Transient Torsional Vibration Research Articles

Shaft fatigue estimation based on characteristics of transient torsional vibration for propulsion shafting system according to variation of passing time in barred speed range

Shaft fatigue estimation based on characteristics of transient torsional vibration for propulsion shafting system according to variation of passing time in barred speed range

Study on Torsional Vibration Response Characteristics of Marine Propulsion Shafting

_ The paper establishes the lumped parameter vibration mathematical model of shafting and uses the system matrix method to calculate and analyze steady-state frequency domain vibration characteristics of the shaft system in the range of diesel engine speed. Then in order to further study the transient torsional vibration of the shaft system under the resonance speed point, the state space method and finite element analysis method were used to compare and analyze the transient time domain response characteristic curve of the shaft system; finally, the test data of the real ship was compared with the theoretical calculation results, which verified the correctness of the mathematical model and the theoretical calculation method. This study has certain theoretical significance for carrying out the design of low-noise and vibration of shaft systems and improving the safety of ship navigation. Keywords shafting torsional vibration; transient time domain; finite element method; vibration test

Suppression of multi-modal torsional vibration of the long-shafting rotor system with nonlinear piecewise NES

Long-shafting rotor systems tend to cross multi-order natural frequencies at start up and coast down, and the multi-order modes of vibration are excited by various excitations. The bending vibration can be limited to the single rotor, but the torsional vibration is obviously coupled between each single rotor, which leads to more problems. Therefore, the current work proposes to suppress the multi-modal torsional vibration of long-shafting rotor system by a single nonlinear piecewise NES (PNES). The dynamic models of long-shafting rotor system and the long-shafting rotor-PNES system are established in which the PNES is used to suppress the first two-order torsional vibration. The genetic algorithm (GA) is used to optimize the multi-modal transient and steady-state torsional vibration suppression results of PNES to obtain optimal parameters design, respectively. And the influences of the parameters of long-shafting rotor-PNES system and the additional position of PNES on the vibration suppression effect of PNES are also discussed. The experimental verification of the suppression of the first two-order steady-state torsional vibration of the long-shafting rotor system by a PNES is carried out. In numerical simulation, the percentage of accumulated energy dissipation of the PNES can reach 52.2 % for the multi-modal transient torsional vibration, and the inhibitions of the three torsional vibrations by the PNES are about 71.6 % and 77.9 %, 67.5 % and 81.2 %, 68.5 % and 69.5 % in the multi-modal steady-state torsional vibration suppression. In the test, only the suppression of the first torsional vibration by PNES is tested, that the PNES can reduce the first two-order steady-state torsional resonances of the first torsional vibration of the long-shafting rotor system by 62.1 % and 65 % respectively.

Dynamic modeling and nonlinear analysis for lateral–torsional coupling vibration in an unbalanced rotor system

Imbalance is a common problem in rotating machinery. In addition to the unbalanced force, lateral–torsional coupling vibration can also be induced by the mass imbalance. However, the related nonlinear behaviors and coupling mechanism are still not well understood, especially when lateral-angular motion is incorporated in a model. In this paper, a model for coupling lateral and torsional vibrations of an unbalanced rotor is developed by Lagrangian dynamics, in which the coupling of lateral-angular and torsional motions is first considered. Based on the model, the lateral responses, torsional responses, coupling excitation characteristics and coupling mechanisms are investigated in detail. The results show that mass imbalance can lead to nonlinear time-varying characteristics in the dynamic equations. When the imbalance is small, the lateral vibration can be degraded to a traditional imbalance problem. Meantime, very small transient torsional vibration with torsional natural frequency ft in frequency domain can be observed at the beginning. The coupling excitation applying on the torsional DOF caused by the lateral synchronous whirling is demonstrated to behave the feature of static torque, consequently, there actually exists no steady-state torsional vibration in small unbalanced rotor. Under largely unbalanced conditions, both resonant and unstable behavior can be observed in the lateral and torsional responses. The combined resonance is induced by the lateral translational–torsional coupling, while the instability is caused by lateral angular–torsional coupling. By increasing the lateral damping, the instability phenomenon can be suppressed, and the lateral amplitude in the resonance region can be effectively reduced.

