The bolt-holes in the assembly discs are designed to limit the circumferential displacement of bolts for the bolt-disc rotor. The position error of circumferential bolt-holes is created in a three-dimensional model of bolt-disc rotor. The distribution of nonuniform stress and deformation is acquired according to finite element approach. Static results demonstrate that the position error of bolt-holes leads to obvious concomitant unbalances including constant mass eccentricity and speed-variant bending under the influence of large tightening force. When these unbalance factors are taken into consideration, dynamic performance such as instability areas and nonlinear motions are analyzed by Newton iterative process and a prediction-correction calculation method. Dynamic results show that rotor flexure enables the systematic stability decreased obviously because of this position error. There is a special phenomenon compared to monobloc rotor that the vibration amplitude proceeds to rise when rotating speed exceeds the critical speed. Moreover, the allowable position error of bolt-holes is obviously smaller than that of monobloc rotor and uneven tightening is a feasible way to reduce adverse effects on the dynamic properties when position error appears. This work proposes a static-dynamic approach to investigate the dynamics of imprecise bolt-disc rotor and establishes the relationship between machining error and dynamic features.

Study on the Vibration Mitigation Characteristic of Dual Clearance Squeeze Film Damper

In this paper, a novel model of dual clearance squeeze film damper (DCSFD) was constructed considering convection effect and the vibration mitigation characteristic of DCSFD was researched. The DCSFD film force linearity r FSFD was proposed. The response characteristics of rigid rotor containing DCSFD were studied based on the DCSFD model. A response experiment of the DCSFD was arranged, and the model was verified. A good consistence was achieved between the simulation and experiment. The experiment and simulation result manifests that the unbalance response of DCSFD was smaller than that of SFD at every excitation frequency. The DCSFD could inhibit the nonlinear vibration such as the bistability and bifurcation due to big mass eccentricity, and nonlinear film force for the DCSFD film force linearity was bigger than that for SFD. The thickness ratio of inner and outer film, pressure loss coefficient, and inner film thickness were the important parameters that have great influence on DCSFD vibration mitigation characteristic.