Dynamic Analysis of Geared Rotors by Finite Elements

Kahraman, Ahmet; Özgüven, H. Nevzat; Houser, Donald R.; Zakrajsek, James J.

doi:10.1115/1.2926579

Cited by 133 publications

(79 citation statements)

References 3 publications

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“…Prior to any modal reduction, the validity of the system model was accessed through a comparison of natural frequencies at low speed and low damping to those previously published in the literature (16,17). As depicted in figure 2, the model provides results consistent with previous experiments.…”

Section: Overviewsupporting

confidence: 70%

Modal Synthesis of a Non-Proportionally Damped, Gyroscopically Influenced, Geared Rotor System via the State-Space

Stringer¹,

Sheth²,

Allaire³

2008

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Approved for public release; distribution unlimited. ii REPORT DOCUMENTATION PAGEForm Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)September 2008 ARL-TR-4582 SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited. SUPPLEMENTARY NOTES ABSTRACTModal synthesis provides for degree-of-freedom reduction and model simplification. This report presents a method for conducting modal synthesis on a geared rotor dynamic system under the influences of non-proportional damping and gyroscopic effects. Based on the familiar first-order, state-space methodology, a coordinate transformation is developed for diagonalizing the state-space equations of motion for each substructure of the system. A modal synthesis procedure then assembles the system equations of motion from the individual substructures. The coupling between the substructures occurs via the gear mesh. Using this methodology, the size and complexity of the model are reduced without incurring any significant loss in accuracy. The reduced model still allows for traditional methods of system analysis: Eigen-solution analysis, frequency domain response, and time domain response. Validation of this methodology occurs through its application to a finite element analysis of a geared system already published in the literature. The application illustrates that the results of the reduced system match almost exactly with the full finite element model. Additionally, the topics of gearing and gyroscopic effects are discussed with respect to limitations that arise from the analysis. In addition to model simplification, this technique also exhibits further potential for use in optimization and system identification schemes.

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Section: Overviewsupporting

confidence: 70%

Modal Synthesis of a Non-Proportionally Damped, Gyroscopically Influenced, Geared Rotor System via the State-Space

Stringer¹,

Sheth²,

Allaire³

2008

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“…investigated a simple geared system with coupled torsional and flexural vibrations. Kahraman [13,14] developed a gear rotor system model, in which the shaft was represented by a finite element model and the flexibility of the bearing was considered. Baud and Velex [15] investigated the dynamics of a gear-shaftbearing system using a nonlinear gear model.…”

Section: Introductionmentioning

confidence: 99%

Rotordynamics analysis of a double-helical gear transmission system

Chen

Tang

et al. 2015

Meccanica

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The rotordynamics of a double-helical gear transmission system is investigated. The equation of motion of the system with bearing and gyroscopic effect is derived by using the finite element method, in which Timoshenko beam finite element is used to represent the shaft, a rigid mass for the gear. Natural frequencies, mode shapes and Campbell diagrams are illustrated to indicate the effects of gear input speed and time varying mesh stiffness. Besides, effects of mesh stiffness on the critical speed of the gear transmission system are analyzed. The numerical results show that the axial force has significant influence on the natural frequency and the mode shape of the double-helical gear transmission system, for which the mix whirling motion dominates the natural characteristics. There are two higher critical speed curves which increase with the mesh stiffness, but one of them is related to the gyroscopic effect.

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“…Iida et al [9] considered a simple geared system with coupled torsional and flexural vibrations. Kahraman et al [2,10] developed a gear rotor system model, in which a finite element model is used to represent shaft and the flexibility of bearing is considered. Baud and Velex [11] investigated the dynamics of gear-shaft-bearing systems using a nonlinear gear model.…”

Section: Introductionmentioning

confidence: 99%

Modal and whirling analysis of coupled lateral and torsional vibration of herringbone gear

Chen

Tang

Zhou

et al. 2013

Int. J. Dynam. Control

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The coupled lateral and torsional motions are significant for the herringbone gear in high-speed applications. The present work attempts to investigate the influences of damping, eccentric mass and time varying mesh stiffness of gear pair on the modal vibration of a herringbone gear pair. Under high-speed condition, the gyroscopic performance as a result of coupled lateral and torsional motions cannot be ignored. To achieve a targeted analysis, the equivalent mesh stiffness of the herringbone gear pair is calculated in preprocessing based on the finite element method by considering the thin rim and web. Subsequently, an analytical model for coupled lateral and torsional motions of the herringbone gear is proposed. Then, the natural frequencies, synchronous whirling speed, critical speed, as well as the transient behaviors with time invariant and time varying stiffness, are calculated numerically. The results in Campbell diagram show that the damping affects the critical speed slightly while the eccentric mass will reduce the critical speed significantly. Transient dynamics analysis shows that no matter which stiffness models are used, the high frequency components are predominant, which may be the results of frequency veering phenomena at high order natural frequency. The present work indicates the necessity of paying attention to the critical speed relative to mesh frequency in high speed gear applications.

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Dynamic Analysis of Geared Rotors by Finite Elements

Cited by 133 publications

References 3 publications

Modal Synthesis of a Non-Proportionally Damped, Gyroscopically Influenced, Geared Rotor System via the State-Space

Modal Synthesis of a Non-Proportionally Damped, Gyroscopically Influenced, Geared Rotor System via the State-Space

Rotordynamics analysis of a double-helical gear transmission system

Modal and whirling analysis of coupled lateral and torsional vibration of herringbone gear

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