Shaft Torsional Vibration Research Articles

Coupling vibration mechanism of rotating shaft–disc–blade system with blade crack—A systematical investigation on the effect of crack, condition, and structure parameters

Rotating shaft–disc–blade (RSDB) system is one of the most important parts of turbomachinery, such as aero-engine, gas turbine, and power plant. Understating and revealing the coupling vibration mechanism of RSDB system is significant for blade health monitoring and blade crack detection. However, the multi-structure, multi-vibration source, and multi-stress coupling makes it a very tough task. This study aims to reveal the coupling vibration mechanism of RSDB system by systematically investigating the steady-state vibration responses under the influences of different blade crack, operation condition, and structure parameters. First and foremost, a coupling vibration model of RSDB system that comprehensively considers the multi-structure, multi-vibration source, and multi-stress coupling effects is presented. And then, a novel condition indicator for blade health monitoring, called blade–blade distance, is proposed to better characterize and analyse the coupling vibration of RSDB system with blade crack. At last, the comprehensive effects of blade crack, operating condition, and structure parameters on the coupling vibration mechanism of the RSDB system with blade crack are systematically studied. The comparative results demonstrate the effectiveness of blade–blade distance and super-harmonic components of shaft torsional vibration and blade bending vibration for indicating the presence of blade crack and tracking the crack severity. Another observation should be noted is that the vibration behaviour including the blade–blade distance, super-harmonic components of shaft torsional vibration and blade bending vibration, the combination frequency components of shaft bending vibration are co-affected by blade crack, operating condition, and structure parameters. It is indicated that the blade health monitoring and crack detection of rotating blade should comprehensively consider different indicators to obtain a more robust and accurate results.

Effect of AVL-based time-domain analysis on torsional vibration of engine shafting

The torsional vibration of the shaft system in hybrid car engines has a significant impact on the overall performance of the vehicle, and it is more complex in hybrid cars compared to traditional cars. Traditional methods for torsional vibration analysis of shaft systems have significant limitations and cannot handle nonlinear and transient problems. To explore the torsional vibration characteristics of hybrid vehicle shaft systems, a simplified engine shaft system torsional vibration equivalent model is innovatively constructed. In addition, a method for quickly determining the confidence level of the torsional vibration equivalent model is proposed. Additionally, the transient dynamic characteristics of a multi-body dynamics model containing a dual mass flywheel are analyzed in depth using the time-domain solver of AVL-exact PU. The results demonstrated that the simulation of 4th and 6th harmonics resonated at critical speeds of 4,195 rpm and 2,771 rpm, respectively, with angular displacement amplitudes of 0.141 deg and 0.047 deg. In fact, resonance was measured at 4,250 rpm and 3,040 rpm, with amplitudes of 0.14 deg and 0.052 deg. These two were basically consistent in key parameters. When the shaft model was started under operating conditions, the amplitudes of harmonics 1, 2, and 4 were basically consistent below 750 rpm, and there were slight differences after 750 rpm. Therefore, the AVL-based engine torsional vibration simulation model constructed has high credibility.

A comparative study on the torsional vibration suppression of rotor system using variable steady state nonlinear energy sink

Current studies have shown that the introduction of bistable nonlinear energy sink (B-NES) and tristable nonlinear energy sink (T-NES) can reduce the effective threshold and alleviate the separation resonance curve compared with traditional NES under the low and higher external excitation respectively. However, there is a lack of comparative studies on the performance of B-NES, T-NES and monostable nonlinear energy sink (M-NES) in the field of torsional vibration engineering application. Aimed at this limitation, a variable steady state nonlinear energy sink (V-NES) is proposed to suppress the torsional vibration of shafting. Negative stiffness is generated by the pre-compression of the spring. The proposed V-NES can be easily switched between monostable, bistable and tristable cases by the moving position of the spring bases. Based on this, the governing equation of torsional vibration coupled with V-NES after proper orthogonal decomposition (POD) reduction is derived. The approximate analytical solution of the coupled system is obtained by using complex averaging method and verified numerically. Then, the vibration reduction effects of M-NES, B-NES and T-NES on the torsional vibration of shafting are compared. Throughout the study, the motion states of strongly modulated response (SMR), interwell oscillation, and chaotic strongly modulated response (CSMR) are observed in the V-NES. Excessively high external excitation amplitudes can make V-NES exhibit CSMR, diminishing the effectiveness of vibration reduction in comparison to inter-well oscillations.

