Torsional Oscillations Research Articles

Exploring the Temporal Variation of the Solar Quadrupole Moment J 2

Recently, Rozelot & Eren pointed out that the first solar gravitational moment (J 2) might exhibit a temporal variation. The suggested explanation is through the temporal variation of the solar rotation with latitude. This issue is deeper developed due to an accurate knowledge of the long-term variations in solar differential rotation regarding solar activity. Here we analyze solar cycles 12–24, investigating the long-term temporal variations in solar differential rotation. It is shown that J 2 exhibits a net modulation over the 13 studied cycles of ≈(89.6 ± 0.1) yr, with a peak-to-peak amplitude of ≈0.1 × 10−7 for a reference value of 2.07 × 10−7). Moreover, J 2 exhibits a positive linear trend in the period of minima solar activity (sunspot number up to around 40) and a marked declining trend in the period of maxima (sunspot number above 50). In absolute magnitude, the mean value of J 2 is more significant during periods of minimum than in periods of maximum. These findings are based on observational results that are not free of errors and can be refined further by considering torsional oscillations for example. They are comforted by identifying a periodic variation of the J 2 term evidenced through the analysis of the perihelion precession of planetary orbits either deduced from ephemerides or computed in the solar equatorial coordinate system instead of the ecliptic coordinate one usually used.

ДОСЛІДЖЕННЯ НЕРЕЗОНАНСНИХ КОЛИВАНЬ СИСТЕМИ «ТЕЛЕСКОПІЧНИЙ ГВИНТ – СИПКЕ СЕРЕДОВИЩЕ»

In the article it is substantiated the value of the angular speeds of rotation of the auger screw, which leads to the breakdown of its lateral vibrations. The dependences describing the law of change of amplitude or natural frequency at slowly variable length of the telescopic screw are deduced. Based on the Van der Paul’s method, in the developed system differential equations are obtained that determine the laws of change of amplitude and frequency of the wave process in the system of a telescopic propeller. It is established that for nonresonant oscillations for this system the main parameters of bending oscillations are a continuous flow of bulk medium - the screw does not depend on its small torsional oscillations and external periodic perturbation. The analysis of the given regression equations shows that to reduce the torque of the auger it is necessary to reduce the frequency of its rotation and the angle of the conveyor. The constructive diagram and the results of theoretical calculations for assessing the influence of constructive-kinematic parameters on the torque indicators of the telescopic screw conveyor are presented.

Impact of Fixed/Variable Speed Hydro, Wind, and Photovoltaic on Sub-Synchronous Torsional Oscillation—A Review

Series compensation is a cost-efficient way to enhance the system reliability and the power transfer capabilities of long transmission lines. As a result of series compensation, the sub-synchronous oscillation (SSO) causes a severe risk of torsional interactions (TI). Therefore, SSO becomes a serious risk factor in grid-integrated renewable energy systems. Numerous researchers have evaluated SSO instances in several types of asynchronous generators in power systems. In this paper, the categorization and the overview of the SSO phenomena have been vital for the different mechanisms, sophisticated systems, analytical techniques, and multiple reviews that have been propagated. This study provides SSO analysis for various types of renewable energy power plants. Finally, while dealing with conventional and new power systems, this study summarizes recent SSO-damping and alleviation techniques for practical perception and future perspectives.

Variations in differential rotation and meridional flow within the Sun’s surface shear layer 1996–2022

