Research on the Critical Speed of a Mixed-Flow Turbocharger with Hybrid Ceramic Ball Bearing

The critical speeds for a vehicle turbocharger with hybrid ceramic ball bearing are researched. The ball bearing-rotor system produces resonance when it working in critical speed and that makes the turbocharger injury working for a long time. The calculation and analysis methods of the critical speed for the vehicle turbocharger are described. The critical speed is computed by two methods including Riccati transfer matrix and DyRoBeS finite element method for a vehicle turbocharger with hybrid ceramic ball bearing. The vibration experiment had been taken to validate the calculating result, Comparison between the results by two calculation methods and the test results show that the first critical speed differences are 6.47 % and 5.66 %, the second critical speed differences are 2.87 % and 2.94 % respectively. And then, the primary factors which influence the critical speed are analyzed, the conclusions will be helpful for the vehicle turbocharger bearing-rotor system design.

FRACTAL DIMENSION OF TIME SERIES APPLIED TO IDENTIFICATION OF CRITICAL SPEED OF JEFFCOTT ROTOR SYSTEM

The dynamical behaviors of logistic map（May＇s model） and duffing equation are studied through fractal dimension of time series at different parameters. It is shown that the parameters of dynamical behaviors can be identified effectively by the curve of fractal dimension with parameter increments. For further verification, the relation between the fractional dimension of time series and rotational speed can be used to identify critical speed effectively by using this method to a plate Jeffoctt rotor system. The numerical and experimental result indicates that the identification of critical parameters is effective.

Calculation of the Critical Speed and Stability Analysis of Cryogenic Turboexpanders with Different Structures

A modularized code based on the Finite Element QZ （FEQZ） method is developed, for a better estimate of the critical speed and a more convenient method of rotor-dynamic stability analysis for a gas bearing high speed turboexpander rotor system with actual structure and application of a cryogenic turboexpander. This code is then validated by the experimental data of a gas bearing turboexpander, with a rotor diameter of 25 mm and a rated speed of 106,400 rpm. With this code, four rotors with different structures, available to the turboexpander, are parametrically analyzed by the available speed range, vibration modes and logarithmic attenuation rate. The results suggest that the rotor with a structure of two thrust collars on the system exhibits a better performance in the designed conditions.

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory （FSDT）. The equations of motion are obtained applying Hamilton＇s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.

Numerical analysis of high‑speed railway slab tracks using calibrated and validated 3D time‑domain modelling

Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a novel slab trackform for high-speed railways is investigated using three-dimensional finite element modelling in Abaqus.It is then compared to the performance of a ballasted track.First,slab and ballasted track models are developed to replicate the full-scale testing of track sections.Once the models are calibrated with the experimental results,the novel slab model is developed and compared against the calibrated slab track results.The slab and ballasted track models are then extended to create linear dynamic models,considering the track geodynamics,and simulating train passages at various speeds,for which the Ledsgard documented case was used to validate the models.Trains travelling at low and high speeds are analysed to investigate the track deflections and the wave propagation in the soil,considering the issues associated with critical speeds.Various train loading methods are discussed,and the most practical approach is retained and described.Moreover,correlations are made between the geotechnical parameters of modern high-speed rail and conventional standards.It is found that considering the same ground condition,the slab track deflections are considerably smaller than those of the ballasted track at high speeds,while they show similar behaviour at low speeds.

ON THE NATURAL FREQUENCIES,COMPLEX MODE FUNCTIONS,AND CRITICAL SPEEDS OF AXIALLY TRAVELING LAMINATED BEAMS:PARAMETRIC STUDY

The dynamic response of an axially traveling laminated composite beam is investigated analytically,with special consideration to natural frequencies,complex mode functions and critical speeds of the system.The equation of motion for a symmetrically laminated system,which is in the form of a continuous gyroscopic system,is considered;the equation of motion is not discretized — no spatial mode function is assumed.This leads to analytical expressions for the complex mode functions and critical speeds.A parametric study has been conducted in order to highlight the effects of system parameters on the above-mentioned vibration characteristics of the system.

