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

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.

Robotica ◽  
2006 ◽  
Vol 25 (3) ◽  
pp. 307-313
Author(s):  
Brian J. Driessen ◽  
Nader Sadegh

SUMMARYIn this paper, we consider the problem of rest-to-rest maneu-ver learning, via iterative learning control (ILC), for single-degree-of-freedom systems with stick-slip Coulomb friction and input bounds. The static coefficient of friction is allowed to be as large as three times the kinetic coefficient of friction. The input is restricted to be a two-pulse one. The desired input's first pulse magnitude is required to be five times the largest possible kinetic (sliding) friction force. The theory therefore allows the stiction force to be as large as the desired second input pulse. Under these conditions, we prove global convergence of a simple iterative learning controller. To the best of our knowledge, such a global-convergence proof has not been presented previously in the literature for the rest-to-rest problem with stick-slip Coulomb friction.


Author(s):  
C. Hunter Cloud ◽  
Eric H. Maslen ◽  
Lloyd E. Barrett

Rotor stability is most commonly estimated using methods derived from a simple single degree of freedom system. When the modes of more complex systems, such as rotors, are closely spaced, we demonstrate that such methods can yield very poor estimates of the modal stability (damping ratio). Multiple output backward autoregression (MOBAR) is proposed as an alternative approach and is demonstrated to yield reasonably accurate estimates of modal damping even when modes are closely spaced. The performance of the MOBAR approach is then examined on an experimental rotor in tilt-pad bearings, demonstrating good performance in a realistic measurement setting.


2010 ◽  
Vol 97-101 ◽  
pp. 1216-1222 ◽  
Author(s):  
Chun Jian Yu ◽  
Xiao Diao Huang ◽  
Cheng Gang Fang ◽  
Ke Fang Dai

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.


Author(s):  
C. Hunter Cloud ◽  
Eric H. Maslen ◽  
Lloyd E. Barrett

Rotor stability is most commonly estimated using methods derived from a simple, single degree of freedom (SDOF) system. When the modes of more complex systems, such as rotors, are closely spaced, we demonstrate that such methods can yield very poor estimates of the modal stability (damping ratio). Multiple output backward autoregression (MOBAR) is proposed as an alternative approach and is demonstrated to yield reasonably accurate estimates of modal damping even when modes are closely spaced. The performance of the MOBAR approach is then examined on an experimental rotor in tilt-pad bearings, demonstrating good performance in a realistic measurement setting.


1978 ◽  
Vol 100 (1) ◽  
pp. 193-198 ◽  
Author(s):  
R. K. Miller

A physical model for hardening hysteresis is presented. An approximate analytical technique is used to determine the steady-state response of a single-degree-of-freedom system and a multi-degree-of-freedom system incorporating this model. Certain critical model parameters which determine the general nature of the responses are identified.


2007 ◽  
Vol 129 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Dara W. Childs ◽  
Avijit Bhattacharya

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.


Author(s):  
D. E. G. Crutcher

The paper deals with a computer program that has been developed to study the dynamic behaviour of poppet valve mechanisms. A theoretical analysis is performed on a single mass, single degree of freedom system subjected to internal and external viscous damping and Coulomb friction, representing a valve mechanism with flexible overhead linkage. Measurements have been made on engines so that computed and experimental results could be compared in order to test the program. The effect on performance of varying the dynamic parameters of valve mechanisms is investigated with the computer program.


2013 ◽  
Vol 791-793 ◽  
pp. 835-838
Author(s):  
Shi Jie Wu ◽  
Lin He ◽  
Xi Zhi Zhao

The traditional shock isolation system is only designed in stiffness regardless of damping, which causes acute contradiction between absolute acceleration amplitude and relative displacement amplitude. Based on the single degree of freedom negative shock isolation system, numerical analysis demonstrates that relative little amplitude of absolute acceleration and relative displacement could be attained within a certain range of damping and frequency ratio. Selecting appropriate damping and stiffness of vibration isolator can resolve contradiction between absolute acceleration amplitude and relative displacement amplitude and consequently improve shock isolation efficiency.


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