Active Control of Shaft Torsional Vibration with a Dynamic Torque Actuator

Active Control of Shaft Torsional Vibration with a Dynamic Torque Actuator

Locating Sources of Sub-Synchronous Oscillations in Wind Farms Based on Instantaneous Energy Supply on Port and Bicoherence

The sub-synchronous oscillation (SSO) which occurred in direct-driven wind generators (DDWG) based wind farms became a research hotspot. The SSO excited the shaft torsional vibration of thermal generators and caused trip failures, leading to economic losses and stabilization problems. However, the existing phasor-based oscillation source locating methods cannot be applied to the SSO since the power system quasi-steady-state assumption was not satisfied in the SSO scenarios. Thus, a novel locating method for SSO sources was urgently required. To fill this gap, this paper proposed an improved method for locating nonlinear sub-synchronous oscillation sources based on Energy Supply on Port (ESP) and bicoherence. The ESP was calculated with the instantaneous values of measured voltages and currents at some predefined network interfaces, i.e., the ports. The tendency of the ESP indicated the transient energy injection from a certain subsystem into the rest of the network during a designated period, which can help figure out the oscillation source of the SSO. After oscillation source localization, the nonlinear index and its threshold were proposed by defining the bicoherence coefficient in consideration of the nonlinear oscillation characteristics. According to the power-quality standard and the comparison of the bicoherence with the threshold, the nonlinearity of the oscillation source was examined. The feasibility and effectiveness of the proposed method were proved in the case study which simulated the oscillation scene of the accident in Hami.

Coupling effect of shaft torsional vibration and advanced injection angle on medium-speed diesel engine block vibration

Engine body vibration is an important safety concern for diesel engines as it can lead to severe engine damages and even catastrophic failures. Traditional methods for excitation computation assume that the rotational speed and the cylinder pressure remain stable under each working cycle, which makes it impossible to precisely predict vibration peaks at certain frequencies. But in practice, the existence of shafting torsional vibration will lead to the fluctuation of rotational speed and cylinder pressure. To predict engine block vibration more accurately, this paper proposes a novel method considering the instantaneous variations in rotational speed and cylinder pressure. It is implemented by two steps. Firstly, an innovative model considering the coupling effect between shaft torsional vibration and advanced injection angle is proposed, it particularly explains how the cylinder pressure and instantaneous rotational speed vary due to the coupling effects. Secondly, the excitation forces that cause block vibration are analyzed and their computational formulas are improved. This method also considers the offset of excitation loading position caused by torsional vibration. The coupling model is experimentally verified and the excitations are loaded into a finite element model of the diesel engine for vibration response prediction. The results reveal that the coupled model can predict vibration peaks at sideband frequencies and thus makes the frequency spectrum much richer than that of the traditional method. Furthermore, it shows that the acceleration results obtained by the coupled model have better prediction accuracy than those obtained from traditional methods, with the deviation percentage reducing from 6.31% and 8.41% to 0.64% and 0.32% in the X and Z direction. It indicates that the coupled model is more reliable in predicting the vibration response of the engine block. Finally, the effect of advanced injection angle on engine block vibration is investigated and the optimal value of the advanced injection angle is determined to be 29 CA, which makes the engine block vibration reduced by 3.60%, 2.72%, and 3.16% in the X, Y, and Z direction comparing to the original advanced injection angle. Overall, this study presents an improved approach for predicting engine block vibrations and offers valuable insights for the design of shafting structures and fuel injection parameters in marine diesel engines.

Analysis of Torsional Vibration of Diesel Shaft System using Hard Coupling with Working Machine

The model is built to analyze and calculate the torsional vibration of the internal combustion engine shaft system and the generator connected by hard coupling to assess the response to the free and forced vibration of the shaft system, thereby serving as a basis for devising a suitable plan to reduce or avoid the problem of shaft torsion vibration. The results of the research include: modeling and building a separate calculation program for shaft torsion vibrations using MATLAB software; free vibration response analysis including calculating the vibration mode frequency and corresponding vibration forms; analyzing the forced vibration response including the amplitude of vibration of the degrees of freedom and the torsion stress of each element.