Critical Speeds of Electric Vehicles for Regenerative Braking

Efficient regenerative braking of electric vehicles(EVs)can enhance the efficiency of an energy storage system(ESS)and reduce the system cost.To ensure swift braking energy recovery,it is paramount to know the upper limit of the regenerative energy during braking.Therefore,this paper,based on 14 typical urban driving cycles,proposes the concept and principle of confidence interval of“probability event”and“likelihood energy”proportion of braking.The critical speeds of EVs for braking energy recovery are defined and studied through case studies.First,high-probability critical braking speed and high-energy critical braking speed are obtained,compared,and analyzed,according to statistical analysis and calculations of the braking randomness and likelihood energy in the urban driving cycles of EVs.Subsequently,a new optimized ESS concept is proposed under the frame of a battery/ultra-capacitor(UC)hybrid energy storage system(HESS)combined with two critical speeds.The battery/UC HESS with 9 UCs can achieve better regenerative braking performances and discharging performances,which indicates that a minimal amount of UCs can be used as auxiliary power source to optimize the ESS.After that,the efficiency regenerative braking model,including the longitudinal dynamics,motor,drivetrain,tire,and wheel slip models,is established.Finally,parameters optimization and performance verification of the optimized HESS are implemented and analyzed using a specific EV.Research results emphasize the significance of the critical speeds of EVs for regenerative braking.

Influence of train speed and its mitigation measures in the short-and long-term performance of a ballastless transition zone

The ballastless track is nowadays the most popular railway system due to the required low number of maintenance opera-tions and costs,despite the high investment.The gradual change from ballasted to ballastless tracks has been occurring in Asia,but also in Europe,increasing the number of transition zones.The transition zones are a special area of the railway networks where there is an accelerated process of track degradation,which is a major concern of the railway infrastructure managers.Thus,the accurate prediction of the short-and long-term performance of ballastless tracks in transition zones is an important topic in the current paradigm of building/rehabilitating high-speed lines.This work purposes the development of an advanced 3D model to study the global performance of a ballastless track in an embankment-tunnel transition zone considering the influence of the train speed(220,360,500,and 600 km/h).Moreover,a mitigation measure is also adopted to reduce the stress and displacements levels of the track in the transition.A resilient mat placed in the tunnel and embank-ment aims to soften the transition.The behaviour of the track with the resilient mat is evaluated considering the influence of the train speed,with special attention regarding the critical speed.The used methodology is a novel and hybrid approach that allows including short-term and long-term performance,through the development of a powerful 3D model combined with the implementation of a calibrated empirical permanent deformation model.

Influence of Vehicle Parameters on Critical Hunting Speed Based on Ruzicka Model

While introducing foreign advanced technology and cooperating with Chinese famous research institutes,the high-speed vehicles are designed and take the major task of passenger transport in China.In high-speed vehicle,the characteristic of shock absorber is an important parameter which determines overall behavior of the vehicle.The most existing researches neglect the influence of the series stiffness of the shock absorber on the vehicle dynamic behavior and have one-sided views on the equivalent conicity of wheel tread.In this paper,a high speed passenger vehicle in China is modeled to investigate the effect of the parameters taking series hydraulic shock absorber stiffness into consideration on Ruzicka model.Using the vehicle dynamic model,the effect of main suspension parameters on critical speed is studied.In order to verify the reasonableness of shock absorber parameter settings,vibration isolation characteristics are calculated and the relationship between suspension parameters and the vehicle critical hunting speed is studied.To study the influence of equivalent conicity on vehicle dynamic behavior,a series of wheel treads with different conicities are set and the vehicle critical hunting speeds with different wheel treads are calculated.The discipline between the equivalent conicity of wheel tread and critical speed are obtained in vehicle nonlinear system.The research results show that the critical speed of vehicle much depends on wheelset positioning stiffness and anti-hunting motion damper,and the series stiffness produces notable effect on the vehicle dynamic behavior.The critical speed has a peak value with the equivalent conicity increasing,which is different from the traditional opinion in which the critical speed will decrease with the conicity increasing.The relationship between critical speed and conicity of wheel tread is effected by the suspension parameters of the vehicle.The study results obtained offer a method and useful data to designing the parameters of the high speed vehicle and simulation study.

Experimental determination of the critical welding speed in high speed MAG welding

In high speed MAG welding process, some weld formation defects may be encountered. To get good weld quality, the critical welding speed beyond which humping or undercutting weld bead can occur must be known for different conditions. In this research, high speed MAG welding tests were carried out to check out the effects of different factors on the critical welding speed. Through observing the weld bead profiles and the macrographs of the transverse sections of MAG welds, the occurrence tendency of humping weld was analyzed, and the values of critical welding speed were determined under different levels of welding current or voltage, and the effect of shielding gas compositions on the critical welding speed was also investigated.

