Torsional Vibration Characteristics Research Articles

Coupled bending and torsional vibration characteristics analysis of inhomogeneous wind turbine tower with variable cross section under elastic constraint

The separation of cross section’ mass center from its centroid will lead to coupled bending and torsional vibration of the wind turbine tower (Referred to as tower). Three governing differential equations of vibration of the tower with inhomogeneous material and variable cross section are formulated based on D'Alembert's principle and Euler-Bernoulli beam theory. Considering the installation and operation factors of the wind turbine, the dimensionless natural frequencies and mode shapes of the tower under multiple constraint conditions are obtained by the differential quadrature method. Compared with those available in the literature, numerical results demonstrate the accuracy and validity of the proposed method. A series of parametric study is accomplished to reveal the influence of the foundation stiffness, wall thickness, eccentricity, and the ratio of the inner diameter of the top and bottom cross section of tower on the vibration characteristics of tower. The frequencies veering for the mode of tower is discussed. These numerical results have guiding significance for the design of tower.

Torsional dynamic response of tapered pile considering compaction effect and stress diffusion effect

Considering both the compaction effect of pile surrounding soil and the stress diffusion effect of pile end soil, this paper theoretically investigates the torsional vibration characteristics of tapered pile. Utilizing the complex stiffness transfer model to simulate compaction effect and tapered fictitious soil pile model to simulate stress diffusion, the analytical solution for the torsional impedance at tapered pile top is obtained by virtue of Laplace transform technique and impedance transfer method. Based on the present solution, a parametric study is conducted to investigate the rationality of the present solution and the influence of soil and pile properties on the torsional vibration characteristics of tapered pile embedded in layered soil. The results show that, both the compaction effect and stress diffusion effect have significant influence on the torsional vibration characteristics of tapered pile, and these two factors should be considered during the dynamic design of pile foundation.

Study on Torsional Vibration Characteristics of Cross Shaft Universal Coupling

In this work, the ship propulsion shaft system with cruciform universal coupling is studied. First, based on the analysis of the structure and characteristics of the cross-axis universal coupling, the motion relations and expressions between the components of the universal coupling are established by using the coordinate transformation method. Second, the characteristics of the four submodels of the head mass point element, the end mass point element, the universal coupling mass point element, and other mass point elements are discussed, and the corresponding torsional vibration differential equations of the four submodels are established. On this basis, the mathematical model of the propulsion shafting system and the differential equations of torsional vibration are established by using the modularization method and lumped parameter method. Finally, the torsional vibration modes and response characteristics of the shafts are calculated and analyzed by using the system matrix method when the external load driving torques of the universal coupling, propeller, and diesel engine are considered. At the same time, the correctness of the mathematical model and calculation method is verified by the test and comparative analysis of ship propulsion shafts. It lays a theoretical foundation for further research on torsional vibration characteristics and mechanisms of the ship propulsion shafting system based on universal coupling. Introduction Universal coupling is a common connection component of mechanical shaft system transmission. It is a common mechanism that can be used to transfer motion and torque. Universal coupling has no requirement for neutrality between the two axes connected. It can be used for intersecting, parallel or staggered multiposition relations, and can still ensure the continuous rotation of the two axes connected. Compared with the belt drive and chain drive, universal coupling has the advantages of large transmission range, compact transmission, high transmission efficiency, and convenient maintenance. Therefore, it is widely used in ships, automobiles, lifting and transportation (Avrigean et al. 2015; Chang et al. 2017), engineering machinery, and other equipment. Because of the manufacturing error, assembly error, and the failure to keep synchronous rotation between the driving shaft and the driven shaft in the working process, additional inertia moment of the universal coupling is generated, which causes the vibration of the system and even leads to the fracture of the universal coupling in serious cases.

