The Dynamical Characteristics of a Gyroscope With a Tuned Elastic Suspension

1980 ◽  
Vol 47 (1) ◽  
pp. 161-166 ◽  
Author(s):  
C. H. J. Fox ◽  
J. S. Burdess
Keyword(s):  
Mathematical Model ◽  
Rigid Body ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Elastic Suspension ◽  
Dynamical Characteristics ◽  
Suspension Parameters ◽  
Lower Natural Frequency ◽  
Two Degree Of Freedom ◽  
Selection Of

This study investigates the dynamics of a gyroscope rotor, supported on a “heavy” elastic suspension, using a mathematical model which allows the gyroscope to be treated as a two-degree-of-freedom rigid body on a light suspension. The natural frequencies are functions of spin rate and it is shown that the lower natural frequency can be reduced to zero by appropriate selection of suspension parameters. In this condition the gyroscope is “tuned” and could provide a useful inertial reference. Some problems associated with predicting the tuning speed of a practical gyroscope are highlighted.

A MEMS-Based Rate Gyro Based on Parametric Resonance

2008 ◽  
Author(s):  
Nicholas J. Miller ◽  
Steven W. Shaw ◽  
Laura A. Oropeza-Ramos ◽  
Kimberly L. Turner
Keyword(s):  
Natural Frequencies ◽  
Proof Mass ◽  
Micro Electro Mechanical System ◽  
Wide Frequency Range ◽  
System Model ◽  
Resonant Response ◽  
Drive Mode ◽  
Rate Gyro ◽  
Two Degree Of Freedom ◽  
Selection Of

This paper describes the dynamics of a microelectromechanical rate gyro whose operation depends on nonlinear parametric resonant response. The basic idea behind this and other similar gyros is that a proof mass is free to move in a plane such that the perpendicular directions of motion are ideally mechanically uncoupled. In one direction, the drive mode, the mass is parametrically driven such that it undergoes a nonlinear resonant response. When rotated about an axis perpendicular to the plane of motion, Coriolis effects couple this drive mode to the other direction, the sense mode, whose response is then measured and calibrated with the rotation rate. Traditional rate gyros of this type require precise matching of the drive and sense linear natural frequencies in order to optimally amplify the sense response. By making use of the wide frequency range of the nonlinear resonant response, many of the difficulties associated with this tuning problem can be avoided. In this paper we emphasize results from a simple two degree-of-freedom micro-electro-mechanical system model that allows one to predict and design the rate response of the gyro by selection of system parameters.

Natural Frequency Analysis in the Workspace of a Six-Axis Industrial Robot Using Design of Experiments

2016 ◽  
Vol 1140 ◽  
pp. 345-352 ◽  
Author(s):  
Paul Glogowski ◽  
Michael Rieger ◽  
Jia Bin Sun ◽  
Bernd Kuhlenkötter
Keyword(s):  
Mathematical Model ◽  
Design Of Experiments ◽  
Modal Analysis ◽  
Natural Frequency ◽  
Frequency Analysis ◽  
Natural Frequencies ◽  
Industrial Robot ◽  
Joint Configuration ◽  
Chatter Vibrations ◽  
Natural Frequency Analysis

This paper deals with a natural frequency distribution of a six-axis industrial robot in order to analyze chatter vibrations in upcoming milling processes. Since the dynamic vibration behavior of the robotic system can be manipulated by changing the robot’s joint configuration, experimental modal analysis is performed to determine the natural frequencies in the entire workspace. In this study, methods of design of experiments are used to derivate a mathematical model that predicts the natural frequencies of the robotic structure for any joint configuration within the considered workspace.

