Shaft Torsional Vibration Research Articles

Torsional vibrations of shafts of mechanical systems

The aim of the research is to compare the calculated dependencies for determining the equivalent rigidity of a mechanical system and to come to an agreement on the methods of compiling dynamic models for systems with elastic reducer couplings in applied and classical oscillation theories. As a result of the analysis, it was revealed that most of the damage in the mechanisms and their details is due to the appearance of oscillations due to the dynamic impact of various factors: shock and alternating loads, unbalanced parts of machines, etc. Therefore, the designer at the design stage, and the engineer in the process of operation should provide the possibility of regulating the oscillatory processes both in details and machines by means of creating rational designs, as well as the use of special devices such as vibration dampers, various vibrators with optimal characteristics. A method is proposed for deriving a formula for determining the equivalent stiffness of a double-mass oscillating system of a multistage reducer with elastic reducer links without taking into account the internal losses and inertia of its elements, which gives a result completely coinciding with the result obtained by the classical theory of small mechanical oscillations and allows eliminating formulas for reducing the moments of inertia of the flywheel masses and the stiffness of the shafts.

Stability Analysis of Rotating Blade Vibrations Using Lyapunov Exponents

This paper presents an analysis of the vibration stability of a rotating blade due to shaft torsional vibration excitation. The governing equation adopted in the study is a Hill’s type linear second order ordinary differential equation with multiple harmonically variable coefficient terms. The differential equation of the system is rewritten as two coupled first order ordinary differential equations. The stable and unstable regions are determined by the Lyapunov characteristics exponents on parameter space (grid) relating to the rotor speed, the torsional vibration excitation frequency and the blade natural frequency. The results are contrasted to those obtained by the strained parameter method (a perturbation technique), an excellent match is observed for small torsional vibration amplitudes .

Magnetostrictive patch sensor system for battery-less real-time measurement of torsional vibrations of rotating shafts

Real-time uninterrupted measurement for torsional vibrations of rotating shafts is crucial for permanent health monitoring. So far, strain gauge systems with telemetry units have been used for real-time monitoring. However, they have a critical disadvantage in that shaft operations must be stopped intermittently to replace telemetry unit batteries. To find an alternative method to carry out battery-less real-time measurement for torsional vibrations of rotating shafts, a magnetostrictive patch sensor system was proposed in the present study. Since the proposed sensor does not use any powered telemetry system, no battery is needed and thus there is no need to stop rotating shafts for battery replacement. The proposed sensor consists of magnetostrictive patches and small magnets tightly bonded onto a shaft. A solenoid coil is placed around the shaft to convert magnetostrictive patch deformation by shaft torsional vibration into electric voltage output. For sensor design and characterization, investigations were performed in a laboratory on relatively small-sized stationary solid shaft. A magnetostrictive patch sensor system was then designed and installed on a large rotating propulsion shaft of an LPG carrier ship in operation. Vibration signals were measured using the proposed sensor system and compared to those measured with a telemetry unit-equipped strain gauge system.

Torsional vibration characteristics analysis of DFIG‐based wind farm and its equivalent model

As large‐scale wind farms (WFs) are integrated with the power grid, the interaction between the WF and the grid may excite torsional vibration of the shaft of the wind turbine. To study the shaft's torsional vibration characteristics of a doubly fed induction generator (DFIG)‐based WF, a detailed small‐signal model of DFIG is established first. Then the small‐signal model for a WF composed of multiple DFIGs is developed on the basis of the single‐machine model. Modal analysis is employed to investigate the torsional vibration characteristics of a WF made up of several identical DFIGs, whose accuracy is also demonstrated through time‐domain simulation. To simplify the torsional vibration analysis for the DFIG‐based WF, a reduced‐order equivalent model is proposed. The results obtained from modal analysis show that the equivalent model not only precisely maintains all the torsional vibration modes of the original small‐signal model but also greatly reduces the computation complexity. With the equivalent model, the ‘curse of dimensionality’ problem is solved in torsional vibration analysis for large WFs, which is of great help in the design of further damping schemes. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Torsional vibration characteristic study of the grid-connected DFIG wind turbine

This paper studies the torsional vibration characteristics of the grid-connected doubly-fed induction generator (DFIG) wind turbine by small signal analysis method. Firstly a detailed small-signal stability union model of the grid-connected DFIG wind turbine is developed, including the mechanical system and electrical system. To study the dynamic characteristic of the blade, gearbox, low speed and high speed shafts, a three mass shaft model for the mechanical system is adopted. At the same time, small signal models of DFIG, the voltage source converter (VSC) and the transmission line of the electrical system are developed respectively. Then, through calculating the eigenvalues of the state matrix A and the corresponding participation factors, the modal analysis is conducted in the shaft torsional vibration issues. And the impact of the system parameters including the series compensation capacitor, the flat-wave reactor, the PI parameters, especially the speed controller of generator rotor on shaft torsional vibration are discussed. The results show that the speed controller strengthens association between the mechanical system and the electrical system, and also produces a low-frequency oscillation mode.