We measure differential rotation and meridional flow in the Sun’s surface shear layer by tracking the motions of the magnetic network seen in magnetograms from SOHO/MDI and SDO/HMI over solar cycles 23, 24, and the start of 25 (1996–2022). We examine the axisymmetric flows derived from 15 to 24 daily measurements averaged over individual 27-day Carrington rotations. Variations in the differential rotation include the equatorial torsional oscillation—cyclonic flows centered on the active latitudes with slower flows on the poleward sides of the active latitudes and faster flows equatorward. The fast flow band starts at ∼45° latitude during the declining phase of the previous cycle and drifts equatorward, terminating at the equator at about the time of cycle minimum. Variations in the differential rotation also include a polar oscillation above 45° with faster rotation at cycle maxima and slower rotation at cycle minima. The equatorial variations were stronger in cycle 24 than in cycle 23 but the polar variations were weaker. Variations in the meridional flow include a slowing of the poleward flow in the active latitudes during cycle rise and maximum and a speeding up of the poleward flow during cycle decline and minimum. The slowing in the active latitudes was less pronounced in cycle 24 than in cycle 23. Polar countercells (equatorward flow) extend from the poles down to ∼60° latitude from time to time (1996–2000 and 2016–2022 in the south and 2001–2011 and 2017–2022 in the north). Both axisymmetric flows vary in strength with depth. The rotation rate increases inward while the meridional flow weakens inward.

Escape through parametric instabilities in a non-ideal motor driven geared rotor shaft driveline

Periodically-varying gear mesh stiffness is a source of parametric excitation, which causes torsional instabilities in geared rotor systems. Unbounded amplitude growth at instability requires energy to be continuously pumped into the torsional modes from some ideal source of infinite power. However, real or non-ideal drives can only provide a limited amount of power; hence, the amplitude growth of torsional oscillations is bounded even at the unstable regions. In this paper, the coupled electro-mechanical dynamics of a geared rotor system driven by a non-ideal DC motor is investigated. It is shown that the system exhibits symptoms of Sommerfeld effect when driven through a torsionally unstable zone. As the system transitions through an unstable speed range, harmful torsional vibrations of the rotor-shafts consume a major part of the motor power, thereby reducing the power available to spin the rotor-shafts. Under some conditions, the spin speed gets captured at the instability zone, from where an escape occurs in the form of a speed jump on supplying a certain minimum threshold power. The design guidelines to suppress this harmful Sommerfeld effect are then proposed.

Drivability Optimization of Electric Vehicle Drivetrains for Brake Blending Maneuvers

Electric vehicle drivetrains are considered a way to reduce greenhouse gas emissions from road traffic. The use of electric drives in automotive vehicles offers advantages, such as the potential to recover energy during braking (regenerative braking). The limitation of the maximum air gap torque of the vehicle drive machine by several factors requires a temporary standalone or simultaneous use of the conventional vehicle wheel brake. In several studies, it is shown that during braking operations, the drive machine and the vehicle wheel brake can induce torsional oscillations in the drivetrain, which have a negative influence on the driving comfort and lead to a high mechanical load. To reduce these oscillations, the simultaneous use of an active anti-jerk control is necessary. Due to the problem of oscillation excitations caused by a brake intervention, the used drivability function (integrated prefilter, anti-jerk control) is investigated and optimized with regard to brake blending maneuvers and the effectiveness for damping torsional oscillations. Therefore, the dynamics of the drivetrain are adapted to the dynamics of the braking system using the prefilter, which leads to precise fulfilment of the driver’s braking desire, even during dynamic brake blending maneuvers. All investigations are carried out with a hardware-in-the-loop test bench to create reproducible results.

High-Frequency Excitations of Drillstring under the Conditions of Periodic Rock Destruction. Self-Excited Oscillator

Abstract —The self-excited oscillator describing high-frequency excitations of a drillstring with high amplitudes of torsional oscillations has been presented. The self-excited oscillator is characterized by discrete degrees of freedom. Fundamentally, the work of the self-excited oscillator is based on the idea of the maximum cutting force during the destruction of rock by PDC bits and the results of laboratory studies by M.I. Vorozhtsov, K.I. Borisov, G.P. Cherepanov. The differential equations of the non-autonomous self-excited oscillator are based on the results of laboratory studies. A typical dynamic mode of the self-excited oscillator operation has been presented. The results have been compared with experimental data.

