Статті в журналах: "Coupled lateral torsional vibration"

1

An, Xue Li, Dong Xiang Jiang, Ming Hao Zhao, and Chao Liu. "Numerical Analysis of Coupled Lateral and Torsional Vibrations of a Vertical Unbalanced Rotor." Applied Mechanics and Materials 20-23 (January 2010): 352–57. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.352.

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A model for the coupled lateral and torsional vibrations of a vertical unbalanced rotor is developed. The equation of motion is obtained using Lagrangian dynamics without considering the external actuating forces and torque. The equation showed coupling and nonlinear interaction between the rotor lateral and torsional vibrations. Most of the earlier work on coupled vibrations has been done for the horizontal rotor model. The coupled vibrations for a vertical rotor have not been reported in the past. An attempt is made to reveal dynamic characteristics of vertical rotor. The results of the simulation showed the coupled between torsional and lateral vibrations is induced by mass eccentricity. Coupled vibrations have appeared in the start period of the vibration. After a transient vibration process, the vibrations are not coupling. The lateral vibration becomes equal amplitude with shafting speed. And the torsional vibration keeps on attenuating until it stops. When the vibration is coupled, the coupling effect on which torsional vibration to lateral vibration is evident. But there’s no coupling effect on the lateral to the torsional. It is also shown that for some operational parameters, the controlling action may excite large lateral vibrations due to coupling with the torsional motion.

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2

Ren, Fushen, Baojin Wang, and Suli Chen. "Nonlinear Modeling and Qualitative Analysis of Coupled Vibrations in a Drill String." International Journal of Bifurcation and Chaos 28, no. 10 (September 2018): 1850119. http://dx.doi.org/10.1142/s0218127418501195.

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A coupled model for axial/torsional/lateral vibrations of the drill string is presented, in which the nonlinear dynamics and qualitative analysis method are employed to find out the key factors and sensitive zone for coupled vibration. The drill string is simplified as an equivalent shell under axial rotation. After dimensionless processing, the mathematical model for coupled axial/torsional/lateral vibrations of the drill string is obtained. The Runge–Kutta–Fehlberg method is employed for the numerical simulation, and the rules that govern the changing of the torsional and axial excitation are revealed. And the stability domains of the explicit Runge–Kutta method are analyzed. Furthermore, the suggestions for field applications are also presented. It is demonstrated by simulation results that the lateral/axial/torsional vibrations exist simultaneously and couple with each other. The system will obtain a stable period motion with an axial excitation zone before the coupled vibration in the three directions, and continue to increase the axial excitation to cause the coupled vibration easily. The torsional excitation of the drill string mainly contributes to the coupled vibration in the three directions when in a specific rotation speed zone. The system is more likely to obtain a periodic motion through adjusting the torsional excitation out of this zone.

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3

Choi, S. H., J. Glienicke, D. C. Han, and K. Urlichs. "Dynamic Gear Loads Due to Coupled Lateral, Torsional and Axial Vibrations in a Helical Geared System." Journal of Vibration and Acoustics 121, no. 2 (April 1, 1999): 141–48. http://dx.doi.org/10.1115/1.2893956.

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In this paper we investigate the rotordynamics of a geared system with coupled lateral, torsional and axial vibrations, with a view toward understanding the severe vibration problems that occurred on a 28-MW turboset consisting of steam turbine, double helical gear and generator. The new dynamic model of the shaft line was based on the most accurate simulation of the static shaft lines, which are influenced by variable steam forces and load-dependent gear forces. The gear forces determine the static shaft position in the bearing shell. Each speed and load condition results in a new static bending line which defines the boundary condition for the dynamic vibration calculation of the coupled lateral, torsional and axial systems. Rigid disks and distributed springs were used for shaft line modeling. The tooth contact was modeled by distributed springs acting normally on the flank surfaces of both helices. A finite element method with distributed mass was used for lateral and torsional vibrations. It was coupled to a lumped mass model describing the axial vibrations. The forced vibrations due to unbalances and static transmission errors were calculated. The eigenvalue problem was solved by means of a stability analysis showing the special behavior of the coupled system examined. The calculation was successfully applied, and the source of the vibration problem could be located as being a gear-related transmission error. Several redesign proposals lead to a reliable and satisfactory vibrational behavior of the turboset.

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4

Krott, Matthew J., Edward C. Smith, and Christopher D. Rahn. "Coupled and Multimode Tailboom Vibration Control Using Fluidic Flexible Matrix Composite Tubes." Journal of the American Helicopter Society 64, no. 4 (October 1, 2019): 1–10. http://dx.doi.org/10.4050/jahs.64.042007.

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This paper covers the modeling and testing of a helicopter tailboom integrated with a fluidic flexible matrix composite (F2MC) damped vibration absorber. In an advance over previous work, the F2MC absorber presented in this paper treats a combination of tailboom lateral, torsional, and vertical vibrations. A finite element structural model of a laboratory-scale tailboom is combined with a model of attached F2MC tubes and a tuned fluidic circuit. Vibration reductions of over 75% in a coupled 26.8-Hz lateral bending/torsion tailboom mode are predicted by the model and measured experimentally. These results demonstrate that F2MC vibration control is viable at higher frequencies and for more complex vibration modes than previous research had explored. A new absorber with a fluidic circuit that targets two tailboom vibration modes is designed and experimentally tested. On the lab-scale tailboom testbed, the absorber with this circuit is shown to provide vibration reductions of over 60% in both a 12.2-Hz vertical mode and a 26.8-Hz lateral bending/torsion mode. Using this new absorber, vertical and lateral/torsion mode damping are achieved with almost no added weight relative to a purely vertical absorber.

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5

Hu, Zehua, Jinyuan Tang, and Siyu Chen. "Analysis of coupled lateral-torsional vibration response of a geared shaft rotor system with and without gyroscopic effect." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 24 (January 22, 2018): 4550–63. http://dx.doi.org/10.1177/0954406217753457.

