Static Misalignment Research Articles

Track Unevenness Prediction Based on Static Track Inspection Data Matching

A track static misalignment prediction model based on track median deviation is created using an IGA-BP neural network in order to precisely predict the trend of ballastless track static misalignment. The historical static track median deviation detection data are matched using actual compensation edit distance (ERP) to finish the correspondence processing of the original data. The precisely matched data are used to train the model, forecast irregularities in the track median, and compare results with other traditional prediction techniques. The outcomes demonstrate that the IGA-BP neural network can more accurately predict the nonlinear time series data development trend. In comparison to other prediction models, the IGA-BP neural network model’s average relative error and root mean square error are 0.091 and 0.110, respectively. The prediction accuracy is raised by between 43% and 60%, demonstrating the IGA-BP neural network model’s efficacy in predicting static upsets on ballastless tracks and presenting a workable strategy for track predictive maintenance.

Dynamic modeling and analysis of the spline joint-flexible coupling-rotor system with misalignment

In the field of aviation and navigation, the spline joint-flexible coupling-rotor system has been widely used. However, the installation of the spline joint and the drive shaft is easy to introduce misalignment, then affecting the safe operation of the system. To solve this problem, this paper studies the dynamic modeling and analysis of the system with misalignment. The finite element dynamic model of the system is established. In this paper, the shaft misalignment is equivalent to the spline static misalignment and the misalignment excitation force of the flexible coupling. And a general model of the spline joint is established, which introduces the static misalignment caused by the installation of the spline joint and the drive shaft, the dynamic misalignment caused by the spline joint vibration, and the tooth surface friction. By solving the dynamic equation, the effect of the misalignment on the system's dynamic characteristics is analyzed, and some suggestions and methods for health monitoring of the system are given. The accuracy of the analysis method proposed in this paper is verified by experiment. The dynamic model and the method proposed in this paper have important theoretical significance for the dynamic design and analysis of rotor systems.

Self-adaptive macroslip array for friction force prediction in contact interfaces with non-conforming meshes

The steady-state nonlinear forced response (NFR) of finite element (FE) models with friction joints is usually computed in the frequency domain through the combination of node-to-node contact elements and the Harmonic Balance Method (HBM). In the current state of the art, rare are the cases where the friction forces are estimated for contact interfaces with non-conforming mesh grids. This need is nowadays taking place due to the improving capability of commercial FE software to manage any kind of boundary condition (i.e., either coupling or contact), without requiring coincident pairs of nodes at the joint interfaces. Such an advantage becomes a drawback when the analysts are requested to investigate the NFR of the assembly by using build-in codes, where the contact forces prediction usually requires node-to-node contact elements whose parameters (i.e., the contact stiffnesses and friction coefficients) can be easily identified by means of experiments. This paper addresses the mentioned limitation, and proposes a novel self-adaptive macroslip array (SAMA) model for the estimation of the nonlinear friction forces on FE contact interfaces with non-conforming meshes. The SAMA model consists on a set of node-to-node contact elements ordered in parallel, whose contact parameters and normal preloads are identified through a step-by-step self-adaptive weighting algorithm that depends on the topology of the meshes in contact. The goodness of the proposed model is assessed on the calculation of the NFR of a bladed disk with shroud contacts, under the hypotheses of cyclic symmetry and HBM. The nonlinear dynamic behavior of the bladed disk is evaluated in two different cases. First, in the case of lack of node-to-node congruence at the contact interface for the structure being in its undeformed configuration, and second, in the case of a relevant static misalignment of the contact interfaces due to the application of large static loads.

Quantitative misalignment detection method for diesel engine based on the average of shaft vibration and shaft shape characteristics

Misalignment is one of the most commonly observed faults in marine diesel engines. Current misalignment detection methods commonly use vibration spectrum analysis, which cannot quantitatively detect misalignment value, and their accuracy is significantly affected by operating conditions. Hence, a mapping model between the shaft radial vibration average and the misalignment value based on shaft shape characteristics is established considering the characteristics of the variable load and compact structure of the diesel engine. Then a monitoring scheme is designed, and a quantitative misalignment detection method is proposed based on the model. The experimental results indicate that the detection accuracy of the new method is greater than 90% and is not affected by the operating conditions. Meanwhile, the relationship between the static misalignment degree and the fluctuation of axle center average position (ACAP) is revealed using this method and can guide static installation and causes analysis of misalignment.

