Shaft Torsional Vibration Research Articles

Mode analysis of structures using the Fourier p-element method

The Fourier p-element method is an improvement to the finite element method, and is particularly suitable for vibration analysis due to the well-behaved Fourier series. In this paper, an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem. Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration, the plate in-plane vibration and annular plate flexural vibration modes, respectively. The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation, especially for higher mode analysis.

Experiments on the extraction of blade vibration signature from the shaft torsional vibration signals

This paper presents experiment results that examine the validity of extracting blade vibration signature from the shaft torsional vibration signals. A special test rig was designed and manufactured for this objective. A set of strain gages were bonded to the shaft and to the blades to measure the shaft twisting and blade bending deformations respectively. A controlled frequency exciter excited the blade vibration. The shaft torsional and blade bending vibration signals were simultaneously recorded and presented in the time and frequency domains. The blade bending vibration frequencies appeared dominantly in the shaft torsional vibration signals for all blade vibration frequencies up to 100Hz. For frequencies higher than 100Hz, less sensitivity of the torsional vibration to blade vibration was observed.

Unbalanced Operation of HVDC Converters in Asynchronous Linksin Torsional Stressing of Turbine-Generator Shafts

This article analyzes the impact of unbalanced and balancedoperation of HVDC link rectifier bridges on ripple current superimposed on the direct current in asynchronous links in the excitation of torsional vibrations in steam turbine-generator-exciter shafts. The effect of nonideal conditions such as unbalanced rectifier ac supply voltage, unbalanced phase inductance and transformer tappings, and firing errors on the spectrum of dc harmonic voltages compared with the ideal case is discussed. These voltages give rise to dc harmonic currents at the rectifier that may excite sympathetic shaft torsional vibrations in the machine shaft.First, frequencies at which sympathetic shaft torsional vibrations would be excited by modulation product harmonic currents due tounbalanced and balanced operation of 50 Hz/50 Hz asynchronous links as a function of deviation in the system frequency are illustrated. Amplitude of shaft torsional torque due to resonant torque excitation due to harmonic current injected into the ac system by the inverter is then discussed. The article thenconsiders how the steady torque excitation depends on the noncharacteristic harmonic current that is injected into the ac system by the inverter. Tables and graphs are presented to illustrate the significance of bridge unbalances on rectifier harmonic ripple voltage (and hence on the associated currents thatare superimposed on the HVDC line current at the rectifier and subsequently at the inverter), which result in torsional torque in turbine-generator shafts. The relative amplitude of noncharacteristic currents injected into the ac system by the inverter operating unbalanced and balanced is indicated. Both 6- and 12-pulse bridges are analyzed.

On the experimental validation of a non-linear shaft damping model

This paper presents an experimental validation of a proposed non-linear damping model for shaft torsional vibration studies, compared to the linear viscous damping model. Nine different shaft configurations were used. The deflection of each shaft exhibiting free vibration was measured for a period of one minute and the signal component at the natural frequency of torsion was found. The experiments showed that the internal shaft damping was highly non-linear. The damping tended to be not only stiffness related but also depended on the material used.

Optimum control to a partially controlled turbogenerator shaft torsional vibration system

The optimal control to a partially controlled turbogenerator shaft torsional vibration system is investigated. The principle of input feedforward control is presented to achieve the minimum of the average vibration energy in a system,and the optimal control matrix of the system is derived. A turbogenerator shaft system is taken as an example to simulate the optimal control process of the torsional vibration. Results from this simulation indicate that the vibration can be effectively controlled by a partial control strategy.

Reduced-Order Nonlinear Dynamic Model of Coupled Shaft-Torsional and Blade-Bending Vibrations in Rotors

In this study, a reduced-order nonlinear dynamic model for shaft-disk-blade unit is developed. The multibody dynamic approach with the small deformation theory for both blade-bending and shaft-torsional deformations is adopted. The equations of motion are developed using Lagrange’s equation in conjunction with the assumed modes method (AMM) for approximating the blade transverse deflection. The model showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearity, modal coupling, stiffening, softening, and parametric excitations. The model is suitable for extensive parametric studies for predesign stage purposes as well as for diagnostics of rotor malfunctions, when blade and shaft torsional vibration interaction is suspected.