Study of Torsional Vibration Bifurcation Characteristics of Direct-Drive Wind Turbine Shaft System

This paper set out to establish the dynamics model of shaft torsional vibration for direct-drive wind turbine with the phenomenon of unstable shaft system torsional vibration. The stability of the equilibrium point of the dynamical model is investigated, and the Routh–Hurwitz stability criterion is used to obtain a range of values for the bifurcation control parameters. For the stable equilibrium point, the stability domain of the system is calculated by constructing the Lyapunov function. The sensitivity analysis of system parameters is carried out to obtain the law of the effect of system parameters on system stability of the torsional vibration system. The results are substituted for example calculations, and the results verify the correctness of the theoretical analysis conclusions. It is proved that it is feasible to analyze the torsional vibration characteristics of the direct-drive wind turbine shaft system by using the principle of Routh–Hurwitz stability, etc., which provides a reference for the structural design of direct-drive wind turbine.

A Predicted-Risk-Based Protection Approach for Turbine Generator Shafts against Fatigue Damage due to Islanding

A distributed generation steam turbine generator (hereafter referred to as turbine generator) improves the supply reliability of the local load when operated as a backup supply during islanding. Interconnection standards recommend removing the utility load from the island. Transient torques induced at the moments of islanding and removing the utility load from the island may cause shaft fatigue life loss and lead to fatigue damage. Therefore, a protection method is proposed in this work. The method is based on predicting the risk of shaft fatigue damage. Induced transient torque is first modeled. Fatigue study determines the local load size required to mitigate shaft torsional vibrations and avoid fatigue life loss during islanding. This is substituted in the torque function to obtain the critical torque. The risk of shaft fatigue damage is predicted by comparing the actual shaft torque with the critical torque. The turbine generator is shut down when the actual shaft torque during islanding exceeds the critical torque. Islanding on the local load is allowed when the actual shaft torque is smaller than the critical torque. The proposed method yields 0.011% shaft fatigue life loss under the most adverse islanding condition against 100% obtained with an online monitoring and protection system (OMPS).

Experimental, Numerical and Analytical Investigation of the Torsional Vibration Suppression of a Shaft with Multiple Optimal Undamped Absorbers

The aim of the present work is to study the suppressed torsional vibration of shafts, with a clamped boundary condition at either end, via single or multiple undamped absorbers. Structures with such features often suffer from failures (e.g. fatigue, wear) caused by excessive vibrations. The shaft considered is under the action of a harmonic point moment. A vibration design benchmark for torsional absorbers is presented. For both cases of the shaft with one and two absorbers, the variation of absorber parameters, including attaching position, moment of inertia and torsional stiffness, are investigated. The optimal values of the absorber control parameters are obtained. First, the governing equation for the torsional vibration of the shaft and its absorbers is derived in a dimensionless form. Next, the free and forced vibrations of the system are investigated and dimensionless natural frequencies are obtained. To absorb the identified natural frequencies, we compute the $${L}_{2}$$ norm of the angular displacement of the shaft at these frequencies and tune the parameters of the absorbers to minimize the norm. A detailed analytical solution framework for determining the torsional vibration response of a shaft equipped with torsional vibration absorbers is developed. Minimizing the established relations for the $${L}_{2}$$ norm of the shaft’s torsion is examined for a wide range of frequencies, as a criterion for determining its absorption frequency. Advantage of using two absorbers over a single absorber is highlighted. Validation of the analytical model is achieved by comparisons to both numerical and experimental results.

Reduction of Torsional Vibrations Excited by Electromechanical Interactions in More Electric Systems

This paper studies the excitation of torsional vibrations by electromechanical interaction after the connection of electrical loads. Electrical generation and power system in aircraft are becoming of key importance, especially considering the current roadmap for aerospace systems' electrification. However, since the drivetrain which links electrical generators to the main engine is relatively flexible in most aircraft structures, torsional vibrations can be excited by the sudden connection or disconnection of electrical loads, thus increasing the drivetrain's fatigue and reducing its reliability and lifetime. Because of the increased amounts of intermittent electrical loads on aircraft systems, which excite torsional vibrations through electromechanical interactions, the electrical load connections are investigated in this paper. Specifically, a method for reducing torsional vibrations in aircraft drivetrains is proposed to extend their lifespan. This method is applied directly to the load being connected and it proposes the connection of the electrical loads following a pulsating pattern, for which the pulse connection time is determined as a function of the drivetrain vibration modes. Simulations results show that the proposed method provides a significant reduction in the drivetrain shaft torsional vibrations. Experimental results validate the simulation data showing the benefits this method can provide in drivetrain reliability, weight reduction and cost.