Numerical simulation of aerodynamic derivatives and critical wind speed for long-span bridges based on simplified steady wind field

Combining the computational fluid dynamics-based numerical simulation with the forced vibration technique for extraction of aerodynamic derivatives, an approach for calculating the aerodynamic derivatives and the critical flutter wind speed for long-span bridges is presented in this paper. The RNG k-ε turbulent model is introduced to establish the governing equations, including the continuity equation and the Navier-Stokes equations, for solving the wind flow field around a two-dimensional bridge section. To illustrate the effectiveness and accuracy of the proposed approach, a simple application to the Hume Bridge in China is provided, and the numerical results show that the aerodynamic derivatives and the critical flutter wind speed obtained agree well with the wind tunnel test results.

Influences of aerodynamic loads on hunting stability of high-speed railway vehicles and parameter studies

The influences of steady aerodynamic loads on hunting stability of high-speed railway vehicles were investigated in this study.A mechanism is suggested to explain the change of hunting behavior due to actions of aerodynamic loads：the aerodynamic loads can change the position of vehicle system（consequently the contact relations）,the wheel/rail normal contact forces,the gravitational restoring forces/moments and the creep forces/moments.A mathematical model for hunting stability incorporating such influences was developed.A computer program capable of incorporating the effects of aerodynamic loads based on the model was written,and the critical speeds were calculated using this program.The dependences of linear and nonlinear critical speeds on suspension parameters considering aerodynamic loads were analyzed by using the orthogonal test method,the results were also compared with the situations without aerodynamic loads.It is shown that the most dominant factors a ff ecting linear and nonlinear critical speeds are different whether the aerodynamic loads considered or not.The damping of yaw damper is the most dominant influencing factor for linear critical speeds,while the damping of lateral damper is most dominant for nonlinear ones.When the influences of aerodynamic loads are considered,the linear critical speeds decrease with the rise of cross wind velocity,whereas it is not the case for the nonlinear critical speeds.The variation trends of critical speeds with suspension parameters can be significantly changed by aerodynamic loads.Combined actions of aerodynamic loads and suspension parameters also a ff ect the critical speeds.The effects of such joint action are more obvious for nonlinear critical speeds.

Motion stability of high-speed maglev systems in consideration of aerodynamic effects: a study of a single magnetic suspension system

In this study, the intrinsic mechanism of aerodynamic effects on the motion stability of a high-speed maglev system was investigated. The concept of a critical speed for maglev vehicles considering the aerodynamic effect is proposed. The study was carried out based on a single magnetic suspension system, which is convenient for proposing relevant concepts and obtaining explicit expressions. This study shows that the motion stability of the suspension system is closely related to the vehicle speed when aerodynamic effects are considered. With increases of the vehicle speed, the stability behavior of the system changes. At a certain vehicle speed,the stability of the system reaches a critical state, followed by instability. The speed corresponding to the critical state is the critical speed. Analysis reveals that when the system reaches the critical state, it takes two forms, with two critical speeds, and thus two expressions for the critical speed are obtained. The conditions of the existence of the critical speed were determined, and the effects of the control parameters and the lift coefficient on the critical speed were analyzed by numerical analysis. The results show that the first critical speed appears when the aerodynamic force is upward,and the second critical speed appears when the aerodynamic force is downward. Moreover, both critical speeds decrease with the increase of the lift coefficient.

Studyon Evaluation Methods for Lateral Stability of High-Speed Trains

Taking a high-speed train in China as an example,using computer simulation technology and comparing with the test data,the three current methods including linear stability analysis method,nonlinear stability analysis method and the field testing criterion are studied to evaluate stability of high-speed trains.A new stability evaluation method is proposed which can be used to evaluate lateral stability of high-speed vehicle based on the codes of UIC 515and UIC 518.From the viewpoint of taking the most unfavorable track conditions into account and improving the safety margin,the new method uses the root mean square of bogie lateral acceleration as a criterion to evaluate the lateral stability of high-speed trains.Numerical example shows that the proposed method not only considers the forced vibration caused by track irregularities in the actual practice,but also takes the instability self-excited vibration into account,so it can realize early warning of bogie slight unstable oscillation,meanwhile the method itself does not involve complex algorithms which has the possibility of engineering applications.

