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1
Al-Tayari, Abdulhameed M. Y., Siyu Chen, and Zhou Sun. "A Coupled Torsional-Transition Nonlinear Vibration and Dynamic Model of a Two-Stage Helical Gearbox Reducer for Electric Vehicles." Shock and Vibration 2020 (August 30, 2020): 1–25. http://dx.doi.org/10.1155/2020/8838521.
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A coupled torsional-transition nonlinear dynamic model of a two-stage helical gear (TSHG) reduction system for electric vehicles (EVs) is presented in this paper. The model consists of 16 degrees of freedom (DOF), which includes factors such as the nonlinearity of backlash, time-varying mesh stiffness (TVMS), mesh damping, supporting bearings, static transmission error (STE), and the torsional damping and stiffness of the intermediate shaft, in which the fourth-order Runge–Kutta numerical integration method was applied to solve the differential equations. With the help of bifurcation diagrams, time-domain histories diagrams, amplitude-frequency spectrums, phase plane diagrams, Poincaré maps, root-mean-square (RMS) curves, peak-peak values (PPVs), and Lyapunov exponents, the effects of pinion rotational speed, backlash, torsional stiffness, and torque fluctuation on the dynamic behavior of TSHG system are investigated. The stability properties of steady-state responses are investigated using Lyapunov exponents. The results reveal various types of dynamic evolution mechanisms and nonlinear phenomena such as periodic-one responses, quasiperiodic responses, jumps phenomena, and chaotic responses. The research presents useful results and information to vibration control and dynamic design of the TSHG transmission system used in EVs.
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Vo, Duy-Quang, and Hoang Lan Ton-That. "Free vibration of simply supported steel I-girders with trapezoidal web corrugations." Reports in Mechanical Engineering 1, no. 1 (2020): 141–50. http://dx.doi.org/10.31181/rme200101141v.
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Natural frequency is essential information required to perform the dynamic analysis. In this study, the straight I-girder element with trapezoidal web corrugations and singly symmetric cross-section is derived based on Kang and Yoo’s thin-walled curved beam with doubly symmetric cross-section theory. Each node of the element has seven degrees of freedom including one warping degree of freedom. Using Hamilton’s principle, governing linear dynamic differential equations of equilibrium, elastic element stiffness matrix, and consistent element mass matrix are established. Matlab code is employed for natural frequency analysis of simply supported steel I-girders with trapezoidal web corrugations. The results are compared with the natural frequencies obtained with ABAQUS. Finally, it is found that the proposed equations provide a good prediction of natural frequency for the first three lateral bending modes and the first five torsional modes.
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Cai, Jun Yan, Xi Jun Liu, and Su Xia Zhang. "Numerical Analysis for Galloping of Iced Quad Bundle Conductors." Applied Mechanics and Materials 226-228 (November 2012): 30–34. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.30.
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In order to attain the purpose of anti-galloping, a simplified model for iced quad bundle conductors of three degrees of freedom in vertical, horizontal and torsional directions is established by means of the Hamilton principle, in which the effect of spacers stiffness and damping is considered. Based on the model, the influence of related parameters such as fluid density, damping ratio on conductor galloping amplitude and critical wind velocity is analyzed. Simultaneously, the relation curve between elastic property of spacers and conductor galloping is obtained. The results indicate that the conductor galloping can be weakened to some degree with the proper enlargement of damping ratio, the reasonable setting of spring stiffness on spacers and the avoidance of areas such as the wind outlet and windward as much as possible when choosing the line path and so on.
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Yoon, Jong-yun, and Hyeongill Lee. "Dynamic vibratory motion analysis of a multi-degree-of-freedom torsional system with strongly stiff nonlinearities." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 8 (2014): 1399–414. http://dx.doi.org/10.1177/0954406214543674.
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Physical driveline systems have inherent nonlinearities such as multiple piecewise linear springs, gear backlashes, and drag torques. The multi-staged clutch dampers, in particular, cause severe problems in simulating the nonlinear dynamic behaviors of multi-degree-of-freedom systems. In order to analyze the nonlinear dynamic behaviors of the system, the harmonic balance method has been employed. This study suggests a method to overcome the convergence problems with strong nonlinearities by employing two distinct smoothening factors for stiffness and hysteresis. First, the dynamic behaviors of the multi-degree-of-freedom torsional system are investigated by employing multi-staged clutch dampers subjected to a sinusoidal excitation. Second, the effects of system parameters are examined with respect to dynamic characteristics of torsional vibration. The regimes of resonance frequencies along with the relevant parameters of the system are investigated by calculating backbone curves, which reduce the calculation time significantly. In order to validate harmonic balance method simulation, the simulated results are compared with those of numerical simulation. Harmonic balance method is shown to be more efficient than numerical simulation in calculating the nonlinear frequency response, as well as in simulating the steady-state responses without transient response effect.
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Liu, Qiaobin, Wenku Shi, and Zhiyong Chen. "Identification of firefly algorithm-based fluctuation coefficient of the exciting torque for vehicle driveline." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 2 (2018): 317–26. http://dx.doi.org/10.1177/1464419318808172.
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The unbalanced excitation force and torque generated by an engine that resonate with the natural frequency of drivetrain often causes vibration and noise problems in vehicles. This study aims to comprehensively employ theoretical modelling and experimental identification methods to obtain the fluctuation coefficients of engine excitation torque when a car is in different gear positions. The inherent characteristics of the system are studied on the basis of the four-degree-of-freedom driveline lumped mass model and the longitudinal dynamics model of vehicle. The correctness of the model is verified by torsional vibration test. The second order's engine torque fluctuation coefficients are identified by firefly algorithm according to the curves of flywheel speed in different gears under the acceleration condition of the whole open throttle. The torque obtained by parameter identification is applied to the model, and the torsional vibration response of the system is analysed. The influence of the key parameters on the torsional vibration response of the system is investigated. The study concludes that proper reduction of clutch stiffness can increase clutch damping and half-axle rigidity, which can help improve the torsional vibration performance of the system. This study can provide reference for vehicle drivetrain modelling and torsional vibration control.
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Lam, Fred C., Michael W. Groff, and Ron N. Alkalay. "The effect of screw head design on rod derotation in the correction of thoracolumbar spinal deformity." Journal of Neurosurgery: Spine 19, no. 3 (2013): 351–59. http://dx.doi.org/10.3171/2013.6.spine12655.
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Object The use of fixed-axis pedicle screws for correction of thoracolumbar deformity in adult surgery is demanding because of the challenge of assembling the bent rod to the screw in order to achieve curve correction. Polyaxial screw designs, providing increased degrees of freedom at the screw-rod interface, were reported to be insufficient in achieving correction of thoracic deformity in the axial plane. Using a multisegment bovine calf spine model, this study investigated the ability of a new uniplanar screw design to achieve derotation correction of the vertebrae and maintain a degree of correction comparable to that of fixed-axis and polyaxial screw designs. Methods Eighteen calf thoracolumbar spine segments from T-6 to L-1 (n = 6 per screw design) underwent bilateral facetectomies at the T9–11 levels and were instrumented bilaterally with pedicle screws and rods. To assess the efficacy of each screw design in imparting rotational correction, each instrumented level was tested under applied torsional moments designed to simulate the motion applied during derotation surgery. Once rotation was achieved, the whole spine was tested to assess the overall stiffness of the construct. Results The fixed-axis construct showed increased efficacy in imparting rotation compared with the uniplanar (115% increase, p > 0.05) and polyaxial (210% increase, p < 0.05) constructs. Uniplanar screws showed a 21% increase in torsional stiffness compared with the polyaxial screws, but this difference was not statistically significant. Conclusions The design of screw heads plays a significant role in affecting the rotation of the vertebrae during the derotation procedure. Uniplanar screws may have the advantage of maintaining construct stiffness after derotation.