Review of Current Research on Shaft Torsional Vibration of Ships

Review of Current Research on Shaft Torsional Vibration of Ships

Exact forced torsional vibration solution of a shaft with multiple discontinuities and arbitrary boundary conditions

In this paper, the method based on Laplace transform and Fourier transform and their inverse transforms is developed to give an exact solution to the forced torsional vibration of a shaft subjected to multiple inertias, multiple elastic supports, arbitrary boundary conditions and arbitrary excitation forces. Two simple cases are used to show in detail how this developed method can obtain an exact analytical solution to the forced torsional vibration of shaft and the results are compared with Eigenfunction Expansion Method and Finite Element Method (FEM) to demonstrate the accuracy and effectiveness of the developed method. Two more complex cases are investigated to further show the superiority of the developed method over FEM in highly efficient and accurate. Finally, using the developed method, the effects of parameters on forced torsional vibration response of shaft are discussed, including the stiffness, the location of elastic supports and the time interval of impact loading. The developed method can provide a reliable theoretical base not only for analysis and fault diagnosis of a shaft system in engineering signal testing projects but also for the verification of other numerical and analytical methods.

Диагностический контроль повреждений валопроводов турбоагрегатов по параметрам крутильных колебаний

The methods of solving the natural frequencies of torsional vibrations of power turbines shaft is done. Determination of shaft damage by changing the natural frequencies of torsional vibrations. A model of a shaft line with a circumferential crack has been created. The calculated torsional vibrations of the shaft line model with a circumferential crack are determined. A technique has been created for determining damage to the shaft line and the necessary measurement accuracy. Calculation of changes in the natural frequencies of torsional vibrations from the location of a circumferential crack. Shafting diagnostics for monitoring changes in the angles of static twisting

Effect of advanced injection angle on diesel engine shaft torsional vibration

In this article, a coupling model of shafting torsional vibration with advanced injection angle is proposed to study the effect of advanced injection angle on shaft torsional vibration. Using Simulink, a model shaft system of a 4190ZL_C medium-speed diesel engine is created to study the effect. The proposed coupling model, the traditional simulation method and the test are conducted on the torsional vibration of the 4190ZL_C medium-speed diesel engine, separately. The results show that the spectrum from the coupling vibration model is more abundant than from the traditional vibration model. Hence, considering the effect of advanced injection angle on shaft torsional vibration, the proposed coupling model can improve the modeling accuracy of shaft torsional vibration. It provides a new approach in engine design.

Ispitivanja ponašanja novog pogona nakon rekonstrukcije broda

The subject of this paper is a detailed qualitative analysis maneuvering and propulsion characteristics of a special purpose river vessel "KOZARA" River war flotillas of the Serbian Army, after reconstruction and modernization. With the modernization of the ship, among other things, the old propulsion group with a classic diesel engine propulsion was replaced by a new diesel electric propulsion. In order to assess the justification of this replacement from the aspect of expected improvements of shunting and propulsion characteristics of the ship, it was necessary to develop and implement a test program and compare the results with available test results of the ship with the old propulsion group in earlier periods of ship operation. The results of measuring the basic maneuvering characteristics: ship speed, stopping distance and turning circle diameter, as well as propulsion characteristics: propeller shaft power, axial and torsional vibrations after six years of operation of the new propulsion confirmed all the advantages of diesel electric propulsion over classic diesel engine propulsion. However, certain problems have been noticed in terms of maintaining this complex plant, and proposed measures to overcome them.

LIDAR-Assisted Wind Turbine Structural Load Reduction by Linear Single Model Predictive Control

LIght Detection And Ranging (LIDAR) sensors provide preview measurements of wind speed in front of the device. This preview may be used to improve important aspects of the operation of wind turbines, such as structural load, while limiting the control effort. In this paper, a single model-based predictive controller, taking advantage of the incoming wind in advance LIDAR measurements, is applied to the generator torque reference of the wind turbine in order to reduce torsional shaft vibrations. The controlled system is tested in a simulation environment that reproduces a set of gusts and turbulent wind fields above the nominal, where the structural loads are higher. The performances obtained are compared with the baseline and with those extracted from a single model predictive controller version without disturbance previsualization. Then, the effect of the coherence between the effective wind estimated from the LIDAR measurements and the real wind is considered. The practical implementation is demonstrated on real-time controller prototypes applied to a Hardware-In-the-Loop Simulator that reproduces realistically the dynamic behavior of the National Renewable Energy Laboratory 5 MW reference wind turbine.