A Computational Model for the Analysis of the Static Forced Performance of Self-Equalizing Tilting Pad Thrust Bearings

Abstract While failure analyses in the archival literature report thrust collar misalignment as a major cause of collapse in oil lubricated thrust bearings (TB), a self-equalizing tilting pad thrust bearing (TPTB) improves operation reliability by adjusting its pads to account for thrust collar tilt. This paper describes a kinematics model for the equalizing mechanism integrated into an existing thermo-elastohydrodynamic (TEHD) analysis tool to deliver load performance predictions for self-equalizing TPTBs. The analysis considers the actual leveling plates geometric model as obtained from a solids modeling commercial software and accounts for the sliding friction forces acting at the contact points of the leveling plates and the rolling friction at their pivots. Further, a Hertz contact analysis model uses the predicted forces to deliver a peak pressure and deformation over the contact area between the leveling plates. Next, this paper presents predictions for an example self-equalizing TPTB operating with a thrust collar static misalignment φ = 0.01 deg. The bearing 126 mm in outer diameter has six pads, operates at 4 krpm (26 m/s maximum surface speed) and under a specific load/pad ranging from 0.5 to 3.5 MPa. Compared to a nonequalizing TPTB, a self-equalizing TPTB operates with up to 50% larger minimum film thickness and about ½ largest elastic deformation. Friction forces acting at the contact points of the leveling plates show a significant effect on the performance of the pad leveling system as they reduce the film clearance and increase a pad peak pressure. Predictions from the Hertz contact analysis agree with those from a commercial finite element analysis tool and show a significantly large peak pressure at the contact points of the leveling plates (> 0.9 GPa) when the bearing supports a 3 MPa/pad specific load. This paper stresses the importance of conducting a comprehensive multiple-pad analysis to accurately evaluate the performance and reliable operation of self-equalizing TPTBs.

Influence of static and dynamic rotor/stator misalignments in axial flux magnetically geared machines

Here, static and dynamic (rotating) misalignments between the low-speed rotor (LSR) and the stator of axial flux magnetically geared machines are studied with the aid of 3-D finite element analysis (FEA). The influence of rotor/stator axis misalignments on machine performance in terms of cogging torque, air-gap flux density, and back-EMF is investigated with reference to the fully healthy condition. The results show that the LSR and HSR cogging torques are significantly affected by such misalignments due to distorted air-gap flux density. However, the amplitude and the harmonics of the back-EMF are only slightly changed. Furthermore, the influence of the misalignments on the machine torque performance is investigated. It is shown that the machine torque is significantly reduced when the LSR axis is misaligned with the axis of the stator. Thus, it is concluded that the torque performance of axial flux magnetically geared machines significantly deteriorates under static and dynamic axis misalignments. In addition, the two types of misalignments have similar effects on machine performance.

Representing Misalignments of the STAR Geometry Model using AgML

The STAR Heavy Flavor Tracker (HFT) was designed to provide high-precision tracking for the identification of charmed hadron decays in heavy-ion collisions at RHIC. It consists of three independently mounted subsystems, providing four precision measurements along the track trajectory, with the goal of pointing decay daughters back to vertices displaced by less than 100 microns from the primary event vertex. The ultimate efficiency and resolution of the physics analysis will be driven by the quality of the simulation and reconstruction of events in heavy-ion collisions. In particular, it is important that the geometry model properly accounts for the relative misalignments of the HFT subsystems, along with the alignment of the HFT relative to STARs primary tracking detector, the Time Projection Chamber (TPC).The Geometry Modeling Language (AgML) provides a single description of the STAR geometry, generating both our simulation (GEANT 3) and reconstruction geometries (ROOT). AgML implements an ideal detector model, while misalignments are stored separately in database tables. These have historically been applied at the hit level. Simulated detector hits are projected from their ideal position along the track’s trajectory, until they intersect the misaligned detector volume, where the struck detector element is calculated for hit digitization. This scheme has worked well as hit errors have been negligible compared with the size of sensitive volumes. The precision and complexity of the HFT detector require us to apply misalignments to the detector volumes themselves. In this paper we summarize the extension of the AgML language and support libraries to enable the static misalignment of our reconstruction and simulation geometries, discussing the design goals, limitations and path to full misalignment support in ROOT/VMC-based simulation.