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A torsional gear dynamic model and a coupled lateral-torsional geared shaft rotor dynamic model are developed considering the time-varying mesh stiffness, backlash, and static transmission error excitation. The torsional dynamic transmission error responses gained from the torsional gear dynamic model and coupled lateral-torsional geared shaft rotor dynamic model are compared. The natural frequencies and mode shapes of the geared shaft rotor system are given and the frequency whirling behaviors are analyzed based on the Campbell diagram. The influences of gyroscopic effects of rotating shafts and meshing gear rotors on the lateral-torsional vibration responses of the geared shaft rotor system are talked about and some conclusions are drawn. (1) The coupled lateral-torsional geared shaft rotor dynamic model could reflect the jump phenomenon of dynamic responses near the critical speed of the gear pair as well as the pure torsional gear dynamic model and it can give more vibration features caused by geared shaft and bearings than the torsional gear dynamic model. (2) When the gear pair is set in the midpoint of the shaft, the influences of the gyroscopic effects on the gear pair’s lateral vibration responses are light and only can be observed near the high critical speeds. However, when the displacements from the gear body to the bearings are not the same, the influences of the gyroscopic effects on the lateral and torsional vibration responses are obvious and can be located both near the low critical speeds and the high critical speeds corresponding to the forward and backward whirling frequency. (3) The influences of the gyroscopic effects on the lateral and torsional vibration responses of the pinion are more obvious than those on the vibration responses of the gear. In addition, relative to the torsional vibration, the lateral vibration of the gear pair is more easily affected by the gyroscopic effect.

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6

Yang, Xu Juan, Guang Heng Xu, Zhao Jun Li, and Ru Gui Wang. "Dynamic Modeling and Response Analysis of Lateral-Torsional Coupling Vibration of the Slewing Mechanism of a Hydraulic Excavator." Advanced Materials Research 753-755 (August 2013): 1755–59. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.1755.

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A lateral-torsional coupled vibration model of the slewing mechanism of a hydraulic excavator is developed with consideration of the effect of lateral vibration and torsional vibration of sun gear and planetary gear on mesh displacement, the mesh stiffness of gear pairs, the bearing stiffness of the planetary and the coupling relationship of two stage planetary gear trains. The dynamic response of the slewing mechanism of a hydraulic excavator is obtained. Compared to the pure torsional vibration, the lateral-torsional vibration model is more reasonable.

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7

Karri, Seshendra Kumar Venkat, and Sree Krishna Sundara Siva Rao Bollapragada. "Influence of lateral vibrations on the whirling characteristics of gear-pinion rotor system." Journal of Vibration and Control 18, no. 11 (October 19, 2011): 1624–30. http://dx.doi.org/10.1177/1077546311423064.

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The proposed work presents a methodology to analyze the influence of lateral vibrations on the whirling characteristics of a rotor-bearing system. A complex variable approach, which is proposed for the analysis of a single rotor system, is very powerful for this purpose. The approach is expanded to the analysis of a combined rotor system to apply it to the gear system analysis. The bearing stiffness and shaft flexibility of the geared rotor system are taken into account in two ways. With regard to the rotor effect, the frequency response functions are obtained for both torsional motions and coupled lateral-torsional motions. By obtaining the differences in the frequency responses of both the models, the effect of neglecting rotor effects in gear dynamics simulation is studied. The lateral stiffness of the system, which reflects the shaft and bearing stiffness, is considered to make a strong lateral and torsional motion coupling. It is shown that the lateral vibrations have considerable effect when the natural frequencies of the lateral vibration and torsional vibration are close to each other, which is expected. The effect of lateral-torsional coupling on gear dynamics is discussed based on the response of the system.

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8

Shen, X. Y., J. H. Jia, M. Zhao, and J. P. Jing. "Coupled torsional-lateral vibration of the unbalanced rotor system with external excitations." Journal of Strain Analysis for Engineering Design 42, no. 6 (August 1, 2007): 423–31. http://dx.doi.org/10.1243/03093247jsa304.

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The coupled torsional-lateral model of the rotor system is set up and governing equations are derived using the Lagrange approach with six degrees of freedom. The gyroscopic effect and gravity are included. Two kinds of unbalance, namely static unbalance and dynamic unbalance, are considered in the rotor system. Torsional and lateral motions are subjected to external excitations. Through numerical simulation, the developed model is used and the coupled torsional-lateral vibrations of the unbalanced rotor system under external excitations are investigated. Some new phenomena are found and discussed.

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9

Choy, F. K., Y. K. Tu, J. J. Zakrajsek, and D. P. Townsend. "Effects of Gear Box Vibration and Mass Imbalance on the Dynamics of Multistage Gear Transmission." Journal of Vibration and Acoustics 113, no. 3 (July 1, 1991): 333–44. http://dx.doi.org/10.1115/1.2930190.

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The objective of this paper is to present a comprehensive approach to analyze the dynamic behavior of multi-stage gear transmission systems with the effects of gear box induced vibrations and rotor mass-imbalances. The modal method, using undamped frequencies and planar mode shapes, is used to reduce the degree of freedom of the system. The various rotor-bearing stages as well as the lateral and torsional vibrations of each individual stage are coupled through localized gear mesh tooth interactions. Gear box vibrations are coupled to the gear stage dynamics through bearing support forces. Transient and steady state dynamics of lateral an torsional vibrations of the geared system are examined in both time and frequency domains. Vibration signature analysis techniques will be developed to interpret the overall system dynamics and individual modal excitations under various operating conditions. A typical 3- staged geared system is used as an example. Effects of mass imbalance and gear box vibrations on the system dynamic behavior are presented in terms of modal excitation functions for both lateral and torsional vibrations. Operational characteristics and conclusions are drawn from the results presented.

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10

Zhou, Shihua, Zhaohui Ren, Guiqiu Song, and Bangchun Wen. "Dynamic Characteristics Analysis of the Coupled Lateral-Torsional Vibration with Spur Gear System." International Journal of Rotating Machinery 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/371408.

