Torsional Coupling Research Articles

Analysis of horizontal vibration characteristics of unequal height twin towers of rigid connected structure

The twin-tower concatenated building with unequal height is highly favored by architects, because of its distinctive appearance and specific building function. Recently, the dynamic characteristics and earthquake action of the unequal height twin towers with the rigid connected structures have been assessed utilizing engineering experience and finite element analysis. However, the technical guidance at the theoretical level is rarely reported. Here, to reveal the dynamic characteristics of unequal height twin towers with the rigid connected structures, the equivalent design method for isolated structures was employed. The Higher Tower (S1) is equivalent to a two-particle two-degree-of-freedom system in the unequal height twin towers with a maximum height of 60 m, while the Lower Tower (S2) is equivalent to a single particle one-degree-of-freedom system. The variation law of their first-order natural vibration periods in the parallel conjoined direction was then analyzed using a simplified structural dynamics method. To investigate the coupling of frequencies and changing law of mode shapes, a three-degree-of-freedom system was established in the vertical conjoined direction. The simplified structural dynamics models were compared to the finite element simulation and validated further by an engineering practice. The results indicate that there are numerous plane and torsion coupling modes in the direction of the vertical rigid connection. The equipment and function area with heavy load should be set in the S1 area when the total stiffness meets the requirements in the direction of the vertical rigid connecting body, whereas the stiffness of the S2 should be controlled to the lowest extent. By analyzing engineering examples and comparing them to numerical simulations, the simplified structural dynamics methods can be used to control and optimize the design scheme to determine a reasonable position for the connecting body within the tower height.

Experimental study on the dynamic modulus of compacted loess under bidirectional dynamic load

The dynamic characteristics of compacted loess are of great significance to the seismic construction of the Loess Plateau area in Northwest China, where earthquakes frequently occur. To study the change in the dynamic modulus of the foundation soil under the combined action of vertical and horizontal earthquakes, a hollow cylindrical torsion shear instrument capable of vibrating in four directions was used to perform two-way coupling of compression and torsion of Xi'an compacted loess under different dry density and deviator stress ratios. The results show that increasing the dry density can improve the initial dynamic compression modulus and initial dynamic shear modulus of compacted loess. With an increase in the deviator stress ratio, the initial dynamic compression modulus increases, to a certain extent, but the initial dynamic shear modulus decreases slightly. The dynamic modulus gradually decreases with the development of dynamic strain and tends to be stable, and the dynamic modulus that reaches the same strain increases with an increasing dry density. At the initial stage of dynamic loading, the attenuation of the dynamic shear modulus with the strain development is faster than that of the dynamic compression modulus. Compared with previous research results, it is determined that the dynamic modulus of loess under bidirectional dynamic loading is lower and the attenuation rate is faster than that under single-direction dynamic loading. The deviator stress ratio has a more obvious effect on the dynamic compression modulus. The increase in the deviator stress ratio can increase the dynamic compression modulus, to a certain extent. However, the deviator stress ratio has almost no effect on the dynamic shear modulus, and can therefore be ignored.

Multi-objective optimization of composite airfoil fibre orientation under bending–torsion coupling for improved aerodynamic efficiency of horizontal axis wind turbine blade

Modern multi-megawatt wind turbines have long, slender and flexible blades, which experience significant vibration due to aerodynamic loads. These blades are generally made of composite layups with cambered airfoil sections, which induce elastic and dynamic coupling between bending and torsional modes. In addition to these phenomena, the aerodynamic pitching moment also arises due to the offset of the blade pitch axis from the aerodynamic centre. With this in mind, the present work aims to develop a computationally efficient complete multi-body dynamic aero-servo-elastic model of an onshore horizontal axis wind turbine, including bending–torsion coupling and aerodynamic pitching moment. 3D wind fields are generated using TurbSim, and the responses of the coupled system are solved under different operational scenarios, which signify the impact of the aforementioned coupling. It is found to be particularly detrimental at higher wind speeds than the rated value. But, proper design and implementation of structural layup can enhance the aerodynamic performance of the blade. Finally, the optimal design of composite fibre orientation of a benchmark turbine blade is investigated to show its beneficial effects in load/response mitigation.