Dynamic modeling of an eccentric face seal including coupled rotordynamics, face contact, and inertial maneuver loads

Mechanical face seals are constitutive components of turbomachines, which in turn can be constitutive to other systems (e.g. aircraft). Furthermore, the rotating element of a face seal is inextricably coupled to the turbomachine via a flexible mount, and the stationary seal element is coupled to the rotating seal element via the fluid film existing between the seal faces. Consequentially, understanding interactions between the seal and turbomachine is important for quantifying seal performance and improving its design. With few exceptions, previous works study the face seal dynamics independent from the rotordynamics. In addition, most prior investigations consider only angular and axial seal dynamics and neglect eccentric (i.e. lateral) deflections of the seal element(s). For the first time, this work develops a comprehensive and novel model of a mechanical face seal in the inertial reference frame including coupled rotordynamics and inertial maneuver loads of the overall system. The model is developed for a general seal geometry where both seal elements, stationary and rotating, are flexibly mounted and allowed to undergo angular, axial, and eccentric deflections. In addition, the seal model presented here accounts for transient operation, fluid shear forces, seal face contact, friction, and thermoelastic deformation. Finally, various faults due to manufacturing imperfections, component flaws, and/or installation errors can be accounted for by incorporating static angular misalignment of both seal elements, dynamic angular misalignment of the rotating seal element, eccentric rotating imbalance, and axial offset of the rotating seal element center of mass. Throughout this work, the equations of motion developed are valid for both steady-state and transient operation. This comprehensive model significantly advances the state of the art in mechanical face seal dynamic modeling and represents a pivotal step towards analyzing seal performance regarding a broad diversity of realistic problems.

On-line dispersion estimation and correction scheme for the Compact Linear Collider

The Compact Linear Collider (CLIC) has stringent component alignment tolerances in order to preserve the ultralow emittance of the utilized particle beams. Beam-based alignment techniques have been designed to relax these tolerances to realizable values. In this paper, a scheme is presented that is capable of mitigating besides the effects of static misalignments also dynamic misalignments caused by ground motion. It is based on the well-known dispersion-free steering (DFS) algorithm, with the peculiarity that it can perform its correction during the usual operation (on-line). This is enabled by performing the necessary dispersion measurements by introducing only negligibly small beam energy changes (per mille level). It has been found that this on-line correction becomes sensitive to the imperfections of transverse wakefields and structure tilts. These sensitivities have been studied via analytical models and in simulations and appropriate countermeasures to improve the robustness of the method have been proposed. The correction performance and robustness properties of the improved algorithm have been studied in detail with respect to all relevant static and dynamic imperfections in a realistic scenario. The presented scheme is not only a potentially important operational tool for CLIC, but the findings with respect to robustness properties for different imperfections are of general interest for the application of the dispersion-free steering algorithm.

On the Predicted Effect of Angular Misalignment on the Performance of Oil Lubricated Thrust Collars in Integrally Geared Compressors

Multiple-stage integrally geared compressors (IGCs) offer improved thermal efficiency and easier access for maintenance and overhaul than single-shaft centrifugal compressors. In an IGC, a main bull shaft drives pinion shafts, each having an impeller at its ends. The compression of process gas in the compressor stages induces axial loads along the pinion shafts that are transmitted via thrust collars (TCs) to the main bull gear (BG) shaft and balanced by a single thrust bearing. Manufacturing inaccuracies and a poor assembly process can lead to static angular misalignments of the TC and BG surfaces that affect the operating film thickness as well as the force and reaction moments of the lubricated mechanical element. In a follow-up to San Andrés et al. (2015, “On the Predicted Performance of Oil Lubricated Thrust Collars in Integrally Geared Compressors,” ASME J. Eng. Gas Turbines Power, 137(5), pp. 1–9), this paper presents an investigation of the performance of a single thrust collar configuration operating with increasing static angular misalignment of either the TC or BG. The flow model solves the Reynolds equation of hydrodynamic lubrication coupled to a thermal energy transport equation to determine the film pressure and bulk temperature fields, respectively. The model predicts performance parameters such as power loss and lubricant flow rate, and force and moment stiffness and damping coefficients. Predictions show that misaligning of either the thrust collar or bull gear alters the load-carrying area in the lubricated zone, shifts the pressure field with peak magnitudes doubling or more depending on the degree and direction of TC or BG misalignment. Static angular misalignment does not significantly affect the power loss, temperature rise, etc., but does have an effect on the dynamic coefficients (both axial and angular). Finally, a reduced complex dynamic stiffness matrix for the lubricated TC shows that some cross-coupled stiffness and moment coefficients are nonzero, indicating hydrodynamic coupling between axial and angular motions for the pinion and bull gear shafts. The coupling could affect the placement of the system natural frequencies and associated mode shapes as well as the system stability.

