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.

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.

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.

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.

The Design, Experimentation, and Simulation of a Novel Coulomb Friction Device for Automotive Valve Spring Damping

1993 ◽  
Vol 115 (4) ◽  
pp. 871-876 ◽  
Author(s):  
J. F. Sefler ◽  
A. P. Pisano
Keyword(s):  
Experimental Data ◽  
Computer Simulation ◽  
Wave Equation ◽  
Computer Modeling ◽  
Coulomb Friction ◽  
Damping Term ◽  
Interference Fit ◽  
Valve Spring ◽  
Coulomb Damping ◽  
Elastomeric Dampers

This investigation contains experimental and computer modeling results of an alternative method for damping automotive valve springs, in which a nondestructive elastomeric sleeve that slides over the spring with an interference fit is used to provide coulomb damping on the outside of the valve spring coils. The damper and valve spring dynamics are modeled using the wave equation with a damping term composed of both viscous and coulomb components. Although the damper is very simple and inexpensive, the reduction in residual spring vibrations are shown to be significant without loss of valve spring performance. Experimental data taken from a 1983 Pontiac family-II, 1.8 liter, four cylinder, single overhead cam engine equipped both with and without the new elastomeric dampers is used to verify the results of the computer simulation and demonstrate the effectiveness of the damper.

Finite Element Simulation of Wheel-Rail Contact Dynamic Instabilities Under Sliding Conditions

2005 ◽  
Author(s):  
A. Saulot ◽  
L. Baillet
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Mechanical Model ◽  
Coulomb Friction ◽  
Rotating Disc ◽  
Contact Conditions ◽  
Rail Corrugation ◽  
Temporal Study ◽  
Element Simulation ◽  
Constant Friction

Using dynamic finite element methods, a temporal study of the dynamic response of a 2D mechanical model composed of a deformable rotating disc (wheel) in contact with a deformable translating body (rail) with constant Coulomb friction is presented. Under global sliding conditions, instabilities at specific frequencies appear in the contact patch even in the case of a constant friction coefficient. The influence of parameters such as global sliding ratio, friction coefficient and transient value of applied sliding on local contact conditions is evaluated. A parallel is then drawn between the frequencies of these instabilities and the modal analysis of the entire mechanical model. Finally, consequences of these instabilities on local rail plastification are presented and correlated with rail corrugation appearing on straight tracks under acceleration or deceleration conditions.

A Finite Element Study on Contact Pressure Distribution in Draw-Bend Friction Test and Its Effect on Friction Measurement

2005 ◽  
Author(s):  
Young Suk Kim ◽  
Don R. Metzger ◽  
Mukesh K. Jain
Keyword(s):  
Finite Element ◽  
Coulomb Friction ◽  
Friction Model ◽  
Friction Test ◽  
Friction Measurement ◽  
Explicit Finite Element ◽  
Constant Friction ◽  
Friction Models ◽  
Bend Tests ◽  
Coulomb Friction Model

Various experimental and numerical works have shown the existence of pressure peaks at the contact interface of draw-bend tests. From this observation, a need has been raised for the re-examination of the methodology to calculate the friction coefficient from the draw-bend friction test. In this paper, the draw-bend friction tests have been simulated by the explicit finite element method. By using 3D finite element models and local axis system, the existence of pressure peaks was confirmed. A non-constant friction model (Stribeck friction model), which is more realistic for sheet metal forming than a constant friction model (Coulomb friction model), was implemented into the finite element code. Simulations were performed with constant and non-constant friction models. From the comparisons, the effect of existence of pressure peaks on the friction measurement was evaluated.

An Efficient, One-Dimensional, Finite Element Helical Spring Model for Use in Planar Multi-Body Dynamics Simulation

2013 ◽  
Vol 6 (2) ◽  
pp. 979-989 ◽  
Author(s):  
Marcin Marek Okarmus ◽  
Rifat Keribar ◽  
Diana-Lucinia Dascalescu ◽  
Rob Zdrodowski
Keyword(s):  
Finite Element ◽  
Dynamics Simulation ◽  
Helical Spring ◽  
Spring Model ◽  
One Dimensional ◽  
Body Dynamics ◽  
Dimensional Finite Element ◽  
Multi Body
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