Chiral metamaterial -inerter nonlinear energy sink for torsional vibration suppression of the rotor system

This paper explores the use of a chiral metamaterial inerter nonlinear energy sink (CINES) for suppressing torsional vibrations in a rotor system. The compress-torsion coupling effect of the chiral metamaterial is adopted to construct the inerter amplification mechanism, which is then combined with the NES to form CINES. The dynamic model of the rotor-CINES coupled system is established, the transient torsional vibrations and steady-state torsional vibrations are optimized by genetic algorithm and the optimal parameters for numerical simulation are obtained. Then, the vibration suppression capability of CINES is evaluated. Moreover, experiments on the CINES are carried out to verify the theoretical results. The results show that the cumulative energy dissipation rate of CINES in transient torsional vibration suppression can reach 89.2 %, and the percentage of vibration suppression in steady-state torsional vibration suppression can reach 88.5 %. Furthermore, the CINES saves more than 10 times its moment of inertia while achieving the same vibration reduction ratio.

Transient Torsional Vibration Characteristic Analysis and Active Suppression of PHEV with Planetary Coupled Transmission System during Mode Transition Process

Transient Torsional Vibration Characteristic Analysis and Active Suppression of PHEV with Planetary Coupled Transmission System during Mode Transition Process

Research on Transient Torsional Vibration Test of Harmonic Reducer

The torsional vibration of harmonic reducer is related to the positioning accuracy and Trajectory Accuracy of industrial robots. Based on this, this paper studies and experiments the impact response of harmonic reducer. By establishing the torsional vibration model with periodic variable stiffness of harmonic reducer, the unit impulse response and characteristics are analyzed; The time-varying torsional stiffness of the harmonic reducer is verified by setting up an experimental platform for the harmonic reducer, and the transient torsional vibration characteristics of the harmonic reducer are obtained The research will provide basic data for the optimal application of harmonic reducer.

An inerter nonlinear energy sink for torsional vibration suppression of the rotor system

To reduce size and weight of the inertial mass required in traditional nonlinear energy sink (NES), an inerter nonlinear energy sink (INES) for suppressing the torsional vibration of the rotor system is developed in this paper. The INES is a combination of a NES with piecewise linear stiffness and an inerter whose vibration can be enlarged by levers. The structure of the INES is introduced, the inerter mechanism is analyzed and the dynamic model of the INES-rotor system is built. Vibration attenuation performance of INES on the rotor system is evaluated by the transient torsional vibration and steady-state torsional vibration, both of which are optimized by the genetic algorithm (GA). It is found that the inerter mass of INES can save about 14.2 times its own rotary inertia when suppressing the torsional vibration of the rotor system. By using the inerter, a significant damping effect also appears. In transient torsional vibration suppression, the percentage of accumulated energy dissipation of INES can reach 95.1%. In steady-state torsional vibration suppression, the peak vibration eliminations of INES for the rotor system can achieve 89.1% in simulation and 80.6% in test.

Study on the Propeller Rope Cutter Concerning Transient Torsional Vibration Due to Cutting Action

Nowadays, damage to ships due to marine debris at sea is increasingly reported. Specifically, a piece of rope or fishing net can wrap around the propeller shaft, stopping it from rotating. Although various efforts have been made, there are still numerous practical challenges. A rope cutter system, which was designed to cut suspended objects wrapped around the propeller shaft, offers a great advantage in protecting the propulsion system. Since the cutting action produces the transient torsional vibration, the connecting bolts should be stable and sufficiently rigid under normal conditions. However, in the event of an encounter with an object that is too hard to cut, the bolts must be broken so that the rope cutter is released. Those kinds of objects may not be long enough to wrap around the shaft, such as a piece of wood. Therefore, this research presents the novelty in maintaining the safety of the propulsion system installed with a rope cutter. In this study, a method for obtaining the maximum diameter of the connecting bolt as a safety device is described, and the torques required to cut ropes of various thicknesses were determined based on actual measurements. Finally, a series of experiments in the laboratory-scale and shipboard test on an actual ship show that the rope cutter does not significantly reduce the ship’s power performance or increase the structural vibration.

Torsional Vibration Stress and Fatigue Strength Analysis of Marine Propulsion Shafting System Based on Engine Operation Patterns

Modern merchant ships use marine propulsion systems equipped with an ultra-long-stroke diesel engine that directly drives a large slow-turning propeller. Such systems use fewer cylinders and generate greater power at slower shaft speeds, which affords improved propulsion performance as well as low repair and maintenance costs. However, this also results in higher torsional vibrations, which can lead to the fatigue of the shafting system. Tests performed on various marine propulsion systems with 5- to 7-cylinder engines have shown that engines with fewer cylinders exhibit a correspondingly wider barred speed range (BSR) and higher torsional vibration stresses. Thus, it is necessary to investigate the optimal engine operation patterns required to quickly pass the BSR with smaller torsional vibration. In this study, we carried out a series of BSR passage experiments during actual sea trials to evaluate the intermediate shaft performance under different engine operation patterns. The fractional damage accumulations due to transient torsional vibration stresses were calculated to estimate the fatigue lifetime of the shafting system. Our analysis results show that the torsional fatigue damage during BSR decelerations are small and negligible; however, the fractional damage during accelerations is a matter of concern. Our study determines the optimal main engine operation pattern for quick passage through the BSR with the smallest torsional vibration amplitudes and the least fractional damage accumulation, which can therefore extend the fatigue lifetime of the entire propulsion shafting system. Based on this analysis, we also suggest the optimum engine pattern for safe BSR passage.