Vibration response analysis caused by rubbing between rotating blade and casing

Two types of blade-tip rubbing due to the static misalignment of the bladed-disk center and casing center and casing deformation are simulated. By applying aerodynamic load in the blade lateral/flexural direction, vibration responses due to blade-casing rubbing are analyzed under the run-up process with constant angular acceleration and the steady-state process at 10000 rev/min. The effects of some parameters, such as the static misalignment e c, casing stiffness k c and casing deformation n p, on the system vibration responses are also illustrated by spectrum cascades, time-domain waveforms of displacement, normal rubbing forces, amplitude spectra and the impulse P in a single blade-casing rubbing period. The results show that blade-tip rubbing will cause amplitude amplification and harmonic resonance phenomena when the multiple frequencies (nf r) of rotational frequency (f r) coincide with the first three flexural dynamic frequencies of the blade (f n1, f n2 and f n3). For example, the displacement amplitudes at 3f r, 14f r and 38f r are large and the vibration is dominant near f n1. In addition, the casing deformation mainly excites the dominant Blade passing frequency (BPF), which is related to the casing deformation coefficient n p. By comparing these impulse values, for the selected parameters in this paper, the casing stiffness has a greater effect on impulse than the static misalignment and casing deformation coefficient. The impulse shows a linear increase trend with the increasing static misalignment, and it decreases under the large n p because the contact time decreases with the increase of n p.

How Geometric Misalignments can affect the Accuracy of Measurements by a Novel Configuration of Self-Tracking LDV

Aim of the paper is to evaluate the reliability of a novel configuration of a Laser Doppler Vibrometer (LDV) for the measurement of vibrations affecting rotating components of machines. In the paper an analysis of errors due to the possible static misalignments of the mirrors utilized in an experimental apparatus has been carried out. This instrument was set up for the estimation of the out of plane vibrations of moving (rotating) objects, in order to give a better characterization of the self-tracking technique employed with the use of a 1D single point LDV and its measurements. The accuracies of the measures are mostly linked to the interaction between environment and instrumentation.

A MODIFIED MODEL OF SQUIRREL CAGE INDUCTION MACHINE UNDER GENERAL ROTOR MISALIGNMENT FAULT

A great deal of researches have so far been conducted on the analysis of eccentricity in induction machines. However, they mostly consider radial non-uniformity and neglect non-uniformity in the axial direction, but in practice, the axial non-uniformity due to rotor misalignment faults is quite common. This paper presents a modifled model of a three-phase squirrel cage induction machine under difierent rotor misalignment conditions. For this purpose, general expressions for air gap and mean radius of induction machine, considering axial non-uniformity, have been developed. The proposed model is able to calculate the time varying inductances versus rotor angle for three-phase squirrel cage induction machines under general rotor misalignment, including static, dynamic and mixed rotor misalignment in the frame of a single program. Simulation results were verifled by the experimental ones. The model presented by Tolyiat et al. (1) has been shown to be accurate for the time domain simulation of AC motors based on the basic geometry and winding layout of stator windings and rotor loops. Contrary to the classical d-q model, this theory can take into account all of the winding magnetomotive force space harmonics. An essential part of this theory is the calculation of machine inductances. These inductances are calculated using winding function and other equations within the theory. By this approach, all space harmonics are taken into account without any restriction concerning symmetry of stator or rotor windings. Hence, this model is widely used for the analysis of

