Shaft Torsional Vibration Research Articles

Simulation Analysis of the Vibration Characteristics of the Parallel Hybrid Shaft System

Abstract. The multi-body dynamics simulation model of the hybrid system with a flexible shaft was established through rationally simplifying the system structure of a parallel hybrid system, assembling the flexible shaft, pulley, piston assembly , rod assembly and the rotor shaft according to the actual constraints, and adding the appropriate connections. The engine cylinder pressure reconstruction model and the motor vector control model were established in MATLAB as system shafting incentives. The simulation analysis of the dynamic characteristics of the system shafting was carried out in the boost mode of the hybrid system. The results show that: the shaft torsional vibration and bending vibration have happened when the hybrid system is running, and the engine cylinder pressure change was the main factor which caused the shaft vibration. Torsional vibration occurs mainly near the even multiple of the frequency of the shaft rotational frequency, and the torsional amplitude decreases gradually with the increase of resonance frequency; radial vibration occurs mainly in the range of 0 to 3 times the rotational frequency.

Tuned viscoelastic damper for hollow shaft's torsional vibration control

This paper presents a piece of work on hollow shaft vibration control using viscoelastic materials in torsional directions. Columned viscoelastic damper is designed as a capsule containing viscoelastic material and elastic material, the outer layer of the capsule is viscoelastic material, the inner layer is elastic material. The damper is mounted somehow into the void of the shaft. When the shaft is vibrating, the damper can provide damping for the passive control of torsional vibrations. The viscoelastic damper is designed based on the principle of dynamic absorber in theoretically. When the damper has been designed, the frequency response functions of the damping system include damper and shaft can be calculated by solving the dynamic equations, then, the damping effect of the viscoelastic damper on the hollow shaft can be obtained. It's shown that the damping effect depends on the loss factor of the viscoelastic material, and the damper can provide large damping for the hollow shaft when the loss factor of the viscoelastic material achieves its optimal value. And these conclusions can also be obtained by ANSYS software.

Research on the Marine Shafting Torsional Vibration with Gears Transmission

Abstract The torsional vibration of marine propulsion shafting has been studied for more than a century. With abundant research achievements and experiences, a systematic approach of vibration calculation has been put forward for ship industrial applications. However, literature review indicates that when processing the gear transmission in the shaft line, the meshing motion has been treated as rigid mass in the equivalent equation of energy conservation, which leads to a certain error between the theoretical and experimental results of torsional vibration. Hence, to improve the calculation accuracy, a new method which considers the gear meshing stiffness is proposed in this paper. By taking the propulsion shafting of 3700DWT IMO TYPE II CHEMICAL TANKER as the research object, the forward computing formula of the shaft torsional vibration was first obtained using gear system dynamics theory. Then, the gear mesh stiffness was derived from the length variation of gear contact line. Finally, the free torsional vibration frequency was calculated considering the influence of the gear meshing force. The real marine test was implemented to verify the proposed method. The calculation results show that the new approach can track the actual torsional vibration more precisely than that without taking the gear meshing impact into account.

A Portable Digital Torsional Vibration Analysis System and its Signal Processing

Shaft torsional vibration is critical to rotating machinery as internal combustion engines because it may cause disasters if we ignore its significance. This paper introduced a portable digital system we developed to derive torsional vibration signal by a Hall Effect transducer. By analyzing the signal in frequency domain, we furthered the study on the influence of torsional vibration in each order under various rotation rates to determine the torsional resonant frequency. Moreover, a comparison between several signal processing methods in frequency domain was investigated and an optimum method for the spectrum correction obtained subsequently. Experiments conducted by this portable digital system showed its good performance in shaft torsional vibration measurements, analysis and trouble diagnosis.

Torsional Vibration of a Shafting System under Electrical Disturbances

Torsional vibration responses of a nonlinear shafting system are studied by a modified Riccati torsional transfer matrix combining with the Newmark-βmethod. Firstly, the system is modeled as a chain consisting of an elastic spring with concentrated mass points, from which a multi-segment lumped mass model is established. Secondly, accumulated errors are eliminated from the eigenfrequencies and responses of the system's torsional vibration by this newly developed procedure. The incremental transfer matrix method, combining the modified Riccati torsional transfer matrix with Newmark-βmethod, is further applied to solve the dynamical equations for the torsional vibration of the nonlinear shafting system. Lastly, the shafting system of a turbine-generator is employed as an illustrating example, and simulation analysis has been performed on the transient responses of the shaft's torsional vibrations during typical power network disturbances, such as three-phase short circuit, two-phase short circuit and asynchronous juxtaposition. The results validate the present method and are instructive for the design of a turbo-generator shaft.