Nonlinear characteristics of a multi-degree-of-freedom wind turbine’s gear transmission system involving friction

In this study, a 42-degree-of-freedom (42-DOF) translation–torsion coupling dynamic model of the wind turbine’s compound gear transmission system considering time-varying meshing friction, time-varying meshing stiffness, meshing damping, meshing error and backlash is proposed. Considering the different meshing between internal and external teeth of planetary gear, the time-varying meshing stiffness is calculated by using the cantilever beam theory. An improved meshing friction model takes into account the mixed elastohydrodynamic lubrication to calculate the time-varying meshing friction. The bifurcation diagram of the excitation frequency is utilized to analyze the bifurcation and chaos characteristics of the system. Meanwhile, the nonlinear dynamic characteristics of the gear system are identified by using the time domain diagrams, phase diagrams, Poincare maps and amplitude–frequency spectrums of the gear system. The results show that the system has complex bifurcation and chaotic behaviors including periodic, quasi-periodic, chaotic motion. The bifurcation characteristics of the system become complicated and the chaotic region increases considering the effects of friction in the high-frequency region.

Exact solutions for thin-walled composite open section beams using a unified state space coupled field formulation

Thin-walled open section composite beams (TWOSCB) used extensively in aerospace structures exhibit several non-classical effects such as torsional warping, warping shear, material coupling, and shear deformation. Arbitrary cross-section and material coupling make the governing equations highly coupled and difficult to solve analytically. In this paper, a unified coupled-field formulation is developed to analyze TWOSCB accommodating all non-classical effects. Using the state-space method to derive analytical expressions for displacements and forces, Vlasov solutions of isotropic beams are recovered. Results obtained for arbitrarily laminated mono-symmetric composite channel and I-section beams subjected to bending and torsion loads show excellent agreement with available results in the literature.

Vibration features of rotor unbalance and rub-impact compound fault

To meet the requirements of improving work efficiency, the rotating machinery represented by gas turbines reduces the gap between rotor and stator, making rub-impact occur frequently. However, a few researchers combined with the current gas turbine condition monitoring concluded that it could diagnose the rub-impact fault. In this study, the vibration features that can help diagnose the compound fault of rotor unbalance and rub-impact are researched. Taking the Jeffcott rotor system as the research object, the mathematical model is constructed considering the coupling of radial and torsion, and the Runge-Kutta method is used to solve the differential equation. Through the analysis of the model results, it is concluded that the compound fault can be diagnosed by the vibration features-reduction of the fundamental frequency amplitude. Finally, the correctness of the model is verified by experiments. At the same time, the vibration features of the rotor and stator are compared to show the consistency of vibration features, which shows that the proposed features can diagnose this compound fault.

Large Torsional Rotation and Rotational Inversion Coupling with Linear Deformation of Electromechanical Actuators Based on Conductive Micro-/Nano-Helices

Large Torsional Rotation and Rotational Inversion Coupling with Linear Deformation of Electromechanical Actuators Based on Conductive Micro-/Nano-Helices

Flutter Analysis of a 3D Box-Wing Aircraft Configuration

The aim of this paper is to present a flutter analysis of a 3D Box-Wing Aircraft (BWA) configuration. The box wing structure is considered as consisting of two wings (front and rear wings) connected with a winglet. Plunge and pitch motions are considered for each wing and the winglet is modeled by a longitudinal spring. In order to exert the effect of the wing-joint interactions (bending and torsion coupling), two ends of the spring are located on the gravity centers of the wings tip sections. Wagner unsteady model is used to simulate the aerodynamic force and moment on the wing. The governing equations are extracted via Hamilton’s variational principle. To transform the resulting partial integro-differential governing equations into a set of ordinary differential equations, the assumed modes method is utilized. In order to confirm the aerodynamic model, the flutter results of a clean wing are compared and validated with the previously published results. Also, for the validation, the 3D box wing aircraft configuration flutter results are compared with MSC NASTRAN software and good agreement is observed. The effects of design parameters such as the winglet tension stiffness, the wing sweep and dihedral angles, and the aircraft altitude on the flutter velocity and frequency are investigated. The results reveal that physical and geometrical properties of the front and rear wings and also the winglet design have a significant influence on BWA aeroelastic stability boundary.