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A sixteen-degree-of-freedom (16-DOF) lumped parameter dynamic model taking into account the gravity, eccentricity, bearing clearance, transmission error, and coupled lateral-torsional vibration is established. Based on the dynamical equation, the dynamic behaviors of the spur gear rotor bearing system are investigated by using Runge-Kutta method. The research focuses on the effect of rotational speed, eccentricity, and bearing clearance and nonlinear response of the coupled multibody dynamics is presented by vibration waveform, spectrum, and 3D frequency spectrum. The results show that the rotational frequency of the driven gear appears in the driving gear, and the dynamic characteristics of gears have obvious differences due to the effects of the gear assembly and the coupled lateral-torsional vibration. The bearing has its own resonance frequency, and the effect of the variable stiffness frequency of the bearings should be avoided during the system design. The results presented in this paper show an analysis of the coupled lateral-torsional vibration of the spur gear system. The study may contribute to a further understanding of the dynamic characteristics of such a spur gear rotor bearing system.

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11

Zheng, Nan, Moli Chen, Guihuo Luo, and Zhifeng Ye. "Coupled Lateral and Torsional Vibration of Rub-Impact Rotor during Hovering Flight." Shock and Vibration 2021 (October 13, 2021): 1–25. http://dx.doi.org/10.1155/2021/4077556.

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When aircraft make a maneuvering during flight, additional loads acting on the engine rotor system are generated, which may induce rub-impact faults between the rotor and stator. To study the rub-impact response characteristics of the rotor system during hovering flight, the dynamic model of a rub-impact rotor system is established with lateral-torsional vibration coupling effect under arbitrary maneuvering flight conditions using the finite element method and Lagrange equation. An implicit numerical integral method combining the Newmark-β and Newton–Raphson methods is used to solve the vibration response. The results indicate that the dynamic characteristics of the rotor system will change during maneuvering flight, and the subharmonic vibrations are amplified in both lateral and torsional vibrations due to maneuvering overload. The form of the rub-impact is different during level and hovering flight conditions: the rub-impact may occur at an arbitrary phase of the whole cycle under the condition of level flight, while only local rub-impact occurs during hovering flight. Under the both flight conditions, the rub-impact has a large effect on the spectral characteristics, periodicity, and stability of the rotor system.

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12

Wang, Zhipeng, Yunbo Yuan, Zhiyong Wang, Wei Liu, Yibin Guo, and Donghua Wang. "Lateral-Torsional Coupling Characteristics of a Two-Stage Planetary Gear Rotor System." Shock and Vibration 2018 (May 31, 2018): 1–15. http://dx.doi.org/10.1155/2018/4293475.

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Planetary gears are one part of the whole transmission chain, and the dynamics and vibration characteristics of them are strongly coupled with external rotors. In this paper, to demonstrate the interaction between multistage planetary gears and external rotors as well as investigate the lateral-torsional coupling characteristics of them, a coupling model of a two-stage planetary gear rotor system is proposed. In such a model, the two-stage planetary gear subsystem is established as a lumped-parameter model and the external rotor subsystem is established as a finite element model. The vibration mode distribution properties and lateral-torsional coupling characteristics are both analyzed by modal strain energy. Three different conditions are considered: uncoupled, partially coupled, and fully coupled. The results indicate that the coupling among multiple subsystems and the lateral-torsional coupling mainly exist in the low-mode region. Natural frequencies dominated by the two-stage planetary gear subsystem are sensitive to coupled conditions, whereas natural frequencies dominated by the input rotor subsystem are remarkably insensitive to coupled conditions. Furthermore, the natural frequency of the first torsional mode can be obtained only in the fully coupled condition. Experiments are implemented to obtain natural frequencies, and the experiment results validate the numerical results.

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13

Ye, Jian Feng, Chun Long Zheng, and Xue Shi Yao. "Analysis of Coupled Bending-Axial Vibration of a Rotor." Advanced Materials Research 662 (February 2013): 608–11. http://dx.doi.org/10.4028/www.scientific.net/amr.662.608.

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Aiming at a rotor model, the coupled bending-axial vibration is being analyzed.Calculation results show that the prestress relative to rotational centrifugal load may influence bending vibration frequencies of a rotor.The bending vibration frequencies will increase when the prestress increases.The axial vibration frequency has not an influence because the direction of the spinning prestress is perpendicular to axis.When a rotor is applies axial force, a compressional force will tend to increase the axial vibration frequencies while a tensile force will decrease the axial vibration frequencies.The effects of the prestress(centrifugal load )of the spinning rotor and the axial prestress can be accounted by an adjustment of the stiffness matrix for analysis.By use of the stiffness matrix,the changed axial and bending vibration frequencies can be explained.The coupled bending-axial vibration may take place when the bending vibration frequencies have increased in the state of the changed prestress.In the end, the coupled bending-axial vibration frequency can be calculated.On the basis of prestress, the coupled lateral-torsional vibration and the coupled torsional-axial vibration frequency can be analysed,similarly.

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14

Ross, Andrew S., Ashraf A. El Damatty, and Ayman M. El Ansary. "Reduced Equivalent Static Wind Loads for Tall Buildings with Tuned Liquid Dampers." Applied Mechanics and Materials 226-228 (November 2012): 1218–27. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1218.

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The tuned liquid damper (TLD) is a proven and an increasingly popular auxiliary device for mitigating the dynamic effects induced by wind loading on tall buildings. As buildings become taller, lighter, and more flexible, there is a greater contribution from the dynamic component. The most reliable tool for assessing the dynamic component is wind tunnel testing. A boundary layer wind tunnel is capable of accurately calculating an equivalent static wind load (ESWL) acting on a building. The current study investigates the reduction in the ESWL of a lateral-torsional coupled building with a TLD system installed. The building is sensitive to torsion in the first two vibration modes. The current investigation uses three unique multi-modal TLD systems designed specifically for a lateral-torsional coupled building. The building ESWL is evaluated with the TLD systems using measurements from tests conducted at the Boundary Layer Wind Tunnel Laboratory at Western University.

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15

Cao, Guohua, Jinjie Wang, and Zhencai Zhu. "Coupled vibrations of rope-guided hoisting system with tension difference between two guiding ropes." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 2 (November 3, 2016): 231–44. http://dx.doi.org/10.1177/0954406216677103.

