Numerical Investigation on Traveling Wave Vibration of Bevel Gears

2007 ◽  
Author(s):  
Costantino Carmignani ◽  
Paola Forte ◽  
Gabriele Melani ◽  
Giovanni Di Carlo
Keyword(s):  
Traveling Wave ◽  
Structural Reliability ◽  
Natural Frequencies ◽  
Contact Condition ◽  
Critical Conditions ◽  
3D Fem ◽  
Bevel Gears ◽  
Numerical Tests ◽  
Natural Modes ◽  
Dynamic Phenomena

Aircraft transmissions have the peculiar characteristics of light structures and high operating speeds, therefore relatively low flexural natural frequencies and high excitation frequencies due to rotation and meshing. Thus some dynamic phenomena, such as traveling wave vibration (TWV), can be more easily encountered. However few papers can be found in the literature on TWV of gears while on the contrary it might be a problem especially for gears having thin rim and disk. This paper deals with the simulation of the disk TWV of bevel gears. 3D FEM is used to obtain the natural modes and frequencies of the gear. The response of a simplified non-rotating model of two meshing gears was entirely simulated in an Ansys environment. The numerical tests were performed considering a variable torque applied to one of the gears, the other being constrained, accounting for the meshing excitation. To simulate the rotating contact condition with respect to the gear reference systems, the dof of the nodes in contact of the two gears were coupled. Preliminary tests were performed considering one of the two gears rigid. The simulation of the TWV of gears makes it possible to identify the most critical conditions for stress and fatigue in the gear disks and therefore estimate the gear structural reliability.

scholarly journals Aspects of Vibration-Based Methods for the Prestressing Estimate in Concrete Beams with Internal Bonded or Unbonded Tendons

2021 ◽  
Vol 6 (6) ◽  
pp. 83
Author(s):  
Angelo Aloisio
Keyword(s):  
Elastic Modulus ◽  
Structural Reliability ◽  
Natural Frequencies ◽  
Concrete Beams ◽  
Experimental Testing ◽  
Hybrid Approach ◽  
Reliable Estimate ◽  
Axial Deformation ◽  
Dynamic Identification ◽  
Concrete Girders

The estimate of internal prestressing in concrete beams is essential for the assessment of their structural reliability. Many scholars have tackled multiple and diverse methods to estimate the measurable effects of prestressing. Among them, many experimented with dynamics-based techniques; however, these clash with the theoretical independence of the natural frequencies of the forces of internally prestressed beams. This paper examines the feasibility of a hybrid approach based on dynamic identification and the knowledge of the elastic modulus. Specifically, the author considered the effect of the axial deformation on the beam length and the weight per unit of volume. It is questioned whether the uncertainties related to the estimate of the elastic modulus and the first natural frequency yield reasonable estimates of the internal prestressing. The experimental testing of a set of full-scale concrete girders with known design prestressing supports a discussion about its practicability. The author found that the uncertainty in estimating the natural frequencies and elastic modulus significantly undermines a reliable estimate of the prestressing state.

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

scholarly journals The modal analysis of cylindrical steel tank with selfsupported roof filled with different level of liquid

2013 ◽  
Vol 12 (2) ◽  
pp. 205-212
Author(s):  
Daniel Burkacki ◽  
Michał Wójcik ◽  
Robert Jankowski
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Environmental Disaster ◽  
Natural Modes ◽  
Liquid Products ◽  
Safety And Reliability ◽  
Steel Tank ◽  
Steel Tanks ◽  
Cylindrical Steel Tanks ◽  
Cylindrical Steel

In technical branches, such as chemical or petroleum industries, cylindrical steel tanks are essential structures used for storage of liquid products. Therefore, their safety and reliability is essential, because any failure might have dangerous consequences, in extreme cases may even lead to an environmental disaster. The aim of the presented paper is to show the results of the modal analysis concerning the cylindrical steel tank with self-supported roof which has been constructed in northern Poland. The investigation was carried out with the use of the FEM commercial computer program Abaqus. The values of natural frequencies, as well as the natural modes, for different levels of liquid filling (empty tank, partly filled and tank fully filled) were determined in the study. The results of the study clearly indicate that the increase in the liquid level leads to the substantial decrease in the natural frequencies of the structure.

Free Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

A Study on the Instability of Disk-Shaped Gear

1999 ◽  
Author(s):  
Guangming Ren ◽  
Litang Yan
Keyword(s):  
Perturbation Method ◽  
Traveling Wave ◽  
Vibration Characteristics ◽  
Exciting Force ◽  
Nonlinear Perturbation ◽  
The Self ◽  
Experimental Investigations ◽  
Damping Force ◽  
Bevel Gears ◽  
Theory And Experiment

Abstract In this paper the theory and experiment concerning vibration instability of disk-shaped gear are presented. At first the self-exciting force of gear is searched and the works done by the exciting force and damping force are analyzed. Then the vibration instability of the disk-shaped plain gear is studied with multiple scale’s method of the nonlinear perturbation method. The vibration characteristics of a coupled pair of bevel gears are investigated experimentally. Both theoretical and experimental investigations show that there are actually self-exciting vibrations on the gear. Under certain conditions the forward traveling wave vibration of the driving gear and the backward traveling wave vibration of the driven gear can be instable.

