Showing papers on "Critical speed published in 2022"

Analysis of Critical Speed for High-Speed Railway Pantograph-Catenary System

Abstract: The pantograph-catenary system is used in modern electrified railways to power electric trains. Common sense is that the increase of train speed leads to a deterioration of the interaction performance. But recent studies indicate that a higher speed may result in a better performance in some local speed regions. This paper is the first attempt to provide a theoretical explanation for this phenomenon. A validated pantograph-catenary model is built to reproduce this phenomenon. Referring the definition of critical speed in moving load problems, the catenary's critical speed is defined. The wavelength components can be extracted through the Fourier transformation to the contact wire's vertical mode shape. The speed that satisfies the resonance condition can be regarded as the potential critical speed. The corresponding contact wire amplitude is further evaluated to determine the critical speeds at a given mode. The analysis indicates that a good interaction performance happens when the speed falls in the transition procedure between the critical two speeds. Based on this idea, a simple indicator that describes the overall contribution of all modes subjected to a moving pantograph at a given speed is proposed to facilitate the determination of the local optimal speed. The variation of the proposed indicator with respect to the speed shows good consistency with the trend of the simulation results. The main finding in this paper can be used in the design phase to determine the optimal speed of the pantograph-catenary system in a local speed range.

Dynamic analysis of the variable stiffness support rotor system with elastic rings

Abstract: Elastic rings are common rotor supporting structure, which have been widely used in aeroengine rotor support system. However, large inertia force and gyroscopic moment may occur during the operation of aeroengine, which may lead to contact between elastic ring and bearing pedestal, and then introduce variable stiffness into the rotor support system. In this paper, a mathematical model of variable stiffness of elastic ring is proposed and this model is subsequently verified by comparison with simulation analysis and experimental results. Based on this model, a variable stiffness model of an elastic ring-supported rotor is developed by coupling the kinetic equations of the rotor with the deformation of the combined support. Then, the spectrum cascades are used to analyze the dynamic characteristics of the rotor system. In addition, the influences of the variable stiffness of elastic ring on the critical speed of the system are also examined. Finally, some simulation results are verified by experiments on a combined test bench of an elastic ring-supported rotor.

Post-resonance backward whirl analysis in cracked overhung rotors

Abstract: Overhung rotors usually exhibit recurrent transitions through critical whirl rotational speeds during startup and coast down operations, which significantly differ from their steady-state whirl responses. The presence of angular acceleration results in a linear-time-varying (LTV) system, which, although technically linear, still presents complexities often evinced by a nonlinear system. In general, backward whirl zones can either precede the critical forward whirl speed (termed as pre-resonance backward whirl, Pr-BW), or immediately follow the critical forward whirl speed (termed as post-resonance backward whirl, Po-BW). The Po-BW in the whirl response of a cracked overhung rotor with a breathing crack is studied here as distinct from that of geometrically symmetric configurations of other rotor systems. The equations of motion from the finite element (FE) model of an overhung rotor system with a breathing crack are numerically integrated to obtain the whirl response. The transient whirl responses with different bearing conditions are thoroughly investigated for excitation of Po-BW. The Po-BW zones of rotational speeds are determined via the wavelet transform method and full spectrum analysis (FSA) and applied to signals with added noise. The results of this work confirm the excitation of the Po-BW in cracked overhung rotors and confirm the robustness of the employed methods.

Post-resonance backward whirl analysis in cracked overhung rotors

Abstract: Overhung rotors usually exhibit recurrent transitions through critical whirl rotational speeds during startup and coast down operations, which significantly differ from their steady-state whirl responses. The presence of angular acceleration results in a linear-time-varying (LTV) system, which, although technically linear, still presents complexities often evinced by a nonlinear system. In general, backward whirl zones can either precede the critical forward whirl speed (termed as pre-resonance backward whirl, Pr-BW), or immediately follow the critical forward whirl speed (termed as post-resonance backward whirl, Po-BW). The Po-BW in the whirl response of a cracked overhung rotor with a breathing crack is studied here as distinct from that of geometrically symmetric configurations of other rotor systems. The equations of motion from the finite element (FE) model of an overhung rotor system with a breathing crack are numerically integrated to obtain the whirl response. The transient whirl responses with different bearing conditions are thoroughly investigated for excitation of Po-BW. The Po-BW zones of rotational speeds are determined via the wavelet transform method and full spectrum analysis (FSA) and applied to signals with added noise. The results of this work confirm the excitation of the Po-BW in cracked overhung rotors and confirm the robustness of the employed methods.