Design, modelling and testing of a compact piezoelectric transducer for railway track vibration energy harvesting

To enable wireless sensor networks to monitor rail infrastructures in real-time, a cost-effective power source is in need. This work presents the design, modelling and testing of a piezo stack energy harvester with frequency up-conversion mechanism for scavenging energy from railway track vibration. The proposed harvester is designed to meet railway track applications’ size, frequency, and stress requirements. A compact design integrating the inertial mass and the piezo stack transducer systems is used to enable the mechanical collision for realising the frequency up-conversion mechanism and ensure the size of the energy harvester is suitable for the limited space on the railway track. The frequency bandwidth of the energy harvester is broadened by utilizing the longitudinal and torsional oscillation of the designed plate springs which enable the system to have two adjacent natural frequencies. The mechanical transformer of the piezo stack transducer system is designed to achieve the required stress level under both the impact force caused by the collision motion and the inertial force generated by the random vibration of the rails. A finite element model (FEM) analysing the free vibration of the piezo stack transducer caused by the frequency up-conversion mechanism is developed to analyse the dynamic characteristics of the coupled system. Lab tests are carried out to validate the proposed FEM and evaluate the impact of different factors such as load resistance, acceleration, initial interval, plate spring, and pulse excitation on power generation. Experimental results show that the energy harvester has two resonant frequencies of 17 Hz and 20 Hz. The frequency up-conversion mechanism can convert this low-frequency vibration into the piezo stack transducer’s high resonant frequency vibration of 94 Hz. A maximum average power of 6.72 mW with a 1-mW-bandwidth of 15 Hz is obtained when actuated at 0.7 RMS g acceleration. • A piezo stack energy harvester for railway track vibration is designed, modelled and tested. • A compact design is proposed to enable the mechanical collision for realising the frequency up-conversion mechanism. • Two adjacent natural frequencies are achieved to broaden the frequency bandwidth. • The mechanical transformer is designed to achieve the required stress level under the impact force and inertial force. • A maximum average power of 6.72 mW with a 1-mW-bandwidth of 15 Hz is obtained when actuated at 0.7 RMS g acceleration.

Loading capacity, rotation loss and torsional oscillation research on an Evershed-type hybrid superconducting bearing used for micro-thrust measurements

Characterized by their very low rotational drag, applications of high-temperature superconductor (HTS) bearings have been expanded in some high-precision instruments. We have developed a sensitive magnetic suspension stand based on an Evershed-type hybrid HTS bearing to measure μN-level thrust. The hybrid HTS bearing uses the strong attractive force of a permanent magnet (PM)-biased bearing to support the main load in the bearing, while instability in the PM-biased bearing is compensated by the magnetic stability from a HTS bearing. Compared with a single PM/HTS bearing, the hybrid HTS bearing is intended not only to support larger loads but also to suppress rotation loss and levitation drift. Loading capacity, loss and damping torque were explored for different design parameters such as bearing gaps L 1, L 2 and the field cooling height (FCH) of bulk HTSs. Spin-down testing suggested that the loss of a hybrid HTS bearing can be reduced by increasing the HTS bearing gap L 2 or reducing the FCH. The hybrid HTS bearing showed a typical oscillation behavior at extreme low frequencies, and torsional pendulum testing suggested that the spring constant k of the hybrid HTS bearing can be as low as 36.39 μN m deg–1. A micro-thrust stand based on the hybrid HTS bearing was established to test an electrospray thruster in a vacuum chamber, and the measurement result of 26.61 μN shows the ability of the micro-thrust stand to achieve μN level testing.

Power system stability improvement considering drive train oscillations of virtual synchronous generator‐regulated type‐4 wind turbines

The type-4 wind turbine generators (WTGs) can provide inertial frequency response by implementing the virtual synchronous generator (VSG) concept. However, unstable torsional oscillations (TOs) would be induced in the multi-mass-spring drive-train which can destabilize the entire power system. In this study, participation factor analyses are performed for a power system inclusive of a thermal unit and aggregated WTG system. The system's eigenvalues are characterized and the possible detrimental impacts of TOs on the inertia provision process and overall power system stability are demonstrated and the related stability limits are identified. A comprehensive active torsional oscillations damper (CA-TOD) and a supercapacitor-based energy storage system (ESS) are presented and discussed to implement the CA-TOD. A state of charge (SoC) regulator is also employed to set the reference speed difference for the turbine-generator. Small-signal studies and electro-magnetic transient (EMT) simulations are performed to evaluate the functionality of the CA-TOD and SoC controller and estimate their impacts on the system's dynamics. The robust performance of the CA-TOD is compared to the band-pass filter-based TOD by sweeping key control parameters of the VSG and emulating drive-train parameter uncertainty. Key results are cross-verified by EMT simulations of a multimachine power system.

