Showing papers on "Critical speed published in 2018"

Nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact

Abstract: In this paper, the nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact are investigated. A novel framework is proposed, in which the sophisticated geometrical structure is considered by finite solid element method and efficient model order reduction is applied to the model. The validity and efficiency of the reduced-order model are verified through critical speed and eigen problems. Its stable and unstable solutions are calculated by means of the assembly technique and the multiple harmonic balance method combined with the alternating frequency/time domain technique (MHB–AFT). The accurate frequency amplitudes are obtained accordingly for each harmonic component. The stabilities of the solutions are checked by the Floquet theory. Through the numerical computations, some complex nonlinear phenomena, such as combined frequency vibration, hysteresis, and resonant peak shifting, are discovered when the rub-impact occurs. The results also show that the control parameters of mass eccentricity, rub-impact stiffness, and rotational speed ratio make significant but different influences on the dynamical characteristics of the system. Therefore, a key innovation of this paper is the marriage of a hybrid modeling method—accurate modeling technique combined with model order reduction and solution method—highly efficient semi-analytic method of MHB–AFT. The proposed framework is benefit for parametric study and provides a better understanding of the nonlinear dynamical behaviors of the real complicated dual-rotor aero-engine with rub-impact.

The stiffening of soft soils on railway lines

Abstract: Railway tracks experience elevated rail deflections when the supporting soil is soft and/or the train speed is greater than approximately 50% of the wave propagation velocity in the track-soil system (i.e. the critical velocity). Such vibrations are undesirable, so soil replacement or soil improvement of the natural soil (or alternatively mini-piles or lime-cement treatment) is often used to increase track-ground stiffness prior to line construction. Although areas of existing soft subgrade might be easily identified on a potential new rail route, it is challenging to determine the type and depth of ground remediation required. Therefore, major cost savings can be made by optimising ground replacement/improvement strategies. This paper presents a numerical railway model, designed for the dynamic analysis of track-ground vibrations induced by high speed rail lines. The model simulates the ground using a thin-layer finite element formulation capable of calculating 3D stresses and strains within the soil during train vehicle passage. The railroad track is modelled using a multi-layered formulation which permits wave propagation in the longitudinal direction, and is coupled with the soil model in the frequency-wavenumber domain. The model is validated using a combination of experimental railway field data, published numerical data and a commercial finite element package. It is shown to predict track and ground behaviour accurately for a range of train speeds. The railway simulation model is computationally efficient and able to quickly assess dynamic, multi-layered soil response in the presence of ballast and slab track structures. Therefore it is well-suited to analysing the effect of different soil replacement strategies on dynamic track behaviour, which is particularly important when close to critical speed. To show this, three soil-embankment examples are used to compare the effect of different combinations of stiffness improvement (stiffness magnitude and remediation depths up to 5 m) on track behaviour. It is found that improvement strategies must be carefully chosen depending upon the track type and existing subgrade layering configuration. Under certain circumstances, soil improvement can have a negligible effect, or possibly even result in elevated track vibration, which may increase long-term settlement. However, large benefits are possible, and if detailed analysis is performed, it is possible to minimise soil improvement depth with respect to construction cost.

Carbon/epoxy filament wound composite drive shafts under torsion and compression

Abstract: Composite cylinders to be used as half shafts must satisfy several requirements, such as critical speed, critical buckling torque, and load carrying ability. This study focused on the investigation...

Design and Characteristic Analysis of a High-Speed Permanent Magnet Synchronous Motor Considering the Mechanical Structure for High-Speed and High-Head Centrifugal Pumps

Abstract: This paper presents design guidelines for a high-speed permanent magnet synchronous motor (PMSM) for a 110 hp and 12 500 r/min centrifugal pump considering the mechanical and electromagnetic characteristics. We selected the size of the rotor based on the torque per unit rotor volume method. The rotor stress analysis was performed using the analytical method and the finite-element method. Based on these results, appropriate sleeve thickness and material were selected considering mechanical stability and electrical performance. The PMSM design was carried out by using the mechanically stable rotating body, and the model with excellent electromagnetic performance was selected based on the iron loss analysis and the eddy current loss analysis using the finite-element method. In addition, the stability of high-speed operation was confirmed by the critical speed analysis of the finally designed PMSM model. The high-speed PMSM verifies the performance through the manufacturing and test it was confirmed that there is no problem when applied to the actual centrifugal pump systems.