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Shi, Wen Ku, Guang Ming Wu, Shi Da Nie, Shi Chao Wang, and Zhi Yong Chen. "The Influence of Torsional Damper Performance Parameter on Transmission System Torsional Vibration." Applied Mechanics and Materials 241-244 (December 2012): 2015–18. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.2015.
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In order to research the influence that the torsional stiffness and damping characteristic of the torsional damper had on the transmission rotational vibration, a multi-degrees-of-freedom model of torsional vibration of a transmission system of an FR type vehicle was built. The frequency of the torsional vibration model of transmission system was calculated, and the forced vibration in the transmission was analyzed; the sensitivity of the torsional stiffness and damping characteristic of the torsional damper on vibration response was researched. This method provides theoretical basis for solving the transmission system rotational vibration of the vehicle, and it has positive meaning in the development of the rear drivetrain NVH.
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Bu, Jian Qing, and Gen Wang Li. "Dynamic Response of Simply-Supported Curved Girder Bridges due to Vehicles." Advanced Materials Research 255-260 (May 2011): 1825–29. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.1825.
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The purpose of this paper, for which a finite element bridge model with 7 degrees of freedom per node and the 1/4 vehicle model with six parameters were established, is to analyze the dynamic response of curved girder bridges under vehicular loads. In the numerical simulation, the vibration characteristics of simply-supported curved girder bridge are analyzed, and the effect to the impact factors were also studied for different radiuses of curvature, eccentricities, ratios between bending and torsion stiffness, and vehicle speeds. The simulated results show that not all the first 5 natural frequencies increase with the variation of radius of curvature. The impact factor variations of vertical deflection and torsion angle are not uniform when parameters changed, and the impact factor of torsion angle would be much larger than that of vertical deflection under the same conditions.
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Hong, Man Bok, and Yong Je Choi. "Design method of planar three-degrees-of-freedom serial compliance device with desired compliance characteristics." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 9 (2012): 2331–44. http://dx.doi.org/10.1177/0954406211432982.
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In this article, a novel method for the systematic design of a planar three-degrees-of-freedom compliance device with desired compliance characteristics is presented. For the realization of desired compliance, the synthesis method of stiffness of a planar mechanism is first derived. The compliance device may be directly realized by means of parallel connections of the synthesized springs. However, the use of several mechanical elements such as joints and guides for spring assemblies for the realization may cause significant complexity in manufacturing the compliance device with high precision and in compact size. In order to resolve the problem, the form of serial connections of three torsional springs which has the same compliance as the form of parallel connections of the synthesized line springs is proposed. The serial form of torsional springs can be physically realized by designing proper shape of the circular flexure hinge corresponding to each of the torsional springs. For the illustration of the proposed design method, a planar serial compliance device with high compliance to the normal contact force is designed and verified by finite element method analysis.
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Xiao, Zheng-Ming, Xing Wu, and Qing Chen. "DYNAMIC MODELING AND ANALYSIS OF MULTI-STAGE PLANETARY GEARS COUPLED WITH CENTRAL BEARINGS AND HOUSING." Transactions of the Canadian Society for Mechanical Engineering 40, no. 5 (2016): 1007–18. http://dx.doi.org/10.1139/tcsme-2016-0083.
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This paper proposes a coupling dynamic model for multi-stage planetary gears train (PGT) based on the gearing theory and Lagrange equation, which is developed by analyzing the displacement relationships of gearing system and the influence of floating components. The time-varying mesh stiffness, bearings in housing, and the torsional support stiffness of ring gears are also considered. This model has 26 degrees-of-freedom (DOF) and adopts three planar DOFs for each central component, mesh phasing relations among planetary gears, and the rotational DOF for the planets of each stage. The modified transverse-torsional model is established in the rotating Cartesian coordinates by using the lumped-parameter method; thus this model is more accurate than the purely torsional model for describing the physical dynamics. The acceleration data is tested by using the scheme of a back-to-back power circulation set-up, and the vibration properties are also studied.
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Hatamzadeh, Mehran, Reza Hassannejad, and Ali Sharifnezhad. "Application of a biomechanical model and combinatorial optimization to determine lower limb joints torsional stiffness in human landing." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 2 (2019): 241–55. http://dx.doi.org/10.1177/1464419319891326.
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Lower limb joint’s torsional stiffness is directly related to the individual’s performance and probability of injury when landing. There are various methods of calculating ankle, knee, and hip joint’s torsional stiffness in which the reliability of the achieved values by them are highly controversial. The purpose of this research is to provide a new method of calculating lower limb joint’s active torsional stiffness based on the body’s four-degrees-of-freedom biomechanical model. For this purpose, a group of subjects performs single-leg landing protocol from the box. In this method, the biomechanical model’s equations of motion are derived in the sagittal plane and are combined with a combinatorial optimization algorithm, which consists of genetic and simulated annealing. By the use of acquired data from the force plate and motion analysis system, combinatorial genetic algorithm–simulated annealing algorithm tries to minimize the differences between the model’s ground reaction force (GRFModel) and the GRFExperimental for each subject and thereby the joint’s torsional stiffness values are obtained. Results show that calculating lower limb joint’s torsional stiffness using the proposed method has good ability in simulating the GRFExperimental in the model. Also, the obtained values by the proposed method have moderate to good reliability and desirable variability in the measurements. Comparing the obtained stiffness values with the values of three conventional computation method in the literature shows that those common methods’ results have high computational errors, low reliability, and high variability in the measurement. Also, their ability to produce GRFModel similar to the GRFExperimental is weaker than the proposed method in single-leg landing protocol.
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Bently, D. E., P. Goldman, and A. Muszynska. "“Snapping” Torsional Response of an Anisotropic Radially Loaded Rotor." Journal of Engineering for Gas Turbines and Power 119, no. 2 (1997): 397–403. http://dx.doi.org/10.1115/1.2815588.
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A rotor system with two orthogonal lateral and two angular (torsional) degrees of freedom is considered. The rotor has asymmetry of the lateral stiffness and is laterally loaded with a constant radial force and a rotating unbalance. Constant driving and load torques are applied to the rotor. The important part of the research includes an analysis of “snapping” action, when, during rotation, the rotor experiences a peak of torsional acceleration. This occurs when the “strong stiffness” axis of the anisotropic rotor passes under the axis of the sideload. The numerical simulation of the analytical model exhibits a snapping (accelerated) torsional response of the rotor at twice synchronous frequency (2×), and it is especially pronounced at 1× and 2× torsional resonances. The snapping response can initiate a rotor crack in the area of stress concentration, can stimulate existing crack propagation, and can be a cause of the coupling failure. The analytical results are obtained by the Averaging Method application. They confirm the numerical results and show the possibility of combination resonance occurrences. The synchronous dynamic stiffness for the frequency range around 1× lateral resonance is analytically obtained. The specific shape of the quadrature dynamic stiffness component can serve as a shaft crack indicator and can be used for early detection of a lateral crack on the rotor.
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Tuo, Jiying, Zhaoxiang Deng, Heshan Zhang, and Jinshan Qiu. "A 3-axis torsion quasi-zero-stiffness-based sensor system for angular vibration measurement." Journal of Vibration and Control 24, no. 18 (2017): 4325–36. http://dx.doi.org/10.1177/1077546317724016.