Twisting an optomechanical cavity

Mechanical rotation and oscillation have far lower frequencies than light does; thus they are not coupled to each other conventionally. In this Letter, we show the torsional mechanical oscillation of an optical cavity can be coupled to the optical modes by introducing birefringence, which produces nondegenerate modes in the cavity: ordinary and extraordinary rays. Twisting the cavity mixes them and modulates the electromagnetic energy. We find torsional optomechanical Hamiltonian by quantising the total energy and reveal the torsional oscillation can be resonantly driven by light.

Self-similarity relations for torsional oscillations of neutron stars

ABSTRACT Self-similarity relations for torsional oscillation frequencies of neutron star crust are discussed. For any neutron star model, the frequencies of fundamental torsional oscillations (with no nodes of radial wavefunction, i.e. at n = 0, and at all possible angular wave numbers ℓ ≥ 2) is determined by a single constant. Frequencies of ordinary torsional oscillations (at any n > 0 with ℓ ≥ 2) are determined by two constants. These constants are easily calculated through radial integrals over the neutron star crust, giving the simplest method to determine full oscillation spectrum. All constants for a star of fixed mass can be accurately interpolated for stars of various masses (but the same equation of state). In addition, the torsional oscillations can be accurately studied in the flat space–time approximation within the crust. The results can be useful for investigating magneto-elastic oscillations of magnetars which are thought to be observed as quasi-periodic oscillations after flares of soft-gamma repeaters.

Stability and Dynamic Analysis of the PMSG-Based WECS With Torsional Oscillation and Power Oscillation Damping Capabilities

The direct-drive permanent-magnet synchronous generator (PMSG) based wind energy conversion system (WECS) with a soft drivetrain shaft is vulnerable to torsional oscillation when it participates in power oscillation damping (POD) services for the AC grid. This paper investigates three possible scenarios of incorporating both torsional oscillation damping (TOD) and POD controllers into PMSG-based WECS. A model of a PMSG-based offshore wind farm (OWF) connected to the IEEE 39-bus AC grid is developed and utilized to analyze the stability and dynamic performances of the WECS within these three scenarios. Comprehensive modal analysis is carried out to analyze the interaction between the torsional and power oscillations, and to tune the TOD and POD controllers to damp these oscillations simultaneously in each scenario. Furthermore, the dynamic performances of the PMSG-based WECS within these scenarios are evaluated through time-domain simulations. Then an optimal scenario for PMSG-based WECS to damp both oscillation types with close frequencies is identified, which is modulating the DC-link voltage for the TOD and the grid-side active power for the POD. This result can provide useful guidance for the future industrial application of the TOD and POD control in the PMSG-based WECS.

The role of boundary conditions in the torsional instability of suspension bridges

We consider a degenerate plate model for suspension bridges, composed by a central beam moving vertically and by a continuum of cross-sections free to rotate around the beam. We study the torsional stability of such structures and we investigate under different boundary conditions how the internal resonances, which depend on the bridge structure only, are the source of torsional oscillations. The stability analysis is carried out by means of standard Floquet theory and via KAM techniques.

Effects of finite sizes of atomic nuclei on shear modulus and torsional oscillations in neutron stars

ABSTRACT The shear modulus of neutron star matter is one of the important properties used for determining torsional oscillations in neutron stars. We take into account the effects of finite sizes of spherical nuclei on the shear modulus and examine the frequencies of crustal torsional oscillations. The shear modulus decreases owing to the finite-size effect, which in turn decreases the frequencies of torsional oscillations. In particular, the finite-size effect becomes more crucial for oscillations with a larger azimuthal quantum number and for neutron star models with a weaker density dependence of nuclear symmetry energy. In practice, when one identifies quasi-periodic oscillations from a neutron star, where magnetic effects are negligible, with crustal torsional oscillations, the finite-size effect can be more significant at frequencies higher than ∼100 Hz.

