Coupled Vibration of Geared Systems

1968 ◽  
Vol 72 (690) ◽  
pp. 522-526 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Natural Frequencies ◽  
Engineering Practice ◽  
Coupled Vibration ◽  
Combined System ◽  
Rotating System ◽  
Rotating Systems ◽  
Epicyclic Gear ◽  
Gear Case ◽  
Gear Box ◽  
Supporting Frame

In the design of geared rotating systems in engineering practice a variety of configurations are used, and their torsional vibration has been extensively studied. Detailed analyses of the modes and frequencies of vibration of these systems have been given by Ker Wilson and Nestorides. When the rotating system is rigidly supported, standard methods may be used to obtain the characteristics of free vibration and the response to impressed forces, from which the transmissibility of the gear-box may be calculated. However, there are many applications in which the gearbox is flexibly mounted. The simple example of a geared engine with a flexibly mounted crankcase has been considered by Den Hartog and Butterfield. In some epicyclic gear-box assemblies, elastic elements are introduced between the reactive element and the gear-case to increase the capacity for absorbing impulsive loads and as a means of varying the natural frequencies of vibration'. Harmonic forces acting on the rotors excite coupled vibration of the rotating system and the supporting frame, and Ker Wilson has shown how the natural frequencies and modes of the combined system may be determined by Holzer-type tabular methods. This involves a trial-and-error technique which may sometimes be tedious. Vibration of geared systems may also be excited by the motion of the frame supporting the gear-box, and an analysis of the response is necessary in the determination of dynamic loads.

Calculation of Natural Frequencies and Modes of Steadily Rotating Systems: A Teaching Note

1973 ◽  
Vol 24 (2) ◽  
pp. 139-146 ◽  
Author(s):  
A Simpson
Keyword(s):  
Special Form ◽  
Natural Frequencies ◽  
Order System ◽  
Symmetric System ◽  
System Matrix ◽  
Rotating System ◽  
First Order ◽  
Natural Frequencies And Modes ◽  
Rotating Systems ◽  
Matrix Vector

SummaryThe linear, second-order, ordinary differential equations governing the free-vibration characteristics, in vacuo, of discretised systems executing, at equilibrium, steady rotational motion about a fixed point may be expressed in the well-known matrix-vector form involving real symmetric and skew-symmetric coefficient matrices. Less well known is the fact that the corresponding Hamiltonian first-order system may be cast into a special form involving a skew-symmetric system matrix. In this paper the computational merits of this special form are exploited in the calculation of the natural frequencies and modes of the rotating system.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

A New Method of Design of Epicyclic Gear Trains

2013 ◽  
Vol 457-458 ◽  
pp. 707-712
Author(s):  
Pei Wen An ◽  
Zhong Liang Lv
Keyword(s):  
New Method ◽  
Combination Method ◽  
Engineering Practice ◽  
Type Number ◽  
Practical Application ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Number Synthesis ◽  
Method Of Design

Epicyclic gear trains have been broadly applied in engineering practice. In this paper, kinematic chains (K.C.) with single-joint (S.J.) were applied to innovative synthesis of the epicyclic gear trains. The method of the innovative synthesis of the epicyclic gear trains was presented. Not only the epicyclic gear trains in common uses were obtained, but some new types of epicyclic gear trains that are got difficultly by means of conventional combination method were gained. Thereby, a new way has been offered for the innovative synthesis of the epicyclic gear trains, at the same time, a way has also been offered for practical application of some multi-link kinematic chains gained by using the theory of type-number synthesis of the K.C. with S.J.. Examples show that the method presented in this paper is right and feasible, and the method is efficient and practical for the innovative synthesis of the epicyclic gear trains.

Epicyclic Gear Vibrations

1976 ◽  
Vol 98 (3) ◽  
pp. 811-815 ◽  
Author(s):  
M. Botman
Keyword(s):  
Natural Frequencies ◽  
Gear Tooth ◽  
Planetary Gear ◽  
Periodic Coefficients ◽  
Plane Vibration ◽  
Epicyclic Gear ◽  
Floquet’S Theory ◽  
Floquet's Theory

The natural frequenices of in-plane vibration of a single planetary gear stage are analyzed. The gear tooth stiffnesses are approximated as linear springs. The effect of planet pin stiffness on the natural frequencies is evaluated. Rotation of the carrier gives rise to a system with periodic coefficients which is solved by means of Floquet’s theory. The rotation of the carrier appears to suppress the nonaxisymmetric modes which are present in the system with nonrotating carrier.

scholarly journals A Structured Approach to Solve the Inverse Eigenvalue Problem for a Beam with Added Mass

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Farhad Mir Hosseini ◽  
Natalie Baddour
Keyword(s):  
Natural Frequencies ◽  
Point Of View ◽  
Inverse Eigenvalue Problem ◽  
Bernoulli Beam ◽  
Combined System ◽  
Vibrational System ◽  
Single Mass ◽  
Inverse Eigenvalue ◽  
Euler Bernoulli Beam ◽  
Structured Approach

The problem of determining the eigenvalues of a vibrational system having multiple lumped attachments has been investigated extensively. However, most of the research conducted in this field focuses on determining the natural frequencies of the combined system assuming that the characteristics of the combined vibrational system are known (forward problem). A problem of great interest from the point of view of engineering design is the ability to impose certain frequencies on the vibrational system or to avoid certain frequencies by modifying the characteristics of the vibrational system (inverse problem). In this paper, a method to impose two natural frequencies on a dynamical system consisting of an Euler-Bernoulli beam and carrying a single mass attachment is evaluated.