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The flexibility of the guiding rope and the tension difference between two guiding ropes cause the lateral and torsional vibrations of the hoisting conveyance in the rope-guided hoisting system, respectively, which are theoretically investigated with two different cases in this paper. The assumed modes method is used to discretize the hoisting rope and two guiding ropes, and Lagrange equations of the first kind is adopted to derive the equations of motion, while the geometric matching conditions at the interfaces of the ropes are accounted for by the Lagrangian multiplier. Considering all the geometric matching conditions are approximately linear, the differential algebraic equations are transformed to a system of ordinary differential equations. The current method can obtain not only the accurate lateral displacements of two guiding ropes, but also the constraint forces between the hoisting conveyance and two guiding ropes. Further, the current method is verified by the ADAMS simulation. Finally, the effects of various parameters on the lateral and torsional vibrations of the hoisting conveyance are analyzed and results indicate that the appropriate tension difference and distance difference could decrease the maximum lateral displacement, which is useful to design super deep rope-guided hoisting system for the decrease of the vibration.

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16

Qin, Wenyuan, Hui Qin, Hongbo Zheng, and Zhiyi Zhang. "The coupled effect of bearing misalignment and friction on vibration characteristics of a propulsion shafting system." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 233, no. 1 (August 2, 2017): 150–63. http://dx.doi.org/10.1177/1475090217722875.

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The propulsion shafting system of ships is usually supported, in part, by water-lubricated rubber bearings, which often work at mixed or boundary lubrication state under heavy-load and low-speed conditions, resulting in strong friction on the bearing–shaft interface and even abnormal vibration in the overall system. In addition, bearing misalignment can further affect the distribution of friction and consequently change the lateral and torsional vibration characteristics of the shafting system. In this work, the rubber bearing was simplified into parallel-distributed springs and the water film was neglected. The dynamic model of the propulsion shafting system was built with the finite element method and reduced by mode truncation. The coupled effect of bearing misalignment and friction was subsequently analyzed with this reduced model and the fourth-order Runge–Kutta method. Finally, lateral and torsional vibration characteristics of the overall system under different bearing misalignment were obtained, which can be used in the identification or diagnosis of abnormal vibration induced by friction.

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17

Lee, Haw-Long, and Win-Jin Chang. "Coupled lateral bending–torsional vibration sensitivity of atomic force microscope cantilever." Ultramicroscopy 108, no. 8 (July 2008): 707–11. http://dx.doi.org/10.1016/j.ultramic.2007.10.012.

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18

Yang, Y. B., Mei Li, Bin Zhang, Yuntian Wu, and Judy P. Yang. "Resonance and Cancellation in Torsional Vibration of Monosymmetric I-Sections Under Moving Loads." International Journal of Structural Stability and Dynamics 18, no. 09 (September 2018): 1850111. http://dx.doi.org/10.1142/s0219455418501110.

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This paper is concerned with the lateral and torsional coupled vibration of monosymmetric I-beams under moving loads. To this end, a train is modeled as two subsystems of eccentric wheel loads of constant intervals to account for the front and rear wheels. By assuming the lateral and torsional displacements to be restrained at the two ends of the beam, both the lateral and torsional displacements are approximated by a series of sine functions. The method of variation of constants is adopted to derive the closed-form solution. For the most severe condition when the last wheel load is acting on the beam, both the conditions of resonance and cancellation are identified. Once the condition of cancellation is enforced, the resonance response can always be suppressed, which represents the optimal design for the beam. Since the condition for suppressing the torsional resonance is exactly the same as that for the vertical resonance, this offers a great advantage in the design of monosymmetric I-beams, as no distinction needs to be made between the suppression of vertical or torsional resonance.

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19

Li, Chao Feng, Shi Hua Zhou, and Jie Liu. "Numerical Simulation of a Bending-Torsion Coupling Gear Transmission System." Applied Mechanics and Materials 448-453 (October 2013): 3403–7. http://dx.doi.org/10.4028/www.scientific.net/amm.448-453.3403.

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Based on the establishment of angular contact ball bearing mechanical model, a nonlinear coupled lateral, torsional and axial dynamic model of helical gear-rotor-bearing system is established, and the dynamic differential equations of the coupled lateral-torsional-axial nonlinear vibration are deduced for imbalance rotors. The investigations are systematically carried out by oscillograms and spectrograms with rotating speed, taking into account eccentricity and nonlinear supporting by rolling bearing. The results show that the rotation frequency of the driven shaft appears in the driving shaft. In addition, the rotation frequencies and meshing frequency appear obviously in torsional direction. It can be seen that the lateral, torsional and axial response characteristics of driving and driven shafts obvious differences are due to the effects of the gear assembly characteristic, gear geometry parameters and the angular contact ball bearings characteristics. As a result, not only appear the rotational frequency and stiffness frequency, but also yield the bearing variable stiffness frequency and conbined frequency in lateral directions. However, the theory of the helical gear-rotor-bearing system still needs further research.

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20

Xu, Jinli, Jiwei Zhu, and Feifan Xia. "Modeling and Analysis of Amplitude-Frequency Characteristics of Torsional Vibration for Automotive Powertrain." Shock and Vibration 2020 (August 29, 2020): 1–17. http://dx.doi.org/10.1155/2020/6403413.

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In the present paper, the amplitude-frequency characteristics of torsional vibration are discussed theoretically and experimentally for automotive powertrain. A bending-torsional-lateral-rocking coupled dynamic model with time-dependent mesh stiffness, backlash, transmission error etc. is proposed by the lumped-mass method to analysis the amplitude-frequency characteristic of torsional vibration for practical purposes, and equations of motive are derived. The Runge–Kutta method is employed to conduct a sweep frequency response analysis numerically. Furthermore, a torsional experiment is performed and validates the feasibility of the theoretical model. As a result, some torsional characteristics of automotive powertrain are obtained. The first three-order nature torsional frequencies are predicted. Torsional behaviors only affect the vibration characteristics of a complete vehicle at low-speed condition and will be reinforced expectedly while increasing torque fluctuation. Gear mesh excitations have little effects on torsional responses for such components located before mesh point but a lot for ones behind it. In particular, it is noted that the torsional system has a stiffness-softening characteristic with respect to torque fluctuation.