Spin tracking studies for polarimetry at the ILC

At the International Linear Collider (ILC), the beam polarization is planned to be measured with a yet unequalled precision of 0.25 % by two Compton polarimeters located 1.8 km upstream and 150 m downstream of the e+e− interaction point (IP). The decisive quantity for the experiments, i.e. the luminosity-weighted average polarization, has to be determined from these measurements. A detailed understanding of the spin tracking and the depolarizing effects is mandatory in order to estimate how precise the polarization at the IP is known from these measurements performed 2 km apart. For that purpose, a beamline simulation including spin tracking has been set up. First results comprise the results of static misalignments, dynamic misalignments and beam-beam interaction are in preparation.

Nonlinear dynamics of a statically misaligned flexible rotor in active magnetic bearings

The response of a statically misaligned flexible rotor mounted in active magnetic bearings is numerically investigated in this work. The mathematical model of the rotor-bearing system incorporates nonlinearity due to the geometric coupling of the magnetic actuators as well as that arising from the magnetic actuator forces that are nonlinear function of the coil current and the air gap between the rotor and the stator. The influence of the rotor’s static misalignment, represented by the gravity parameter, W, on its response was found to be dependent on the magnitude of the geometric coupling parameter, α. Numerical results showed that for α = 0, the response of the rotor was always synchronous regardless of the values of W. For moderate values of α, nonsynchronous vibration was seen in the response of the rotor for the case of W ≠ 0. For large values of α, nonsynchronous vibration was observed in the response of the rotor irrespective of the values of W. For the values of design and operating parameters of the rotor-bearing system investigated in this work, the response of the rotor displayed a rich variety of nonlinear dynamical phenomena including sub-synchronous vibrations of period-2, -3, -4, -6, -8, -12, -14 and -16, quasi-periodicity and chaos. Numerical results further revealed the existence of multiple attractors within certain ranges of the speed parameter, Ω. Co-existence of attractors has serious implications on the safe operation of magnetically supported rotating machinery as synchronous response of the rotor may become nonsynchronous or even chaotic when excited by external forces that cause the rotor’s position to move from one basin of attraction to another.

Augmented Reality for Art, Design and Cultural Heritage—System Design and Evaluation

This paper describes the design of an optical see-through head-mounted display (HMD) system for Augmented Reality (AR). Our goals were to make virtual objects perfectly indistinguishable from real objects, wherever the user roams, and to find out to which extent imperfections are hindering applications in art and design. For AR, fast and accurate measuring of head motions is crucial. We made a head-pose tracker for the HMD that uses error-state Kalman filters to fuse data from an inertia tracker with data from a camera that tracks visual markers. This makes on-line head-pose based rendering of dynamic virtual content possible.We measured our system, and found that with an A4-sized marker viewed from > 20° at 5 m distance with an SXGA camera (FOV 108°), the RMS error in the tracker angle was < 0.5° when moving the head slowly. Our Kalman filters suppressed the pose error due to camera delay, which is proportional to the angular and linear velocities, and the dynamic misalignment was comparable to the static misalignment. Applications of artists and designers lead to observations on the profitable use of our AR system. Their exhibitions at world-class museums showed that AR is a powerful tool for disclosing cultural heritage.

Axial Wedge Effect in Tilted Hydrodynamic Journal Bearings

Hydrodynamic journal bearings are susceptible to static angular misalignment, resulting from improper assemblage, elastic and thermal distortion of the shaft and bearing housing, and also manufacturing errors. Several previous works on the theme, both theoretical and experimental, focused on the determination of the static properties of angular misaligned bearings. Although some reports show agreement between theoretical and experimental results, the increasingly severe operating conditions of hydrodynamic bearings (heavy loads and high rotational speeds) require more reliable theoretical formulations for the evaluation of the journal performance during the design process. The consideration of the angular misalignment in the derivation of the Reynolds equation is presented here in detail, showing that properly conducted geometric and magnitude-order analyses lead to the inclusion of an axial wedge effect term that influences the velocity and pressure fields in the lubricant film. Numerical results evidence that this axial wedge effect more significantly affects the hydrodynamic forces and static operational properties of tilted short journal bearings.