Torsional Vibration of a Shafting System under Electrical Disturbances

Torsional vibration responses of a nonlinear shafting system are studied by a modified Riccati torsional transfer matrix combining with the Newmark-β method. Firstly, the system is modeled as a chain consisting of an elastic spring with concentrated mass points, from which a multi-segment lumped mass model is established. Secondly, accumulated errors are eliminated from the eigenfrequencies and responses of the system's torsional vibration by this newly developed procedure. The incremental transfer matrix method, combining the modified Riccati torsional transfer matrix with Newmark-β method, is further applied to solve the dynamical equations for the torsional vibration of the nonlinear shafting system. Lastly, the shafting system of a turbine-generator is employed as an illustrating example, and simulation analysis has been performed on the transient responses of the shaft's torsional vibrations during typical power network disturbances, such as three-phase short circuit, two-phase short circuit and asynchronous juxtaposition. The results validate the present method and are instructive for the design of a turbo-generator shaft.

Design and Experimental Test of Fiber Bragg Grating Rotate Speed Sensor Elastomer

This paper presents a rotate speed sensor using fiber Bragg grating (FBG) as sensitive component and constant strength cantilever structure as elastomer. The sensor is applied in large rotating experimental platform testing changes of impeller rotate speed through the vibration of the sensor's elastomer. The center reflection wavelength of FBG enters fiber grating demodulation device sm130, where light signal is demodulated. Experimental results demonstrate that the sensor can test the rotate speed of rotating machine repeatedly and sensitively. In addition, the sensor's easy theory and portable structure lay the foundation for further study on shaft torsional vibration detection of rotating machinery.

RESPONS GETARAN TORSIONAL POROS MODEL TURBIN ARUS LAUT SUMBU VERTIKAL AKIBAT EKSITASI MOMEN PUNTIR

Shaft Torsional Vibration Response of Vertical Axis Ocean Current Turbine Model Due to Torque Excitation. The current research aimed to study the torsional vibration response of Vertical Axis Ocean Current Turbine due torandomly torque excitation pattern, owing to the variety of ocean current velocity. The turbine model is composed of 3 aluminum blades of NACA 0018 connected to steel shaft. Turbine dimensions are 10 cm of chord, 1.8 cm of chamber and 100 cm of span. The variation of ocean current velocity is 0.5 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s, 2.5 m/s and 3.0 m/s. The Model has 2 degree of freedom which is described into two 2nd order differential equations. The eigenvalue solution yields the model’s natural frequencies; 201,38 rad/s and 457.91 rad/s. Fourier series is used to define the equation of torsional excitation, whilst the vibration equation is solved using Laplace Transform. According to analysis, there is no resonance occur. That because of the system’s natural frequencies is diverse to the magnitude of excitation frequencies. Model will be statically twisted first before vibrated. The response will be transient first then constantly steady. Furthermore, the bigger torque excitation will cause the bigger angular displacement as well the amplitude.

Analysis of Electromechanical Interactions in a Flywheel System With a Doubly Fed Induction Machine

This paper analyzes the electromechanical interaction in a flywheel system with a doubly fed induction machine, used for wind farm power smoothing or grid frequency response control. The grid-connected electrical machine is subject to power control, and this can cause it to produce negative damping to the shaft torsional vibration. Resonance must be prevented, and this paper proposes a solution by coordinating the design of the electrical controller and mechanical shaft. Computer simulations are used to demonstrate the problem and the proposed solution.

Analysis of Flexural and Torsional Vibration for Turbogenerator Shafts on Power Impact

Based on a Jeffcott rotor system with rigid support, the math models of flexural and torsional vibration were built, and their vibration characteristics were concluded. A simulation experiment in this paper was designed about the flexural and torsional vibration of shafts on a simulated turbine generator during network impacts. By analysis, flexural and torsional vibration characteristics were obtained, and the results showed the shafts flexural vibration and torsional vibration were interacted with each other. It was provided that torsional vibration could inhibit the complex shafts exercise. A new idea was suggested that the characteristics of torsion vibration should be considered as the symptom of faults diagnosis

Experimental Investigation of Characteristic Frequency in Unsteady Hydraulic Behaviour of a Large Hydraulic Turbine

The features of unsteady flow such as pressure variation and fluctuation in a large hydraulic turbine usually lead to the instability of operation. This article reports the recent in site investigation concerning the characteristic frequencies in pressure fluctuation, shaft torsional oscillation and structural vibration of a prototype 700 MW Francis turbine unit. The investigation was carried out for a wide load range of 200 MW-700 MW in the condition of water head 57 m-90 m. An extensive analysis of both time-history and frequency data of these unsteady hydraulic behaviours was conducted. It was observed that the pressure fluctuation in a draft tube is stronger than that in upstream flow passage. The low frequency with about one third of rotation frequency is dominative for the pressure fluctuation in part load range. Also the unsteady features of vibration of head cover and torsional oscillation of shaft exhibited the similar features. Numerical analysis showed that the vibration and oscillation are caused by vortex rope in the draft tube. In addition, a strong vibration with special characteristic frequency was observed for the head cover in middle load range. The pressure fluctuation in the draft tube with the same frequency was also recorded. Because this special vibration has appeared in the designed normal running condition, it should be avoided by carefully allocating power load in the future operation.