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21

Chen, Chin-Shong, S. Natsiavas, and H. D. Nelson. "Coupled Lateral-Torsional Vibration of a Gear-Pair System Supported by a Squeeze Film Damper." Journal of Vibration and Acoustics 120, no. 4 (October 1, 1998): 860–67. http://dx.doi.org/10.1115/1.2893912.

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This paper presents a model and analysis of the coupled lateral-torsional vibration of a gear-pair system supported by a squeeze film damper (SFD). Steady state dynamic characteristics of the system are considered. First, insight is gained into the dynamics of the system and the model is partially verified by investigating the linear characteristics of a specific configuration. Then, the response of the nonlinear system is examined for rotating unbalance excitation. The trigonometric collocation method (TCM) is employed to obtain steady-state responses, while direct integration is used to verify these results. The sensitivity of the system to lateral-torsional coupling is examined by comparing steady response with and without this effect. The response sensitivity to various system parameters, e.g., gear mesh stiffness and damping, SFD clearance to diameter ratio, and gear mass unbalance, is also studied. As expected, the numerical results reveal that the lateral motion dominant modes may be significantly attenuated by using an SFD, while the torsional motion dominant modes are sensitive to gear mesh damping. The strong nonlinearity of the SFD is responsible for complex dynamic response in some frequency ranges.

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22

XU, LIZHONG, and YAOWU LI. "LATERAL-FLEXURAL AND TORSIONAL VIBRATIONS OF FLEXIBLE RING FOR ELECTROMECHANICAL INTEGRATED ELECTROSTATIC HARMONIC ACTUATOR." International Journal of Structural Stability and Dynamics 09, no. 03 (September 2009): 391–409. http://dx.doi.org/10.1142/s0219455409003144.

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This paper presents an electromechanical coupled dynamic equation for the lateral-flexural and torsional vibrations of a flexible ring for an electromechanical integrated electrostatic harmonic actuator as well as the equation of the forced response of the electromechanical integrated electrostatic harmonic actuator to voltage excitation. By solving these equations, the natural frequency and vibration modes of the flexible ring for the actuator are investigated. Changes in the natural frequency with respect to the main system parameters are also examined and the dynamic responses of the actuator to voltage excitation obtained.

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23

Muszynska, Agnes. "Vibrational Diagnostics of Rotating Machinery Malfunctions." International Journal of Rotating Machinery 1, no. 3-4 (1995): 237–66. http://dx.doi.org/10.1155/s1023621x95000108.

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This paper outlines rotating machinery malfunction diagnostics using vibration data in correlation with operational process data. The advantages of vibration monitoring systems as a part of preventive/predictive maintenance programs are emphasized. After presenting basic principles of machinery diagnostics, several specific malfunction symptoms supported by simple mathematical models are given. These malfunctions include unbalance, excessive radial load, rotor-to-stator rubbing, fluid-induced vibrations, loose stationary and rotating parts, coupled torsional/lateral vibration excitation, and rotor cracking. The experimental results and actual field data illustrate the rotor vibration responses for individual malfunctions. Application of synchronous and nonsynchronous perturbation testing used for identification of basic dynamic characteristics of rotors is presented. Future advancements in vibration monitoring and diagnostics of rotating machinery health are discussed. In the Appendix, basic instrumentation for machine monitoring is outlined.

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24

Ananda Rao, M., J. Srinivas, V. B. V. Rama Raju, and K. V. S. S. Kumar. "Coupled torsional–lateral vibration analysis of geared shaft systems using mode synthesis." Journal of Sound and Vibration 261, no. 2 (March 2003): 359–64. http://dx.doi.org/10.1016/s0022-460x(02)01240-3.

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25

Shiau, T. N., J. S. Rao, J. R. Chang, and S. T. Choi. "Dynamic Behavior of Geared Rotors." Journal of Engineering for Gas Turbines and Power 121, no. 3 (July 1, 1999): 494–503. http://dx.doi.org/10.1115/1.2818500.

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This paper is concerned with the dynamic behavior of geared rotor systems supported by squeeze film dampers, wherein coupled bending torsion vibrations occur. Considering the imbalance forces and gravity, it is shown that geared rotors exhibit chaotic behavior due to nonlinearity of damper forces. The route to chaos in such systems is established. In geared rotor systems, it is shown that torsional excitation can induce lateral vibrations. It is shown that squeeze film dampers can suppress large amplitudes of whirl arising out of torsional excitation.

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26

Jrad, Wassim, Foudil Mohri, Guillaume Robin, El Mostafa Daya, and Jihad Al-Hajjar. "Analytical and finite element solutions of free and forced vibration of unrestrained and braced thin-walled beams." Journal of Vibration and Control 26, no. 5-6 (November 13, 2019): 255–76. http://dx.doi.org/10.1177/1077546319878901.

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In this article, vibration of thin-walled beams with arbitrary open cross-section shape is investigated. Based on the beam element model accounting for warping and flexural–torsional coupling, analytical solutions for different boundary conditions are derived for higher free vibration modes in bending, torsion and flexural–torsional coupled modes. In the model, the effects of rotational inertial kinematic terms are considered. The finite element approach of the model is also investigated. Three-dimensional beams with seven degrees of freedom per node are adopted in the mesh process. Free vibration and forced vibration analyses are possible. In forced vibration, the behaviour of the beams is studied in the frequency domain using the steady-state method (modal analysis). Damping is considered using the Rayleigh model. The model is validated by comparing the results to benchmark solutions found in the literature and to other recent numerical and experimental results. Additional finite element simulations are performed by means of commercial softwares (Abaqus and Adina). In slender unrestrained beams, the vibration behaviour is predominated by torsion and lateral bending modes. In design, recourse to braces is a good compromise. This solution is discussed, and improvement of the vibration behaviour in the presence of intermediate braces is confirmed. Application of higher vibration modes in building and bridge design is outlined. The effects of the number and distribution of the intermediate braces to improve structural stability against vibration behaviour is outlined.