Diagnosing Coupled Lateral-Torsional Vibrations in Turbomachinery

2008 ◽  
Author(s):  
Vinayaka N. Rajagopalan ◽  
John M. Vance
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Real World ◽  
Diagnostic Method ◽  
Natural Frequencies ◽  
The Other ◽  
Torsional Vibrations ◽  
Test Rig ◽  
Objective Being ◽  
Heavy Damage

Rotordynamic instability, commonly observed as subsynchronous vibration, is a serious problem that can cause heavy damage to a turbomachine or make it incapable of operation due to high vibration levels. However, all subsynchronous vibrations are not necessarily unstable. A way to quickly diagnose them would be helpful. In an earlier paper, the authors presented data from experiments that simulated various causes of sub-synchronous vibrations, some causes being genuine rotordynamic instabilities and some others being benign (stable), and identified ways to diagnose and classify the subsynchronous motions. In a continuation of the same study, subsynchronous vibrations due to coupled lateral-torsional effects are experimentally simulated, the objective being to signal-analyze these vibrations to find unique signatures that identify this cause and also be able to recognize if they are a true rotordynamic instability or not. To this end, a test rig was built with parallel shafts coupled by gears, driven by a DC motor at one end and loaded at the other end, to closely simulate a real-world machine. A torsional mathematical model for the test rig is also presented to predict its torsional natural frequencies. Experiments were conducted wherein the first torsional natural frequency was externally excited, with the shaft spinning at a higher speed. The result was a false sub-synchronous “instability” signal in the lateral measurements. A method to distinguish these vibrations from a genuine lateral non-synchronous instability is presented. Also, a new diagnostic method to classify the subsynchronous vibration as benign is elucidated.

Effects of Elevated Temperatures on Rocking Vibration of Rotating Disk and Spindle Systems

2002 ◽  
Vol 124 (4) ◽  
pp. 794-800 ◽  
Author(s):  
Chaw-Wu Tseng ◽  
Jr-Yi Shen ◽  
C.-P. R. Ku ◽  
I. Y. Shen
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Elevated Temperatures ◽  
Natural Frequencies ◽  
Rotating Disk ◽  
Temperature Variations ◽  
Spindle System ◽  
Radial Bearing ◽  
Bearing Stiffness ◽  
Rocking Vibration

This paper studies how temperature variations affect natural frequencies of rocking vibration of a rotating disk and spindle system through mathematical modeling and experimental measurements. Existing literature has shown that both radial bearing stiffness krr and natural frequency ω01B of one-nodal-diameter disk modes could substantially affect natural frequencies ω01U of rocking vibration. In this paper, a preliminary experiment first identifies that relaxation of bearing stiffness krr is the dominating factor to shift the natural frequency ω01U at elevated temperatures. In addition, the bearing relaxation primarily results from thermal mismatch between the bearing raceways and the rotating hub. Guided by the experimental results, a mathematical model is developed to determine how temperature variations affect bearing contact angles, bearing preloads, and subsequently the radial bearing stiffness krr. Based on the bearing stiffness krr and disk frequency ω01B at elevated temperatures, one can predict natural frequency ω01U of rocking vibration through the mathematical model by Shen and Ku (1997). Finally, ω01U of a rotating disk and spindle system are measured in a thermal chamber to validate the theoretical predictions.

Vibrating Beam Technique for Measuring Animal Natural Frequency

1995 ◽  
Vol 14 (3) ◽  
pp. 119-133 ◽  
Author(s):  
John M Randall ◽  
Chaoying Peng
Keyword(s):  
Resonant Frequency ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Frequency Measurement ◽  
System Response ◽  
Single System ◽  
Design Requirements ◽  
Modal Mass ◽  
Two Degree Of Freedom ◽  
Beam Technique

The discomfort to animals arising from vibration during transport is likely to be greatest at their natural resonant frequency. This frequency can be measured without compromising animal welfare by placing them on a simple beam support at each end which is caused to vibrate by a small impulse. The optimum beam to give stable and accurate results for this technique is evaluated using a two-degree-of-freedom model. Some design requirements are contradictory, for example sensitivity to the resolution of frequency measurement and the benefits of having a single system response. These problems are alleviated by specifying a unified accuracy at both of the system natural frequencies. In this case the natural frequency of the beam should be twice that of the animal and the modal mass of the beam should equal that of the animal.