Stability Analysis of Rotating Blade Vibration due to Torsional Excitation

This paper presents an approximate 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 strained parameters method, a perturbation technique, is utilized in developing the stability transition curves in the plane of parameters related to the rotor speed, the torsional vibration excitation frequency and the blade natural frequency. The stable and unstable regions obtained by perturbations are contrasted to those obtained by numerical stability analysis performed using Floquet theory and an excellent match is observed for small torsional vibration amplitudes. Numerical integration of the original equation at selected points in the predicted stable and unstable regions showed that the predicted behavior of the responses is correct, wherein the unstable regions growing blade vibration is exhibited.

Damping Property and Vibration Analysis of Blades with Viscoelastic Layers

This paper showed the damping effect and the vibration analysis of a shaft-disk-blade system with viscoelastic layers on blades. The focus of the research is on the shaft's torsional vibration and the blade's bending vibration. The equations of motion were derived from the energy approach. This model, unlike the previous, used only two displacement functions for layered blades. Then, the assumed-modes method was employed to discretize the equations. The analyses of natural frequencies damping property were discussed afterwards. The numerical results showed the damping effects due to various constraining layer (CL) thickness and viscoelastic material (VEM) thickness. The research also compared FRF's of the systems with and without viscoelastic layers. It is concluded that both CL and VEM layers promote the damping capability but the marginal effect decreases with their thickness. The CLD treatment also found drop the natural frequencies slightly.

Blades condition monitoring using shaft torsional vibration signals

PurposeThe purpose of this paper is to validate mathematically the feasibility of extracting the rotating blades vibration condition from the shaft torsional vibration measurement.Design/methodology/approachA mathematical model is developed and simulated for extracting rotating blades vibration signatures from the shaft torsional vibration signals. The model simulates n‐blades attached to a rigid disk at setting angles and the shaft drives the disk is flexible in torsion. The model is developed using the multi‐body dynamics approach in conjunction with the Lagrangian dynamics. A three‐blade rotor system example is simulated for blades free and forced vibration under stationary and rotating conditions. Frequency spectrums for the shaft torsional and blades bending vibration are represented and studied for analysis verification purposes.FindingsThe torsional vibration frequency spectrums showed blades free and forced vibration signatures. The blade setting angle is shown to reduce the sensitivity of torsional vibration signal to blades vibration signatures as it increases. The torsional vibration signals captured the variation in blades properties and produced broadband frequency components for mistuned system. The shaft torsional rigidity is shown to reduce the sensitivity of torsional vibration signal to blades vibration if increased to extremely high values (approaching rigid shaft). The rotor inertia is shown to have less effect on the torsional vibration signals sensitivity. The method of torsional vibration as a tool for rotating blades vibration measurement, based on the proposed mathematical model and its simulation, is feasible.Practical implicationsThere is a growing need for reliable predictive maintenance programs that in turn requires continuous development in methods for machinery health monitoring through vibration data collection and analysis. Turbo machinery and bladed assemblies like fans, marine propellers and wind turbine systems usually suffer from the problem of blades high vibration that is difficult to measure. The proposed new method for blades vibration measurement depends on the shaft torsional vibration signals and can be used also for verifying the signals from other types of bearings sensors for possible blades vibration condition monitoring.Originality/valueThis paper presents a unique mathematical model and simulation results for the rotating blades vibration monitoring. The developed model can be simulated for studying coupled blades vibration problems in the design stage as well as for condition monitoring in maintenance applications.

Torsional Vibration Control of the Main Drive System of a Rolling Mill Based on an Extended State Observer and Linear Quadratic Control

In the main drive system of a rolling mill, shaft torsional vibration is often generated when a motor and a roll are connected with a flexible shaft. State feedback control can effectively suppress the torsional vibration of the main drive system of a rolling mill. Because of the difficulty of measuring the load speed and the shaft torque, and moreover the sensitivity of the Luenberger observer to the model uncertainties and the noise include in the detected signal, in this paper, we propose an extended state observer (ESO), a new observer, to estimate the unknown states and the load torque disturbance. We propose an ESO and linear quadratic (LQ) based speed controller with an integrator and load torque feedforward compensation for torsional vibration suppression in a two-mass main drive system of a rolling mill. The simulation results show the controller effectively improves the performances of command following, torsional vibration suppression, and robustness to parameter variation. This is the first time that the ESO has been utilized in torsional vibration control of the main drive system of a rolling mill, and its validity and superiority is verified in comparison with the conventional proportional integral (PI) controller and the state feedback controller based on a reduced-order state observer.