New clutch oil-pressure establishing method design of PHEVs during mode transition process for transient torsional vibration suppression of planetary power-split system

For plug-in hybrid electric vehicles (PHEVs), mode transition might be the most effective way of energy conservation. However, the transient torsional vibration (TTV) during mode transition process, which is unavoidable, usually affect the drive comfort. This paper presents an innovative planetary hybrid power-split system (PHPS), which comprised of an epicyclic gear system, two compact clutches and a wedge brake device, and will been applied Chery PHEVs. First, powertrain vibration during mode transition process, as influenced by dynamic transfer friction torque of clutch, angle-varying mesh stiffness of epicyclic gear and external loads of multi-power sources, are investigated through a nonlinear TTV model. Then, the dynamic equations of mode transition process are established and numerically solved to get TTV response as well as vehicle jerk, and further new clutch oil-pressure establishing method design of PHEVs during mode transition process for relative torsional oscillation suppression of PHPS is presented. At last, bench tests are carried out, and results indicated that the proposed optimization model effectively suppressed PHPS torsional oscillation, vehicle longitudinal jerk, and improved driving smoothness during mode transition process.

New teeth surface and back (TSB) modification method for transient torsional vibration suppression of planetary gear powertrain for an electric vehicle

Advantages of planetary gear powertrain (PGT) for electric vehicles (EVs) are the high degree of efficiency, various reduction ratio, stress distribution by the planet gear and compaction in designing driving system. However there is noise in running at high rotational speed, so the transient torsional vibration suppression of the PGT for EVs become extremely essential and urgent. This study presents a 4 + N degree of freedom (DOF) nonlinear torsional system that essentially describes a PGT of EVs example, and further study on influence of novel TSB modification on transient vibration of planetary gear powertrain for an electric vehicle. In particular, the vibration of the PGT during the speed-up process, as excited by dynamic torque of motor generator (MG), time-varying mesh stiffness of front and back gear teeth, and also teeth backlashes, are investigated using a nonlinear torsional transient model. Then a full PGT model during the speed-up process is proposed and numerically solved to obtain the transient vibration acceleration. Dynamic response results of the PGT are also successfully compared and analyzed under different teeth backlashes. Finally, an improved genetic algorithm is applied to construct optimal relationship between the transient vibration and the TSB modification, and further the optimum three-dimensional TSB modification of sun-gear is finally obtained. The simulation and experiment results indicated that the proposed novel TSB modification method effectively suppressed the PGT transient vibration and vehicle jerk, at the same time, improved the ride comfort during the high-speed driving mode.

Study on Forced Torsional Vibration of CFRP Drive-Line System with Internal Damping

The use of CFRP transmission shaft has positive effect on the weight and flexural vibration reduction of drive-line system. However, the application of CFRP transmission shaft will greatly reduce the torsional stiffness of the drive-line, and may cause strong transient torsional vibration. Which will seriously affect the performance of CFRP drive-line. In this study, the forced torsional vibration of the CFRP drive-line system is carried out using the lumped parameter model. In addition, the effect of rotary inertia, internal damping, coupling due to the composite laminate, and excitation torque are incorporated in the modified transfer matrix model (TMM). Then, the modified TMM is used to predict the torsional frequency and forced torsional vibration of a CFRP drive-line with three-segment drive shafts. The results of modified TMM shown that the rotational speed difference of the CFRP transmission shaft segment is much larger than metal transmission shaft segment under excitation torque. And compared the results from finite element simulation, modified TMM and torsional vibration experiment respectively, and it has shown that the modified TMM can accurately predict forced torsional vibration behaviors of the CFRP drive-line system.

Analysis and validation of a procedure for a lumped model of Polar Class ship shafting systems for transient torsional vibrations

In this paper, the authors discuss the development of a procedure for modeling the transient torsional loads on shafting systems induced by an ice impact sequence on Polar Class vessels propellers. The procedure was used to solve the transient torsional vibration using a lumped masses model of shafting systems driven by electric motors. After a description of the methodology and procedure used to model the vibratory behavior of a shafting system, the discussion will focus on a sensitivity analysis performed on the relevant parameters that allows a proper description of the shaft’s dynamics. The model has then been benchmarked and validated against the results from a finite element code, using an R-Class icebreaker from the Canadian Coast Guard as a case study. The results show promising outcomes for the assessment of the transient torque loads, and the model will be used in the future to aid the upcoming experimental activity.

