Showing papers on "Critical speed published in 2015"

Critical Speed of Railway Tracks. Detailed and Simplified Approaches

Abstract: The dynamic amplification effects of the response due to a moving load on the surface of an elastic solid has been object of research for more than a century. However, if in the beginning of the last century the problem had only theoretical interest, this is no longer true. Indeed, the recent advancements in the rolling stock, which can now reach speeds higher than 500 km/h, brought this kind of problems to the engineering practice, mainly to high speed railway engineering. The present paper approaches this problem focusing on railway engineering. The departing point is the theoretical formulation of the critical speed problem of a moving load on the surface of an elastic solid. From the usage of 2.5D detailed models it was possible to understand the influence of the embankment and track properties on the critical speed. However, to avoid complex numerical models, which are very demanding from the computational point of view, a simplified approach is proposed for the computation of the critical speed of track–embankment–ground systems. The results of the simplified approach are compared to those achieved by detailed methods, also presented in this paper, and the proposed expedite methodology is found to be very accurate.

Optimization of Damping Compensation for a Flexible Rotor System With Active Magnetic Bearing Considering Gyroscopic Effect

Abstract: Active magnetic bearing (AMB) levitated rotating machineries are always required to operate above the rotor first bending critical speed to achieve a high power density. It is important to ensure safe rotor run-down through critical speeds. This paper presents an optimization of damping compensation for a flexible rotor to make maximal use of the limited electromagnetic force to retain flexible deformation. The design, rotor modal properties, and bending model test for an AMB test rig which typifies a 10-kW centrifugal compressor are described in detail. The optimal compensation phase angle with and without considering the gyroscopic effect is first derived from a theoretical model. The flexible deformations with the different control radius and phase are also analyzed. Then, the phase angle from flexible deformation to electromagnetic force in the existing control system is experimentally identified. A phase-shift filter is designed to compensate the corresponding phase difference around the bending frequency. The damping compensation experiments validate the proposed optimization approach.

Dynamic characteristics of a disk–drum–shaft rotor system with rub-impact

Abstract: The dynamic model of a disk–drum–shaft rotor system with rub-impact is established and its dynamic characteristics are analyzed. According to an elastic impact model and Coulomb’s friction law, two rub-impact force models are firstly developed which corresponding to the disk–stator contact and the drum–stator contact, respectively. Taking into account, the coupling of the whole rotor whirl and the local drum vibration, the dynamic model of a disk–drum–shaft rotor system with the disk–stator and the drum–stator rubbing is established by employing Sanders’ shell theory and Lagrange equation. The numeric results reveal that the continuous increase in rotating speed, disk mass eccentricity, and stator radial stiffness induces alternation of periodic-one motion of the disk without disk–stator contact, periodic-one motion with disk–stator full annular rubbing and the disk–stator partial rubbing region in which the quasi-periodic and periodic motions of the disk appear alternately. In addition, the motion of the drum is synchronous with that of the disk and has three situations, i.e., un-deformation, deformation with one circumferential wave, and periodic and quasi-periodic vibration with drum–stator rubbing. Due to the effects of the drum, the rotating speed corresponding to the start of the disk–stator full annular rubbing in the disk–drum–shaft rotor system is smaller than that in the disk–shaft rotor system, and there is only one disk–stator partial rubbing region which is near the critical speed of rotor system. What is more, compared with parameters of the disk, those of the drum can only affect the motion of the rotor system slightly.

Design of a Halbach Array Permanent Magnet Damping System for High Speed Compressor With Large Thrust Load

Abstract: Many magnetically suspended compressors operate above the first bending critical speed, which gives rise to high vibration problems and introduces complications in designing controllers for radial magnetic bearings; besides, a significant axial load always exists in high-speed compressors, which requires a high load capacity in the thrust bearings and introduces complications in designing axial magnetic bearings. In this paper, a passive damper with the Halbach magnet array is proposed. The Halbach damper can provide radial damping force without control system, and can also provide a large axial force to reduce the burden of axial bearing. Firstly, the effect of the location of dampers on response amplitude is studied and the optimum convenient location is obtained. Then, an analytical model of the Halbach damper is established and the effects of some important structure parameters on the system performance are discussed. Finally, a design example for a high-speed compressor with flexible rotor and a large thrust load is given. The analytical and design results, which are verified by the finite element result, show that the Halbach damper can provide the required axial force, and it is effective in controlling the first bending vibration of the flexible rotor.