Modeling and Analysis of Amplitude-Frequency Characteristics of Torsional Vibration for Automotive Powertrain

In the present paper, the amplitude-frequency characteristics of torsional vibration are discussed theoretically and experimentally for automotive powertrain. A bending-torsional-lateral-rocking coupled dynamic model with time-dependent mesh stiffness, backlash, transmission error etc. is proposed by the lumped-mass method to analysis the amplitude-frequency characteristic of torsional vibration for practical purposes, and equations of motive are derived. The Runge–Kutta method is employed to conduct a sweep frequency response analysis numerically. Furthermore, a torsional experiment is performed and validates the feasibility of the theoretical model. As a result, some torsional characteristics of automotive powertrain are obtained. The first three-order nature torsional frequencies are predicted. Torsional behaviors only affect the vibration characteristics of a complete vehicle at low-speed condition and will be reinforced expectedly while increasing torque fluctuation. Gear mesh excitations have little effects on torsional responses for such components located before mesh point but a lot for ones behind it. In particular, it is noted that the torsional system has a stiffness-softening characteristic with respect to torque fluctuation.

Torsional dynamics of bi-directional functionally graded small-scale tubes possessing a variable length scale parameter

The aim of the current study is to investigate torsional vibrations of bi-directional functionally graded (FG) small-scale tubes. The size effect is captured using the modified couple stress theory (MCST). Through-the-thickness distribution profile of material properties are characterized by employing a power-law function, which incorporates a gradation index, β, and longitudinal varation in material properties is featured by an exponential function which employs a gradient parameter, α. Similar to other material properties, continuous spatial variation of the length scale parameter is also incorporated into the analysis of two-dimensionally FG tubes. The model, including governing equations of motion and boundary conditions, is developed through the utilization of Hamilton’s principle. By employing differential quadrature method (DQM) numerical results regarding torsional vibrations are provided. Accuracy of the proposed model and procedures are verified through verification comparisons made to limiting cases available in the literature. Numerical results reveal effects of various material and geometric parameters on natural frequencies and indicate that torsional free vibration characteristics of small-sized tubes are sensitive to distribution profile of constituents, geometric aspect ratios and effective length scale parameter. Results also demonstrate that length scale parameter variation has significant influence on natural frequencies which justifies the necessity of its consideration in analyses.

Torque distribution method based on vibration instability of PS-HEV transmission system

The power-split hybrid electric vehicle has multiple working modes, which can be switched to different working mode according to different working conditions. The main switching process involved in the vehicle driving is the switch from the pure electric mode to the hybrid driving mode. This paper studies the mode switching process involved in the power-split hybrid electric vehicle driving process, and a nonlinear dynamic equation of the electromechanical coupling of the corresponding transmission system is established. Then the multi-scale method is employed to solve the dynamic equation, and the amplitude-frequency response curve is drawn. According to the curve, the effects of load, mechanical input excitation of the engine and motor electromagnetic excitation on the electromechanical coupling torsional vibration of the transmission system are studied. The engine and motor torque distribution schemes are obtained by analyzing the amplitude-frequency response curve of the torsional vibration characteristics of the system. The analysis results show that the vibration instability phenomenon of the transmission system can be avoided by establishing the nonlinear dynamic equation of the transmission system, analyzing the vibration characteristics of the vibration system, and optimizing the torque distribution of a PS-HEV at different working modes.

Torsional vibration characteristics and experimental study of cracked rotor system with torsional oscillation

Root causes of numerous crack failures are attributed to the torsional oscillation between the turbine generator and the grid. To prevent such kind of failures, torsional vibration monitoring system has been intensively installed in reality and the torsional vibration is more and more observed in the operation. However, the mechanism of the characteristics of torsional vibration of the rotor system with and without cracks has not been well explored. Therefore this work presents the dynamic analysis and experimental study on the rotor system with transverse and slant cracks. For simulating the torsional oscillation in reality, excitation device is designed in the experiments and torsional vibration is measured. Based on this, the characteristics of lateral and torsional vibration of the rotor system are compared. The results show that, (i) although the slant crack presents more significant later-torsional vibration (especially for the breathing crack), the transverse cracked rotor system show higher amplitudes in the fundamental frequency and harmonic components (especially for the open crack) and (ii) the torsional excitation introduces more obvious vibration fluctuation in the rotor system with cracks (observed from the orbits and the torsional vibration).