Research on Fast and Precise Positioning Strategy of an Ultrasonic Motor Based on the Ultrasonic Friction Reduction Theory.

To address the problems of the large positioning error and long positioning time of the traditional positioning strategy, namely, the two-phase simultaneous power-off method (TPSPM), a new positioning strategy, called the first single-phase then two-phase power-off method (FSPTTPPM), based on the ultrasonic friction reduction theory, has been proposed in this work. This method realizes zero sliding displacement between the friction material and the stator during the torsional oscillation of the shaft by controlling the driving circle frequency and the duration of the single-phase power-off period, which reduces the deviation of the displacement reservation value. In order to verify the correctness of the driving mechanism, a test platform has been built, and two positioning strategies have been used for experimental verification. The following experimental results have been obtained: compared to TPSPM, FSPTTPPM has the advantages of higher positioning accuracy and short positioning time. In terms of the positioning accuracy, the relative errors of the displacement reservation values of FSPTTPPM and TPSPM vary with the initial angular velocity (0.24 to 1.18 rad/s) in the range of −0.4 to 0.1 and −0.8 to 0.8, respectively. In addition, the relative error of the displacement reservation value is closer to zero than that of TPSPM at the same initial angular velocity. In terms of the positioning time, when the initial angular velocity is greater than 0.7 rad/s, the positioning time of the FSPTTPPM is approximately 10 ms smaller than that of the TPSPM.

Polar Upwelling at Three Sunspot Minima

We summarize the analysis methods used to derive differential rotation leading to the Torsional Oscillations (TO) and a new method for determining Meridional Circulation (MC). The new MC results show a reversal of the flow direction at near-polar latitudes with the time of reversal corresponding closely to the time of sunspot Minima.

Case Study: Automated Stringer Detection Boosts Drilling Efficiency With Less Downtime

_ Horizontal drilling has evolved over decades to become a trusted well construction technique in mature oil-producing regions. However, many challenges remain in geologically complex drilling environments. One challenging drilling scenario arises when the drill bit encounters hard stringers interbedded within softer formations like sandstone. The sudden change in rock mechanics in moving from the formation to the stringer often results in deflection of the drill bit and a deviation in the well path known as a dogleg. The rapid directional changes caused by doglegs lower drilling efficiency by moving the drilling assembly off its planned path, and sometimes, out of the desired reservoir zone. The static loads generated in a dogleg can damage the bottomhole assembly (BHA) and lead to premature bit wear, shortened run life, higher maintenance costs, and more trips downhole. The curved path also increases the risk of stuck casing or completions strings, which can prevent the well from being completed to planned target depth (TD). An operator of a mature field in the North Sea faced such challenges while drilling multilateral wells through reservoir sections containing hard calcite stringers interspersed in sand formations with low unconfined compressive strength. The operator aimed to keep its lifting costs low by increasing the gross rate of penetration (ROP) through these sections. But the doglegs created at each stringer often required pulling back to perform a costly, time-consuming reaming operation to smooth out the well path and allow drilling to continue to TD. On average, the operator amassed 2.7 hours of invisible lost time (ILT) on reaming for every 3,300 ft (1000 m) drilled and achieved significantly lower gross ROP—both of which increased the operator’s per-well lifting costs above plan. Working with the operator, Baker Hughes developed an automated stringer detection service that would identify stringers earlier than previously possible to minimize local doglegs, reduce reaming time, and efficiently deliver wells to plan. Developing an Early-Warning Stringer Detection Service With operator input, the service provider developed an automated service that provided reliable, consistent, and early stringer detection to guide fast corrective action. The service includes an automated stringer-detection module embedded in an advanced measurement-while-drilling (MWD) sensor sub. The sub contains several dynamic sensors that collect a range of vibration and load measurements. The detection module uses a physics-based algorithm that combines two MWD measurements—tangential acceleration and dynamic torque at the bit—to calculate a value for high-frequency torsional oscillation (HFTO) in the BHA. HFTOs are torsional vibrations with frequencies between 50 Hz and 450 Hz that only occur during bit-rock interactions in hard formations. The distinct change in HFTO response during the transition from soft formations to hard formations makes it a leading indicator for detecting stringers in real time during drilling.