Natural Frequncies of Coupled Blade‐Bending and Shaft‐Torsional Vibrations

In this study, the coupled shaft‐torsional and blade‐bending natural frequencies are investigated using a reduced order mathematical model. The system‐coupled model is developed using the Lagrangian approach in conjunction with the assumed modes method to discretize the blade bending deflection. The model accounts for the blade stagger (setting) angle, the system rotating speed and its induced stiffening effect. The coupled equations of motion are linearized based on the small deformation theory for the blade bending and shaft torsional deformation to enable calculation of the system natural frequencies for various combinations of system parameters. The obtained coupled eignvalue system is ready for use as a reference for comparison for larger size finite element simulations and for the use as a fast check on natural frequencies for the coupled blade bending and shaft torsional vibrations in the design and diagnostics processes. Some results on the predicted natural frequencies are graphically presented and discussed pertinent to the coupling controlling factors and their effects. In addition, the predicted coupled natural frequencies are validated using the Finite Element Commercial Package (Pro‐Mechanica) where good agreements are found.

유연체 로터-커플링-블레이드 시스템의 로터 축과 블레이드의 연성 진동에 관한 연구

In this paper, a dynamic model for the rotor shaft-coupling-blade system was developed. The blades are attached to a disk and driven by an electric motor shaft which is flexible in torsion. We assumed that the shaft torsional flexibility was lumped in the flexible coupling which is usually adopted in rotor systems. The Lagrangian approach with the small deformation theory for both blade-bending and shaft-torsional deformations was employed for developing the equation of the motion. The Assumed Modes Method was used for estimating the blade transverse deflection. The numerical results highlight the effects of both structural damping of the system and the torsional stiffness of the flexible coupling to the dynamic response of the blade. The results showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearity, stiffness hardening and softening.

Compensation for encoder geometry and shaft speed variation in time interval torsional vibration measurement

Digital time interval techniques for the measurement of torsional vibrations in rotating shafts have been used in a variety of applications. The techniques use high-speed timers to detect the passage times (often referred to as “zero crossings”) in a carrier signal from a multiple pulse per revolution encoder on the shaft. Next, a reference array is created by computing the passage times for an encoder with geometrically uniform segments rotating at a constant speed. The measured times are compared against the reference array and the time difference processed to yield the shaft torsional vibration. If the reference array differs from the encoder passage times, the calculated torsional vibration will be subject to bias errors manifested as high-level order content. There are two potential causes for inconsistency in the reference signal: (1) geometric variation in angular encoding device and (2) a non-constant shaft speed. Procedures to handle these situations are addressed. An in situ encoder calibration method is presented that creates a reference array representative of the actual encoder angular intervals. The method uses time synchronous averaging of the encoder zero crossing over many shaft revolutions. The process causes the time passage variations induced by the torsional vibration to average to zero, ultimately yielding the time stamps caused by the passage of each respective encoder segment. The synchronous averaged encoder passage times are then used to correct the reference array to calculate the torsional vibration. Variation of the encoder geometry and changes in shaft running speed cause the torsional vibration be sampled on a non-uniform time interval basis. The non-uniform time sampling would cause errors if used with fixed sampling interval algorithms such as the DFT. A resampling algorithm is applied to create an array sampled with a constant time interval basis to minimize the error. The background and implementation details of time interval torsional vibration measurement enhancements are first presented. The capabilities are then demonstrated with experimental results from several pieces of rotating equipment. The tests show the successive improvement in the torsional vibration data as the proposed compensation methods are sequentially applied.

Stability analysis of rotating blade bending vibration due to torsional excitation

This paper studies the forced vibrations of a flexible rotating blade under the excitation of shaft torsional vibration. A reduced order nonlinear dynamic model is adopted, wherein the torsional vibration degree of freedom is substituted by a simple harmonic motion with a frequency that is function of the system rotating speed. The resulting system of second-order ordinary differential equation with harmonically varying coefficients is solved using the method of harmonic balance. The forced response solution is compared to the numerical integration results. Agreement is found with respect to stable and unstable regions of the blade vibrations. The solution is useful for defining dangerous operating speed ranges and for quantifying the relationship between shaft torsional and blade bending natural frequencies.

Parametric stability of continuous shafts, connected to mechanisms with position-dependent inertia

Stability of the parametrically excited torsional vibrations of shafts connected to mechanisms with position-dependent inertia is studied via a version of Bolotin's method. The shafts are considered to be torsionally elastic, distributed parameter systems and discretized through a finite element scheme. The mechanisms are modelled by a linearized Eksergian equation of motion. A general method of analysis is described and applied to examples with slider–crank and Scotch-yoke mechanisms.