Resonance of torsional vibrations of centrifugal pump shafts due to cavitation erosion of pump impellers

Abstract Selected results were gathered during investigation of centrifugal pumps used in a sea water cooling system of one of Diesel power stations are presented in the paper. The main goal of research was to explain the reason of occurring fractures in pump shafts. The investigation has shown that the fractures were caused mainly by the resonance between pump shaft torsional natural vibrations and those following from the pressure fluctuations related to the frequency of the shaft rotational speed and the number of impeller blades. The resonance occurred as a result of intense erosion of pump impellers derived mainly from cavitation phenomenon that caused about 20% of the impeller mass decrease. The scope of the investigation has covered among others: erosion damage recognition, tests of the investigated pumps operating conditions, spectral analysis of pressure fluctuation generated by the pump blade system as well as strength analysis of the pump shaft and the frequencies of its natural bending and torsional vibrations.

Numerical and experimental investigation of the torsional stiffness of flexible disc couplings

Disc couplings are widely used in compressors, gas turbines, and aerospace applications because of their flexibility and their consequent ability to compensate in almost all directions. The torsional stiffness of disc coupling has a great influence on shaft torsional vibration, and in many applications low-order torsional resonance may occur due to insufficient stiffness in the disc coupling. Investigation of the factors influencing the torsional stiffness of disc coupling will help to improve the design and control of shaft torsional vibration. In this paper, a 3D finite element (FE) model was built to estimate the stiffness of a disc coupling, taking the behavior of friction and contact into consideration. Based on this model, the curve of torque vs. angular displacement was obtained by applying a series of torsional load steps to the coupling. The effects of diaphragm shape, bolt preload, and fluctuation of torque were evaluated. A test rig was established to validate the simulated results. Both the simulated and experimental results demonstrated a strong nonlinear relationship between the torque and angular displacement during both the loading and unloading processes. The results also showed that the bending and inclining of flanges and diaphragms were mainly responsible for the varied stiffness of the disc coupling. In addition, load fluctuation, bolt preload, and shape of diaphragms could lead to variation in the stiffness of disc couplings.

Study on Vibration of Marine Diesel-Electric Hybrid Propulsion System

This study analyzes the characteristics of hybrid propulsion shafting and builds mathematical models and vibration equations of shafting using the lumped parameter method. Main focus is on the asymmetric double diesel propulsion shafting operation process and the impact of the phase angle and motor excitation on torsional vibration of shafting. Model result is validated by testing results conducted on double diesel propulsion shafting bench. Mathematical model and model-building methods of shafting are correct.

Structural Modifications for Torsional Vibration Control of Shafting Systems Based on Torsional Receptances

Torsional vibration of shafts is a very important problem in engineering, in particular in ship engines and aeroengines. Due to their high levels of integration and complexity, it is hard to get their accurate structural data or accurate modal data. This lack of data is unhelpful to vibration control in the form of structural modifications. Besides, many parts in shaft systems are not allowed to be modified such as rotary inertia of a pump or an engine, which is designed for achieving certain functions. This paper presents a strategy for torsional vibration control of shaft systems in the form of structural modifications based on receptances, which does not need analytical or modal models of the systems under investigation. It only needs the torsional receptances of the system, which can be obtained by testing simple auxiliary structure attached to relevant locations of the shaft system and using the finite element model (FEM) of the simple structure. An optimization problem is constructed to determine the required structural modifications, based on the actual requirements of modal frequencies and mode shapes. A numerical experiment is set up and the influence of several system parameters is analysed. Several scenarios of constraints in practice are considered. The numerical simulation results demonstrate the effectiveness of this method and its feasibility in solving torsional vibration problems in practice.

Online Identification and Verification of the Elastic Coupling Torsional Stiffness

To analyze the torsional vibration of a diesel engine shaft, the torsional stiffness of the flexible coupling is a key kinetic parameter. Since the material properties of the elastic element of the coupling might change after a long-time operation due to the severe working environment or improper use and the variation of such properties will change dynamic feature of the coupling, it will cause a relative large calculation error of torsional vibration to the shaft system. Moreover, the torsional stiffness of the elastic coupling is difficult to be determined, and it is inappropriate to measure this parameter by disassembling the power unit while it is under normal operation. To solve these problems, this paper comes up with a method which combines the torsional vibration test with the calculation of the diesel shafting and uses the inherent characteristics of shaft torsional vibration to identify the dynamic stiffness of the elastic coupling without disassembling the unit. Analysis results show that it is reasonable and feasible to identify the elastic coupling dynamic torsional stiffness with this method and the identified stiffness is accurate. Besides, this method provides a convenient and practical approach to examine the dynamic behavior of the long running elastic coupling.