Hunting stability analysis of high-speed train bogie under the frame lateral vibration active control

Abstract: In this paper, we study a multi-objective optimal design of three different frame vibration control configurations and compare their performances in improving the lateral stability of a high-speed train bogie. The existence of the time-delay in the control system and its impact on the bogie hunting stability are also investigated. The continuous time approximation method is used to approximate the time-delay system dynamics and then the root locus curves of the system before and after applying control are depicted. The analysis results show that the three control cases could improve the bogie hunting stability effectively. But the root locus of low- frequency hunting mode of bogie which determinates the system critical speed is different, thus affecting the system stability with the increasing of speed. Based on the stability analysis at different bogie dynamics parameters, the robustness of the control case (1) is the strongest. However, the case (2) is more suitable for the dynamic performance requireme...

Influence of probe dynamic characteristics on the scanning speed for white light interference based AFM

Abstract: The dynamic characteristics of an atomic force probe are important for rapid and accurate measurement in white light interference (WLI) based atomic force microscope (AFM). The tip of the probe will fly from the surface when its dynamic characteristics are poor, which will cause measurement error. Generally such tip flight can be avoided by reducing the scanning speed, which will decrease the error at the cost of measurement efficiency. In this paper, a dynamical model of atomic force probe is presented to analyze the causes of tip flight in the measurement process. A numerical simulation is performed on a typical sample surface to investigate the influence of profile, preloading and probe parameters on scanning speed. Experimental testing is conducted on a self-developed WLI based AFM, and the experimental results agree well with that of the theory. The maximum scanning speeds of the probe for a sample are tested under certain conditions. It is shown that for a certain probe, the tip flight occurs at the upwards points of the measured sample when the scanning speed exceeds the critical speed, which is constrained by the preloading.

Design, modeling, and robust control of the flexible rotor to pass the first bending critical speed with active magnetic bearing:

Abstract: Recently, magnetic bearings have been applied to many rotating machines such as turbo-molecular pumps, cooling gas compressor, flywheel energy storage systems. And high-power density is the future ...

Axial Vibration Suppression by Field Flux Regulation in Two-Axis Actively Positioned Permanent Magnet Bearingless Motors With Axial Position Estimation

Abstract: This paper presents a novel axial vibration suppression method in two-axis actively positioned permanent magnet bearingless motors. Only radial directions are actively positioned. The axial and tilting directions are passively stabilized by the magnetic attraction force between the stator core and the rotor permanent magnet. Generally, a damping force is considerably low in the axial and tilting directions. Therefore, when an axial disturbance force is applied to the rotor, the axial vibration is generated, and then, the vibration cannot be suppressed at a critical speed. In this paper, a novel axial vibration suppression method by d -axis current is proposed. The damping force is generated by d -axis current regulation. In this proposed method, the rotor axial position is estimated from the flux linkage variation in the motor winding. Therefore, an additional displacement sensor is not necessary. In experiments, it is confirmed that the rotor axial vibration is successfully suppressed by the proposed method.