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27

Kiciński, Jan. "Assessment of Materials and Operational Imperfections in Rotating Machinery." Key Engineering Materials 293-294 (September 2005): 391–400. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.391.

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Presented have been the methods of modelling of the selected materials and operational imperfections (defects) like rotor cracks and hydrodynamic instability in rotating machines. Despite abundant information on this topic, there are still numerous problems to be solved. This regards primarily to the analysis of characteristic symptoms of such defects in the form of e.g. nonlinear vibrations and coupled forms of lateral, axial and torsional vibrations. The paper presents also author’s opinions concerning the one of the most intriguing operational imperfections, namely the formation of oil whirls and oil whips in slide bearings of a rotating machine. Coupled forms of vibration are generally a result of different kinds of couplings taking place in the system and interactions between construction and material imperfections.

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28

Gong, L., and H. Hao. "Analysis of Coupled Lateral-Torsional-Pounding Responses of One-Storey Asymmetric Adjacent Structures Subjected to Bi-Directional Ground Motions Part I: Uniform Ground Motion Input." Advances in Structural Engineering 8, no. 5 (October 2005): 463–79. http://dx.doi.org/10.1260/136943305774858043.

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This paper presents results of a parametric study of seismic induced lateral-torsional-pounding responses of an asymmetric and a symmetric one-storey system subjected to bi-directional ground motion. The properties of the symmetric model are fixed, while the vibration frequency and eccentricity of the asymmetric model vary in the numerical computation. 20 sets of bi-directional horizontal earthquake ground motion time histories are numerically simulated for the analysis. All the simulated motions are compatible individually with the Newmark-Hall design response spectrum with 5% damping and normalized to 0.5g. Ensemble mean peak responses of the two systems to the 20 sets ground motions are estimated. Both linear elastic and nonlinear inelastic behaviours are studied. Effects of torsional stiffness, structural vibration frequency, eccentricities, and initial gap between two structures are investigated. Numerical results are presented in dimensionless form and compared with the code torsional provisions. In this paper, the input ground motion time histories at all the structural supports are assumed to be uniform. An accompany paper of this study is devoted to discuss the effect of the spatially varying ground motion on coupled lateral-torsional-pounding responses of the adjacent structures (Hao and Gong 2005).

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29

Zhou, Shihua, Guiqiu Song, Mengnan Sun, and Zhaohui Ren. "Nonlinear dynamic response analysis on gear-rotor-bearing transmission system." Journal of Vibration and Control 24, no. 9 (August 30, 2016): 1632–51. http://dx.doi.org/10.1177/1077546316667178.

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A coupled lateral-torsional nonlinear dynamic model with 16-degree-of-freedom (16-DOF) of gear-rotor-bearing transmission system (GRBTS) is developed after comprehensive considering the nonlinear features associated with time-varying meshing stiffness, backlash, transmission error, friction force, input/output load, gravity and gear eccentricity. Based on the nonlinear differential equations, the coupled multi-body dynamic responses of the GRBTS are demonstrated using the Runge-Kutta numerical method, and the effects of friction coefficient and mean load on the dynamic characteristics are investigated. The results show that the friction force could enlarge the vibration amplitude and affect the low frequency components seriously. The mean load excitation has a complicated influence on the coupled GRBTS, and the torsional vibration is the dominate response. Whereas the mean load excitation has a certain extent vibration suppression, and light load and heavy load could no longer effectively control the nonlinear vibration of the GRBTS. With the increasing of rotational speed, the friction coefficient and mean load ranges of the chaotic behavior widen and the chaotic characteristics strengthens. It is shown that small parameter random perturbation might be propagated in the vibration system and lead to relatively large vibration of the system. The contribution to provide a reference for the design and study of gear system.

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30

Szolc, Tomasz. "On the Discrete–Continuous Modeling of Rotor Systems for the Analysis of Coupled Lateral Torsional Vibrations." International Journal of Rotating Machinery 6, no. 2 (2000): 135–49. http://dx.doi.org/10.1155/s1023621x00000130.

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In the paper, dynamic investigations of the rotor shaft systems are performed by means of the discrete-continuous mechanical models. In these models the rotor shaft segments are represented by the rotating cylindrical flexurally and torsionally deformable continuous viscoelastic elements. These elements are mutually connected according to the structure of the real system in the form of a stepped shaft which is suspended on concentrated inertial viscoelastic supports of linear or non-linear characteristics. At appropriate shaft crosssections, by means of massless membranes, there are attached rigid rings representing rotors, disks, gears, flywheels and others. The proposed model enables us to investigate coupled linear or non-linear lateral torsional Vibrations of the rotating systems in steady-state and transient operating conditions. As demonstrative examples, for the steam turbo-compressor under coupled lateral torsional vibrations, the transient response due to a blade falling out from the turbine rotor as well as the steady-state response in the form of parametric resonance caused by residual unbalances are presented.

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31

Schwibinger, P., and R. Nordmann. "The Influence of Torsional-Lateral Coupling on the Stability Behavior of Geared Rotor Systems." Journal of Engineering for Gas Turbines and Power 110, no. 4 (October 1, 1988): 563–71. http://dx.doi.org/10.1115/1.3240172.

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In high-performance turbomachinery trouble often arises due to unstable asynchronous lateral vibrations. The instabilities are mostly caused by oil film bearings, clearance excitation, internal damping, annular pressure seals in pumps, or labyrinth seals in turbocompressors. In recent times as an additional influence the coupling between torsional and lateral vibrations is considered, which is of practical importance in geared rotor systems. In the literature [1, 2], some field problems are described, where in geared drive trains unstable lateral vibrations occurred together with torsional oscillations. This presentation studies the influence of torsional-lateral coupling on the stability behavior of a simple geared system supported by oil film bearings. The coupling effect is investigated by parameter studies and a sensitivity analysis for the uncoupled and the coupled system.