Multidimensional vibration reduction control of the frame structure with magnetorheological damper

To analyze the multidimensional vibration reduction performance and torsional vibration characteristics of frame structures with magnetorheological damper (MRD), the space models of the reinforced concrete (RC) frame structure with and without MRD, based on the space beam element and shell element model, are established and programmed by using MATLAB software. Then, comparisons on results of modal analysis and dynamic time history response calculated from self-programmed space model and finite element model established by ANSYS software are carried out. The comparison results show that the self-programmed space model is validity and reliability. Finally, the dynamic time history analyses on the structures with and without MRD under bidirectional seismic wave action are presented; the multidimensional dynamic time history response and torsional vibration response between the uncontrolled and the controlled structures are then compared. The comparison results show that MRD can effectively reduce the three-dimensional displacement response and restraint the torsional vibration response of the space frame structure.

Analysis of torsional vibration characteristics and time delay feedback control of semi-direct drive cutting transmission system in shearer

Abstract The semi-direct drive cutting transmission system driven by low speed and high torque permanent magnet synchronous motor (PMSM) in shearer is a typical electromechanical coupling system. In this paper, the torsional vibration characteristics of the transmission system with internal parameter and external cutting load excitation changes are studied. Considering the torsional vibration angle and the air gap magnetic field energy of the PMSM, the torsional vibration model of the electromechanical coupling transmission system is derived by the Lagrange-Maxwell equation. Then, in the case of 1:1 internal resonance and external resonance, the first-order approximate solution is obtained by multiple scale method, and the influence of cutting load excitation and current on the torsional vibration characteristics of the rotor system is analyzed. In addition, the numerical simulation is used to study the vibration jump phenomenon of the nonlinear electromechanical coupling system. The influence of the cutting load excitation on the chaos motion is obtained by the bifurcation diagram and maximum Lyapunov index map. Finally, the vibration amplitude and chaos motion of the rotor system are suppressed by the time delay feedback controller. The research results can provide a theoretical basis for the design and manufacture of the shearer semi-direct drive cutting transmission system.

Beam Approximation for Dynamic Analysis of Launch Vehicles Modelled as Stiffened Cylindrical Shells

A beam approximation method for dynamic analysis of launch vehicles modelled as stiffened cylindrical shells is proposed. Firstly, an initial beam model of the stiffened cylindrical shell is established based on the cross-sectional area equivalence principle that represents the shell skin and its longitudinal ribs as a beam with annular cross-section, and the circumferential ribs as lumped masses at the nodes of the beam elements. Then, a fine finite element model (FE model) of the stiffened cylindrical shell is constructed and a modal analysis is carried out. Finally, the initial beam model is improved through model updating against the natural frequencies and mode shapes of the fine FE model of the shell. To facilitate the comparison between the mode shapes of the fine FE model of the stiffened shell and the equivalent beam model, a weighted nodal displacement coupling relationship is introduced. To prevent the design parameters used in model updating from converging to incorrect values, a pre-model updating procedure is added before the proper model updating. The results of two examples demonstrate that the beam approximation method presented in this paper can build equivalent beam models of stiffened cylindrical shells which can reflect the global longitudinal, lateral and torsional vibration characteristics very well in terms of the natural frequencies.