Nonlinear dynamic analysis of a rotor-bearing system with porous tilting pad bearing support

Abstract: Porous tilting pad bearings (PTPBs) show a potential for using in high-speed, high precision rotating machinery that requires high bearing stiffness and good stability. In this study, the nonlinear characteristics of a rotor supported on PTPBs are investigated. The Darcy equations and the modified Reynolds equations are adopted to establish the gas flow model in porous materials and gas film region, respectively. The pad motions and rotor motions are also included in the numerical nonlinear model. The advantages of PTPBs over tilting pad journal bearings are discussed. PTPBs with externally pressurized gas can avoid friction during startup and shutdown, improve the load capacity at low rotational speeds, and effectively suppress subsynchronous vibrations at high rotational speeds. The nonlinear characteristics of the rotor-bearing system with various bearing parameters, such as supply pressure ratio, nominal bearing clearance, pad tilting and radial stiffness, are analyzed. Poincare maps, predicted rotor orbit and bifurcation diagrams are used. High supply pressure ratio and small nominal bearing clearance can significantly decrease the orbit size and increase the critical speed. Low tilting and high radial stiffness can improve system stability. This study reveals the complex nonlinear characteristics of the system and provides guidance for designing PTPBs for using in high-speed rotating machinery.

Dimensionless modeling and nonlinear analysis of a coupled pitch–plunge–leadlag airfoil-based piezoaeroelastic energy harvesting system

Abstract: In this paper, an airfoil-based piezoaeroelastic energy harvesting system is proposed with an additional supporting device to harvest the mechanical energy from the leadlag motion. A dimensionless dynamic model is built considering the large-effective-angle-of-attack vibrations causing (1) the nonlinear coupling between the pitch–plunge–leadlag motions, (2) the inertia nonlinearity, and (3) the aerodynamic nonlinearity modeled by the ONERA dynamic stall model. Cubic hardening stiffness is introduced in the pitch degree of freedom for persistent vibrations with acceptable amplitude beyond the flutter boundary. The nonlinear aeroelastic response and the average power output are numerically studied. Limit cycle oscillations are observed and, as the flow velocity exceeds a secondary critical speed, the system experiences complex vibrations. The power output from the leadlag motion is smaller than that from the plunge motion, whereas the gap is narrowed with increasing flow velocity. Case studies are performed toward the effects of several dimensionless system parameters, including the nonlinear torsional stiffness, airfoil mass eccentricity, airfoil radius of gyration, mass of the supporting devices, and load resistances in the external circuits. The optimal parameter values for the power outputs from the plunge and leadlag motions are, respectively, obtained. Beyond the secondary critical speed, it is shown that the variations of the power outputs with those parameters become irregular with fluctuations and multiple local maximums. The bifurcation analysis shows the mutual transitions between the limit cycle oscillations, multi-periodic vibrations, and possible chaos. The influences of these complex vibrations on the power outputs are discussed.

Active Vibration Control of a Flexible Rotor by Flexibly Mounted Internal-Stator Magnetic Actuators

Abstract: This paper demonstrates vibration reduction in a hollow rotating shaft by means of internal-stator active magnetic actuators, which are resiliently mounted This problem requires further consideration over and above classic rotor/magnetic bearing systems on account of the flexible behavior of the magnetic actuator support structure This paper presents an experimental facility conforming to the proposed topology, with a particular focus on the control problem such a system presents The unique challenges are discussed, and a solution is presented in the form of H $_\infty$ -based control Ultimately, experimental results demonstrate the system to be capable of substantial rotor vibration suppression, including while passing the rotor's first critical speed, which was not obtainable with simpler classical control techniques This means the top achievable rotor speed was increased from approximately 3000 r/min without magnetic actuator vibration suppression to over 9000 r/min with vibration suppression active At the rotor critical speed, the magnetic actuators affect a reduction in rotor vibration amplitude of over 70% compared to the rotor supported purely on mechanical bearings, while simultaneously avoiding excessive excitation of the flexible active magnetic actuator support structure

Asymptotic theory of fluid entrainment in dip coating

Abstract: When a contact line moves with a sufficiently large speed, liquid or gas films can be entrained on a solid depending on the direction of contact-line movement. In this work, the contact-line dynamics in the situation of a generic two-fluid system is investigated. We demonstrate that the hydrodynamics of a contact line, no matter whether advancing or receding, can formally reduce to that of a receding one with small interfacial slopes. Since the latter can be well treated under the classical lubrication approximation, this analogy allows us to derive an asymptotic solution of the interfacial profiles for arbitrary values of contact angle and viscosity ratio. For the dip-coating geometry, we obtain, with no adjustable parameters, an analytical formula for the critical speed of wetting transition, which in particular predicts the onset of both liquid and gas entrainment. Moreover, the present analysis also builds a novel connection between the Cox–Voinov law and classical lubrication theory for moving contact lines.