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32

Chen, Siyu, Jinyuan Tang, Changjiang Zhou, and Zehua Hu. "Modal and whirling analysis of coupled lateral and torsional vibration of herringbone gear." International Journal of Dynamics and Control 2, no. 3 (December 10, 2013): 404–14. http://dx.doi.org/10.1007/s40435-013-0042-9.

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33

Simmons, H. R., and A. J. Smalley. "Effective Tools for Diagnosing Elusive Turbomachinery Dynamics Problems in the Field." Journal of Engineering for Gas Turbines and Power 112, no. 4 (October 1, 1990): 470–77. http://dx.doi.org/10.1115/1.2906191.

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This paper describes and discusses techniques that can effectively diagnose dynamics problems in turbomachinery. A variety of elusive dynamics problems are identified that require definition, quantification, diagnosis, and monitoring. The state of the art in measurement and signal processing techniques is discussed with reference to such factors as the directness of the measurement, the degree of intrusion required, the difficulty of installation, and the reliability or durability of the sensor. Several examples of techniques are provided that have proved to be effective in diagnosing elusive dynamics problems; some examples allow comparison of alternative techniques with different degrees of effectiveness. Problems addressed include rotating stall in the compressor section of a gas turbine, coupled lateral/torsional vibration in a gas turbine driven pipeline compressor, forced vibration of combustor parts, strain gage telemetry of blade vibrations, and nonintrusive measurement of blade vibrations using bearing-mounted accelerometers.

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34

REN, Zhaohui. "Vibration Characteristic Analysis of Helical Gear-rotor-bearing System with Coupled Lateral-torsional-axial." Journal of Mechanical Engineering 51, no. 15 (2015): 75. http://dx.doi.org/10.3901/jme.2015.15.075.

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35

Lee, An Sung, Jin Woong Ha, and Dong-Hoon Choi. "Coupled lateral and torsional vibration characteristics of a speed increasing geared rotor-bearing system." Journal of Sound and Vibration 263, no. 4 (June 2003): 725–42. http://dx.doi.org/10.1016/s0022-460x(02)01103-3.

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36

HONG, Jie, Pingchao YU, Yanhong MA, and Dayi ZHANG. "Investigation on nonlinear lateral-torsional coupled vibration of a rotor system with substantial unbalance." Chinese Journal of Aeronautics 33, no. 6 (June 2020): 1642–60. http://dx.doi.org/10.1016/j.cja.2020.02.023.

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37

Shum, K. M., and Y. L. Xu. "Multiple tuned liquid column dampers for reducing coupled lateral and torsional vibration of structures." Engineering Structures 26, no. 6 (May 2004): 745–58. http://dx.doi.org/10.1016/j.engstruct.2004.01.006.

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38

Luo, Z., X. Sun, and J. N. Fawcett. "Coupled torsional-lateral-axial vibration analysis of a geared shaft system using substructure synthesis." Mechanism and Machine Theory 31, no. 3 (April 1996): 345–52. http://dx.doi.org/10.1016/0094-114x(95)00012-n.

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39

ZHANG, KUNPENG, and QIAN DING. "LATERAL AND TORSIONAL VIBRATIONS OF A TWO-DISK ROTOR-STATOR SYSTEM WITH AXIAL CONTACT/RUBS." International Journal of Applied Mechanics 01, no. 02 (June 2009): 305–26. http://dx.doi.org/10.1142/s1758825109000137.

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The dynamics of a rotor system with axial contact/rub events between the disks and stator are investigated by numerical simulations. The formula for determining the contact/rub points, axial contact forces and dry friction forces are deduced. To account for their influence, the axial contact forces are substituted by equivalent forces acting at the disk centers, based on the equivalent moment rule. One-parametric model is used to estimate the contact-induced dry friction forces. The coupled equations of lateral and torsional motions of rotor and the lateral motion of disk are then established. Numerical simulations are carried out to reveal the lateral and torsional vibrations for both two-disk contact/rubs with different axial clearances, and one disk contact/rubs. Bifurcation diagrams, orbits, phase portraits, amplitude-frequency spectra and Poincaré maps are adopted to demonstrate the dynamical behaviors of the system. The results show that though both the lateral and torsional vibrations can reflect the influences of contact/rubs on rotor dynamics, the spectrum analyses of the torsional vibrations are more suitable to determine straight the extent of their effect.

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40

Thiyyakkandi, Sudheesh, Michael McVay, Peter Lai, and Rodrigo Herrera. "Suitability of jetted and grouted precast pile for supporting mast arm structures." Canadian Geotechnical Journal 54, no. 9 (September 2017): 1231–44. http://dx.doi.org/10.1139/cgj-2016-0467.

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Jetted and grouted precast piles (JGPPs) are prefabricated piles installed utilizing jetting and pressure grouting. These piles are well-suited for urban environments as they overcome the inherent drawbacks of currently chosen deep foundations (e.g., noise and vibration disturbances due to pile driving, quality control issue with cast-in-place construction). Past studies in a large test chamber facility have shown that JGPPs can support very high axial and torsional loads owing to their improved skin and tip resistances subsequent to the side- and tip-grouting. However, this new pile has not yet been implemented in practice due to the lack of field verification of its constructability as well as load resistance. This paper presents the full-scale field construction of two JGPPs and the load test program performed to investigate the applicability of the new pile as a foundation for miscellaneous structures. As such structures are subjected to high torsion and lateral load during severe wind-loading (e.g., hurricanes), the test program included combined torsion and lateral loading as well as simple lateral loading. An actual pole – mast arm assembly was used in the coupled torsion and lateral load test to simulate the typical field-loading scenario. The load was applied using a crane and the pile’s rotations and translations were monitored using the novel instrumentation systems. The field tests showed that JGPPs possess high torsion and lateral resistances compared to identically sized drilled shafts, which is a common foundation type used for such structures. The two methods available for predicting axial resistance of the new pile are found to be suitable for the estimation of torsional resistance as well. It was also found that the concurrent application of torsion significantly reduces lateral resistance of the new pile foundation as observed for drilled shafts. In general, the study reveals that the JGPPs are well-suited foundations for miscellaneous structures.