Stress-deformation analysis of rail substructure under moving wheel load

Abstract: A three-dimensional (3D) finite element (FE) analysis is developed to study the effect of moving wheel load on the dynamic response of track with the key objective of determining the accurate stress-deformation response of the substructure. The 3D FEM model is first calibrated and then validated with two independent set of field measurements. The computed transient displacements and vertical stresses corroborate well with the field data from the selected case studies, endorsing the reliability of the current numerical model. The changes attributed to dynamic stress paths and the angle of principal stress rotation are also analysed with respect to the train speed in the range, 60–450 km/h. The results show some limitations of the existing dynamic amplification factor in relation to the design of railway track. This traditional approach will only be appropriate when the train speeds are relatively low, but it will not be accurate at significantly higher speeds at which significant principal stress rotation occurs, resulting in correspondingly increased shear stresses. The current FEM model enables a limiting train speed to be determined to prevent shear failure of the ballast layer when the dynamic response in relation to ballast properties is interpreted based on the proposed R-wave speed /critical track speed ratio.

Double-parameter Hopf bifurcation analysis of a high-speed rail vehicle with an alternative wheel/rail contact approximation

Abstract: This investigation integrates an alternative fully-parameterized approximation of nonlinear wheel/rail interaction into a simplified vehicle model, and a two-parameter Hopf bifurcation analysis is conducted to reveal the influence of the wheel/rail contact geometry and secondary suspension parameters for high-speed rail vehicles. The bifurcation diagram is compared among the 6 DOFs bogie model, linear and nonlinear 7 DOFs vehicle model, nonlinear 17 DOFs vehicle model, and 3D full DOFs vehicle model. It shows that the nonlinear 7 DOFs vehicle model can meet the requirement of both carbody hunting and bogie hunting simulations. 6 DOFs bogie model can only be used in bogie hunting bifurcation analysis. Linear vehicle model would bring errors in either critical speed or limit circle magnitude. The divergences in the linear terms of rolling radius and contact angle polynomials are significant enough in field operation to cause a noticeable difference in Hopf bifurcation speed. Attention shall be paid to the shape of equivalent conicity and contact angle curve. The crucial parameters to the Hopf bifurcation include the series stiffness and damping coefficient of the yaw damper and the lateral damper damping. However, the requirement of suspension parameters for stability can conflict in carbody hunting and bogie hunting cases.

All-round responses and boundaries of a shaft and dry friction damper assembly

Abstract: A helicopter tailrotor driveline is equipped with dampers to suppress the resonance of transmission shafts. A dry friction damper and a slender shaft form an assembly The comprehensive understanding of different responses of the assembly provides the basis for a more reasonable parameter configuration of the damper. To this end, the assembly is modeled as a dynamic system with rub impact between a rotor with continuous parameter distribution and a suspended elastic stator. Boundaries of rub impact and condition of Hopf bifurcation are derived. Pinned natural frequencies and backward whirl frequencies are solved by analytical deduction. The critical speed for triggering a backward whirl with consideration of eccentric excitation is obtained by the multiple scale perturbation method. Then, all-round responses and boundaries are solved by both analytical and numerical approaches based on the parameters of a helicopter. The effects of friction coefficient, internal damping, suspension stiffness, variable impact stiffness, etc. on the boundaries are presented in detail with the discussion of relationships between physical reasons and analytical conditions. Results show that smaller impact stiffness difference and friction coefficient, a greater mass damping ring, moderate suspension stiffness, greater internal and external damping are the key factors for the damper design. This study has reference significance not only for the assembly in a helicopter but also for similar mechanical systems.

Rotor strength and critical speed analysis of a vertical long shaft fire pump connected with different shaft lengths

Abstract: The vertical long shaft fire pump (VLSFP) is mainly used in fire-fighting places far away from land and lacking large amounts of water supply. The paper selected the XBC18-178-240LC3 model of VLSFP as the research object. First, the experimental-numerical hydraulic performance of the single-VLSFP was carried out, and then the hydraulic performance of the multi-VLSFP was analyzed by the same numerical simulation method as single-VLSFP. After that, three rotor models (Z4 model, Z5 model-original model and Z6 model) were designed by modeling software, connected by different length and number of the shaft section under the same total length of the intermediate shafts. Finally, the rotor's strength and critical speed of three models were analyzed and checked via the CFD simulation and the Workbench software. The study mainly found: (1) Through the strength check of the impeller, maximum equivalent stress of the three models was less than the allowable stress of the rotor material, which indicated the structural design of them met the safety requirement; (2) Through the critical speed check of the shafting rotor, the working speed of the VLSFP was lower than 0.8 times the first-order critical speed of the three models, which indicated the rotor could avoid the resonance and the structure of the three models met the dynamic design requirement. According to the stress check of the impeller and the critical speed check of the shafting rotor, combining the time and labor cost when the VLSFP was installed and disassembled many times before and after the test or operation, the paper selected the Z4 model to be the optimal model, which could provide a theoretical support for the subsequent structure design optimization of the vertical long shaft fire pump.