Dynamic response of a cracked rotor with an unbalance influenced breathing mechanism

Abstract: The vast majority of studies on cracked rotors assume that the breathing response of a fatigue crack is weight-dominant i.e. the effect of dynamic forces on the breathing response is negligible. In this study, the assumption of weight-dominance is removed and the coupling effect of unbalance angle and magnitude on the breathing behaviour of a crack is examined. The proposed breathing model is shown to be greatly influenced by unbalance eccentricity and rotor speed, whereas weight-dominant breathing models are unaffected by these factors. A significant difference in the vibration behaviour of a weight-dominant model and the proposed model was particularly seen around the critical speed of deeply cracked rotors. High unbalance eccentricity and a 180° placement of the unbalanced mass resulted in the disappearance of 2X and/or 3X harmonic components at one-half and one-third of the rotor critical speed when the vibration was predicted using the proposed model. This result suggests careful placement and size of the unbalance mass may allow for the isolation of rotor cracks from other rotor faults in the frequency domain by negating the effects of the crack breathing.

A new method for estimation of critical speed for railway tracks on soft ground

Abstract: This paper presents a new method, ETL (EBER Track Lab), which allows for estimation of critical speed from measurements from a running train at normal speeds. Hence, large distances can be covered ...

Rotor Dynamic Analysis of Ultra-high Speed Switched Reluctance Machines over 1 Million rpm

Abstract: Ultra-high speed machines have drawn more and more interest for researchers in recent times. Switched reluctance machines (SRMs) are of particular interest due to their simple rotor geometry. For ultra-high speed machines, rotor dynamics are a major component and must be considered in the design stage. In this paper, a rotor dynamic study of an ultra-high speed SRM with a rated speed of 1 million rpm is presented. First, different rotors built with isotropic and orthotropic materials are studied, using both analytical and numerical methods. Then, the impact of using a laminated stack versus a solid stack is studied. Finally, three different geometries of single, tandem, and bilateral rotor shafts are proposed, analyzed and compared based on their cost, torque density, manufacturing complexity, and rotor dynamic stability.

Calculated estimation of railway wheels equivalent conicity influence on critical speed of railway passenger car

Abstract: The article presents the results of determining the equivalent conicity characterizing the geometric interaction of wheels and rails on 1520 mm track gauge. The cases of interactions of rails and wheelsets, wheels of which have different profiles, are considered. The computer model of the motion speeds of the passenger car is developed. According to the results of computer simulation, critical speeds for the bogie moving through the tracks of intended gauge are received. Based on the results of the simulation anslysis, the significant dependence of the value of the equivalent conicity on the critical speed is confirmed. The necessity of considering the limit values of equivalent conicity in tests of high speed rolling stock is emphasized. This work is supported by: KEGA

Towards robust design optimization of automotive turbocharger rotor-bearing systems