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In this paper, a novel 3-axis torsion quasi-zero-stiffness (TQZS)-based sensor system is proposed for absolute rotation measurement in vibration systems. Analysis on the applied torque and structural parameters shows that the proposed mechanism with two concentric spheres connected by six symmetry distributed springs could approximately achieve TQZS features in three rotational degrees of freedom simultaneously, thus a remarkable torsional vibration measurement performance can be guaranteed. Although due to high stiffness, the mechanism also has high anti-interference ability about force or vibration in translational directions. Mathematical modeling and numerical simulations are carried out to show the effectiveness of the proposed 3-axis sensor system in different base vibrations. In consideration of its feasibility and high performance, it can be foreseen that the proposed TQZS-based sensor will get more and more implementations in various engineering practices with torsional vibration measurements.
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Idehara, Sérgio J., Fernando L. Flach, and Douglas Lemes. "Modeling of nonlinear torsional vibration of the automotive powertrain." Journal of Vibration and Control 24, no. 9 (2016): 1774–86. http://dx.doi.org/10.1177/1077546316668687.
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A vibration model of the powertrain can be used to predict its dynamic behavior when excited by fluctuations in the engine torque and speed. The torsional vibration resulting from torque and speed fluctuations increases the rattle noise in the gearbox and it should be controlled or minimized in order to gain acceptance by clients and manufactures. The fact that the proprieties of the torsional damper integrated into the clutch disc alter the dynamic characteristic of the system is important in the automotive industry for design purposes. In this study, bench test results for the characteristics of a torsional damper for a clutch system (torsional stiffness and friction moment) and powertrain torsional vibration measurements taken in a passenger car were used to verify and calibrate the model. The adjusted model estimates the driveline natural frequency and the time response vibration. The analysis uses order tracking signal processing to isolate the response from the engine excitation (second-order). It is shown that a decrease in the stiffness of the clutch disc torsional damper lowers the natural frequency and an increase in the friction moment reduces the peak amplitude of the gearbox torsional vibration. The formulation and model adjustment showed that a nonlinear model with three degrees of freedom can represent satisfactorily the powertrain dynamics of a front-wheel drive passenger car.
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Hammami, Maroua, Nabih Feki, Olfa Ksentini, Taissir Hentati, Mohamed Slim Abbes, and Mohamed Haddar. "Dynamic effects on spur gear pairs power loss lubricated with axle gear oils." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 5 (2019): 1069–84. http://dx.doi.org/10.1177/0954406219888236.
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The dynamic model of 12-degrees-of-freedom for spur gears pair accounting for nonlinear time-varying stiffness, damping, and coefficient of friction along the path of contact obtained from experimental tests is investigated. The Newmark's integration method is used to solve the equations and obtain the dynamic responses. Elementary mass, stiffness, and damping matrices with torsional and translational coupled effects were detailed. The lens of this work is to start from a nonlinear dynamic model to evaluate the influence of dynamic effects and lubrication on meshing gears power loss for different spur gear geometries within various operating conditions. The results reveal some useful references to vibration control, dynamic design, and efficiency improvement.
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Matyja, Tomasz, and Bogusław Łazarz. "Simulation Studies of the Effect of Shaft's Nonlinear Flexural Stiffness Parameters for Critical States of Rotating Power Transmission Systems." Solid State Phenomena 236 (July 2015): 62–69. http://dx.doi.org/10.4028/www.scientific.net/ssp.236.62.
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The paper presents simulation studies, performed using Simulink, the impact of nonlinear flexural stiffness of shafts for critical speed range and amplitude of vibration. The tests were performed on the selected model of a rotating machine, consisting of a drive, two torsional vibration dampers, shaft with mounted on it two rigid rotors (discs), supported on a three self-aligning roller bearings and mechanical power receiver (brake). The machine startup and braking with crossing the critical states was simulated using specialized Simulink library, which was developed by authors for analysis of transient states in rotating machines and flexural-torsional couplings. In accordance with the concept of modeling adopted by the authors, rotating system is divided into inertial rigid elements (rotors, bearings, clutches, etc..) and compliance elements (parts of the shaft). The main component of the currently developed library is block modeling rigid rotor with 6 degrees of freedom and with the static and dynamic unbalance. By assumption the library is a modular, expandable and allows modeling the systems of any configuration. The goal of the simulation was to verify how nonlinear flexural stiffness of shaft influences the values of critical speeds and the level of flexural and torsional vibrations.
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Xu, Jinli, Jiwei Zhu, and Lei Wan. "Effects of intermediate support stiffness on nonlinear dynamic response of transmission system." Journal of Vibration and Control 26, no. 9-10 (2020): 851–62. http://dx.doi.org/10.1177/1077546319889872.
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This study is aimed at investigating the effects of intermediate support stiffness on nonlinear vibration response of transmission system. A coupled bending–torsional–lateral dynamic model with 14 degrees of freedom of transmission system is proposed comprehensively considering rubber dynamic stiffness, time-varying stiffness, static transmission error, and backlash. Meanwhile, a model of intermediate support with rubber nonlinear properties is developed to improve the accuracy of analysis. On the basis of the nonlinear differential equations derived by the lumped-parameter method, the dynamic responses of the key parts in the transmission system are obtained using the Runge–Kutta method and the effects of intermediate support stiffness on the dynamic characteristics are analyzed. Numerical results show that complicated interaction occurs and intermediate support stiffness has a great influence on the vibration of the coupled system. With the increase in the intermediate support stiffness, the vibration displacements in the three directions of the gear are progressively reduced and the nature frequencies are changed. The influence of the radial stiffness is greater than that of the axial stiffness. An experiment is performed subsequently to validate the effect of intermediate support stiffness on system, and the experimental results are consistent with numerical ones.
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Jia, Shengxiang, Ian Howard, and Jiande Wang. "The Dynamic Modeling of Multiple Pairs of Spur Gears in Mesh, Including Friction and Geometrical Errors." International Journal of Rotating Machinery 9, no. 6 (2003): 437–42. http://dx.doi.org/10.1155/s1023621x03000423.
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This article presents a dynamic model of three shafts and two pair of gears in mesh, with 26 degrees of freedom, including the effects of variable tooth stiffness, pitch and profile errors, friction, and a localized tooth crack on one of the gears. The article also details howgeometrical errors in teeth can be included in a model. The model incorporates the effects of variations in torsional mesh stiffness in gear teeth by using a common formula to describe stiffness that occurs as the gears mesh together. The comparison between the presence and absence of geometrical errors in teeth was made by using Matlab and Simulink models, which were developed from the equations of motion. The effects of pitch and profile errors on the resultant input pinion angular velocity coherent-signal of the input pinion's average are discussed by investigating some of the common diagnostic functions and changes to the frequency spectra results.
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Panny, Matthias, Andreas Mayr, Marco Nagiller, and Yeongmi Kim. "A domestic robotic rehabilitation device for assessment of wrist function for outpatients." Journal of Rehabilitation and Assistive Technologies Engineering 7 (January 2020): 205566832096123. http://dx.doi.org/10.1177/2055668320961233.
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Introduction Available robot-assisted stroke rehabilitation systems are often limited in their utilization in the home environment, due to several barriers such as high cost, absence of therapists, tedious training tasks, or encumbering interfaces. This paper presents a low-cost robotic rehabilitation and assessment device for restoring wrist function, offering wrist exercises incorporating pronation-supination and flexion-extension movements. Furthermore, the device is designed for the assessment of joint stiffness of the wrist, and range of motion in two degrees of freedom. Methods: Mechanical/electrical design of the device as well as the control system is described. A preliminary evaluation focused on the measurement of the torsional stiffness of the limb is presented. It is evaluated by reconstructing the known stiffness values of torsional springs by measuring the motor current required to displace them. Results The device demonstrates the ability to determine the stiffness of an object with low-cost hardware. Use case scenarios of the device for training and assessment of the wrist are presented, allowing for a range of motion of [Formula: see text] and [Formula: see text], for pronation-supination and flexion-extension respectively. Conclusion The device shows potential to help objectively quantify the stiffness of the wrist movement, which consecutively could be used to represent and quantify the degree of impairment of patients after stroke in a more objective manner. Further clinical study is necessary to examine this.