Meshing Force of Misaligned Spline Coupling and the Influence on Rotor System

Meshing force of misaligned spline coupling is derived, dynamic equation of rotor‐spline coupling system is established based on finite element analysis, the influence of meshing force on rotor‐spline coupling system is simulated by numerical integral method. According to the theoretical analysis, meshing force of spline coupling is related to coupling parameters, misalignment, transmitting torque, static misalignment, dynamic vibration displacement, and so on. The meshing force increases nonlinearly with increasing the spline thickness and static misalignment or decreasing alignment meshing distance (AMD). Stiffness of coupling relates to dynamic vibration displacement, and static misalignment is not a constant. Dynamic behaviors of rotor‐spline coupling system reveal the following: 1X‐rotating speed is the main response frequency of system when there is no misalignment; while 2X‐rotating speed appears when misalignment is present. Moreover, when misalignment increases, vibration of the system gets intricate; shaft orbit departs from origin, and magnitudes of all frequencies increase. Research results can provide important criterions on both optimization design of spline coupling and trouble shooting of rotor systems.

The role of research in the development of athletic footwear

The three main needs of athletes are performance, injury protection and comfort. Footwear enhances performance through increases in traction and biomechanical efficiency. Footwear protects the foot at the interface with the ground and the entire body against the forces resulting from repeated feet-ground impacts. Footwear can also reduce injuries by correcting for the locomotor system static structural misalignments. Footwear uppers, insoles or sockliners being considered upper elements, are responsible to maintain the feet over the shoe soles. Uppers fit is most important to athletes' comfort. Athletes' needs as well as their relative importance are defined by the 'critical' maneuvers performed during sporting activities. 'Critical' maneuvers are maneuvers that must be performed to succeed in a sport and/or maneuvers that have been linked to the highest incidence of injury observed in that sport. Focus group research and surveys help to identify critical maneuvers. 3D motion capture systems, force plateforms and pressure insoles are used to study the critical maneuvers associated to different sporting activities. The results of these studies lead to design criteria that are shared with designers and developers. Prototypes are created and evaluated using the same batteries of biomechanical tests to assess how well they meet the design criteria. Therefore, footwear designed for different sporting activities can readily be differentiated. Gender, skill level, and environmental conditions add further requirements upon footwear design thus allowing for differentiation even within a given sporting activity. Footwear intended for use in multiple sporting activities represent non-trivial design challenges. Typically, such designs lead to shoes that feature some level of compromise to address the competing requirements of each different sporting activity. This holds true even within a sport when injury protection and performance needs conflict, or when different injury protection needs require somewhat contradictory solutions. Considering running footwear as an example, it is generally believed that shoes currently designed to offer maximal cushioning lack rearfoot stability and vice-versa, shoes designed to resist injury inducing excessive rearfoot motion lack cushioning. Yet, recent research and novel design approaches have shown that the magnitude of the compromises in footwear design can be significantly reduced if not eliminated.

A Static Geometrical Illusion Contributes Largely to the Footsteps Illusion

When a black and a white rectangle drifts across a stationary striped background with constant velocity, the rectangles appear to alternately speed up and slow down. Anstis (2001, Perception 30 785-794; 2004, Vision Research 44 2171-2178) suggested that this 'footsteps' illusion is due to confusion between contrast and velocity signaling in the motion detectors of the human visual system. To test this explanation, three experiments were carried out. In experiment 1, the magnitudes of the footsteps illusion in dynamic and static conditions was compared. If motion detectors play an important role in causing the illusion, it should be reduced in the static condition. Remarkably, however, we found that the illusory misalignment between the black and the white rectangle was even more prominent in the static condition than in the dynamic condition. In experiment 2, we measured the temporal-frequency properties of the footsteps illusion. The results showed that the footsteps illusion was tuned to low temporal frequencies. This suggests that the static illusory misalignment can contribute sufficiently to the dynamic illusory misalignment. In experiment 3, the magnitude of the illusion was measured with the rectangles drifting on a temporally modulated background instead of a spatially modulated background. If contrast affects the apparent velocity of the rectangles, temporal modulation of a uniform background should also cause the footsteps illusion. However, the results showed that the magnitude of the illusion was much reduced in this condition. Taken together, the results indicate that the footsteps illusion can be regarded as a static geometrical illusion induced by the striped background and that motion detectors play a minor role at best.