Prediction of Dry-Friction Whirl and Whip Between a Rotor and a Stator

2007 ◽  
Vol 129 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Dara W. Childs ◽  
Avijit Bhattacharya
Keyword(s):  
Friction Force ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Coulomb Force ◽  
Test Results ◽  
Jeffcott Rotor ◽  
Transient Simulations ◽  
Force Direction ◽  
Function Definition ◽  
Coulomb Friction Force

This paper addresses recent test results for dry-friction whip and whirl. Authors of these publications suggest that predictions from Black’s 1968 paper (J. Mech. Eng. Sci., 10(1), pp. 1–12) are deficient in predicting their observed transition speeds from whirl to whip and the associated precession frequencies of whirl and whip motion. Predictions from Black’s simple Jeffcott-rotor/point-mass stator are cited. This model is extended here to a multimode rotor and stator model with an arbitrary axial location for rotor-stator rubbing. Predictions obtained from this new model are quite close to experimental observations in terms of the transition from whip to whirl and observed precession frequencies. Paradoxically, nonlinear numerical simulations using Black’s model fail to produce the whirl and whip solutions. The Coulomb friction force in Black’s model has a fixed direction, and Bartha showed in 2000 (“Dry Friction Backward Whirl of Rotors,” Dissertation, THE No. 13817, ETH Zurich) that by making the friction-force direction depend on the relative sliding velocity, nonlinear simulations would produce the predicted whirl solutions. He also showed that Black’s proposed whip solution at the upper precession-frequency transition from whirl to whip was unstable. The multimode extension of Black’s model predicts a complicated range of whirl and whip possibilities; however, nonlinear time-transient simulations (including the sgn function definition for the Coulomb force) only produce the initial whirl precession range, initial whirl-whip transition, and initial whip frequency. Simulation results for these values agree well with predictions. However, none of the predicted higher-frequency whirl results are obtained. Also, the initial whip frequency persists to quite high running speeds and does not (as predicted) transition to higher frequencies. Hence, despite its deficiencies, correct and very useful predictions are obtained from a reasonable extension of Black’s model.

Prediction of Dry-Friction Whirl and Whip Between a Rotor and a Stator

2006 ◽  
Author(s):  
Dara W. Childs ◽  
Avijit Bhattacharya
Keyword(s):  
Friction Force ◽  
Dry Friction ◽  
Coulomb Force ◽  
Test Results ◽  
Jeffcott Rotor ◽  
Transient Simulations ◽  
Force Direction ◽  
Function Definition ◽  
Multi Mode ◽  
Coulomb Friction Force

This paper addresses recent test results for dry-friction whip and whirl. Authors of these publications suggest that predictions from Black’s 1968 paper are deficient in predicting their observed transition speeds from whirl to whip and the associated precession frequencies of whirl and whip motion. Predictions from Black’s simple Jeffcott-rotor/point-mass stator are cited. This model is extended here to a multi-mode rotor and stator model with an arbitrary axial location for rotor-stator rubbing. Predictions obtained from this new model are quite close to experimental observations in terms of the transition from whip to whirl and observed precession frequencies. Paradoxically, nonlinear numerical simulations using Black’s model fail to produce the whirl and whip solutions. The Coulomb friction force in Black’s model has a fixed direction, and Bartha showed in 2000 that by making the friction-force direction depend on the relative sliding velocity, nonlinear simulations would produce the predicted whirl solutions. He also showed that Black’s proposed whip solution at the upper precession-frequency transition from whirl to whip was unstable. Results presented here show that Black’s whirl solutions are unstable for all whirl precession frequencies, not just the whirl-whip transition frequency. The multi-mode extension of Black’s model predicts a complicated range of whirl and whip possibilities; however, nonlinear time-transient simulations (including the sgn function definition for the Coulomb force) only produce the initial whirl precession range, the initial whirl-whip transition, and the initial whip frequency. Simulation results for these values agree well with predictions. However, none of the predicted higher-frequency whirl results are obtained. Also, the initial whip frequency persists to quite high running speeds and does not (as predicted) transition to higher frequencies. Hence, despite its deficiencies, correct and very useful predictions are obtained from a reasonable extension of Black’s model.