Separate critical condition for ultrasonic vibration assisted grinding

Separate characteristic of the tangential ultrasonic vibration assisted grinding (TUAG) machining is analyzed based on TUAG process, and a critical speed formula is given to correctly set the machining parameters to insure the separate characteristics of TUAG process. The critical speed is not only related to the ultrasonic vibration amplitude and frequency, but also to the grinding wheel velocity and the cutting point space, and the grinding force can be decreased during the TUAG process with separability. Grinding force experiments are conducted, and the experimental results are in good agreement with the theoretical results.

Implementation of high speed arc welding with DE-GMAW

Modern manufacturing industry demands low cost and high efficient welding processes to remain competitiveness in the time of globalization. In this study, conventional gas metal arc welding （GMAW） was modified, a double-electrode GMAW （DE-GMAW） system is developed and DE-GMAW process is implemented through optimization of the design and process parameters and suitable selection of igniting sequence of double arcs. High speed welding tests were carried out to examine the effects of different factors on occurrence of weld formation defects. Through observing the weld bead appearance in DE-GMA W, the values of critical welding speed were determined under different levels of welding current and welding speed.

Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems:mechanism and numerical and experimental studies

The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e.,the dynamic stiffness).However,the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system.Therefore,this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system.Then,the numerical study and experimental verification are conducted on the dynamic stiffness characteristics of a squirrel cage,which is a common support structure for aero-engine.Moreover,the static stiffness experiment is also performed for comparison.Finally,a rotor system model considering the dynamic stiffness of the support structure is presented.The presented rotor model is used to validate the results of the theoretical analysis.The results illustrate that the dynamic stiffness reduces the critical speed of the rotor system and may lead to a new resonance.

Study on the effect of thermal deformation on the liquid seal of high-temperature molten salt pump in molten salt reactor

The high-temperature molten salt pump is the core equipment in a molten salt reactor that drives the flow of the molten salt coolant.Rotor stability is key to the continuous and reliable operation of the molten salt pump,and the liquid seal at the wear ring can affect the dynamic characteristics of the rotor system.When the molten salt pump is operated in the hightemperature molten salt medium,thermal deformation of the submerged parts inevitably occurs,changing clearance between the stator and rotor,affecting the leakage and dynamic characteristics of the seal.In this study,the seal leakage,seal dynamic characteristics,and rotor system dynamic characteristics are simulated and analyzed using finite element simulation software based on two cases of considering the effect of seal thermal deformation effect or not.The results show a significant difference in the leakage characteristics and dynamic characteristics of the seal obtained by considering the effect of seal thermal deformation and neglecting the effect of thermal deformation.The leakage flow rate decreases,and the first-order critical speed of the seal-bearing-rotor system decrease after considering the seal’s thermal deformation.

Nonlinear Dynamic Characteristic Analysis of the Shaft System in Water Turbine Generator Set

A 3D finite element vibration model of water turbine generator set is constructed considering the coupling with hydropower house foundation. The method of determining guide bearing dynamic characteristic coefficients according to the swing of the shaft is proposed, which can be used for studying the self-vibration characteristic and stability of the water turbine generator set. The method fully considers the complex supporting boundary and loading conditions; especially the nonlinear variation of guide bearing dynamic characteristic coefficients and the coupling effect of the whole power-house foundation. The swing and critical rotating speed of an actual generator set shaft system are calculated. The simulated results of the generator set indicate that the coupling vibration model and calculation method presented in this paper are suitable for stability analysis of the water turbine generator set.

Analysis on Dynamic Performance for Active Magnetic Bearing-Rotor System

In the application of active magnetic bearings (AMB), one of the key problems to be solved is the safety and stability in the sense of rotor dynamics. The project related to the present paper deals with the method for analyzing bearing rotor systems with high rotation speed and specially supported by active magnetic bearings, and studies its rotor dynamics performance, including calculation of the natural frequencies with their distribution characteristics, and the critical speeds of the system. One of the targets of this project is to formulate a theory and method valid for the analysis of the dynamic performance of the active magnetic bearing rotor system by combining the traditional theory and method of rotor dynamics with the analytical theory and design method based on modern control theory of the AMB system.