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.

Rocking Vibration of Rotating Disk and Spindle Systems With Asymmetric Bearings

2003 ◽  
Vol 70 (2) ◽  
pp. 299-302 ◽  
Author(s):  
J. S. Park ◽  
I. Y. Shen ◽  
C.-P. R. Ku
Keyword(s):  
Rigid Body ◽  
Perturbation Analysis ◽  
Natural Frequencies ◽  
Rotating Disk ◽  
Mode Shapes ◽  
Nodal Diameter ◽  
Spindle System ◽  
Rocking Motion ◽  
Rocking Vibration

This note presents how bearing asymmetry affects natural frequencies and mode shapes of a rotating disk/spindle system through a perturbation analysis. The analysis will focus on rocking motion of the disk/spindle system that consists of rigid-body rocking of the spindle, one-nodal-diameter modes of each disk, and deformation of spindle bearings.

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.

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.

Negative Selection Algorithm Using Natural Frequency for Novelty Detection under Temperature Variations

2010 ◽  
Vol 163-167 ◽  
pp. 2747-2750
Author(s):  
Miao Li ◽  
Wei Xin Ren
Keyword(s):  
Natural Frequency ◽  
Negative Selection ◽  
Euclidean Distance ◽  
Natural Frequencies ◽  
Novelty Detection ◽  
Selection Algorithm ◽  
Temperature Variations ◽  
Negative Selection Algorithm ◽  
Environment Effects ◽  
Anomalous Condition

The vibration features are affected by damage in structure and environmental conditions while the bridges are in the operation. Environment effects should not be ignored in making correct diagnoses of structures. Negative selection algorithm inspired by immune system has the capability for self-nonself discrimination. Temperature effect on natural frequency is analyzed in the paper, and the algorithm based on Euclidean distance is applied to natural frequencies of structures under temperature variations. The results indicate that negative selection algorithm using natural frequency passes the false-positive tests, and effectively detect the anomalous condition of structure under varying temperature.

Rocking Vibration of Rotating Disk and Spindle Systems With Asymmetric Bearings

2001 ◽  
Author(s):  
Jung Seo Park ◽  
I. Y. Shen ◽  
C.-P. Roger Ku
Keyword(s):  
Numerical Simulation ◽  
Rotational Speed ◽  
Natural Frequencies ◽  
Rotating Disk ◽  
Mode Shapes ◽  
Unperturbed System ◽  
High Rotational Speed ◽  
Spindle System ◽  
Rocking Motion ◽  
Gyroscopic Effects

Abstract This paper studies how bearing asymmetry affects natural frequencies and mode shapes of a rotating disk/spindle system through a numerical simulation and a perturbation analysis. Existing literature has shown that rocking motion of a rotating disk/spindle system with symmetric bearings consists of rigid body rocking of the spindle, one-nodal-diameter modes of each disk, and deformation of spindle bearings. The rocking motion, characterized by (0,1) unbalanced modes, has repeated natural frequencies when the spindle is stationary, because the disk/spindle system is axisymmetric. For a rotating spindle, (0,1) unbalanced modes evolve into forward and backward precession with circular orbits. In this paper, the numerical simulation shows that bearing asymmetry splits a pair of repeated (0,1) unbalanced modes into two modes with distinct frequencies when the spindle is stationary. Moreover, when the rotational speed increases from zero, the (0,1) unbalanced mode with lower frequency evolves into backward precession and the (0,1) unbalanced mode with higher frequency evolves into forward precession. The precession orbits are elliptical because of the bearing asymmetry. Two perturbation schemes are developed to prove the phenomena observed in the numerical simulation. For low rotational speed, a stationary disk/spindle system with symmetric bearings serves as the unperturbed system. Both the bearing asymmetry and gyroscopic effects from rotation form the perturbation. A contraction iteration predicts the effects of bearing asymmetry on natural frequencies and mode shapes. For high rotational speed, a rotating (gyroscopic) disk/spindle system with symmetric bearings serves as the unperturbed system. The bearing asymmetry forms the perturbation. To obtain a perturbation solution, the solvability condition is first derived for the unperturbed gyroscopic system. Lindsted-Poincaré approach then predicts the effects of bearing asymmetry on natural frequencies and mode shapes of the rotating disk/spindle system.