On the repeated natural frequencies for torsional vibration of shafts

To investigate the repeated frequency condition (RFC) for torsional vibration of shafts' system, the transfer matrix method was adopted. Firstly, the transfer relationship from the boundary to engaging disks of double shafts' system (DSS) was constructed. Secondly, the RFC of DSS was deduced out and the methods to select mode shape were presented. Finally, the relationship was extended to multilevel transmission system (MTS), and the RFC of this system was explored. The conclusions is this: 1) the necessary RFC requires the existence of joint engaging couple (JEC); 2) for DSS, the sufficient is the number of boundary transfer factors (fB) larger than 2; 3) the whole system can be split into independent groups, the total multiplicity is the sum of independent solution number of every group, the latter is the number of independent fB=0 inside the group minus 1.

Performance of HVDC Converters in Enhancing Transient Stability of Power Systems and in the Torsional Stressing of Generator Shafts Due to Balanced and Unbalanced Operation of the Rectifier

This paper examines performance of HVDC converters with respect to real and reactive power at the inverter or rectifier following a command for power injected into or taken from the AC system to enhance power system stability. It also considers the effect balanced and unbalanced operation of inverters in asynchronous links has on torsional stressing of large turbine-generator shafts. First a 6-pulse bridge is modeledto determine characteristics for reactive power at both the inverter and rectifier as a function of AC power at the inverter or rectifier. Responses for real and reactive power following transient commands for AC real power are determined for a range of commands for real power to enhance transient performance of the power system. The characteristics relate to a link with typical parameters rated at 200 MW ~ 1000 MW. Performance of a 12-pulse bridge configuration that was modeled is then summarized. Noncharacteristic harmonic currents injected by the inverter into the AC system due to balanced and unbalanced operation of the rectifier in an asynchronous link is then reviewed. Excitation of turbine-generator shaft torsional vibrations by noncharacteristic currents injected into the AC system on account of balanced and unbalanced operation of the rectifier is then discussed.

Calculation and Measurement of Torsional Vibrations in Large Steam Turbosets – New Technique

ABB has been carrying out torsional vibration test on steam turbine sets for many years, with sizes ranging from 350MW coal fired steam turbines to 1000MW nuclear steam turbines. Rated speeds have been 1,800 rpm and 3600 rpm. Torsional shaft vibrations are excited in large steam turbine generators sets by electrical disturbance torques occurring in the active part of the generators. Due to the low torsional damping of the shaft trains, resonance can cause high torsional vibration amplitudes. Some thermal power plant operators require experimental verification of the natural torsional shaft frequencies. ABB has developed a new measurement technique which allows torsional vibration to be measured in a selected measurement plane along the shaft. With today's highly sensitive sensors and modern measurement and data analysis equipment, the excitation due to normal random disturbances in the electrical grid provides sufficiently good results. All natural torsional frequencies in the range of interest are obtained with an accuracy of ± 0.2 Hz and identified using the calculated natural frequencies. The new measurement technique, places no restrictions on normal power plant operation.

TORQUES IN MULTI-MACHINE GENERATOR SHAFTS DUE TO HVOC RECTIFIER RIPPLE CURRENTS SUPERIMPOSED ON THE DC CURRENT IN ASYNCHRONOUS LINKS

ABSTRACT This paper analyses torsional vibrations in steam turbine-generator-exciter shafts of machines in multi-machine power systems in close proximity to the inverter station due to rectifier ripple currents superimposed on the DC current in asynchronous DC links. It extends earlier work to include an in-depth analysis of system scaling factors for modulation product harmonic currents impressed on generators not examined in the literature heretofore by an inverter in an asynchronous link. Frequency at which shaft torsional vibrations would be excited by modulation product harmonics in 50Hz/50Hz asynchronous links as a function of deviation in system frequency is first reviewed. Amplitude of shaft torque due to steady resonant torque excitation which is a function of initial rate of increase of vibration at adjacent cells where the steady resonant torque excitation is applied, the time constant for decay of the vibration and stiffness between adjacent cells is then discussed. The paper then shows that torque in shafts of machines in multi-machine networks may be estimated by proportioning HVDC Link inverter modulation product harmonic disturbance current appropriately to each machine at risk. A three phase fault studies programme to proportion converter harmonic current to each machine is discussed. System scaling factors are evaluated for different scenarios : (i) neglecting system loads, (ii) using a lumped load at the inverter, and (iii) employing distributed system loads for (a) constant impedance loads and (b) subtransient reactance dynamic loads. The effect of tappings of transformers is also discussed. On the basis of these evaluations, generators are identified which are most at risk. Torques in shafts of the machines in Ireland due to rectifier ripple currents superimposed on the DC current of the proposed North Wales/Ireland Link are then analysed and discussed.