Abstract: In the competitive automotive market, the performance of turbochargers is constantly being pushed towards their theoretical optimum. One of the key components of the turbocharger is the rotor-bearing system, which determines the friction losses and noise output and furthermore affects the overall turbocharger efficiency, reliability and cost. In order to fulfil the demands of the automotive market, developing methods to optimize the rotor-bearing system is the focus of this study, where particular attention is paid to taking into account the product-to-product variations that are inevitable in cost-effective mass-produced parts, as well as the variations in turbocharger operating conditions. First, a model of the rotor-bearing system was developed to predict the rotordynamic response over the operating range. The model is constructed in a step-by-step fashion, starting with a simple test case: a Laval rotor supported by plain journal bearings. As the behavior of the rotor-bearing system varies over its rotation speed range, run-up simulations were performed by a time-transient multi-physical model. In this model, several sub-models are coupled: a rotordynamic sub-model, a thermo-hydrodynamic submodel and a thermal network model. Once a satisfactory correlation was found between numerical simulation results and measurement results, the test case progressed to a Laval rotor with floating ring bearings instead of plain journal bearings. Correspondingly, the bearing model was extended to include the dynamics of the floating ring and its two oil films. The resulting run-ups showed a response consisting of a critical speed, an oil whirl and an oil whip. Analysis of a turbocharger rotor-bearing system was subsequently performed, showing a more complex response, consisting of multiple critical speeds and the co-existence of sub-synchronous whirling modes. The effect of the rotor-bearing operating conditions, unbalance configuration, the thrust bearing and the bearing cylindricity were investigated. Most of the trends are correctly predicted by the model, however the correlation between measurement results and simulation results was clearly inferior to the case of the Laval rotor, most likely due to the uncertainties in the actual turbocharger geometry and the actual unbalance distribution. Lastly, an optimization of a Laval rotor-bearing system was performed. The resulting robust optimum design ensures optimum rotor-bearing performance, even at the most severe operating conditions and even if all manufacturing tolerances represent the worst case scenario. Particularly the uncertainties in rotor unbalance and oil supply temperature were found to have a significant influence on the optimum design.

Nonstationary analysis of nonlinear rotating shafts passing through critical speed excited by a nonideal energy source

Abstract: In this paper, the effect of nonlinearity on vibration of a rotating shaft passing through critical speed excited by nonideal energy source is investigated. Here, the interaction between a nonlinear gyroscopic continuous system (i.e. rotating shaft) and the energy source is considered. In the shaft model, the rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The nonlinearity is due to large deflection of the shaft. Firstly, nonlinear equations of motion governing the flexural–flexural–extensional vibrations of the rotating shaft with nonconstant spin are derived by the Hamilton principle. Then, the equations are simplified using stretching assumption. To analyze the nonstationary vibration of the nonideal system, multiple-scale method is directly applied to the equations expressed in complex coordinates. Three analytical expressions that describe variation of amplitude, phase, and angular acceleration during passage through critical speed are derived. It is shown that...

Effects of rotary inertia on sub- and super-critical free vibration of an axially moving beam

Abstract: The most important issue in the vibration study of an engineering system is dynamics modeling. Axially moving continua is often discussed without the inertia produced by the rotation of the continua section. The main goal of this paper is to discover the effects of rotary inertia on the free vibration characteristics of an axially moving beam in the sub-critical and super-critical regime. Specifically, an integro-partial-differential nonlinear equation is modeled for the transverse vibration of the moving beam based on the generalized Hamilton principle. Then the effects of rotary inertia on the natural frequencies, the critical speed, post-buckling vibration frequencies are presented. Two kinds of boundary conditions are also compared. In super-critical speed range, the straight configuration of the axially moving beam loses its stability. The buckling configurations are derived from the corresponding nonlinear static equilibrium equation. Then the natural frequencies of the post-buckling vibration of the super-critical moving beam are calculated by using local linearization theory. By comparing the critical speed and the vibration frequencies in the sub-critical and super-critical regime, the effects of the inertia moment due to beam section rotation are investigated. Several interesting phenomena are disclosed. For examples, without rotary inertia, the study overestimates the stability of the axially moving beam. Moreover, the relative differences between the super-critical fundamental frequencies of the two theories may increase with an increasing beam length.