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Lin, B. C., and A. S. Papageorgiou. "Demonstration of Torsional Coupling Caused by Closely Spaced Periods—1984 Morgan Hill Earthquake Response of the Santa Clara County Building." Earthquake Spectra 5, no. 3 (1989): 539–56. http://dx.doi.org/10.1193/1.1585539.
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The parameters of the dominant modes of vibration of the steel-framed Santa Clara County Office Building in San Jose, California, are determined using “the modal minimization method” for structural identification. The optimal estimates of the model parameters are determined by minimizing a selected measure-of-fit between the responses of the structure and the model. Two types of models are used: (1) A planar linear model with classical damping and (2) A three dimensional linear model consisting of rigid floor decks, where each floor is allowed three degrees of freedom - two orthogonal translations plus a rotation. The Santa Clara County Office Building continued vibrating in a free vibration manner with very low damping, long after the intense part of ground motion had ended. The records of its torsional motion exhibit a strong beating effect which is explained by the strong coupling of torsional and translational modes of vibration. Such a strong coupling of modes of vibration is attributed to the proximity of the value of torsional stiffness to that of translational stiffnesses.
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Xu, Jinli, Fancong Zeng, and Xingyi Su. "Coupled Bending-Torsional Nonlinear Vibration and Bifurcation Characteristics of Spiral Bevel Gear System." Shock and Vibration 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/6835301.
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A spiral bevel gear system supported on thrust bearings considering the coupled bending-torsional nonlinear vibration is proposed and an eight degrees of freedom (8DOF) lumped parameter dynamic model of the spiral bevel gear system combined with time-varying stiffness, static transmission error, gear backlash, and bearing clearances is investigated. The spiral bevel gear system is analyzed with the equations of motion and the dynamic response is solved using the Runge-Kutta method. The effects of mesh frequency, mesh damping coefficient, load coefficient, and gear backlash are revealed, which describe the true mesh characteristics of the spiral bevel gear system. The bifurcation characteristics as jump discontinuities, periodic windows, and chaos are obtained by studying time histories, phase plane portraits, Poincaré maps, Fourier spectra, and global bifurcation diagrams of the gear system. The results presented in this study provide some useful information for engineers in designing and controlling such gear systems.
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Gao, Zhi Ying, Yong Zang, and Tian Han. "Hopf Bifurcation and Stability Analysis on the Mill Drive System." Applied Mechanics and Materials 121-126 (October 2011): 1514–20. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.1514.
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According to the lumped mass method, the drive system of rolling mill can be simplified as a three-degree-of-freedom spring-mass model. The nonlinear dynamics equations are established considering nonlinear torsion stiffness of connecting shaft and nonlinear friction force between roller and strip, and Hopf bifurcation and critical parameters are analyzed by applying the Hurwitz algorithm criterion. Furthermore, the system stability is numerically simulated through time-history and phase plots. The results indicate that the system motion can be stable in some range of parameters, and the bifurcation phenomenon occurs and the stability may be lost across the critical points. In addition, at different bifurcation points the phase orbit run along diverse skeleton curves of revolution. These conclusions are significant to reveal the mechanism of system bifurcation and stability, and help for optimization of technology condition in practical application.
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Srikanth, P., and AS Sekhar. "Dynamic analysis of wind turbine drive train subjected to nonstationary wind load excitation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 3 (2014): 429–46. http://dx.doi.org/10.1177/0954406214536547.
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The dynamic analysis of wind turbine drive train is presented in this paper. A typical wind turbine drive train consists of a rotor, gearbox and generator. The dynamic modelling of epicyclic gearbox that exists in wind turbine is challenging due to the fact that it has both rotating and orbiting gears. The dynamic equations of motion are obtained based on the rigid multibody modelling with discrete flexibility approach by Lagrange’s formulation. The dynamic model accounts for the time varying gear tooth mesh stiffness, linear stiffness of bearings and torsional shaft stiffness. The aerodynamic torque that a wind turbine drive train subjected to, is modelled based on the simplified method for load calculation in wind turbine, Danish Standard DS472. The characteristic load value acting per unit length at the two-thirds length of the blade is used for calculating the total load of the torsional moment. The vibration signals that are obtained from wind turbine drive train are nonlinear and nonstationary in nature. This is due to the fact that the applied torque load on drive train is nonlinear and nonstationary in nature. The coupled dynamic model of 18 degrees of freedom is solved for responses in time and frequency domains for some nonstationary wind load realizations. The dynamic responses of the system, contact forces between gear tooth pairs in time and frequency domains are obtained numerically. The study envisages that this dynamic model of wind turbine drive train is very useful for subsequent studies on condition monitoring.
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Liu, Zhansheng, Senlin Huang, and Jiexian Su. "Nonlinear Dynamic Analysis of an Unsymmetrical Generator-Bearing System." Journal of Vibration and Acoustics 129, no. 4 (2007): 448–57. http://dx.doi.org/10.1115/1.2731407.
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Considering both nonlinear oil film force and unsymmetrical stiffness, this paper presents a mechanical model of a generator-bearing system. The complex mode synthesis method is used to reduce the linear degrees of freedom of the high order model in the rotating coordinates, and one-order modal differential equations are obtained which may not be solved directly by Newmark-β method. To solve this problem, a modified Newmark-β method is presented to investigate dynamic effects of the asymmetry of rotor stiffness, the viscosity of oil, the rotor unbalance and the ratio of length to diameter of bearings. Three-dimension diagrams and unfiltered vibration curves are used as tools to examine the dynamic behavior of the system, and some insights into the dynamic behavior are given. Numerical results show that instability of the system may be improved by modifying these parameters.
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Zhang, Haibo, Shijing Wu, and Zeming Peng. "A nonlinear dynamic model for analysis of the combined influences of nonlinear internal excitations on the load sharing behavior of a compound planetary gear set." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 7-8 (2015): 1048–68. http://dx.doi.org/10.1177/0954406215597958.
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Nonlinear internal excitations, which include meshing stiffness, backlash, and bearing clearance, may cause nonuniform load distribution in compound planetary gear transmission. To quantify the influence of nonlinear internal excitations on load sharing behavior, and to study the combined effects of meshing stiffness, backlash, and bearing clearance on load sharing behavior, this paper develops a nonlinear dynamic model of a Ravigneaux compound planetary gear set with all members possessing translational and torsional vibration degrees of freedom, as an extend dynamic model to the prior research for compound planetary gear set. In detail, the dynamic model is derived on the basis of the second Lagrange equations, and the load sharing coefficients for different meshing pairs are defined and calculated. Single factor analysis is introduced to investigate the influence of each nonlinear internal excitation on load sharing coefficient ( LSC). On the basis of single factor analysis, Taguchi method is incorporated with the nonlinear dynamic model to study the combined effects of nonlinear internal excitation and figure out the most significant control factor affecting LSC among meshing stiffness, backlash, and bearing clearance. The calculation results are evaluated by using signal-to-noise ( S/ N) analysis and ANOVA method. The results indicate that backlash affects the load sharing behavior most significantly, compared with mean value of meshing stiffness and bearing clearance.
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Zhang, W., R. Q. Wu, and B. Siriguleng. "Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom." Shock and Vibration 2020 (January 14, 2020): 1–29. http://dx.doi.org/10.1155/2020/5282904.