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41

Lee, Kyoung-Hyun, Hyung-Suk Han, and Sungho Park. "Bifurcation analysis of coupled lateral/torsional vibrations of rotor systems." Journal of Sound and Vibration 386 (January 2017): 372–89. http://dx.doi.org/10.1016/j.jsv.2016.10.002.

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42

Al-Bedoor, B. O. "Modeling the coupled torsional and lateral vibrations of unbalanced rotors." Computer Methods in Applied Mechanics and Engineering 190, no. 45 (August 2001): 5999–6008. http://dx.doi.org/10.1016/s0045-7825(01)00209-2.

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43

Al-Said, Samer A. M. "Crake Effect on the Dynamic Characteristics of Elastically Coupled Beams." Applied Mechanics and Materials 110-116 (October 2011): 328–36. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.328.

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Simple mathematical model that describes the lateral vibration of elastically coupled cracked cantilever beams carrying rigid disk at their tips is derived. The derived model is used to study the effect of elastic coupling, crack depth and location on the dynamic characteristics of the system. The cracked beam is presented as two beams connected with torsional spring at the crack location. Model verification is carried out using three dimensional finite element analysis using ANSYS program, the verification results showed good agreement with that obtained from the proposed model. The study reveals that the first system natural frequency is affected by the crack and the elastic coupling.

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44

Han, HyungSuk, and KyoungHyun Lee. "Experimental verification for lateral-torsional coupled vibration of the propulsion shaft system in a ship." Engineering Failure Analysis 104 (October 2019): 758–71. http://dx.doi.org/10.1016/j.engfailanal.2019.06.059.

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45

Salehi-Khojin, Amin, Nader Jalili, and S. Nima Mahmoodi. "Vibration analysis of vector piezoresponse force microscopy with coupled flexural-longitudinal and lateral-torsional motions." Journal of Sound and Vibration 322, no. 4-5 (May 2009): 1081–99. http://dx.doi.org/10.1016/j.jsv.2008.11.039.

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46

Lee, An-Chen, and Tien-Dat Hoang. "Coupled lateral and torsional vibrations of the micro-drilling spindle systems." International Journal of Advanced Manufacturing Technology 87, no. 5-8 (March 17, 2016): 2063–79. http://dx.doi.org/10.1007/s00170-016-8463-1.

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47

Kuang, J. S., and S. C. Ng. "Coupled lateral-torsion vibration of asymmetric shear-wall structures." Thin-Walled Structures 38, no. 2 (October 2000): 93–104. http://dx.doi.org/10.1016/s0263-8231(00)00033-1.

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48

Bigdeli, Yasser, and Dookie Kim. "Investigation of the Performance of Two Passive Controllers in Mitigating the Rotational Response of Irregular Buildings." Advances in Materials Science and Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/1898792.

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Two passive vibration control devices (i.e., circle type tuned liquid damper (C-TLD) and a circle type tuned liquid column damper (C-TLCD)) were experimentally investigated for their performance when attached to the irregular building structure subjected to dynamic loads. The specific directions where the maximum response of the structure is expected were experimentally identified for x- and y-directions as well as for rotational direction. The power spectral density (PSD) was computed for the response of the structure based on the frequency of the first three modes and also water level changes in the device container by using fast Fourier transform (FFT). The performances of these two controllers regarding suppressing the structural vibration were compared for the seismic loads applied in an experimentally identified critical direction. The results show that these systems are effective in terms of mitigating the coupled lateral and torsional vibrations of a scaled three-story irregular model.

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49

Li, Chao-Feng, Shi-Hua Zhou, Jie Liu, and Bang-Chun Wen. "Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system." Acta Mechanica Sinica 30, no. 5 (October 2014): 746–61. http://dx.doi.org/10.1007/s10409-014-0063-4.

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50

Zhu, Xiuxing, Weixia Zhou, Yujian Lei, Peng Jia, Shifeng Xue, Bo Zhou, and Yuanbo Xia. "A Nonlinear Dynamic Model for Characterizing the Downhole Motions of the Sidetracking Tool in a Multilateral Well." Energies 16, no. 2 (January 4, 2023): 588. http://dx.doi.org/10.3390/en16020588.

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It is of practical interest to investigate the mechanical behaviors of a sidetracking tool system and to describe the sidetracking tool’s vibration mechanical response, as this can provide an important basis for evaluating and optimizing the tool structure and effectively controlling the profile of the sidetracking window. In this article, three nonlinear dynamic models with ten, six, and two degrees of freedom, respectively, are established using the Lagrange method to characterize the behavior of the sidetracking tool. It should be noted that in these models, the axial, lateral, and torsional vibration of the tool system are fully coupled. The process of the sidetracking tool mills in the casing-pipe wall is divide into three typical stages, i.e., the window mill, pilot mill, and watermelon mill grinding the casing, respectively. The dynamic response of the three stages is studied to more effectively analyze the influence of the sidetracking tool vibration deformation on the window width. The Runge–Kutta method, which is easy to implement, is applied to solve the supposed nonlinear dynamic model, and some useful findings are as follows. The effects of sidetracking tool vibrations at different stages on window widening size are illustrated quantitatively. The vibration trajectory pattern of the sidetracking tool is different from that of the conventional drilling tool due to the influence of the whipstock, which changes from the general whirling motion pattern to the X reciprocating pattern, and the vibration amplitude decreases. Due to the influence of the tool’s lateral amplitude, the window profile is widened. The widened window size of the window mill and the pilot mill are 3.30 mm and 2.74 mm, respectively, and the extended window size of the watermelon mill is 0.07 mm, while the maximum window width formed by the sidetracking tool is 374.34 mm. This work proposes, for the first time, the coupled vibration model of the sidetracking tool system, which is helpful to better understand the nonlinear dynamic effects of the sidetracking tool, laying the foundation for the optimization of the sidetracking parameters.

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