Parametric study to identify the cause of high torsional vibration of the propulsion shaft in the ship

AbstractSince torsional vibration can lead to fatigue failure of the propulsion shaft in a ship, it should be restricted from the first step of the design through calculation and verified at the sea trial test step through measurement. Considering that the torsional vibration of the shaft is a system characteristic, it is strongly related to the vibration modes at the natural frequencies of the shaft. Therefore, the actual torsional vibration problem can occur due to the variation of parameters such as those of the vibration system, including mass of inertia, damping, and stiffness, which differ from the design.In this research, the root cause analysis of the high torsional vibration which occurred in the actual ship is described through a parametric study performed using numerical analysis. Parameters that can increase the torsional vibration of the propulsion shaft are selected, including coupling stiffness, shaft stiffness, coupling damping, and shaft damping. Through the torsional vibration calculations with variations of these parameters, the extent of the effect of these parameters on the torsional vibration of the propulsion shaft is investigated and the cause of the increased torsional vibration is identified.

Analysis of Turbine Generator Shaft Torsional Vibration Caused by Self‐Commutated Converters

SUMMARYThis paper presents a simple analysis tool for torsional vibration of the rotor shaft of a turbine generator which is interconnected with a power system with self‐commutated converters. The evaluation is based on analysis of measurement data in the field and instantaneous value‐based power system simulation. A number of power converters with large capacity are installed in industrial power systems. Especially, interharmonics originating from self‐commutated converters cause torsional vibration at the rotor shaft of rotating machines. The interaction between rotating machines and converters is known as sub‐synchronous torsional interaction. The resonance between interharmonics from converters and the natural frequency of the rotor shaft causes large torsional vibrations, leading to shaft damage. In this paper, the influence of interharmonics on turbine generators is investigated. If there were air gap torque fluctuations with a frequency near the natural frequency caused by interharmonics, which have frequencies below 100 Hz of the sideband wave caused by asynchronous pulse width modulation, the rotor shaft may be damaged by the torsional vibration. In this paper, the emerging condition of the torsional vibration and the impact on the generator are investigated.

Small-signal Modeling and Modal Analysis of Wind Turbine Based on Three-mass Shaft Model

—One critical task in wind turbine shaft torsional vibration study involves the modeling of a wind turbine and power grid. With a focus on the mechanical rotational system of wind turbine, this article provides a three-mass shaft model upon which one wind turbine to infinite bus model can be developed. The model, based on small-signal stability analysis, is used to study the wind turbine shaft torsional vibration. For this reason, this article concentrates on the union model of stall wind turbine and power grid. The small-signal stability model includes the mechanical system and electrical system. Data for the turbine's blades and shaft as well as electrical generator are given to allow replication of the model in its entirety. Each of the component blocks of the wind turbine and power grid is modeled separately so that one can easily expand and modify the model to simulate variable-speed wind turbines or multi-turbines system to suit their needs. This is then followed by a case study that explains how the small-signal stability model can be used to study wind turbine shaft torsional vibration issues. Results obtained from the case study show that the model performs as expected.

Experimental study of coupled shaft bending - blade umbrella mode vibration of a turbine rotor model

This paper describes an experimental study on the characteristics of blade-shaft coupled bending vibration of a rotor system with a bladed disk. In a rotor with relatively long blades such as low-pressure steam turbines, the coupled vibration of shaft torsional and blade bending vibration with nodal diameter of zero (umbrella mode) must be considered in terms of reliability. The bending-torsion coupled resonance of rotor systems occurs under specific conditions, when the rotational speed is equal to the sum and/or difference of the bending natural frequency and torsional natural frequency. In this study, a test apparatus with a flexible rotor equipped with a bladed disk which simulates actual turbine blade structure was developed to study the coupled vibration characteristics of shaft bending and blade (κ=0). The rotor was excited with an active magnetic bearing for lateral direction and a servomotor for torsional direction. Resonance of a bladed disk with nodal diameter (κ) of zero, which was coupled with the rotor’s torsional vibration, occurred under the above specific condition with lateral excitation force where frequency was equal to the rotor’s bending natural frequency. In addition, resonance of rotor bending vibration was found when the rotor was excited in torsional direction of its natural frequency.