Dynamic Characteristic Analysis of the Multi-Stage Centrifugal Pump Rotor System with Uncertain Sliding Bearing Structural Parameters

Abstract: The traditional dynamic characteristic analysis of the multi-stage centrifugal pump rotor system is developed assuming the bearing structural parameters with constant values. However, the manufacturing errors will cause the structural parameters to vary around their nominal values and then affect the dynamic characteristics of the bearing-rotor system. Thus, this paper proposes a method for analyzing the dynamic characteristics of the bearing-rotor system with uncertain bearing structural parameters. First, dynamic characteristic coefficients of the sliding bearing are identified to establish the dynamic model of the rotor system, and its dynamic characteristics are analyzed through finite element simulations. Next, the sliding bearing structural parameters are taken as the variables to establish an optimization model, which is solved by the improved particle swarming optimization algorithm to obtain the extreme critical speed of the rotor system. A case study was carried out on a multi-stage centrifugal pump. The obtained extreme values of the critical speeds were close to those calculated using the multiple samples generated by the Monte Carlo method, indicating that the proposed method can provide accurate variation ranges of critical speeds efficiently and lay a theoretical basis for selecting robust operational speeds and designing the rotor system of the multi-stage centrifugal pump.

Stability of Hydrogen Turbopump Rotor Shaft Axially Self-Balanced

Abstract: Controlling the vibration levels of turbopump rotor shafts is a key feature for the reliability of space engines. Turbopump components are exposed to high static and dynamic stress levels, and therefore are particularly sensitive to High-Cycle Fatigues. Among the numerous dynamic excitations that affect the turbopump, self-induced instabilities are the most critical ones because of the exponential growth rate of vibration levels. These flutter-like phenomena may account for rotor shaft instabilities of turbopumps designed with an Axial Balancing System (ABS). Such a system is necessary to avoid heavy static loads on bearings and is commonly used in high power turbopumps in the space industry. It consists of a fluid cavity located in the back of a centrifugal compressor. Instabilities induced by the ABS have been studied within the framework of a Research and Technology program using a reduced scale Hydrogen turbopump demonstrator called TPtech. This paper focuses on experimental and numerical analysis of rotor instabilities induced by the ABS. A coupled dynamic model of the rotor shaft and the ABS cavity is presented. It shows instabilities of the rigid rotor axial mode, but also of an axisymmetric rotor mode. This result is consistent with the data acquired during TPtech test campaign. The instability mechanism is complex as it involves the rotor modes, the flow in the ABS cavity and its acoustic modes. Therefore, TPtech tests performed in representative conditions are valuable. They have permitted tool validation and have provided design rules to prevent occurrence of such phenomena.

Modelling and analysis of passenger rail vehicle for the improvement of critical speed using MR damper based semi-active suspension

Abstract: Developing economies focus to enhance train speed by introducing high speed corridors and upgrading existing rail infrastructure. Higher speed has adverse impact on vehicle stability and ride comfort. Therefore, in order to improve critical speed and ride comfort magneto-rheological (MR) based dampers are used. Here, the lateral dynamics of an Indian passenger rail vehicle is expressed with 17 degrees of freedom model and after validation, it is used to examine the effect of suspension parameters such as damping and stiffness on critical speed. Moreover, a sensitivity analysis is performed and it is found that critical speed is the most sensitive to secondary lateral damping coefficient. Therefore, these dampers are replaced with MR fluid dampers to evaluate improvement in stability and critical speed. The modified Bouc-Wen model is formulated to characterise the behaviour of the MR damper. Herein, two distinct controllers: disturbance refusal and damper force tracking control algorithms are employed to govern the entire system. Measured random track irregularities are applied as an input to simulate the system. The results reveal that the semi-active suspension improves the critical speed by 19.38 km/h (9.89%) when compared to the existing passive suspension, and significantly reduces the vibration responses of the carbody in a wide frequency spectrum at higher speeds of the train.