Experimental Investigation of Surge and Stall in a High-Speed Centrifugal Compressor

Abstract: Flow instability, known as surge and stall, limits the stable operating range of compressors. In this paper, a panoramic map of instability evolution across all typical operations is experimentally demonstrated for the first time in a high-speed centrifugal compressor with a maximum speed of 185,000 r/min and a corresponding rotation velocity at the impeller outlet of 593 m/s. Twelve high-response Kulite pressure probes are mounted on the internal surface of the compressor’s casing. The experimental results show that the instability phenomena are quite complex and diverse at different operations. At low speed (<70% of the maximum speed), high-frequency and low-frequency stall successively occurs at the impeller, and is followed by surge as mass flow rate reduced. The transient process of surge is a transient stall/unstall self-loop, with the “self-similarity” to the sustainable stall/unstall conditions. At 70% of the maximum speed, the system exhibits two types of surge, a minor-amplitude periodic surge...

Application of Coupled Train-Track Modelling of Critical Speeds for High-Speed Trains using Three-Dimensional Non-Linear Finite Elements

Abstract: It is known that as trains traverse soft soils a critical point can be reached whereby the train speed will exceed the Rayleigh ground wave velocity leading to critical velocity issues. If track structures are present, such as stiffened embankments, increases in the train's critical speed can occur. This higher ground wave velocity is termed the critical track velocity. Approaching a critical speed will lead to an increase in the transient track deflection when compared to the quasi-static case. As resonant conditions develop, very high transient track displacements will occur, including the potential for track uplift. In the past, these sites were few in number as the train speeds were relatively low, however as train speeds continue to increase critical speed issues will become more of an issue. This paper first presents simple graphs and equations of the permissible train speed versus Young's modulus and undrained shear strength for typical homogenous clay subgrades. However, for nonhomogenous soils (layered soils), it is necessary to understand the development of the dynamic interaction and hence determine the most cost effective mitigation strategy. For layered soils, this can become difficult to determine without more sophisticated analysis. The development of critical velocities is studied in this paper using a threedimensional time domain finite element program in which the train and track are coupled and the soil is simulated using non-linear soil constitutive models where the stiffness is a function of the isotropic and deviatoric stress, and the damping ratio is a function of the deviatoric strain. This paper benchmarks the analyses using measured data from the Ledsgard site and shows that this approach is able to model the development of track dynamic conditions with train speed through plots of the transient sleeper deflection, and displacement contour plots of the overall ground surface behaviour. The non-linear variation in the different layers' stiffness is highlighted through plots of the time histories of Young's modulus with train speed and depth.

World-line geometry probed by fast spinning particle

Abstract: Interaction of spin with electromagnetic field yields an effective metric along the world-line of spinning particle with anomalous magnetic moment. If we insist to preserve the usual special relativity definitions of time and distance, critical speed which the particle cannot overcome during its evolution in electromagnetic field differs from the speed of light. Instead, we can follow the general relativity prescription to define time and distance. With these definitions, critical speed coincides with the speed of light. But intervals of time and distance probed by the particle in the presence of electromagnetic field slightly differ from those in empty space. Effective metric arises also when spin interacts with gravitational field.

Dynamic characteristics of magnetorheological fluid lubricated journal bearing and its application to rotor vibration control

Abstract: Application of smart lubricants like magnetorheological (MR) fluids is always considered to be a promising field of realizing smart bearings with semi-active controllable capability. For bearings lubricated with MR fluid, the dynamic characteristics i.e. the stiffness and damping coefficients are important, while few studies have focused on this field. The present work adopts the Herschel-Bulkley model to describe the rheological behavior of MR fluid. The shearing-thinning effect incorporated in this model leads to different result compared to that from the Bingham model. Stiffness and damping coefficients of bearings lubricated with Newtonian fluid, Bingham fluid are calculated. Calculations show that shear-thinning effect has great influences on both static and dynamic characteristics of the journal bearing. Simulations of rotordynamics of a turbo-expander rotor with different bearing properties are performed to investigate the possibility of MR fluid as lubricants to control the behavior of rotor. Results show that MR fluids are applicable to change performances of the rotor system. Vibration amplitude suppression and critical speed alteration can be achieved by MR fluids.