A new torsional vibration coupling model for transmission system in diesel generator

The coupling between the crankshaft and the camshaft is neglected before in fault diagnosis which may lead to incomplete fault information. In this paper, a new torsional coupling model of a diesel generator transmission system is proposed for fault diagnosis. The natural frequency and forced torsional vibration response of the model are obtained by the system matrix method and Newmark-β method. For the system without considering the lumped mass of camshafts, some key natural frequencies are lost. The vibration dynamics are compared for the transmission system with and without the new coupling model. And important frequency responses are missed in the spectrums of the forced torsional vibration without the new coupling model. Finally, the new coupling model is implemented in fault diagnosis and the cause of an unusual vibration fault is deduced in the simulation, which confirms the feasibility of the proposed model in fault diagnosis.

Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures

The design of complex, competing effects in magnetic systems—be it via the introduction of nonlinear interactions1–4, or the patterning of three-dimensional geometries5,6—is an emerging route to achieve new functionalities. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states7, ultrafast chiral domain wall dynamics8–10 and spin textures with new spin topologies7,11. Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography12,13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall14. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials15, unconventional computing2,16, particle trapping17,18 and magnetic imaging19.

Establishment and analysis of nonlinear frequency response model of planetary gear transmission system

Abstract. Based on the lumped parameter theory, a nonlinear bending torsion coupling dynamic model of planetary gear transmission system was established by considering the backlash, support clearance, time-varying meshing stiffness, meshing damping, transmission error and external periodic excitation. The model was solved by the Runge–Kutta method, the dynamic response was analyzed by a time domain diagram and phase diagram, and the nonlinear vibration characteristics were studied by the response curve of the speed vibration displacement. The vibration test of the planetary gearbox was carried out to verify the correctness of frequency domain response characteristics. The results show that the vibration response in the planetary gear system changes from a multiple periodic response to a single periodic response with the increase in input speed. Under the action of the backlash, time-varying meshing stiffness and meshing damping, the speed vibration displacement response curves of internal and external meshing pairs appear to form a nonlinear jump phenomenon and have a unilateral impact area, and the system presents nonlinear characteristics. The nonlinear vibration of the system can be effectively suppressed by decreasing the mesh stiffness or increasing the mesh resistance, while the vibration response displacement of the system increases by increasing the external exciting force, and the nonlinear characteristics of the system remain basically unchanged. The backlash is the main factor affecting the nonlinear frequency response of the system, but it can restrain the resonance of the system in a certain range. The spectrum characteristics of the vibration displacement signal of the planetary gearbox at different speeds are similar to the simulation results, which proves the validity of the simulation analysis model and the simulation results. It can provide a theoretical basis for the system vibration and noise reduction and a dynamic structural stability design optimization.

A hybrid linear actuator based on screw clamp operation principle: Design and experimental verification

This paper presents a hybrid linear actuator using screw clamp operation principle. The actuator mainly consists of a hollow electromagnetic torque motor located between two clamping nuts, two hollow cylindrical shaped piezoelectric stacks symmetrically configured at two ends of the actuator and a feed-screw (also considered as the mover of the actuator) assembled throughout all the parts. The torque motor is symmetrically connected to two clamping nuts via two torsion coupling springs located at either end of the motor spindle. Two piezoelectric stacks can work independently to propel the opposing loads, which effectively take advantage of the anti-compression and non-tensile characteristics of piezoelectric element. The special feature of the actuator is the screw clamp mechanism, the operation of which involves intermittent rotation of two nuts (driven by the torque motor) on a feed-screw to achieve the bi-direction piezoelectric motion accumulation. Furthermore, the application of feed-screw could decrease the actuator’s sensitivity to wear, in order to realize a rigid self-locking and thus ensure the actuator’s holding capacity. A prototype was fabricated and the experimental results show that the no-load speed, maximum thrust, and peak power of the actuator were 20 mm/s, 280 N, and 1.54 W, respectively.

Applications of the asymptotic homogenization to materials with periodic and non‐periodic micro structures

AbstractThe first part of the paper presents the application of the asymptotic homogenization for determining the effective elastic and elasto‐plastic properties and stress concentrations in the B4C/2024Al composite using 3D x‐ray images of the internal structure. For comparison, calculations were performed for a dispersed composite with an aluminum matrix, in which boron carbide inclusions were simulated by ellipsoids. The elasto‐plastic behavior of the real structure of the B4C/2024Al composite was investigated in computational experiments on uniform compression, uniaxial tension, and a combination of pure shear and uniform compression. The calculation results were compared with experimental data. The second study concerns the application of asymptotic homogenization to metamaterials. Metamaterials may have unusual behaviour such as tension–bending coupling or tension–torsion coupling. Most metamaterials have a periodic structure in Cartesian coordinates. We studied tension‐compression‐shear coupling provided by the metamaterial using second order asymptotic representation.