Flexural Vibration of Cylindrical Shells Partially Coupled With External and Internal Fluids

1997 ◽  
Vol 119 (3) ◽  
pp. 476-484 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Good Accuracy ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Flexural Vibration ◽  
Rayleigh Quotient ◽  
Mode Shapes ◽  
Virtual Mass ◽  
Coupled Vibration ◽  
Theory Of Shells ◽  
Shell Axis

In this paper, the free flexural vibrations of a partially fluid-loaded simply supported circular cylindrical shell are studied; the fluid is assumed to be inviscid and to present a free-surface parallel to the shell axis. The presence of external and internal fluids are both studied and the problem for incompressible and compressible fluid are both discussed by using the added virtual mass approach. Circumferential dependence of displacement is extended in a Fourier series. The maximum potential energy of the cylinder is evaluated using a sum of reference kinetic energies of the shell vibrating in vacuum; this fact allows the proposed method to be independent from the theory of shells used. Then, the Rayleigh quotient for fluid-shell coupled vibration is formulated and minimized to obtain the Galerkin equation whose solution gives the natural frequencies and mode shapes. Numerical computations are performed to obtain the modal characteristics as functions of the level of water in contact with the shell in the range of good accuracy of the theory, that is around the half-wet shell level. Results for both a shell partially surrounded and filled with water are obtained and compared.

Dynamics of a Rotating System With a Nonlinear Eddy-Current Damper

1998 ◽  
Vol 120 (4) ◽  
pp. 848-853 ◽  
Author(s):  
Y. Kligerman ◽  
O. Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Eddy Current ◽  
Eddy Currents ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
System Response ◽  
Rotating System ◽  
Restoring Force ◽  
Rotating Systems ◽  
Eddy Current Damper

We investigate the nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact eddy-current damper. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the imbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

Free vibration analysis of rotating tapered Timoshenko beams via variational iteration method

2016 ◽  
Vol 23 (2) ◽  
pp. 220-234 ◽  
Author(s):  
Yanfei Chen ◽  
Juan Zhang ◽  
Hong Zhang
Keyword(s):  
Free Vibration ◽  
Iteration Method ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Accurate Determination ◽  
Variational Iteration Method ◽  
Mode Shapes ◽  
Engineering Practice ◽  
Timoshenko Beams ◽  
Variational Iteration

Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tapered Timoshenko beams using the technique of variational iteration, which is relatively new and is capable of providing accurate solutions for eigenvalue problems in a quite easy way. Natural frequencies and mode shapes for rotating tapered Timoshenko beams with linearly varying height as well as linearly varying height and width are investigated via two numerical examples, and solutions are compared with results published in literature where available. Since the method constitutes a numerical procedure, the convergence of solutions which is important for practical implementation is evaluated as well, where efficiency and accuracy of variational iteration method in solving high order eigenvalue problems are demonstrated.

scholarly journals Mössbauer experiments in a rotating system and physical interpretation of their results

2021 ◽  
pp. 34-43
Author(s):  
Alexander L. Kholmetskii ◽  
Tolga Yarman ◽  
Ozan Yarman ◽  
Metin Arik
Keyword(s):  
Energy Shift ◽  
Special Theory ◽  
Relativistic Energy ◽  
Theory Of Relativity ◽  
Rotating System ◽  
Rotating Systems ◽  
Extra Energy ◽  
Quantum Mechanical Description ◽  
Dilation Effect ◽  
The Moment

We discuss the results of modern Mössbauer experiments in a rotating system, which show the presence of an extra energy shift between the emitted and absorbed resonant radiation in addition to the relativistic energy shift of the resonant lines due to the time dilation effect in the co-rotating source and absorber with different radial coordinates. We analyse the available attempts to explain the origin of the extra energy shift, which include some extensions of special theory of relativity with hypothesis about the existence of limited acceleration in nature, with hypothesis about a so-called «time-dependent Doppler effect», as well as in the framework of the general theory of relativity under re-analysis of the metric effects in the rotating system, which is focused to the problem of correct synchronisation of clocks in a rotating system with a laboratory clock. We show that all such attempts remain unsuccessful until the moment, and we indicate possible ways of solving this problem, which should combine metric effects in rotating systems with quantum mechanical description of resonant nuclei confined in crystal cells.

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