Study on the non-contact FBG vibration sensor and its application

Abstract: A non-contact vibration sensor based on the fiber Bragg grating (FBG) sensor has been presented, and it is used to monitor the vibration of rotating shaft. In the paper, we describe the principle of the sensor and make some experimental analyses. The analysis results show that the sensitivity and linearity of the sensor are −1.5 pm/μm and 4.11% within a measuring range of 2 mm–2.6 mm, respectively. When it is used to monitor the vibration of the rotating shaft, the analysis signals of vibration of the rotating shaft and the critical speed of rotation obtained are the same as that obtained from the eddy current sensor. It verifies that the sensor can be used for the non-contact measurement of vibration of the rotating shaft system and for fault monitoring and diagnosis of rotating machinery.

Transverse Vibration of Axially Moving Functionally Graded Materials Based on Timoshenko Beam Theory

Abstract: The transverse free vibration of an axially moving beam made of functionally graded materials (FGM) is investigated using a Timoshenko beam theory. Natural frequencies, vibration modes, and critical speeds of such axially moving systems are determined and discussed in detail. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. Hamilton’s principle is employed to derive the governing equation and a complex mode approach is utilized to obtain the transverse dynamical behaviors including the vibration modes and natural frequencies. Effects of the axially moving speed and the power-law exponent on the dynamic responses are examined. Some numerical examples are presented to reveal the differences of natural frequencies for Timoshenko beam model and Euler beam model. Moreover, the critical speed is determined numerically to indicate its variation with respect to the power-law exponent, axial initial stress, and length to thickness ratio.

Dynamic design methodology of high speed micro-spindles for micro/meso-scale machine tools

Abstract: With the increasing demands for high manufacturing accuracy and processing efficiency, micro/meso-scale machine tool systems are proposed. The availability of micro-spindles with ultra-high rotating angular speeds and ultra-small run-out are a key technology for micro/meso-scale cutting processes. Well-established design methods exist for traditional spindle systems, but there is a strong demand for a methodology to predict the dynamic characteristics, particularly at the micro-scale, which will dictate manufacturing accuracy. In this respect, the minimization of run-out is of paramount importance. In response to this, two problem areas are considered in this paper: (a) hybrid air bearing systems—a methodology related to the calculation of the load capacity and stiffness of hybrid air journal and thrust bearings, and (b) spindle rotor system—a methodology for the rotor dynamic analysis including critical speed, mode shape, and unbalanced response predictions. Mathematical models and simulation procedures are given, followed by explanations of their use. Finally, the proposed dynamic design method is demonstrated on a realized micro-spindle system model. Two designs namely the original design and a modified design are analyzed and comparisons are carried out. The numerical simulations and the experimental evidence available for the original design have substantiated the validity of the proposed dynamic design method. The proposed methodology lays the foundation for controlling run-out of the high speed micro-spindles in micro/meso-scale machine tools.

Curved road safe speed calculating method and caution system based on vehicle infrastructure cooperation

Abstract: The invention discloses a curved road safe speed calculating method and caution system based on vehicle infrastructure cooperation. The method includes the following steps of calculating the sideslip critical speed of a vehicle; calculating the rollover critical speed of the vehicle; comparing the small values of the two critical speeds and determining the safe speed when the vehicle runs into the curve; and calculating the safe vehicle speed when the vehicle runs into the curve after considering the behavior characteristics of a driver. The invention provides a method for accurately calculating the safe vehicle speed when the vehicle runs into the curve on the basis of fully considering the influences of people, vehicles and roads. Through the comprehensive considering of the vehicle motion characteristics and driver behavior characteristics, the safe vehicle speed of the vehicle at the curved road is analyzed by means of a vehicle dynamics theory. The method has the advantages of simple calculation, fast operation speed, and high reliability, and provides the theoretical method support for the design and development of a curved road safe driving caution system.

Effective approach for calculating critical speeds of high-speed permanent magnet motor rotor-shaft assemblies

Abstract: An effective approach is presented for large errors in calculating critical speed of rotor-shaft assembly with the commercial finite element software, is intended to develop the discrete model of the rotor-shaft assembly by using lumped mass method, which is supported by active magnetic bearings. The first two bending critical speeds are analysed by optimising the flexural rigidity coefficient based on transfer matrix method. Compared with experimental modal testing and finite element analysis, the results of the transfer matrix method are in good agreement with modal measurement, the percentage errors of the first two bending natural frequencies are 0.21 and 2.1%, respectively. Owing to the higher accuracy and numerical stability, the method used in this study is an effective way to calculate the critical speed of the rotor-shaft assembly.