Monitoring Torsional Vibrations of Electro-mechanical Systems Using Stator Currents

A method is proposed to detect shaft torsional vibrations in AC motors and generators from their stator currents. This is achieved by extracting current components at specific frequencies which are the modulation products of the power system frequency and the vibrating frequency. A general closed form proof of this principle is given for both induction and synchronous machines, and the principle is verified quantitatively by digital simulation and experimental results. The effect of the machine operating point is also investigated. The method is applicable to torsional vibrations induced by different causes. When the oscillating torque is developing and the measured stator current is nonstationary, the Wavelet Transform can be used to extend the application of the proposed method to transient conditions.

Milling Cutter Wear Monitoring Using Spindle Shaft Vibration

With the intent of continuously monitoring cutting tool condition in intermittent machining operations in a benign manner, a noncontacting measurement system was assembled to measure spindle shaft torsional vibration. Spindle vibration was measured using an optical system and analysis of it in the frequency domain resulted in a measure of spectral power which corresponded to amount of cutter wear.

TORQUES IN TURBINE-GENERATOR-EXCITER SHAFTS DUE TO DC CURRENTS IN ASYNCHRONOUS HVDC LINKS

ABSTRACT This paper makes an indepth analysis of excitation of shaft torsional vibrations in steam turbine-generator-exciter shafts by variable-frequency ripple currents superimposed on DC currents in asynchronous Links. First, frequencies at which sympathetic shaft torsional vibrations would be excited by modulation product harmonics in 50Hz/50Hz asynchronous Links as a function of deviation in system frequency is illustrated. Then steady-state torque excitation due to injected harmonic stator currents due to the DC ripple currents is analysed. Time constants for decay of shaft torsional vibrations based on electrical and steam viscous damping for generators operating at full-load and no-load for reduced shaft models which are used with the torque excitation to give amplitude of modal torque are also evaluated. Amplitude of shaft torque for a given torque excitation using reduced shaft models is illustated. The effect of generator load on shaft torque which results from resonant excitation for reduced shaft models is also illustrated. Typical shaft torques for generators connected close to HVDC Link inverters which results from resonant excitation by non-characteristic currents at full-load and no-load are also illustrated. Shaft torques in multi-machine networks are estimated by proportioning HVDC Link disturbance current to each machine at risk using system network data, generator data, fault analysis data and load flow data, considering the frequency dependence of the system parameters. 660MW andlOOOMWmachines are considered in the analyses that are made.

Bending vibration measurement on rotors by laser vibrometry

A new technique is proposed for noncontact measurement of bending vibration directly from a rotating component. This notoriously difficult and previously unattained measurement is a further development of laser Doppler vibrometry. Simultaneously the technique provides an accurate measure of shaft torsional vibration in situations in which measurements of torsional vibration have shown significant sensitivity to bending vibration. Experimental results validate the theory developed, and a conservative estimate of the minimum measurable bending vibration is made at 20 millidegrees.

Active Vibration Control of 2 Stand Skin Pass Mill by Observer

Skin pass mill is the equipment for the thermal-refing metal rolling of stainless plants, etc. Usually, rolling mill is elastically coupled with the motor driving a rolling mill. Shaft torsional vibration is often generated, when we attempt to get the high control performance of the rolling mill. Such a vibration causes degradation of product quality. In this paper, we propose a method of suppressing the vibrations of steel plate tension using Observer. This method has the excellent characteristic that the vibration-suppressive system is easily constructed just by adding the observer to the conventional control system. This is detailed hereunder.