Partial Frequency Assignment for Torsional Vibration Control of Complex Marine Propulsion Shafting Systems

With the large-scale and complexity of ship propulsion shafting, it is more difficult to analyze and control the torsional vibration of shafting. Therefore, an effective control method for the torsional vibration of shafting is of great significance in the field of ship engineering. The main strategy of torsional vibration control adopted in this paper is to keep the natural frequency of a shaft system away from the excitation frequency through structural modifications. In addition, because the basic parameters of much of the equipment in engineering applications cannot be changed, this restriction cannot be ignored when seeking solutions related to structural modifications. This paper studies the partial eigenvalue assignment for the torsional vibration control of complex ship propulsion shafting using the gradient flow method, which can shift a “dangerous” natural frequency to a safe value, while satisfying complex physical constraints. The models of a ship propulsion system and a diesel generator set are established to demonstrate several different desired modification schemes and constraint conditions in practice. In particular, close frequencies are shifted. The numerical simulation results demonstrate that it is effective and feasible to make a partial frequency assignment of torsional vibration, which provides a reliable approach for the control of torsional vibration for complex shaft systems in practical engineering.

Study of Torsional Vibrations of Turbomachine Shafts: Part 1. Algorithm Optimization for the Determination of the Parameters of Natural and Forced Torsional Vibrations of Shafts

This article is concerned with the issues of the development and optimization of algorithms for the control and calculation of the torsional vibration parameters of turbomachine shaftings. For the control of shaft torsional vibrations, the discrete phase method (DPM) is used. Depending on the natural shafting vibration forms determined by calculation, the necessary number of informational surfaces (control cross-sections) with labels, which are alternating crest–valley pairs (“gears”), or holes in special perforated disks, are made along its length. The DPM features that must be considered when using it for the control of the torsional vibration parameters are observed. It is shown that the said method can only determine the mean integral angular speed values at angles of rotation of a rotor between labels in informational cross-sections, but it does not provide the direct instantaneous measurement of the shaft torsional vibration parameters. The approximation of the instantaneous torsional vibration parameters by their mean integral values leads, in case when the fast Fourier transform (FFT) is used, to significant errors, especially in the higher harmonics range. In this case, the accuracy of the angular vibration spectrum determination depends significantly on the conversion order, i.e., on the number of labels in an informational cross-section in fact. It is noted that additional errors of the FFT algorithms are caused by the use of data with nonconstant discretization frequency (data on a variable grid). The problems of the DPM determination of the harmonic amplitudes multiple to the rotation frequency (order harmonics) are discussed. It is shown that they can be determined only using angular masks of informational cross-sections. In addition, angular masks that are in compliance with the established rules help to significantly decrease the label pitch difference effect on the calculation results for the torsional vibration parameters. The algorithms for the conversion of the measurement results are presented. The relations for the determination of the angular amplitudes (swirl angles) of a shaft in control cross-sections are obtained with consideration of the chosen number of labels and the torsional vibration frequency. Examples of the results for the numerical modeling and analysis of shaft torsional vibrations using the proposed algorithms are given.

Measurement and Evaluation of Shaft Torsional Vibrations Using Shaft Instantaneous Angular Velocity

Online evaluation of possible failures of a turbine is a key factor for a successful long-term turbine operation. Fluctuations of generator air-gap torque, caused for example by nonstationary conditions of electrical power grid, influence shaft torsional vibrations as well as rotating blades vibrations. Symptoms of shaft torsional vibrations are not measurable by normally used relative shaft vibrations sensors, so special measurement must be used. The direct consequence of shaft torsional vibrations is local acceleration or deceleration of shaft circumference when it is measured by a stationary sensor. This paper deals with a measurement method using an optical probe measuring the passage of black and white stripes of a zebra tape, which is stuck on the rotor. The shaft torsional vibrations manifest themselves as a phase modulation of the optical probe output signal, so the sampling rate influence the achievable resolution of the calculated shaft vibrations. The presented method for the calculation of the shaft torsional vibrations is based on the evaluation of shaft instantaneous angular velocity. The advantage of this method is a direct compensation of possible nonregular geometry of the zebra tape. The analysis of shaft torsional vibrations evaluation using this method is supplemented by two case studies from the authors' current work.