G/T 500톤급 차도선 추진축계시스템의 비틀림진동 특성과 안전성 평가

In South Korea, which is surrounded by the sea on three sides, many passenger and car ferries operate around the coasts where there are many islands. Until recently, passenger and car ferries of the 200 gross tonnage (G/T) class were mainly built by small shipbuilding companies. In recent years, with the improvement of the berth facilities of islands, passenger and car ferries of the 500 G/T class have been built and operated to improve economic and operational efficiency. The propulsion shafting system applied to these ships requires a high speed of more than 1500 r/min and more than 1 MW of power for the main engine system, which consists of two engines and two shafts. In South Korea, D company manufactures and supplies high-speed engines of up to 800 kW depending on market demand, but domestic brand engines of greater power are still difficult to obtain. Therefore, main engines are mostly imported and propulsion shafting systems are designed and manufactured according to the sales policies and guides of various domestic dealers. Furthermore, due to the high prices of main engines, ship owners purchase them directly and supply them to shipyards. Consequently, the overall design of propulsion shafting systems considering torsional vibration is not being performed. As a result, accidents related to the main engine and shafting system occur frequently because the torsional vibration characteristics of the engine are not fully examined. This study evaluates the torsional vibration characteristics and safety of three engine models applied to the propulsion shafting system focusing on the recently increasing number of passenger and car ferries of the 500 G/T class.

Torsional Vibration and Bifurcation Characteristics of Automotive Main Reducer Based on Nonlinear Hybrid Model

In the view of integrating dynamics of systems with dynamics of structures, the pinion shaft of automobile main reducer is divided into several torsion rod elements to establish its dynamic model, while the torsional vibration dynamic model of hypoid gears is still built with lumped mass method, thus the hybrid dynamic model of automotive main reducer is obtained by the combination of two kinds of dynamic models. Considering the nonlinear factors such as time-varying mesh stiffness, backlash and static transmission error of gear pairs, Runge-Kutta method is applied to obtain the time domain spectrum, spectrum graph, phase-plane diagram, Poincaré maps, and bifurcation diagrams of the system. The dynamic response characteristics of system with different parameters such as input rotational speed and mesh stiffness are systematically investigated by numerical simulations.

Torsional vibration solution of tapered pile considering stress diffusion effect of pile end soil

Based on the torsional plane strain model and tapered fictitious soil pile model, the torsional vibration characteristics of tapered pile considering stress diffusion effect of pile end soil is investigated theoretically. Considering the coupling conditions of pile-soil system, the torsional impedance at the tapered pile head is obtained by means of Laplace transform and impedance transfer method. A parametric study is performed, the rationality of the tapered fictitious soil model is verified and the influence of the cone angle of tapered fictitious soil pile on the torsional vibration characteristics of tapered pile embedded in layered soil is studied. The results show that: the cone angle of tapered fictitious soil pile has obvious effect on the torsional vibration characteristics of tapered pile with the shorter length.

Fatigue damage assessment method of turbine shafts' torsional vibrations under SSO incidents

Sub-Synchronous Oscillation (SSO) can pose severe threat to the steam turbine shafting system, which in particular is the torsional vibrations leading to the hazard or shut down of the power units. A method is developed to evaluate fatigue damage under SSO incidents, which utilizes field data and modal decomposition and superposition concepts, and combines the structural full-size FEA (finite element analysis) modal analysis with refined finite element structural analysis of specific parts. Applying such method to a 330 MW steam turbine shafting system, our study illustrates its torsional vibration characteristics under different modes of SSO incidents. The results indicate that the proposed method is faster than conventional full-size transient analysis, decreasing the computational cost. We find that coupling shrinkage structure is the most vulnerable part, which is consistent with engineering practice and thus perfects our traditional understanding that connecting parts in journals are the only vulnerable parts. At the end of this paper, we also point out that with the presence of SSO incident, decreasing the load on shafts in time would help alleviate the damage.

Manufacturing quality assurance for a rotate vector reducer with vibration technology

To improve the product quality of rotate vector (RV) reducer at a low cost, a kind of vibration technology is introduced to investigate the quality assurance of RV. It includes a torsional vibration test to assess the vibration performance of the reducer and vibration analysis to recognize the manufacturing defects in the reducer’s mechanical components. The mechanical components with manufacturing defects are diagnosed through the signal processing on torsional vibration and defect characteristics recognition, and they are removed from the RV reducer by a reassembling process. As a result, the dynamic behavior of the reducer is evidently improved, the torsional vibration of the reducer is kept within a low level, and the feedback control is realized for product quality during the production process. Therefore, the presented vibration technology is highly recommended to the manufacture quality assurance of RV reducers applied in an industrial robot.