Analysis of Turbine Generator Shaft Torsional Vibration Caused by Self-commutated Converters

SUMMARY This paper presents a simple analysis tool for torsional vibration of the rotor shaft of a turbine generator which is interconnected with a power system with self-commutated converters. The evaluation is based on analysis of measurement data in the field and instantaneous value-based power system simulation. A number of power converters with large capacity are installed in industrial power systems. Especially, interharmonics originating from self-commutated converters cause torsional vibration at the rotor shaft of rotating machines. The interaction between rotating machines and converters is known as sub-synchronous torsional interaction. The resonance between interharmonics from converters and the natural frequency of the rotor shaft causes large torsional vibrations, leading to shaft damage. In this paper, the influence of interharmonics on turbine generators is investigated. If there were air gap torque fluctuations with a frequency near the natural frequency caused by interharmonics, which have frequencies below 100 Hz of the sideband wave caused by asynchronous pulse width modulation, the rotor shaft may be damaged by the torsional vibration. In this paper, the emerging condition of the torsional vibration and the impact on the generator are investigated.

Small Signal Stability Analysis of Wind Turbine for Shaft Torsional Vibration Studies

One critical task in wind turbine shaft torsional vibration study involves the modelling of wind turbine and power grid. Focus on the mechanical rotational system of wind turbine, this paper provides three-mass shaft model upon which one wind turbine to infinite bus model can be developed. The model based on small signal stability analysis is used to study the wind turbine shaft torsional vibration. For this reason, this paper concentrates on the union model of stall wind turbine and power grid. The small-signal stability model includes the mechanical system and electrical system. Each of the component-blocks of the wind turbine and power grid is modelled separately so that one can easily expand and modify the model to suit their needs. Then, this is followed by one case study to explain how the small-signal stability model can be used to study wind turbine shaft torsional vibration issues.

PMSG 풍력발전시스템에서 전원 저전압 발생시 비틀림 진동 동특성 시뮬레이션 및 실험

A wind generator system model includes wind model, rotor dynamics, synchronous generator, power converter, distribution line and infinite bus. This paper investigates the low-Voltage Ride-Through capability of PMSG wind turbine in a variable speed. The drive train of a wind turbine on 2-mass modeling can observe the shaft torsional vibration when the low-voltage occur. To reduce the torsional vibration when the low-voltage occur, this paper designs suppression control algorithm of the torsional vibration and implements simulation. The simulation based on MATLAB/SIMULINK has validated at the transient state of the PMSG and an experiment using 3kW simulator has validated the LVRT control.

Shaft instantaneous angular speed for blade vibration in rotating machine

Reliable blade health monitoring (BHM) in rotating machines like steam turbines and gas turbines, is a topic of research since decades to reduce machine down time, maintenance costs and to maintain the overall safety. Transverse blade vibration is often transmitted to the shaft as torsional vibration. The shaft instantaneous angular speed (IAS) is nothing but the representing the shaft torsional vibration. Hence the shaft IAS has been extracted from the measured encoder data during machine run-up to understand the blade vibration and to explore the possibility of reliable assessment of blade health. A number of experiments on an experimental rig with a bladed disk were conducted with healthy but mistuned blades and with different faults simulation in the blades. The measured shaft torsional vibration shows a distinct difference between the healthy and the faulty blade conditions. Hence, the observations are useful for the BHM in future. The paper presents the experimental setup, simulation of blade faults, experiments conducted, observations and results.

Approximate Galerkin method applied to an analysis of vibration of continuous mechanical systems

AbstractPaper presents fundamental assumptions of the approximate Galerkin method application in order to vibration analysis of continuous mechanical systems with different form of vibration and different boundary conditions. Flexural vibration of beams, longitudinal vibration of rods and torsional vibration of shafts with all possible ways of fixing were considered. Analyzed mechanical systems were treated as subsystems of mechatronic systems with piezoelectric transducers. This work was done as an introduction to the analysis of mechatronic systems with piezoelectric transducers used as actuators or passive vibration dampers [1–3]. It is impossible to use an exact Fourier method in this case. This is the reason why the approximate Galerkin method was chosen and analysis of its exactness was done as a first step of this work. Dynamic flexibilities of considered mechanical systems were calculated twice, using exact and approximate methods. Obtained results were juxtaposed and it was proved that in some cases the approximate method should be corrected while in the other it is precise enough. A correction method was proposed and it was assumed that the approximate method can be used in mechatronic systems analysis. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Fiber Measuring Method for Rotating Parts Comprehensive Vibration

Light propagation in the air is easily affected by the environment. Shaft bending vibration and torsional vibration are needed to be measured at the same time. The different vibration state are coupled each other. For these reasons, it is necessary to design the optical fiber laser Doppler measurement system and develop the integrated optical fiber system, which is in favor of various vibration modes decoupling and can improve the signal-to-noise ratio. The double parallel beam differential scheme is adopted in the torsional vibration measurement, which the light exposed in the air is coupled into the optical fiber. The optical fiber heterodyne Doppler interference measuring method is adopted in the bending vibration measurement. The laser Doppler vibration measurement technology is applied to a rotating shaft vibration measurement. Comprehensive measuring technology is developed, which can simultaneously measure bending vibration, torsional vibration and the rotation speed of shaft.