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The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.
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ElMaraghy, H. A., and B. Johns. "An Investigation Into the Compliance of SCARA Robots. Part I: Analytical Model." Journal of Dynamic Systems, Measurement, and Control 110, no. 1 (1988): 18–22. http://dx.doi.org/10.1115/1.3152641.
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A special class of robots suited for assembly tasks called SCARA (Selective Compliance Assembly Robot Arm) provides a degree of built-in flexibility due to robot structure. In such robots there are three revolute joints and a prismatic joint. They offer four degrees of freedom consisting of rotation about two vertical and parallel axes at the revolute joints, and translation and rotation about the tool axis. Some models offer additional degrees of freedom at the end effector. Structural compliance can arise due to the stiffness of the robot links, drive system, grippers as well as the assembled parts. The largest effect is due to the drive torsional stiffness followed by the grippers, workpieces and the robot tool link. Knowledge of the inherent flexibility is extremely useful in designing tooling and fixtures, in laying out the assembly work cell according to the amount of compliance available in various regions of the robot work envelope, in guarding against wedging and jamming and in specifying external Remote Centre Compliance devices (RCC) if necessary. In this paper the various sources of compliance built into a SCARA robot system are outlined together with their relative significance. A mathematical model which expresses the end effector deflection as a function of the robot Jacobian and the drive compliance parameters in Cartesian coordinates has been developed. The modified generalized assembly force model developed for the Selective Compliance Assembly Robot Arms (SCARA), used in this investigation, is described. Constraints required to prevent jamming and wedging of parts during assembly are outlined. The application of this compliance model for both rotational and prismatic part insertion is described. The conditions required to obtain true or semi-compliance centres for the SCARA robot end effector are derived and discussed.
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MARZOUK, S. S., A. S. GENDY, S. N. MIKHAIEL, and A. F. SALEEB. "MODELING WITH INCREASED EFFICIENCY AND VERSATILITY FOR FLEXURAL-TORSIONAL BUCKLING OF UNSYMMETRICAL THIN-WALLED STRUCTURES." International Journal of Structural Stability and Dynamics 02, no. 04 (2002): 431–56. http://dx.doi.org/10.1142/s0219455402000658.
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Aiming at the performance-enhancement in coarse mesh modeling, we utilize a number of closed form solutions of a class of torsionally loaded thin-walled bars to formulate a two-noded element for spatial buckling analysis. The key in this relates to the use of the "exact" solution for the displacement fields (as oppose to the more conventional finite element approach where polynomial/Lagrangian-type interpolation is employed). That is, in addition to the well known "exact" solution for the coupled flexure/transverse-shear problem, we utilize a new "exact" solution for the more difficult case of coupled system of differential equations governing a torsionally loaded thin-walled beam using the higher-order theories of non-uniform twist/bi-moment with coupled warping-shear deformations. For the linear analysis, convergence and accuracy study indicated that the proposed model to be rapidly convergent, stable and computationally efficient; i.e. one element is sufficient to exactly represent an end loaded part of the beam. Such model has been extended to account for nonlinear analysis, in particular, the flexural torsional buckling of thin-walled structures. To this end, the effect of finite rotations in space is accounted for as per the modern theories of spatial buckling, resulting in second-order accurate geometric stiffness matrices. Compared with the classical theory of thin-walled structures, the present approach is more general in that all significant modes of stretching, bending, shear (due to both flexure and torsional/warping), torsion, and warping are accounted for. The inclusion of non-uniform torsion is accomplished through adoption of the principle sectorial area. This requires incorporation of a warping degree of freedom in addition to the conventional six degrees of freedom at each node. The element is derived for general cross sections including the Wagner-effect contributions. The model's properties and performance, particularly with regard to the resulting (significant) improvements in mesh accuracy, are assessed in a fairly complete set of numerical simulations.
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Han, Zejun, Mi Zhou, Xiaowen Zhou, and Linqing Yang. "Dynamic Response of 3D Surface/Embedded Rigid Foundations of Arbitrary Shapes on Multi-Layered Soils in Time Domain." International Journal of Structural Stability and Dynamics 19, no. 09 (2019): 1950106. http://dx.doi.org/10.1142/s0219455419501062.
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Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.
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Rong, Qiang. "Optimum parameters of a five-story building supported by lead-rubber bearings under near-fault ground motions." Journal of Low Frequency Noise, Vibration and Active Control 39, no. 1 (2019): 98–113. http://dx.doi.org/10.1177/1461348419845829.
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Seismic response of five-story frame structure supported by lead-rubber bearings isolation system is investigated subjected to near-fault ground motions. The main structure is modeled as a simple linear multi-degrees-of-freedom vibration system with lumped masses, excited by near-fault ground motions in the horizontal direction. The variation curves of peak top floor acceleration and peak bearing displacement of isolated building are plotted under different yield shear coefficient. The objective function selected for optimality is to maximize the seismic energy dissipated by the lead-rubber bearings. The main constraint conditions selected for optimality are the minimization of both peak bearing displacement and peak top floor acceleration. Optimum parameters of lead-rubber bearing isolation system are investigated and found that optimum yield shear coefficient of lead-rubber bearings is found to be in the range of 0.10–0.14 under near-fault ground motions. Optimum yield shear coefficient decreases with the increase of second isolation period. Optimum yield shear coefficient of lead-rubber bearings with higher yield displacement is larger than that of lead-rubber bearings with low yield displacement. Optimum ratio of pre-yield stiffness to post-yield stiffness of lead-rubber bearings is found to be in the range of 16–35. Optimum stiffness ratio increases proportionally with the decrease of yield displacement. Optimum stiffness ratio increases slightly with the increase of yield shear coefficient. Excluding the effect of pre-yield stiffness, the optimum second isolation period is recommended to be in the range of 4–6 s.
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He, Y., H. Elmaraghy, and W. Elmaraghy. "A Design Analysis Approach for Improving the Stability of Dynamic Systems with Application to the Design of Car-Trailer Systems." Journal of Vibration and Control 11, no. 12 (2005): 1487–509. http://dx.doi.org/10.1177/1077546305060832.
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A design analysis approach is developed for improving the stability of dynamic systems subject to non-conservative forces. It combines genetic algorithms, sequential quadratic programming (SQP), and dynamic mode tracking (DMT). The proposed approach automatically optimizes the stability criterion and is applicable to rotor dynamics, wind turbine dynamics, aeronautics, and ground vehicle dynamics. The Routh-Hurwitz criterion has traditionally been used for determining the stability characteristics of these dynamic systems. In the conventional trial and error approaches, designers iteratively change the values of the design variables and reanalyze until an acceptable stability characteristic is achieved. This is both time-consuming and tedious. The proposed approach automates the design/analysis cycle by using the DMT technique to identify the modes; then, the SQP algorithm determines the stability criterion; and finally a genetic algorithm is applied to optimize design variables. The proposed integrated approach has been tested and evaluated numerically using a linearized car-trailer model with three degrees of freedom and the results demonstrate its feasibility and efficacy. The performed parametric sensitivity analysis revealed that the geometric parameters have a much greater influence on the lateral stability of the vehicle systems, compared with inertia parameters and torsional spring stiffness coefficients.
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Yardimoglu, Bulent, and Daniel J. Inman. "Coupled Bending-Bending-Torsion Vibration of a Pre-Twisted Beam with Aerofoil Cross-Section by the Finite Element Method." Shock and Vibration 10, no. 4 (2003): 223–30. http://dx.doi.org/10.1155/2003/354074.