Determination Methodology for Stability Domain of Hybrid Electric Power System with Multiple Excitation Sources

Irregular internal excitation (engine excitation and motor excitation) and external load excitation can cause torsional vibration in hybrid electric propulsion system which even leads to the break of shaft. The objective of this paper is to determinate the stability domain of hybrid electric power system under different drive mode with multiple excitation sources. To achieve the goal, the simplified three-mass torsional model of hybrid electric power system is established. Then we apply the multi-scale method to solve the nonlinear torsional model. Finally we set different parameters of engine speed to simulate torsional vibration characteristics of hybrid electric power system. The simulation results exhibit that the torsional vibration characteristics of hybrid electric power system under two drive mode are different because the directional relationship of the moment of engine and permanent magnet synchronous motor (PMSM) is distinctive. It’s hard to eliminate the torsional vibration of hybrid electric propulsion system due to phase difference between the engine excitation and the load excitation.

Evaluation of Torsional Vibration Characteristics of Ship Propeller-Engine Shaft System Based on Theoretical Sensitivity Analysis

Evaluation of Torsional Vibration Characteristics of Ship Propeller-Engine Shaft System Based on Theoretical Sensitivity Analysis

Torsional vibration of an end bearing pile embedded in radially inhomogeneous saturated soil

This paper is concerned with the torsional dynamic response of an end bearing pile embedded in radially inhomogeneous saturated soil. The soil is simulated using Biot’s two-phase linear theory and its radial inhomogeneity due to the construction disturbance effect is considered by radially gradual variation of soil parameters. Then, the governing equations for the pile–soil system are established to derive an analytical solution for the torsional vibration of the pile. The reliability of the proposed solution is verified and parametric studies are performed to analyze the torsional vibration characteristics of the pile.

Design Torsional Vibration Damper of Engine based on Classical Optimal Approach

The torsional vibration of crankshaft is an important factor in the vibration caused by the engine and causing fracture. An inline 4-cylinder engine crankshaft system will be the object to research. Finite element model of crankshaft is built by ANSYS. And analysis torsional vibration characteristics of shafting are based on the model, which include natural vibration and forced vibration. It gets main harmonic times, minor main harmonic times and corresponding engine speed in commonly used speed range. Designs parameters of torsional vibration damper (TVD) based on classical optimal approach. And tests the damping effect under different conditions based on the finite element model. The results show that the design meets the requirements of the damper, and has good damping effect. Research methods and conclusions can be applied to actual research. It can be used in similar crankshaft torsional vibration system analysis, design and analysis of torsional damper.

Analysis of the electromechanical coupling mechanism and torsional vibration characteristics of a high‐speed train drive system

The high-speed train transmission system is a complex electromechanical coupling system, which consists of a motor, a universal shaft, a gearbox, and a wheel set. In order to solve dynamic problems such as torsion vibration caused by a high-speed train transmission system, the simplified model and equivalent mechanics model of the system were established, the natural vibration frequency was solved, and the simulation results of the system under a fixed torque input were analysed. The results showed that the natural vibration frequency of the universal shaft was 4.19 Hz, the natural vibration frequency of the pinion was 7.54 Hz, the natural vibration frequency of the big gear was 35.6 Hz, and the natural vibration frequency of the wheel set was 107.45 Hz. The natural vibration frequency of each part of the system increased gradually during the transmission from the motor to the wheel set. A fixed torque was added to the input end of the simulation model. The simulation results showed that the change amplitude of the torsion angle displacement of the big gear and the wheel set decreases. It is known that the angular displacement caused by the torsional vibration is weakened by the larger torsion stiffness of the axle.