Torsional fatigue of turbine-generator shafts owing to network faults

Many studies have been made of the fatigue processes resulting from cyclic stress which metal for making turbine generator shafts has to bear. In the paper a modified dynamic program written on the basis of the theories is used to simulate the shaft torsional vibrations resulting from four types of network fault. The purpose is to study the influence of a safety factor, selected in the first stage of design, on the damage accumulated following worst-case fault clearance and synchronising of the simulated machines.

Analysis of variable-frequency currents superimposed on DC currents in asynchronous HVDC links in stressing turbine-generator-exciter shafts

The paper makes an indepth analysis of the excitation of shaft torsional vibrations in steam turbine-generator-exciter shafts by variable-frequency ripple currents superimposed on DC currents in asynchronous links using the finite element and reduced models of the machine shafts. Frequencies at which sympathetic shaft torsional vibrations would be excited by modulation product harmonics in 50 Hz/50 Hz and 50 Hz/60 Hz asynchronous links as a function of deviation in system frequency are illustrated. It is shown that amplitude of shaft torque due to steady resonant torque excitation is a function of initial rate of increase of vibrations at adjacent cells, the time constant for decay of the vibration, and stiffness between adjacent shaft cells.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Power links with Ireland-excitation of turbine-generator shaft torsional vibrations by variable frequency currents superimposed on DC currents in asynchronous HVDC links

The paper describes an in-depth analysis of excitation of shaft torsional vibrations in steam-turbine-generator-exciter shafts in close proximity to HVDC converter stations by variable-frequency ripple currents superimposed on the DC currents in asynchronous links. It extends earlier work to include an in depth analysis of system scaling factors for harmonic currents impressed on generators in Northern Ireland by an inverter and to investigate the phenomena for possible torsional vibrations in the generators by the link. It is concluded that variable-frequency ripple currents superimposed on the DC current in asynchronous links can excite sympathetic torsional vibrations in turbine-generator-exciter shafts. Subtransient generator reactances may be used to approximately proportion injected harmonic current to each machine of a multi-machine network. Very small noncharacteristic currents could result in serious damage to the machine although possibility of two power systems operating with fixed deviation in system frequencies long enough for the vibrations to build up is remote. Studies should be undertaken as routine on all machines in close proximity to HVDC converter stations to ascertain whether or not the machines are at risk.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Active vibration control of a motor system by using H∞ control theory

AbstractThis paper considers the vibration control of a motor system which has a motor and a load connected with a flexible shaft. However, this system often generates a shaft torsional vibration. Traditional methods of treating this problem to adjust the PID controller so that the closed‐loop frequency response is slower than that of the vibration mode. On the other hand, one method has already been proposed in which the vibration is suppressed by a disturbance observer.This paper proposes a new approach based on H∞ control theory. For comparison, a PI control system based on classical control theory also is constructed.The results of several experiments show that compared with the PI control system, the H∞ control system is effective in suppressing the vibration. Further, the H∞ controller obtained in the study consists of a PI controller and a series compensator that functions as an active vibration controller.

Stressing of turbine-generator-exciter shafts by variable-frequency currents superimposed on DC currents in asynchronous HVDC links and following disturbances at converter stations

Ripple currents on the DC side of both HVDC synchronous and asynchronous links together with cleared HVDC and AC system disturbances can excite in some circumstances onerous torsional vibrations in large steam generator shafts. The problem has assumed importance in recent months on account of the HVDC link between Scotland and Northern Ireland going ahead, on account of the proposed Eire/Wales link, and because AC/DC/AC couplers are to be installed extensively to interconnect the East and West European grid systems. This paper discusses and analyses excitation of shaft torsional vibrations in steam turbine-generator-exciter shafts in close proximity to HVDC power converter substations by: (i) variable-frequency ripple currents superimposed on the DC currents in asynchronous links; and (ii) disturbances at bi-polar converter stations. Detailed simulation of the HVDC converter and generator is necessary for precise assessments of shaft torsional response following HVDC converter station faults. 500 MW, 660 MW, 1000 MW and 1300 MW machines are considered in the analyses that are made. >