Multi-crack detection in general cross-section swept wings based on natural frequency changes

2020 ◽  
pp. 107754632096401
Author(s):  
Fatemeh Barzegar ◽  
Saeedreza Mohebpour ◽  
Hekmat Alighanbari
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Cross Section ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Detection Method ◽  
Mode Shapes ◽  
Modal Strain Energy ◽  
Torsional Mode ◽  
Frequency Changes

In this article, a multi-crack detection method, which is based on natural frequency changes and the concept of modal strain energy, is for the first time developed for the general cross-section swept tapered wings under coupled bending-torsional vibration and applied to the solid and thin-walled airfoil cross-section wings. The presented method is able to handle the problems with an unknown number of cracks and predicts the number of existent cracks, their locations and depths by optimization of an appropriate objective function. The stress intensity factors of airfoil-shaped crack surfaces are obtained using an approximation method. Inputs of the detection method are natural frequencies of uncracked and cracked wings which are calculated by using a mathematical model and finite element method software ANSYS, respectively, and validated by comparison with former research studies. In the mathematical model, the Rayleigh–Ritz method is used to calculate the coupled bending-torsional mode shapes of the uncracked wing and their corresponding natural frequencies. Results demonstrate that the proposed method has precisely predicted the number, locations and depths of cracks in all case studies.

Natural Frequencies and Mode Shapes of Beams Carrying a Two Degree-of-Freedom Spring-Mass System

1993 ◽  
Vol 115 (2) ◽  
pp. 202-209 ◽  
Author(s):  
Ming Une Jen ◽  
E. B. Magrab
Keyword(s):  
Exact Solution ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Attached Mass ◽  
Approximate Methods ◽  
Mass System ◽  
The Laplace Transform ◽  
Rigid Mass ◽  
Two Degree Of Freedom

An exact solution for the natural frequencies and mode shapes for a beam elastically constrained at its ends and to which a rigid mass is elastically mounted is obtained. The attached mass can both translate and rotate. The general solution is obtained using the Laplace transform with respect to the spatial variable and yields the exact solutions to several previously published simpler configurations that were obtained using approximate methods. Numerous numerical results are presented for the natural frequency coefficients that extend previously reported results and that show the transition between various limiting cases. In addition, values are presented for the lowest two natural frequency coefficients for a beam that is clamped at both ends and is carrying a two dof spring-mass system. Representative mode shapes at selected values of the system’s parameters are also given.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

scholarly journals A Vibration-Based Structural Health Monitoring System for Transmission Line Towers

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 515 ◽  
Author(s):  
Long Zhao ◽  
Xinbo Huang ◽  
Ye Zhang ◽  
Yi Tian ◽  
Yu Zhao
Keyword(s):  
Structural Health Monitoring ◽  
Transmission Line ◽  
Natural Frequency ◽  
Health Monitoring ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Transmission Tower ◽  
Health Monitoring System ◽  
Wind Speeds ◽  
Before And After

In this paper, we present a vibration-based transmission tower structural health monitoring system consisting of two parts that identifies structural changes in towers. An accelerometer group realizes vibration response acquisition at different positions and reduces the risk of data loss by data compression technology. A solar cell provides the power supply. An analyser receives the data from the acceleration sensor group and calculates the transmission tower natural frequencies, and the change in the structure is determined based on natural frequencies. Then, the data are sent to the monitoring center. Furthermore, analysis of the vibration signal and the calculation method of natural frequencies are proposed. The response and natural frequencies of vibration at different wind speeds are analysed by time-domain signal, power spectral density (PSD), root mean square (RMS) and short-time Fouier transform (STFT). The natural frequency identification of the overall structure by the stochastic subspace identification (SSI) method reveals that the number of natural frequencies that can be calculated at different wind speeds is different, but the 2nd, 3rd and 4th natural frequencies can be excited. Finally, the system was tested on a 110 kV experimental transmission line. After 18 h of experimentation, the natural frequency of the overall structure of the transmission tower was determined before and after the tower leg was lifted. The results show that before and after the tower leg is lifted, the natural frequencies of each order exhibit obvious changes, and the differences in the average values can be used as the basis for judging the structural changes of the tower.

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