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The present study deals with a finite element model for coupled bending-bending-torsion vibration analysis of a pretwisted Timoshenko beam with varying aerofoil cross-section. The element derived in this paper has two nodes, with seven degrees of freedom at each node. The nodal variables are transverse displacements, cross-section rotations and the shear angles in two planes and torsional displacement. The advantage of the present element is the exclusion of unnecessary derivatives of fundamental nodal variables, which were included to obtain invertable square matrix by other researchers, by choosing proper displacement functions and using relationship between cross-sectional rotation and the shear deformation. Element stiffness and mass matrices are developed from strain and kinetic energy expressions by assigning proper order polynomial expressions for cross-section properties and considering higher order coupling coefficients. The correctness of the present model is confirmed by the experimental results available in the literature. Comparison of the proposed model results with those in the literature indicates that a faster convergence is obtained. The results presented also provide some insights in the formulation by clearly indicating that higher order coupling terms have considerable influence on the natural frequencies.
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Dinh, Ngoc Hieu, Joo-Young Kim, Seung-Jae Lee, and Kyoung-Kyu Choi. "Seismic Vulnerability Assessment of Hybrid Mold Transformer Based on Dynamic Analyses." Applied Sciences 9, no. 15 (2019): 3180. http://dx.doi.org/10.3390/app9153180.
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In the present study, the seismic vulnerability of a hybrid mold transformer was investigated using a dynamic analytical approach incorporating the experimental results of shaking table tests. The analytical model consisted of linear springs and plastic beam elements, and it has six degrees of freedom simulating the hybrid mold transformer. The dynamic characteristics of the analytical model were determined based on the shaking table tests. The reliability of the analytical model was verified by comparing the test results and analytical results. In order to assess the seismic vulnerability, three critical damage states observed during the shaking table tests were investigated by incorporating the three performance levels specified in ASCE 41-17. Comprehensive dynamic analyses were performed with a set of twenty earthquakes in consideration of the variation of the uncertain parameters (such as the effective stiffness and coil mass) of the mold transformer. Based on the analytical results, fragility curves were established to predict the specified exceedance probability of the mold transformer according to the performance levels.
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Muhayudin, Nor Amalina, Khairul Salleh Basaruddin, Ruslizam Daud, Fiona McEvoy, and Tansey. "Experimental Analysis of Fabricated Synthetic Midthoracic Paediatric Spine as Compared to the Porcine Spine Based on Range of Motion (ROM)." Applied Bionics and Biomechanics 2021 (September 24, 2021): 1–10. http://dx.doi.org/10.1155/2021/2799415.
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The present study is aimed at investigating the mechanical behaviour of fabricated synthetic midthoracic paediatric spine based on range of motion (ROM) as compared to porcine spine as the biological specimen. The main interest was to ensure that the fabricated synthetic model could mimic the biological specimen behaviour. The synthetic paediatric spine was designed as a 200% scaled-up model to fit into the Bionix Servohydraulic spine simulator. Biomechanical tests were conducted to measure the ROM and nonlinearity of sigmoidal curves at six degrees of freedom (DOF) with moments at ±4 Nm before the specimens failed. Results were compared with the porcine spine (biological specimen). The differences found between the lateral bending and axial rotation of synthetic paediatric spine as compared to the porcine spine were 18% and 3%, respectively, but was still within the range. Flexion extension of the synthetic spine is a bit stiff in comparison of porcine spine with 45% different. The ROM curves of the synthetic paediatric spine exhibited nonlinearities for all motions as the measurements of neutral zone (NZ) and elastic zone (EZ) stiffness were below “1.” Therefore, it showed that the proposed synthetic paediatric spine behaved similarly to the biological specimen, particularly on ROM.
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Shirahama, Yusaku, Ryuta Sato, Yusuke Takasuka, Hidenori Nakatsuji, and Keiichi Shirase. "Machine Bed Support with Sliding Surface for Improving the Motion Accuracy." International Journal of Automation Technology 10, no. 3 (2016): 447–54. http://dx.doi.org/10.20965/ijat.2016.p0447.
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The purpose of this study is to develop a new machine bed support mechanism for reducing the vibration generated during the high-speed tracking motion of numerical control machine tools. In order to achieve this, the frequency response and motion trajectory of a machine tool with the proposed machine bed, which has a sliding surface, are measured and compared with that of the conventional support. Based on the modal analysis of the machine tool structure, a mathematical model representing the influence of the machine bed characteristics on the vibration is also developed. The model consists of a bed, saddle, table, column, and spindle head. Every component has three degrees of freedom for each of the translational and rotational axes. In order to evaluate the characteristics of the machine bed, the mathematical model determines the stiffness and damping along the X-, Y-, and Z-axis between the bed and the ground. The frequency response curves simulated by using the mathematical model are compared with that of the measured ones. From the results of the experiments and simulations, it is confirmed that the vibration generated during high-speed tracking motions can be reduced by using the proposed machine bed with a sliding surface.
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Gilmore, Paul, and Umesh Gandhi. "Development of disc spring stack containment methods for vibration isolation." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 2 (2021): 4871–79. http://dx.doi.org/10.3397/in-2021-2865.
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Cone disc springs exhibit quasi-zero stiffness behavior that is useful in isolating objects from low frequency vibrations. However, the stroke of a single disc spring is too low for most applications, and springs are stacked to increase the displacement. A method to contain the isolator stack then becomes critical for practical uses. Many challenges in developing these containment methods have been identified and can be collectively described as how to appropriately contain the stack without affecting isolation performance. In this work, three designs are considered: a retaining ring design, tube and shaft design, and zero poisson ratio sleeve design. Disc spring stacks with containment method are built, and load-deflection curves are measured and compared with standalone stacks. Under quasi-static compression testing, each containment method has minimal effect on the standalone stack load-deflection curve. However, significant differences in isolation performance are observed in vibration testing and found to depend on characteristics such as lateral stability, lateral strength, and degrees of freedom. Lastly, advantages, disadvantages, and appropriate applications for each containment method are summarized. The conclusions of this work are that containment method is an important variable in the application of disc spring isolators and robust, versatile containment designs have been demonstrated.
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Yang, Hui, Hairong Fang, Yuefa Fang, and Haibo Qu. "Kinematics Performance and Dynamics Analysis of a Novel Parallel Perfusion Manipulator with Passive Link." Mathematical Problems in Engineering 2018 (November 25, 2018): 1–18. http://dx.doi.org/10.1155/2018/6768947.
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In order to solve the problem of the honeycombs perfusion in the thermal protection system of the spacecraft, this paper presents a novel parallel perfusion manipulator with one translational and two rotational (1T2R) degrees of freedom (DOFs), which can be used to construct a 5-DOF hybrid perfusion system for the perfusion of the honeycombs. The proposed 3PSS&PU parallel perfusion manipulator is mainly utilized as the main body of the hybrid perfusion system. The inverse kinematics and the Jacobian matrix of the proposed parallel manipulator are obtained. The analysis of kinematics performance for the proposed parallel manipulator including workspace, singularity, dexterity, and stiffness is conducted. Based on the virtual work principle and the link Jacobian matrix, the dynamic model of the parallel perfusion manipulator is carried out. With reference to dynamic equations, the relationship between the driving force and the mechanism parameters can be derived. In order to verify the correctness of the kinematics and dynamics model, the comparison of theoretical and simulation curves of the motion parameters related to the driving sliders is performed. Corresponding analyses illustrate that the proposed parallel perfusion possesses good kinematics performance and could satisfy the perfusion requirements of the honeycombs. The correctness of the established kinematics and dynamics models is proved, which has great significance for the experimental research of the perfusion system.