Vibration control of a bi-disk rotor using electro-rheological elastomers

Abstract: Abstract Smart materials are widely used for vibration control of rotating machines. This paper considers the control of vibration of a bi-disk rotor bearing system using electro-rheological elastomer (ERE) rings inserted in the bearings. The bi-disk rotor is selected so that vibration response can be studied in a rotating speed range which includes the first two critical speeds. The rotor bearing system is modelled using the finite element method taking into account the gyroscopic effect of the rotor and the internal damping of the shaft. The influence of the active elastomer when it is subjected to different levels of the electric field on the critical speeds is first investigated. Then, the vibration response is determined for both steady-state and transient running up and running down conditions. Simulation results show the potentials of the ERE when used in passive mode for vibration reduction in the steady-state and transient running up and down conditions of the rotor system. In the active mode, the application of an electric field to the EREs shifts slightly the resonant speeds to higher frequencies due to the increase of the stiffness of the bearings while increasing the vibration amplitudes in the steady-state and transient running up and down conditions in the vicinity of the resonant speeds. Nevertheless, it has been shown that the rotor steady-state vibration response can be reduced at other rotating speed range when an electric field is applied.

Non-stationary Resonance Transition of the Gyroscopic Rigid Rotor with Nonlinear Damping and Non-ideal Energy Source

Abstract: The article constructs differential equations of motion of a gyroscopic rigid unbalanced rotor with nonlinear cubic damping and nonlinear stiffness, taking into account the anisotropy of the linear stiffness of the elastic support material and interaction with a non-ideal DC motor with a linear characteristic, and the dynamics of the rotor is studied by a numerical method. Two jumping nonlinear effects are observed during the accelerated resonant transition from a large amplitude to a smaller one, accompanied by Sommerfeld effects, during the resonant transition with the decelerated motor from a smaller amplitude of oscillations to a larger one, corresponding to two critical speeds. Nonlinear cubic damping suppresses the maximum amplitudes in the regions of critical velocity and amplitude after similar resonant increasing and damping beats oscillations. At sufficiently close critical velocities, exit from the resonance at a lower critical velocity can lead to capture at another resonance at a higher critical velocity, the severity of the Sommerfeld effect on each of the resonant regions becomes comparable. Therefore, the evaluation of the response of the dynamics of resonant transients is of paramount importance for the correct design of the vibration insulation of the rotor machine.

Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay

Abstract: <p style='text-indent:20px;'>This paper is concerned with a nonlocal time-space periodic reaction diffusion model with age structure. We first prove the existence and global attractivity of time-space periodic solution for the model. Next, by a family of principal eigenvalues associated with linear operators, we characterize the asymptotic speed of spread of the model in the monotone and non-monotone cases. Furthermore, we introduce a notion of transition semi-waves for the model, and then by constructing appropriate upper and lower solutions, and using the results of the asymptotic speed of spread, we show that transition semi-waves of the model in the non-monotone case exist when their wave speed is above a critical speed, and transition semi-waves do not exist anymore when their wave speed is less than the critical speed. It turns out that the asymptotic speed of spread coincides with the critical wave speed of transition semi-waves in the non-monotone case. In addition, we show that the obtained transition semi-waves are actually transition waves in the monotone case. Finally, numerical simulations for various cases are carried out to support our theoretical results.</p>

Gyroscopic effect on a scaled rotor-bearing system

Abstract: This paper deals with scale-fullscale models of rotor-bearing systems on rotating condition. The investigation is focused on the gyroscopic effect, which causes forward and backward whirl frequencies. When the rotor-bearing system is scaled proportionally in its dimension (height, length, and width), the scaling factor of whirl frequencies can be derived. It depends on the ratio between a transverse and polar moment of inertia on its rotating axis called the gyroscopic factor. The experimental study is conducted to validate it on three scaled rotor-bearing systems, which shifts its disc from the middle of the shaft on the scale of 1:1, 2:1, and 3:1 to clearly show the gyroscopic effect on first bending natural frequency. The scaling factor is then validated using the Campbell diagram by finding its critical speed. From this critical speed, the whirl frequencies along the range of the full-scale model speed can be obtained. The result also shows that the scaling factor remains the same whether it is at rotation or rest condition. Consideration must be made on the effect of the structural design, that is, blade and support, because of its unsymmetric stiffness that can cause backward whirl frequencies. The bearing stiffness must be ensured to be scaled proportionally, especially on journal bearing cases. This finding can be used by engineers to deal with scaling method implementation on rotating machinery design.