Research on Damping and Vibration Characteristic of the Large and Precision NC Rotary Table

2010 ◽  
Vol 97-101 ◽  
pp. 1216-1222 ◽  
Author(s):  
Chun Jian Yu ◽  
Xiao Diao Huang ◽  
Cheng Gang Fang ◽  
Ke Fang Dai
Keyword(s):  
Cutting Force ◽  
Dynamic Model ◽  
Friction Force ◽  
High Frequency ◽  
Coulomb Friction ◽  
Vibration Characteristic ◽  
Rotary Table ◽  
Online Test ◽  
Cutting Chatter ◽  
Coulomb Friction Force

According to the current situation of acicular chip and high-frequency chattering of the NC rotary table while gear milling, rigidity and damping performances of the table were analyzed and the damping program of Coulomb friction was bring up. Online test of the gear milling cutting force can be used to establish dynamic model of circumferential vibration of the table with Coulomb friction. Then mechanism of restraining gear cutting chatter by damping of Coulomb friction and acicular chip generating mechanism were exposed. Furthermore, relationship between backlash and rotary rigidity of the table was also analyzed. A kind of floating apparatus with friction damping was designed to optimize circumferential damping of the table by adjusting Coulomb friction force, which reduces the influence of high-frequency chattering on gear milling. As a result, efficiency of gear milling was increased 1.5 times and the noise was reduced from 105dB to 91dB.

Forced Vibration of a Base-Excited Single-Degree-of-Freedom System With Coulomb Friction

1984 ◽  
Vol 106 (4) ◽  
pp. 280-285 ◽  
Author(s):  
Etsuo Marui ◽  
Shinobu Kato
Keyword(s):  
Friction Force ◽  
Coulomb Friction ◽  
Damping Ratio ◽  
Force Frequency ◽  
Vibratory System ◽  
Single Degree Of Freedom ◽  
Analytical Technique ◽  
Single Degree ◽  
Dimensional Parameters ◽  
Coulomb Friction Force

Using the “stopping region of motion” concept, a brief analytical technique is worked out for the behavior of the linear forced vibratory system under the influence of a Coulomb friction force. The following points are clarified by the above technique: 1. The behavior of the system is completely determined by the three non-dimensional parameters of nondimensional friction force, frequency ratio and damping ratio. 2. The vibratory system undergoes a periodic vibration with stopping periods when the mass cannot move. These stopping periods increase at lower exciting frequencies, owing to Coulomb friction. 3. The relation between the kind of motion occurring in the system and the above three parameters can be obtained theoretically and verified experimentally.

Dynamics of a Coulomb Damped Helical Spring: A Finite Element Approach

2004 ◽  
Author(s):  
Majid Rashidi ◽  
Sachin P. Budhabhatti ◽  
John L. Frater
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Friction Force ◽  
Coulomb Friction ◽  
Helical Spring ◽  
Radial Expansion ◽  
Damping Force ◽  
Coulomb Damping ◽  
Constant Friction ◽  
Coulomb Friction Force

This work presents the results of a mathematical modeling to study the dynamic behavior of a helical spring under a periodic excitation induced by a rotating cam. The spring is sleeved over a mandrel; thereby it is further subjected to a Coulomb damping force as it oscillates. Helical springs expand radially when they are compressed. The effect of this radial expansion is included in the mathematical model. Standard wave equation that includes variable Coulomb damping was used to examine the vibratory behavior of the spring. Numerical solution to the no-friction, constant-friction, and varying-friction forces were obtained from the wave equation, using Explicit Finite Difference method. Finite Element was used to model the radial expansion of the spring to determine the variations of the Coulomb friction force. The spring response to the prescribed cam excitation, under the variable Coulomb friction force, was found not to be significantly different from that of a previously assumed constant friction force, for the cases that were studied in this work. In case of postulating a variable damping force the residual vibrations of spring loops are slightly higher than of the constant damping force.