Numerical Analysis of Bladed Disk–Casing Contact With Friction and Wear

Abstract: In order to increase the aerodynamic performances of their engines, aircraft engine manufacturers try to minimize the clearance between rotating and stationary parts in axial and centrifugal compressors. Consequently, the probability of contact increases, leading to undesirable phenomena caused by forced excitation of the natural modes, or by modal interaction. Due to the complexity of these phenomena, many numerical studies have been conducted to gain a better understanding of the physics associated with them, looking primarily at their respective influence on potential unstable behaviors. However, the influence of other physical phenomena, such as friction and wear, remains poorly understood. The aim of this work is to show some effects associated with friction and wear on the dynamic behavior resulting from blade-to-casing interaction.The numerical study reported here is based on a simplified finite element model of a rotating bladed disk and a flexible casing. The contact algorithm uses an explicit time marching scheme with the Lagrange multipliers method. Friction and wear are formulated using respectively Coulomb’s and Archard’s Laws. The rotational speed is set to critical speed giving rise to modal interaction between a backward mode of the casing and a counter-rotating mode of the bladed disk with one nodal diameter. Contact is initiated by a dynamic excitation of the stator.In the presence of friction, the system becomes unstable when a sideband of the excitation frequency coincides with a one nodal diameter mode of the bladed disk. The introduction of wear leads to a vibration reduction, while the abradable material is removed by the wear process. The number of wear lobes produced on the casing is related to the ratio between the vibration frequency of the blades and the rotating speed. The ratio obtained by means of the FE model corroborates experimental observations.Copyright © 2015 by ASME

Robust rotor dynamics for high-speed air bearing spindles

Abstract: For ultra-precision machining machine tool components need to operate outside critical frequencies of the machining system to avoid insufficient surface finish caused by vibrations. This particularly applies to tooling spindles as those are generally the component of a machine tool with low stiffness and damping values. Surface finish and shape of a machined part rely directly on the overall accuracy in motion of the tooling spindle over the entire machining parameter and speed range. Thus spindle designs for an operation outside critical frequencies combined with high stiffness and damping values are crucial for ultra-precision machining. For sufficient stiffness properties bearing gaps of gas bearings have to have a size of only a few microns and show a distinct sensitivity on temperature and for journal bearings also on speed. This again means that bearing properties change with temperature and speed. Considering a spindle system comprising a rigid shaft rotating in a radial/axial bearing system with changing stiffness and damping properties leads to a resonance speed map with changing rigid mode resonance speeds. This paper treats the influence of shaft speed and temperature on bearing gaps from which rigid mode resonance speeds for a shaft spinning in a bearing system are derived. The quoted influence of centrifugal load and temperature on bearing stiffness, damping and load capacity can be applied to any kind of gas bearing. Therefore the calculation of bearing stiffness, damping or load capacity is not treated in detail. The reader will be shown that there are simple design rules for air bearing systems and shafts of high-speed tooling spindles to avoid critical speeds through the entire speed range. Finally, methods of how to prove the initial design goals and how to verify dynamics of high-speed spindles in production will be presented to the reader. It will also be shown that there are production high-speed spindles available which do not include any critical speed within their speed range and thus show robust rotor dynamics with extremely low errors in motion. Procedures in design, validation and application treated in this paper shall give the reader not only design guidelines for spindles to avoid critical spindle speeds within its speed range, but also recommendations for machine tool builders and end-users for a machine operation taking machine and rotor dynamics into account. As the knowledge for this paper is predominantly based on the experience and work of the author himself only a few references are used. However presented testing results entirely confirm the approach presented in this paper.

A critical review on the self-excitation process and steady state analysis of an SEIG driven by wind turbine

Abstract: This paper presents a critical review on the self-excitation process and steady state analysis of a self-excited induction generator driven by the wind turbine. The physics of self-excitation is crucial for the interpretation of the voltage build-up process of self-excited induction generators (SEIGs). During the initial phase of build-up the machine behaves as if it be a synchronous machine with weak permanent magnet in the form of remnant magnetization. In this paper the MMF approach as well as the synchronous resonance approach has been proposed to know the fact that how the machine relinquishes the initial synchronous mode and enters into the final asynchronous mode. The process of self-excitation is initiated by the resonating interaction between the terminal capacitor and machine׳s magnetizing reactance. The steady state analysis has been reviewed and proposed based on input/output impedance method to find the steady state reactive VAR need of the SEIG. The minimum and maximum critical capacitance has been evaluated theoretically. Finally the value of critical speed and critical load impedance has been evaluated.