Stick slip characteristics analysis of drill string system with longitudinal and torsional coupling tool

Due to the complexity and uncertainty of downhole conditions during drilling, the torsional vibration generated at the drill bit may cause the bottom hole assembly (BHA) to excite high frequency longitudinal vibration, which may lead to the longitudinal bounce of the drill string in severe cases. The excessive vibration will seriously affects the service life of the drill bit or other downhole tools. To avoid these problems and reduce the stick-slip phenomenon, this paper proposed an innovative longitudinal-torsional coupling tool, which can generate appropriate coupling vibration. With analysis of working mechanism, theoretical research includes establishment of dynamic model of BHA connected with the tool. The cases study is carried out based on Lagrangian theory. The results show the tool can effectively suppress stick-slip vibration. By adjusting the internal design parameter, the innovative design can achieve appropriate vibration, which can enable the drilling smoother, increase the mechanical efficiency, and reduce the wear of drill bit. The innovative design can provide reference for avoiding downhole accidents and improving of drilling safety. The theoretical research results can present new ideas for the development of drill string dynamics under new situations.

Fault Feature Analysis of Gear Tooth Spalling Based on Dynamic Simulation and Experiments.

Gear dynamics analysis based on time-varying meshing stiffness (TMS) is an important means to understand the gear fault mechanism. Based on Jones bearing theory, a bearing statics model was established and introduced into a gear system. The lateral–torsion coupling vibration model of the gear shaft was built by using a Timoshenko beam element. The lumped parameter method was used to build the dynamic model of a gear pair. The dynamic model of a spur gear system was formed by integrating the component model mentioned above. The influence of rectangular and elliptical spalling on TMS was analyzed by the potential energy method (PEM). The fault feature of tooth spalling was studied by dynamic simulation and verified by experiments. It is found that the gear system will produce a periodic shock response owing to the periodic change of the number of meshing gear teeth. Due to the contact loss and the decrease of TMS, a stronger shock response will be generated when the spalling area is engaged. In the spectrum, some sidebands will appear in the resonance region. The results can provide a theoretical guide for the health monitoring and diagnosis of gear systems.

A novel mechanical metamaterial with tailorable Poisson’s ratio and thermal expansion based on a chiral torsion unit

Auxetic and negative thermal expansion metamaterials have a wide range of applications in flexible electronics, aerospace, biomedicine. Based on the compression/thermal–torsion coupling effects, and combining the special deformation mechanism of the planar anti-tetrachiral structure, this work proposed a novel 3D mechanical metamaterial with negative Poisson’s ratio (PR) and negative coefficient of thermal expansion. The mechanical design method of the metamaterial is demonstrated, and the coordinated deformation theory between its in-plane and out-of-plane deformations is established. By numerical simulation, the torsional deformation response of torsion unit of the metamaterials is explored, and Poisson’s characteristics and thermal expansion effect of the metamaterials are analyzed. The results show that the PR and thermal expansion effect of the metamaterial can be adjusted and switched, and its deformation behavior can be programmed. The coupling design method for metamaterials provides a good design strategy for engineering applications such as intelligent actuators, flexible robots, and biomedical sensors.

Comment on "Electronic, vibrational and torsional couplings in N-methylpyrrole: Ground, first excited and cation states" [J. Chem. Phys. 154, 224305 (2021)

Two-color (1 + 1') zero-electron-kinetic-energy (ZEKE) and photoionization efficiency (PIE) spectra are reported via different levels in the S1 ← S0 (Ã1A2←X̃1A1) one-photon transition of jet-cooled N-methylpyrrole. The laser radiation is produced using two dye lasers, one with an 1800 l/mm grating and one with 2400 l/mm. We report spectra where the excitation and ionization radiation are produced with both combinations of the dye lasers; these spectra differ markedly. This is attributed to Wood's anomalies with the 2400 l/mm grating: one aspect is a loss in light intensity over a range of wavelengths, attributed to a resonance anomaly. Another is the appearance of a "shadow" ZEKE spectrum and PIE curve at apparently higher ionization wavenumbers; under some conditions, a third ZEKE spectrum was observed-these latter observations arise from higher-order dispersion effects, likely caused by a Rayleigh anomaly. We comment on these observations and report more representative ZEKE and PIE spectra than those presented in a recent paper by our group [A. R. Davies, D. J. Kemp, and T. G. Wright, J. Chem. Phys. 154, 224305 (2021)] for four intermediate S1 levels.