Dynamic bifurcations analysis of a micro rotating shaft considering non-classical theory and internal damping

Abstract: In this study, the dynamic bifurcation of a viscoelastic micro rotating shaft is investigated. The non-classical theory (the modified couple stress theory) and the Kelvin Voigt model are used for modeling the viscoelastic micro shaft. The transverse equations of motion are derived using the variational approach. The reduced order model of the system is obtained by the Galerkin method. Using the Routh–Hurwitz criteria the stability regions of the system are extracted in which the effect of the length scale parameter is significant. Using the center manifold theory and the normal form method the double zero eigenvalue bifurcation is analyzed. The results show that the internal and external damping coefficients, the rotational speed and the material length scale parameter influence the critical speed, amplitude, and phase of a non-trivial solution, and radius of limit cycle (periodic solution). Also, it is seen that by increasing the dimensionless length scale parameter (material length scale per radius of the shaft) the radius of the limit cycle is decreased, whereas the critical rotational speed and the rate of the phase are increased. However, the radius of the limit cycle concerning the classical theory is higher than that of regarding the modified couple stress theory. Furthermore, with an increase of the external damping coefficient the radius of the limit cycle is linearly decreased; however, the critical speed of the system is increased. Additionally, by decreasing length scale parameter the results of the modified couple stress theory approach the classical theory ones.

Dynamic Characteristics of Air Cycle Machine Rotor System

Abstract: Parameters optimization in the critical speed region has the important influence on operational stability of an air cycle machine. Effects of bearing stiffness and unbalanced exciting force on critical speed and response characteristics are investigated by the modal method and harmonic response analysis. Resonance separation phenomenon in the critical speed region is analyzed in detail. When difference exists in the phase of unbalanced exciting force, resonance separation appears in the conical whirling speed region. The characteristics after resonance separation are closely related to the phase difference value and amplitude of unbalanced exciting force. The paper provides theoretical and experimental foundations for resonance separation analysis and also provides data support for dynamic balance and dynamic design of the rotor system.

Research on Friction Vibration of Marine Water Lubricated Rubber Bearing

Abstract: Marine water-lubricated rubber bearing is used to support the stern shaft of surface vessels and underwater vehicles, whose friction vibration and noise directly influence the stealth, security of the vessels and both physical and psychological health of occupants. In order to investigate the this problem, the kinds of water-lubricated bearings with different rubber material were tested on the bearing testing machine, and friction coefficient, noise, vibration frequency and amplitude were measured under different working conditions. The results show that friction coefficient of water-lubricated rubber bearings are affected with the rubber material, operating speed, applied load and cooling water temperature, which results in the change of bearing vibration state. The component content of carbon black and self-lubricated materials can affect the deformation size, frictional performances and friction coefficients of bearings. The higher the speed, the smaller the friction coefficient, and friction vibration state is changed. With the increase of the specific pressure in some range, the contact pressure between tested bearing and shaft decreases due to the augment of the contact area so that the friction coefficient and vibration amplitude are changed. As cooling water temperature is enhanced, sometimes friction vibration declines, but the critical speed producing noise increases due to softened rubber.

Analysis of resonance effect for a railway track on a layered ground

Abstract: When a train runs on soft ground it can approach or even exceed the speed of surface waves in the ground. Under such conditions the amplitudes of the track response increase considerably. Moreover, a resonance-like phenomenon can occur in which a clear oscillation trail can be observed behind the moving axle loads. An investigation is presented of this resonance frequency and the critical speed effect for a track on a layered half-space subject to a moving load. Three different methods are used to investigate this resonance frequency: (i) the spectrum of the response to a moving load, (ii) analysis of the dispersion curves of the ground, and (iii) frequency analysis of the response to a stationary load. A parameter study is presented of a layered half-space ground with different P-wave speeds, S-wave speeds, and depth of the upper layer. The critical speeds are found in each case; in such a layered ground, the critical speed is greater than the Rayleigh wave speed of the soft upper layer due to the influence of the underlying half-space. The oscillating frequencies are shown to vary with the speed of the moving load, tending to reduce when the load speed increases. The P-wave speeds of both the upper layer and the underlying half-space are found to have negligible influence on the critical velocity and on the oscillating frequency; the S-wave speed of the half-space has only a small influence. Larger differences are found when the depth of the layer is varied. Finally, a formula for calculating this resonance frequency is proposed.