Transient and Steady State Torsional Vibration Analysis of Large Bore Diesel Engines

Transient and Steady State Torsional Vibration Analysis of Large Bore Diesel Engines

Studying the Stressed State of the Turbine Shafting at Short-Circuit

The stressed state in the most dangerous sections of shafting rotors at torsional vibrations caused by sudden loading of the generator rotor has been investigated. Consideration was given to transient torsional vibrations of the turbo-unit shafting at two-phase and three-phase short circuits. Shafting sections are simulated using the rods of piecewise constant cross-section with the distributed mass, the rotor discs and flanges are presented as the lumped mass and the moments of inertia. To construct the design models of the rotors we take into consideration all their structural peculiarities, dead load pressure, lumped forces and moments and the kinematic influence of the foundation via the bearings. These loadings can be constant, periodically alternating and/ or arbitrarily assigned in time. The computations were done using the bundled software that was developed using the method of finite elements with the direct-time integration of motion equations by the step-type Newmark method used to solve problems on induced, bending, longitudinal and torsional vibrations of shafting installed on complicated elastically strained supports. For the junction points of adjacent rotors we take into consideration the rigidity of docking elements and junction imperfections, in particular the radial clearance or the fracture of section axes. The investigations carried out showed that for involved turbo-units the shafting sections between the turbine and the generator are the most dangerous. The obtained data can be used to assess the fatigue damageability of turbine shafting due to the high level of stresses that arise at torsional vibrations caused by short-circuit.

전기 모터 구동 대빙급 추진 시스템의 과도 비틀림 진동 분석

A ship’s propulsion shafting system is subjected to varying magnitudes of intermittent loadings that pose great risks such as failure. Consequently, the dynamic characteristic of a propulsion shafting system must be designed to withstand the resonance that occurs during operation. This resonance results from hydrodynamic interaction between the propeller and fluid. For ice-class vessels, this interaction takes place between the propeller and ice. Producing load- and resonance-induced stresses, the propeller-ice interaction is the primary source of excitation, making it a major focus in the design requirements of propulsion shafting systems. This paper examines the transient torsional vibration response of the propulsion shafting system of an ice-class research vessel. The propulsion train is composed of an electric motor, flexible coupling, spherical gears, and a propeller configuration. In this paper, the theoretical analysis of transient torsional vibration and propeller?ice interaction loading is first discussed, followed by an explanation of the actual transient torsional vibration measurements. Measurement data for the analysis were compared with an applied estimation factor for the propulsion shafting design torque limit, and they were evaluated using an existing international standard. Addressing the transient torsional vibration of a propulsion shafting system with an electric motor, this paper also illustrates the influence of flexible coupling stiffness design on resulting resonance. Lastly, the paper concludes with a proposal to further study the existence of negative torque on a gear train and its overall effect on propulsion shafting systems.

Transient torsional vibration responses of finite, semi-infinite and infinite hollow cylinders

Torsional guided waves are often used to detect the defects in a hollow cylinder. To realize the excitation of the torsional guided waves with high efficiency, the transient vibration responses of finite, semi-infinite and infinite hollow cylinders to external torsional forces must be clarified theoretically. In this study, the method of eigenfunction expansion is employed to solve the above problems. The exact analytical solutions derived by this method are not only explicit but also concise. Furthermore, the analytical solution of the transient torsional vibration of the finite hollow cylinder is numerically evaluated. The results obtained agree well with those simulated by the finite element method.

A novel method for improving analysis precision of transient torsional vibration of engine

For transient torsional vibration analysis of an engine, the Revolution Tracking Analysis (RTA) method cannot accurately estimate harmonic amplitudes of torsional vibration signal, owing to the Low Frequency Rolling Vibration (LFRV) caused by radial vibration of the crankshaft. To overcome the disadvantage of the RTA method, the Windowed Revolution Tracking Analysis (WRTA) method is proposed. Simulation and experiment results show that, except for the 0.5th harmonic, amplitude precision of the other harmonics of transient torsional vibration signal in a four-stroke engine are greatly improved using the proposed method.

Transient torsional wave in finite hollow cylinder with initial axial stress

An analytical solution is obtained for transient torsional vibration of a finite hollow cylinder with initial axial stress. The cylinder is subjected to dynamic shearing stress at the internal surface and is fixed at the external surface. The basic equations are presented and the solution is obtained by means of Fourier series expansion technique and the separation of variables method. The effects of the initial stress on the natural frequencies and transient torsional responses are presented and discussed.