Multi-objective Optimization of Hybrid Carbon/Glass Fiber Reinforced Epoxy Composite Automotive Drive Shaft

Abstract: In design and fabricate drive shafts with high value of fundamental natural frequency that represented high value of critical speed; using composite materials instead of typical metallic materials could provide longer length shafts with lighter weight. In this paper, multi-objective optimization (MOP) of a composite drive shaft is performed considering three conflicting objectives: fundamental natural frequency, critical buckling torque and weight of the shaft. Fiber orientation angle, ply thickness and stacking sequence are also considered as the design variables in this MOP. To solve this MOP, Modified Non-Dominated Sorting Genetic Algorithm (modified NSGA II) is employed. To calculate fundamental natural frequency and critical buckling torque, finite element model of a truck composite drive shaft has been carried out using commercial software ABAQUS/Standard. Finally optimum design points are obtained and from all non-dominated optimum design points, some trade-off points are picked using multi-criteria decision analysis methods and the points are discussed.

The research on mechanical properties of direct drive high-speed permanent-magnet machine for compression

Abstract: The high speed permanent-magnet (HSPM) machine is appropriate for high speed operation due to its simple structure and high power density. In order to avoid stress damage to rotor caused by the centrifugal force and thermal stress, the strength analysis is very important. The rotor should have enough stability to avoid spaning the critical speed of bending mode. In addition, the structural vibration associated characteristics between the parts and the whole machine needs to be studied. This paper introduces a kind of hybrid rotor with carbon/glass fibre sleeve and compressor impeller. The three ply composite rotor is deduced by the 3D finite element method (FEM) model. Design guidelines of the high speed interference fit rotor that offers theory base for optimal design was generalized. Finite element (FE) analysis is used to study structural vibration associated characteristics for a HSPM machine with 315 kW, 18000 rpm.

Forward and Backward Whirling of a Rotor with Gyroscopic Effect

Abstract: The determination of whirling frequencies of high speed turbines is always challenging in rotor dynamics. The natural frequencies of a Jeffcott rotor are split in the presence of gyroscopic effect. It is quite well known that the lower branch corresponds to the backward whirl and the upper branch corresponds to forward whirl. The forward whirl mode of the rotor has been observed experimentally, however, the backward whirl has not been observed. In this study it is shown that the backward whirl can be observed when the rotor is coasting down to rest from above the critical speed corresponding to the backward whirl. In order to illustrate the forward and the backward critical speeds of a simple Jeffcott rotor, the natural frequencies are obtained analytically for the second natural frequency of the system because of the large gyroscopic effect present in that mode. An experimental set up was used to verify the presence of backward whirl while the rotor is coasting down to rest. The rotor is also simulated using finite element method by ANSYS, and Campbell diagram is plotted. The analytical, experimental and ANSYS simulations confirm the existence of the backward whirl when the rotor is coasting down.

Active Vibration Control of the Flexible Rotor in High Energy Density Magnetically Suspended Motor With Mode Separation Method

Abstract: Since the mass of the rotor in high energy density magnetically suspended motor (HEDMSM) is always large and there are only three balancing planes on the flexible rotor restricted by the structure of the motor, which means that the second bending mode cannot be balanced using N + 1 planes method which is always applied to balance the flexible rotor. Then, the rotor displacements maybe large and this situation will make the system consume large amplifier currents when the rotor passes the first bending critical speed. Therefore, the mode separation method is proposed to separate the first and the second bending modes in rotor displacement and reconstruct the displacement signal nearby the first bending mode. Then, the original rotor displacement signal used by the digital controller is substituted by the reconstructed displacement signal and the amplifier current is reduced a lot when the rotor passes the first bending critical speed. Finally, the experiment of mode separation is carried out in 100 kW magnetically suspended motor and the experiment results show the effectiveness and superiority of the mode separation method in reducing the amplifier current when the rotor passes the first bending critical speed.