Nonlinear Vibration Characteristics of the Involute Spline Coupling in Aeroengine with the Parallel Misalignment

In order to control the vibration of the involute spline coupling in aeroengine well and reduce the fretting wear, a bending–torsion coupling nonlinear vibration model of the involute spline coupling with the misalignment was proposed, and a dynamic meshing stiffness function with multiteeth engagement was established. Then, the influence of different misalignment, wear, and rotation speeds with different misalignment on the nonlinear vibration characteristics of the involute aviation spline coupling was explored. The result shows that with an increase of the parallel misalignment, the system experienced the state of a single period, a quasiperiod, multiperiod, and chaos but finally only alternated between the quasiperiod and the chaos state. The uneven wear of each tooth of the spline displayed a significant influence on the vibration of the spline coupling, and the influence of the uniform wear was smaller under given conditions here. Furthermore, with an increase of the speed, the larger the misalignment was, the more times the system entered or left the chaos state were. The model proposed here is found to be closer to the actual working conditions, and the analysis results can provide more accurate external load conditions for the prediction of the fretting damage of the spline coupling in aeroengine.

Effects of aerodynamic coupling and non-linear behaviour on galloping of ice-accreted conductors

Wind action on ice-covered transmission lines causes galloping, which is a problem because it can introduce interphase short circuits and cause fatigue of the cross-arms of the power line’s towers and insulators. The galloping phenomenon is characterised by a combination of large-amplitude, low-frequency vertical, horizontal, and torsional oscillations. To better understand the dynamic responses of vertical, horizontal and torsional 3-degree-of-freedom (DoF) galloping on four-bundled conductors, time–history analyses were conducted for 2D systems of varying DoFs and frequency ratios. The fundamental characteristics of the conductor’s non-linear 1-DoF vertical response were analysed via time–history analysis, indicating that large oscillations were caused by inclusion of an angular range of relative angle of attack with a high negative lift-coefficient slope. By considering the energy balance of the vertical motion over one oscillation period, we estimated the stable and unstable limit-cycle amplitudes. Then, by comparing the results of the 1-, 2-, and 3-DoF systems, we clarified the effect of aerodynamic coupling on 3-DoF galloping. The oscillation types in the 3-DoF systems were categorised as vertical–horizontal 2-DoF coupling oscillations, vertical–torsional 2-DoF coupling oscillations, and vertical 1-DoF oscillations according to the stationary torsional angle. Finally, we indicated the coupling effects on vertical oscillation by considering the energy balance of the vertical motion with the defined amplitudes and phase differences of the horizontal and torsional motions. The vertical amplitude of the vertical–horizontal 2-DoF coupling oscillation can become very large if the horizontal amplitude increases and the phase difference between horizontal and vertical displacements approaches 180°. Meanwhile, the range of the stationary torsional angle in which the vertical–torsional 2-DoF coupling oscillation occurs becomes wide as the phase difference between the torsional and vertical displacements approaches 90°. However, without horizontal motion, the vertical amplitude has a limited value, even if the torsional amplitude becomes large.

Multispan bridges with distributed deck and pier mass and pier‐flexure‐deck‐torsion coupling under transverse excitation—Analytical solution, parametric studies, design implications

AbstractAn “exact” analytical dynamic model is developed for symmetric bridges with two to five spans under transverse earthquake. It considers the mass as distributed along the deck and the piers and accounts for coupling of deck torsion with pier bending in vertical planes normal to the deck's axis. The characteristic equation is formulated in terms of (up to) seven dimensionless parameters which fully define a bridge and is solved numerically. Commercial software is used to validate the solution. Parametric studies of 225 bridge layouts produce response results of key importance for seismic design. Specific and general conclusions are drawn for conceptual design of multispan bridges for transverse earthquake.