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 Frequency Clusters in Planetary Gear Vibration

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Tristan M. Ericson ◽  
Robert G. Parker
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
The Other ◽  
Or Groups ◽  
Mass Moment ◽  
Mass Moment Of Inertia ◽  
Bearing Stiffness ◽  
Planet Gear ◽  
Central Member

This paper investigates how the natural frequencies of planetary gears tend to gather into clusters (or groups). This behavior is observed experimentally and analyzed in further detail by numerical analysis. There are three natural frequency clusters at relatively high frequencies. The modes at these natural frequencies are marked by planet gear motion and contain strain energy in the tooth meshes and planet bearings. Each cluster contains one rotational, one translational, and one planet mode type discussed in previous research. The clustering phenomenon is robust, continuing through parameter variations of several orders of magnitude. The natural frequency clusters move together as a group when planet parameters change. They never intersect, but when the natural frequencies clusters approach each other, they exchange modal properties and veer away. When central member parameters are varied, the clusters remain nearly constant except for regions in which natural frequencies simultaneously shift to different cluster groups. There are two conditions that disrupt the clustering effect or diminish its prominence. One is when the planet parameters are similar to those of the other components, and the other is when there are large differences in mass, moment of inertia, bearing stiffness, or mesh stiffness among the planet gears. The clusters remain grouped together with arbitrary planet spacing.

Analysis of Vibration Caused by Ball Bearing in a HDD Spindle System at Elevated Temperature

2006 ◽  
Vol 321-323 ◽  
pp. 1624-1628 ◽  
Author(s):  
D.K. Kim ◽  
G.H. Jang
Keyword(s):  
Elevated Temperature ◽  
Frequency Distribution ◽  
Natural Vibration ◽  
Ball Bearing ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Spindle System ◽  
Bearing Stiffness ◽  
Natural Vibration Characteristics

This research investigates the vibration caused by ball bearing in a HDD spindle system, specifically non-repeatable runout (NRRO), at elevated temperature by analyzing the characteristics of ball bearing and the natural vibration characteristics of the spindle system due to the effect of elevated temperature. It shows that the elevated temperature results in the decrease of bearing deformation in the spindle system, which reduces the bearing stiffness and the natural frequencies of the spindle system consequently. It has a significant effect on the amplitude and the frequency distribution of NRRO at elevated temperature.

Influence of Bearing Configuration on Spindle Modal Characteristics

2014 ◽  
Author(s):  
Jun Hong ◽  
Guanghui Liu ◽  
Xiaohu Li ◽  
Wenwu Wu ◽  
Shaoke Wan ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Machine Tools ◽  
Test Bench ◽  
Natural Frequencies ◽  
Dynamic Performance ◽  
Radial Deformation ◽  
Spindle System ◽  
Modal Characteristics ◽  
Spindle Bearing ◽  
Simulation And Experiment

Since bearing configuration has significant influence on the spindle modal characteristics which can reflect the dynamic performance of spindle system in machine tools, so it would be of extraordinary importance and necessity to analyze the spindle modal characteristics through simulation and experiment when it comes to designing spindle system. In this paper, the number and span of bearings, the spacer of bearing set and the overhang of spindle are considered as the main designing parameters of the spindle system. Firstly, a coupled spindle-bearing model is established considering the radial deformation of the bearing inner ring caused by interference fits of spindle assembly, as well as the centrifugal and thermal deformations. Based on the model, the modal characteristics of different bearing configurations are analyzed. Secondly, a spindle test bench is designed and constructed. Finally, modal characteristics of the spindle system are tested with different bearing configurations. From the simulation and experimental results, it’s indicated that there is a correlation between the natural frequency and the number of bearings. The using of short spacer inside the bearing set can increase spindle natural frequency slightly. Besides, the first natural frequency of the spindle system rises with the bearing span, whereas the second one tends to decrease. And shortening the overhang of spindle can also increase its natural frequencies, which can be taken into account in spindle design.

Sign in / Sign up

Export Citation Format

Share Document