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Wang, Meiling, Qingkai Han, Baogang Wen, Hao Zhang, and Tianmin Guan. "Modal characteristics and unbalance responses of fan rotor system with flexible support structures in aero-engine." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 9 (2016): 1686–705. http://dx.doi.org/10.1177/0954410016658076.
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This paper investigates the vibration patterns, i.e. rigid motions of shaft and elastic deformation of support structures, of fan rotor system in aero-engine, which differs from traditional flexible rotor systems, and together with its shaft transverse motions due to unbalanced mass. The fan rotor system commonly is composed of one rigid shaft and two flexible support structures (such as squirrel cages), which is effective to decrease the critical speeds avoiding serious shaft vibration due to unbalance. Scaled test rig for realistic fan rotor system is set up according to similarity principles, governing differential equations of which are deduced by means of Lagrangian approach with four degrees of freedom. In contrast to modeling a traditional flexible rotor system, the system stiffness is not determined by the shaft but the two flexible support structures. The rigid shaft only contributes to the inertial items of the governing equations. Parameter values of dynamic model are identified from measurements on the scaled test rig, the modal shapes and the modal energy distributions are calculated. These modal characteristics of the fan rotor system are quite different from those of a traditional flexible rotor system whose stiffness mainly contributed by its elastic shaft even the system values are consistent. The obtained modal characteristics are compared and confirmed by using the simulation results of a corresponding finite element model, in which shaft is built by rotating beam elements and its flexible structures are built by equivalent spring elements. Campbell diagrams of the fan rotor system are used to illustrate the gyroscopic effect with the increasing speeds. And then the unbalance responses are calculated through the deduced analytical formula rapidly and comparisons, including the response spectrum and orbits, the amplitude and phase frequency response curves, and operating deflection shapes, are carried out in the sub- and super-critical range.
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Jafari, M., and M. J. Mahjoob. "An Exact Three-Dimensional Beam Element With Nonuniform Cross Section." Journal of Applied Mechanics 77, no. 6 (2010). http://dx.doi.org/10.1115/1.4002000.
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In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.
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Zheng, Yisheng, Xinong Zhang, Yajun Luo, Shilin Xie, and Yahong Zhang. "Harnessing the compressed-spring mechanism for a six-degrees-of-freedom quasi-zero-stiffness vibration isolation platform." Journal of Vibration and Control, August 18, 2020, 107754632094839. http://dx.doi.org/10.1177/1077546320948399.
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The compressed-spring structure is a simple and reliable mechanism to achieve negative stiffness, which has been vastly investigated for achieving quasi-zero-stiffness isolation. However, six-degrees-of-freedom quasi-zero-stiffness isolators based on this kind of negative-stiffness mechanism still have not been touched. In this study, we propose a six-degrees-of-freedom quasi-zero-stiffness isolation platform constructed by six modules that use compressed-spring structures. Its underlying quasi-zero-stiffness principles in the translational and torsional directions are explained. By establishing the static model of the platform and linearizing it at the static equilibrium position, we find that the linear cross-coupling effects appear if the static load exists. Linearized dynamic analysis of the isolation platform is then performed and the results demonstrate that by applying spring compression, the isolation frequency band can be expanded to lower frequency range in six directions. Because of cross-coupling effects resulted from the static load, the platform cannot achieve whole-frequency-range isolation in the coupling directions even if the spring compressions satisfy quasi-zero-stiffness conditions.
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Chen, Jun-Xin, Yun-He Li, Jian Wen, Zhen Li, Bin-Sheng Yu, and Yong-Can Huang. "Annular Defects Impair the Mechanical Stability of the Intervertebral Disc." Global Spine Journal, March 30, 2021, 219256822110060. http://dx.doi.org/10.1177/21925682211006061.
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Study Design: A biomechanical study. Objectives: The purpose of this study was to investigate the effects of cruciform and square incisions of annulus fibrosus (AF) on the mechanical stability of bovine intervertebral disc (IVD) in multiple degrees of freedom. Methods: Eight bovine caudal IVD motion segments (bone-disc-bone) were obtained from the local abattoir. Cruciform and square incisions were made at the right side of the specimen’s annulus using a surgical scalpel. Biomechanical testing of three-dimensional 6 degrees of freedom was then performed on the bovine caudal motion segments using the mechanical testing and simulation (MTS) machine. Force, displacement, torque and angle were recorded synchronously by the MTS system. P value <.05 was considered statistically significant. Results: Cruciform and square incisions of the AF reduced both axial compressive and torsional stiffness of the IVD and were significantly lower than those of the intact specimens ( P < .01). Left-side axial torsional stiffness of the cruciform incision was significantly higher than a square incision ( P < .01). Neither incision methods impacted flexional-extensional stiffness or lateral-bending stiffness. Conclusions: The cruciform and square incisions of the AF obviously reduced axial compression and axial rotation, but they did not change the flexion-extension and lateral-bending stiffness of the bovine caudal IVD. This mechanical study will be meaningful for the development of new approaches to AF repair and the rehabilitation of the patients after receiving discectomy.
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Chao, Lin, Wang Yu, Hu Yanan, and Yu Yongquan. "Dynamic Characteristics Analysis of the Composite Motion of Curve-Face Gear." Journal of Computational and Nonlinear Dynamics 16, no. 6 (2021). http://dx.doi.org/10.1115/1.4050702.
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Abstract The unified model was proposed for the three configurations of the composite motion of curve-face gear pair. A coupled bending-torsional-axial dynamic model with multi degree-of-freedom transmission system was proposed comprehensively considering nonlinear parameters such as tooth mesh stiffness, static transmission error and backlash. The fourth-order Runge–Kutta numerical method was applied to solve the dimensionless dynamic differential equations of the system, and then the dynamic responses of the system were investigated by time history, phase-plane portrait, poincare map, FFT spectrum and bifurcation diagram. It was found that the dynamic responses of the three configurations were complex. It presented quasi-periodic motion only under certain configuration and parameter conditions. With the increase of meshing frequency, the system state was characterized by the alternation between chaotic motion and periodic motion. Eccentricity ratio of displacement curve of curve-face gear pair mainly affected the rotational frequency of the system. As the eccentricity ratio increased, the dominant frequency of the system gradually changed from meshing frequency to rotational frequency. The correctness of the theoretical model was verified through corresponding experimental studies.
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Yoon, Jong-yun, and Iljae Lee. "Nonlinear Analysis of Vibro-Impacts for Unloaded Gear Pairs With Various Excitations and System Parameters." Journal of Vibration and Acoustics 136, no. 3 (2014). http://dx.doi.org/10.1115/1.4026927.
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Torsional systems with clearance-type nonlinearities have inherent vibratory problems such as gear rattle. Such vibro-impacts generally occur on the unloaded gear pairs of a vehicle correlated with the firing excitation of an engine. This study investigates the gear rattle phenomena on unloaded gear pairs with different excitation conditions and various system parameters. First, a linear time-invariant system model with six degrees of freedom is constructed and then a numerical analysis is applied to the gear rattle motion. Smoothening factors for clutch stiffness and hysteresis are employed for the stability of numerical simulations. Second, the dynamic characteristics of vibro-impacts are studied by examining the fast Fourier transform (FFT) components of the gear mesh force in a high frequency range. The effects of various system parameters on the vibro-impacts are examined using a nonlinear system model. Finally, the vibro-impacts, in terms of “single-sided” and “double-sided” impacts, are identified in phase planes.
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Su, Biao, Karl Gunnar Aarsæther, and David Kristiansen. "Numerical Study of a Moored Structure in Moving Broken Ice Driven by Current and Wave." Journal of Offshore Mechanics and Arctic Engineering 141, no. 3 (2019). http://dx.doi.org/10.1115/1.4042263.