Вплив імпульсних рульових двигунів на динаміку твердопаливної ракети

The object of this study is a rocket with a solid propellant engine launched from a vehicle launcher. The current work studies the oscillations of a rocket airframe in flight under the influence of impulses of the steering motors and the effectiveness of flight control along the trajectory by the steering motors located in the head of the solid rocket. Analytical and numerical methods for determining the frequencies of free vibrations of a rigid body and analytical methods for integrating differential equations of motion are applied. A mathematical model of rocket flexural oscillations has been constructed. Methods for determining the modes and frequencies of natural oscillations have been analyzed. Three lower frequencies and modes of natural oscillations of the rocket were calculated. The discrepancy between the results of the calculation by the computer program and the analytical calculation of the first approximation is 3%. The calculation of oscillations of a rocket with a caliber of 30 mm and a length of 7655 mm showed that torsional and longitudinal oscillations have relatively high frequencies and have little effect on the stability and controllability of the rocket flight. The vibrations of the rocket airframe, which has a gas-dynamic flight control system with the help of rudders and a gas-jet one with the help of steering engines, are studied. Steering motors are small-sized disposable solid propellant motors, which are located in five rows around the perimeter of the rocket airframe at the head. Methods for calculating the forced oscillations of a rocket during the operation of steering engines have been developed. Under the action of the control pulse, transverse oscillations of the rocket airframe y are excited and simultaneously, the rocket rotates as a solid body around the center of mass. Airframe oscillations quickly decay, and rotation changes the pitch or slip angle. To stop the rotation and leave some required angle of inclination or azimuth of the trajectory, a second impulse of force must be given by the steering motor mounted on the opposite side of the hull. The dependence of the change in pitch and slip angles on the duration of time intervals between control pulses was studied. The analysis of the dependence obtained shows that, although the weight of the fuel charge is approximately half the weight of the rocket, the controllability by the steering engines is equally effective at any fuel consumption.

A novel virtual synchronous machine implementation and verification of its effectiveness to mitigate renewable generation connection issues at weak transmission grid locations

AbstractLarge‐scale penetration of renewable resource based generation will displace conventional synchronous machine‐based power generation. This will lower the overall system inertia and will result in lower short circuit levels at point of connection (POC) of renewable resources. Renewable resources such as wind and solar photovoltaic (PV) are interfaced to the power system via power electronic inverters. Operation of inverter‐based equipment under low inertia and low short circuit conditions is challenging. Specific challenges include fault recovery response, unstable oscillatory interactions, and impact on torsional oscillations of thermal generating units. In this paper, the effectiveness of inverters, controlled as a virtual synchronous machine (VSM), to overcome some of these issues is investigated. A battery energy storage system (BESS) inverter is controlled as a VSM. The input signals provided to the BESS inverter are derived from solving the time domain equations of a synchronous machine. The response of exciter, governor, and power system stabilizer (PSS) are also included in the VSM strategy. The dynamic characteristics of the proposed VSM are verified using a single machine infinite bus (SMIB) test model. The effectiveness of the proposed VSM approach to mitigate specific technical challenges is verified by performing dynamic response studies on two test systems. The two test systems represent selected regions of practical power systems with high renewable penetration. The VSM response is compared with a conventional synchronous machine response in all test cases, to demonstrate the close correlation of dynamic response. The simulation results demonstrate that the VSM's response is as expected and is capable of mitigating stability‐related issues due to low system inertia and low short circuit strength.