A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

2021 ◽  
Author(s):  
Gregory L. Altamirano ◽  
Meng-Hsuan Tien ◽  
Kiran D'Souza
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Nonlinear Response ◽  
Piecewise Linear ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Forced Response ◽  
New Method ◽  
Analysis Tools ◽  
Compatibility Constraint

Abstract Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

Tribology research of the turned zirconium-dioxide ceramics

2012 ◽  
Vol 3 (3) ◽  
pp. 181-190
Author(s):  
G. Fledrich ◽  
R. Keresztes ◽  
L. Zsidai
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Dry Friction ◽  
Zirconium Dioxide ◽  
Steel Specimen ◽  
Friction Condition ◽  
Normal Direction ◽  
Basic Material ◽  
Series Production ◽  
Ceramic Specimen

The zirconium dioxide as basic material is suitable to machine by tool with regular edge derivingfrom lower ceramic hardness and from other characteristics so in case of piece production or small – andmedium series production, at quick prototype production can become potential material alike. The aims tocompare the arising frictional characteristics in case of dry friction condition in case of ceramic – steelsurface pairs machined with different sets. We have developed for an equipment to carry out tribologicaltests. During the test we pressure the steel counter face with determined normal direction force thecasing surface of the rotating ceramic specimen and in the meantime we measure the value of the frictionforce with force meter cell. We have calculated the friction coefficient characterizing the system from thenormal direction force and the friction force as well as we measured the wear of the steel specimen andits deformation.

scholarly journals Effect of adding mass to rotor on in-plane squeal in automotive disc brake

2018 ◽  
Vol 211 ◽  
pp. 13006
Author(s):  
Takashi Nakae ◽  
Takahiro Ryu ◽  
Hiroki Goto ◽  
Daisuke Sato
Keyword(s):  
Dry Friction ◽  
Coulomb Friction ◽  
Disc Brake ◽  
Vibration Modes ◽  
Concentrated Mass ◽  
Mass Model ◽  
Out Of Plane ◽  
The Relationship

This study experimentally examined disc brake-generated inplane squeal by looking at vibration modes. The in-plane squeal was determined to be closely related to both the out-of-plane squeal that has directionality caused by Coulomb friction and the in-plane squeal caused by dry friction. The characteristics of in-plane squeal were also analytically investigated using a concentrated mass model formed by connected massless beams, and the relationship between mass added to the rotor and squeal suppression was clarified.

A General Model for Two-Point Contact Dry-Friction Whip and Whirl: Further Advancements and Experimental Test Results

2015 ◽  
Author(s):  
Jason C. Wilkes ◽  
Tim Allison
Keyword(s):  
Experimental Test ◽  
General Model ◽  
Dry Friction ◽  
Point Contact ◽  
Current Work ◽  
Test Results ◽  
Air Bearings ◽  
Test Rig ◽  
Single Location ◽  
Arbitrary Phase

Numerous papers have investigated the behavior of dry-friction whip and whirl; most of them consider contact between a rotor and stator at a single location. For rotors running on multiple magnetic bearings, air bearings, or bushings, equipment failure may result in rub at more than one location. For these cases, it is important to have an analytical model that characterizes possible regions of two-point contact dry-friction whip and whirl. The current work presents a general model to predict possible whirl regions for multi-contact dry-friction whip and whirl, allowing for an arbitrary phase between contact locations. In theory this method can be applied to more than two contact locations; however, a two-point contact example case is developed and compared to results from an experimental test rig developed to demonstrate multi-contact dry-friction whip and whirl in the current work.

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