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This paper presents a numerical model intended to simulate the mooring force and the dynamic response of a moored structure in drifting ice. The mooring lines were explicitly modeled by using a generic cable model with a set of constraint equations providing desired structural properties such as the axial, bending, and torsional stiffness. The six degrees-of-freedom (DOF) rigid body motions of the structure were simulated by considering its interactions with the mooring lines and the drifting ice. In this simulation, a fragmented ice field of broken ice pieces could be considered under the effects of current and wave. The ice–ice and ice–structure interaction forces were calculated based on a viscoelastic-plastic rheological model. The hydrodynamic forces acting on the floating structure, mooring line, and drifting ice were simplified and calculated appropriately. The present study, in general, demonstrates the potential of developing an integrated numerical model for the coupled analysis of a moored structure in a broken ice field with current and wave.
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Lu, Yi, Ling Ding, Shuyan Li, and Jianping Yu. "Derivation of Topological Graphs of Some Planar 4DOF Redundant Closed Mechanisms by Contracted Graphs and Arrays." Journal of Mechanisms and Robotics 2, no. 3 (2010). http://dx.doi.org/10.1115/1.4001735.
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Some planar redundantly closed mechanisms (RCMs) have better dexterity, less singular configuration, and higher stiffness. In this paper, the derivation of valid topology graphs (TGs) of some planar four degrees of freedom (4DOF) RCMs is studied based on the contracted graph (CG), arrays, and topology graph with digits (DTG). First, some CGs without any binary links are constructed for the planar 4DOF RCMs, some curves with only binary links are distributed over CGs, and some valid TGs of the planar 4DOF RCMs are derived. Second, a complicated derivation of TG is transformed into an easy derivation of array and DTG, and some programs are compiled in VISUAL BASIC; all valid arrays corresponding to nonisomorphic TGs are derived, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined and removed by the compiled programs. Third, many valid TGs of the planar 4DOF RCMs with various basic links are derived from valid arrays and DTGs. Finally, some application examples are illustrated.
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Arghavan, S., and A. V. Singh. "Free Vibration of Single Layer Graphene Sheets: Lattice Structure Versus Continuum Plate Theories." Journal of Nanotechnology in Engineering and Medicine 2, no. 3 (2011). http://dx.doi.org/10.1115/1.4004323.
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Prospect of applications of graphene sheets in composites and other advanced materials have drawn attention from a broad spectrum of research fields. This paper deals with the methods to find mechanical properties of such nanoscale structures. First, the lattice structure method with the Poisson’s ratio of 0.16 and the thickness of 3.4 Å is used to obtain the Young’s moduli for the in-plane and out-of-plane deformation states. This method has the accuracy of molecular dynamics simulations and efficiency of the finite element method. The graphene sheet is modeled as a plane grid of carbon atoms taken as the nodal points, each of which carries the mass of the carbon atom and is assigned as a six degrees of freedom. The covalent bond between two adjacent carbon atoms is treated as an extremely stiff frame element with all three axial, bending, and torsional stiffness components. Subsequently, the computed Young’s moduli, approximately 0.11 TPa for bending and 1.04 TPa for the in-plane condition, are used for studying the vibrational behaviors of graphene sheets by the continuum plate theory. The natural frequencies and corresponding mode shapes of various shaped single layer graphene sheet ), such as rectangular, skewed, and circular, are computed by the two methods which are found to yield very close results. Results of the well-established continuum plate theory are very consistent with the lattice structure method, which is based on accurate interatomic forces.
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Sharei, Hoda, Jeroen Kieft, Kazuto Takashima, Norihiro Hayashida, John J. van den Dobbelsteen, and Jenny Dankelman. "A Rigid Multibody Model to Study the Translational Motion of Guidewires Based on Their Mechanical Properties." Journal of Computational and Nonlinear Dynamics 14, no. 10 (2019). http://dx.doi.org/10.1115/1.4043618.
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Abstract During percutaneous coronary interventions (PCI), a guidewire is used as an initial way of accessing a specific vasculature. There are varieties of guidewires on the market and choosing an appropriate one for each case is critical for a safe and successful intervention. The main objective of this study is to predict the behavior of the guidewire and its performance in a vasculature prior to the procedure. Therefore, we evaluate the effectiveness of different mechanical properties of the guidewire on its behavior. A two-dimensional (2D) model has been developed in which a guidewire is considered as a set of small rigid segments connected to each other by revolute joints. These joints have two degrees-of-freedom to allow rotation. Linear torsional springs and dampers are applied in each joint to account for the elastic properties of the guidewire; the elastic properties have been measured for two commercially available guidewires (Hi-Torque Balance Middleweight Universal II—Abbot and Amplatz Super Stiff—Boston Scientific) and these are used in the model. Only translational motion has been applied to the guidewires and the effect of bending stiffness of the guidewire and also friction between guidewire and vasculature on its behavior are investigated. The results are validated with actual movement of the guidewires in a simple phantom model. Behavior of a guidewire in a vasculature was predicted using the developed model. The results of both simulation and experiment show that the behavior of a guidewire is influenced by its mechanical properties and by the friction between the guidewire and vasculature. This study is the first step to develop a complete model, which can predict the behavior of a guidewire inside the vasculature. We compared the tip trajectory for two commercial guidewires in one vasculature geometry. In future, this kind of knowledge might support not only the interventionist in choosing the best suitable guidewire for a procedure but also the designer to optimize new instrument to have the desired behavior.
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Ertas, Bugra, Keith Gary, and Adolfo Delgado. "Additively Manufactured Compliant Hybrid Gas Thrust Bearing for Supercritical Carbon Dioxide Turbomachinery: Experimental Evaluation and Fluid–Structure Model Predictions." Journal of Engineering for Gas Turbines and Power 143, no. 8 (2021). http://dx.doi.org/10.1115/1.4050864.
Full textAbstract:
Abstract This paper presents rotating test results and advances an analytical predictive fluid–structure model for a new type of gas-lubricated thrust bearing fabricated using direct metal laser melting. The bearing concept in this study is a compliant hybrid gas thrust bearing that uses external pressurization to increase load carrying capacity, where the testing campaign in this study was only focused on steady-state static performance. The need for the bearing concept comes from enabling highly efficient supercritical carbon dioxide (sCO2) turbomachinery by replacing oil-lubricated bearings with process gas lubrication. Leveraging the process gas of the turbomachine for bearing lubrication results in lowered bearing power loss, simplified mechanical design, and allows for novel oil-free hermetic drivetrains resulting in an efficient emission-free system. The new concept utilizes hydrostatic pressurization on individual tilting pads flexibly mounted with hermetic squeeze film dampers (HSFDs). This paper focuses on rotating tests of a 173 mm outer diameter gas thrust bearing in air up to 10 krpm and hydrostatic inlet pressures to 365 psi (2.52 MPa). The influence of thrust runner speed and bearing inlet pressure on force deflection characteristics and load carrying capability of the gas film were experimentally evaluated. This work also advances a predictive fluid–structure thrust bearing model using an isothermal ideal-gas-based compressible Reynolds flow equation directly coupled to a lumped stiffness element possessing axial and rotational degrees-of-freedom. The rotating testing demonstrated load capability of 1816 lbs (8.1 kN), which equates to a thrust bearing unit load of 67 psi (0.46 MPa). Gas film force–deflection curves reveal a nonlinear relationship between thrust load and film clearance. Comparison of film thickness values with the predictive model show good agreement under high load and inlet pressure, however deviate as load and pressure decrease. Load capability was shown to increase with increasing hydrostatic inlet pressure, while the increase in thrust runner speed revealed a small decrease in load capacity.