Sensor Egregium – An Atomic Force Microscope Sensor for Continuously Variable Resonance Amplification

2021 ◽  
pp. 1-23
Author(s):  
Rafiul Shihab ◽  
Tasmirul Jalil ◽  
Burak Gulsacan ◽  
Matteo Aureli ◽  
Ryan Tung
Keyword(s):  
Finite Element Analysis ◽  
Atomic Force Microscope ◽  
Natural Frequencies ◽  
Proof Of Concept ◽  
Element Analysis ◽  
Force Microscopy ◽  
Atomic Force ◽  
Wide Range ◽  
Curve Veering ◽  
Dynamic Phenomena

Abstract Numerous nanometrology techniques concerned with probing a wide range of frequency dependent properties would benefit from a cantilevered sensor with tunable natural frequencies. In this work, we propose a method to arbitrarily tune the stiffness and natural frequencies of a microplate sensor for atomic force microscope applications, thereby allowing resonance amplification at a broad range of frequencies. This method is predicated on the principle of curvature-based stiffening. A macroscale experiment is conducted to verify the feasibility of the method. Next, a microscale finite element analysis is conducted on a proof-of-concept device. We show that both the stiffness and various natural frequencies of the device can be highly controlled through applied transverse curvature. Dynamic phenomena encountered in the method, such as eigenvalue curve veering, are discussed and methods are presented to accommodate these phenomena. We believe that this study will facilitate the development of future curvature-based microscale sensors for atomic force microscopy applications.

Modal Properties of Hybrid Carbon/Kevlar Composite Thin Plate and Hollow Wing Model

2013 ◽  
Vol 446-447 ◽  
pp. 597-601
Author(s):  
H. Haidzir ◽  
Dayang Laila Majid ◽  
A.S.M. Rafie ◽  
M.Y. Harmin
Keyword(s):  
Mechanical Properties ◽  
Thin Plate ◽  
Composite Plate ◽  
Natural Frequencies ◽  
Computational Procedure ◽  
Modal Testing ◽  
Wing Model ◽  
Natural Modes ◽  
Superior Mechanical Properties ◽  
Hybrid Carbon

In any flutter prediction analysis, modal testing is necessary because flutter, a resonant like vibration occurs at a flutter frequency and adopts a mode shape akin to its structural natural modes. Modal testing can be performed computationally with knowledge of the mechanical properties of the structure. In the present work, computational modal analysis is first performed on a cantilevered hybrid composite thin plate and validated experimentally. Then, the computational procedure is demonstrated on a composite hollow wing model of same material. The concept of hollow wing is explored due to the superior mechanical properties of carbon/kevlar composite plate. It is observed that the natural frequencies of the hollow wing model are higher than thin plate due to stiffer configuration. A breathing mode was also observed at mode 4 for the hollow wing.

Node Control of Uniform Beams Subject to Various Boundary Conditions

1992 ◽  
Vol 59 (4) ◽  
pp. 983-990 ◽  
Author(s):  
L. Weaver ◽  
L. Silverberg
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Controlled System ◽  
Free Boundary Conditions ◽  
Various Boundary Conditions ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Control Forces ◽  
Direct Feedback

This paper introduces node control, whereby discrete direct feedback control forces are placed at the nodes of the N+1th mode (the lowest N modes participate in the response). Node control is motivated by the node control theorem which states, under certain conditions, that node control preserves the natural frequencies and natural modes of vibration of the controlled system while achieving uniform damping. The node control theorem is verified for uniform beams with pinned-pinned, cantilevered, and free-free boundary conditions, and two cases of beams with springs on the boundaries. A general proof of the node control theorem remains elusive.

Motion Characteristics of Loop Type Elliptic Resonator

2008 ◽  
Vol 20 (1) ◽  
pp. 61-67
Author(s):  
Tohru Sasaki ◽  
◽  
Kunio Koizumi ◽  
Motofumi Sasaki
Keyword(s):  
Natural Frequencies ◽  
Torsional Stiffness ◽  
Elliptic Motion ◽  
Natural Modes ◽  
Center Point ◽  
Elliptic Vibration ◽  
Arbitrary Phase ◽  
Piezoelectric Bimorphs ◽  
Motion Characteristics

This paper deals with characteristics of the elliptic resonator. The resonator consists of loop and leg part, respectively. Each part was actuated by bimorph type piezoelectric member. The deflection of loop part and the bending of leg part generated by piezoelectric bimorphs makes an elliptic motion at the center point of the upper member. If resonators are put in a train and are actuated at the same frequency, it can feed objects on the upper surface of its train. There are two type of resonator, arch type and pentagonal type. Arch type resonator generates big amplitude on the center of upper surface. Bending its under member, pentagonal type resonator generates amplitude on the whole upper surface. Calculated results show that a shape of resonator influences on natural modes and natural frequencies. The trial one could generate elliptic motion in arbitrary phase with both type resonator. A pentagonal type resonator with notch reinforces its torsional stiffness and can generate necessary natural modes and an elliptic vibration without generating other natural modes.

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