Forced Vibrations of a Single-Degree-of-Freedom System With Coulomb Bearing Friction

1969 ◽  
Vol 36 (4) ◽  
pp. 871-873 ◽  
Author(s):  
E. V. Wilms
Keyword(s):  
Coulomb Friction ◽  
Degree Of Freedom ◽  
Half Cycle ◽  
Piecewise Linearization ◽  
Single Degree Of Freedom ◽  
State Response ◽  
Single Degree ◽  
Forcing Function ◽  
Bearing Friction

The equation of motion of a single-degree-of-freedom mechanical system with Coulomb friction acting at two bearings is derived. The equation is nonlinear, but may be solved by piecewise linearization. For the case of transient oscillations, the amplitude decreases by a constant ratio every half cycle and, in this respect, the behavior resembles that of viscous damping rather than the type of Coulomb damping which has previously been investigated. The steady-state response with a forcing function is determined for the case of small damping. In addition to the amplitude and phase angle of the motion, a solution requires the determination of a second angle which defines the linearized regions.

Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems

2019 ◽  
Vol 24 (12) ◽  
pp. 3843-3861 ◽  
Author(s):  
Mario Lázaro
Keyword(s):  
Past History ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Critical Curves ◽  
History Of ◽  
Definition Of ◽  
Analytical Expressions ◽  
Critical Damping

In this paper, exact closed forms of critical damping manifolds for multiple-kernel-based nonviscous single-degree-of-freedom oscillators are derived. The dissipative forces are assumed to depend on the past history of the velocity response via hereditary exponential kernels. The damping model depends on several parameters, considered variables in the context of this paper. Those parameter combinations which establish thresholds between induced overdamped and underdamped motion are called critical damping manifolds. If such manifolds are represented on a coordinate plane of two damping parameters, then they are named critical curves, so that overdamped regions are bounded by them. Analytical expressions of critical curves are deduced in parametric form, considering certain local nondimensional parameters based on the Laplace variable in the frequency domain. The definition of the new parameter (called the critical parameter) is supported by several theoretical results. The proposed expressions are validated through numerical examples showing perfect fitting of the determined critical curves and overdamped regions.

Global convergence for two-pulse rest-to-rest learning for single-degree-of-freedom systems with stick-slip Coulomb friction

Robotica ◽  
2006 ◽  
Vol 25 (3) ◽  
pp. 307-313
Author(s):  
Brian J. Driessen ◽  
Nader Sadegh
Keyword(s):  
Global Convergence ◽  
Coefficient Of Friction ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Input Pulse ◽  
Iterative Learning ◽  
Degree Of Freedom ◽  
Stick Slip ◽  
Single Degree Of Freedom ◽  
Single Degree

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.

A Computationally Efficient Numerical Algorithm for the Transient Response of High-Speed Elastic Linkages

1979 ◽  
Vol 101 (1) ◽  
pp. 138-148 ◽  
Author(s):  
A. Midha ◽  
A. G. Erdman ◽  
D. A. Frohrib
Keyword(s):  
Transient Response ◽  
Numerical Algorithm ◽  
High Speed ◽  
Relative Size ◽  
Degree Of Freedom ◽  
Time Dependent ◽  
Computationally Efficient ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Forcing Function

A new numerical algorithm, easily adaptable for computer simulation, is developed to approximate the transient response of a single degree-of-freedom vibrating system; governing differential equation is linear and second order with time-dependent and periodic coefficients. This is accomplished by first solving the classical linear single degree-of-freedom problem with constant coefficients. The system is excited by a periodic forcing function possessing a certain degree of smoothness. The integration terms in the solution are systematically expanded into two groups of terms: one consists of non-integral terms while the other contains only integral terms. The final integral terms are bounded. For certain combinations of frequency and damping, within the sub-resonant frequency range, the relative size of the integral terms are demonstrated to be small. The algebraic expansion (non-integral) terms then approximate the solution. The solution to a single degree-of-freedom system with time-dependent and periodic parameters is made possible by discretizing the forcing period into a number of intervals and assuming the system parameters as constant over each interval. The numerical algorithm is then employed to solve an elastic linkage problem via modal superposition. Convergence of the solution is verified by refining the number of intervals of discretization.

The Steady State Response of Systems With Hardening Hysteresis

1978 ◽  
Vol 100 (1) ◽  
pp. 193-198 ◽  
Author(s):  
R. K. Miller
Keyword(s):  
Steady State ◽  
Degree Of Freedom ◽  
General Nature ◽  
Model Parameters ◽  
Steady State Response ◽  
Single Degree Of Freedom ◽  
Analytical Technique ◽  
State Response ◽  
Single Degree ◽  
Critical Model

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.

Analysis and Determination of Associated Linkage, Redundant Constraint, and Degree of Freedom of Closed Mechanisms With Redundant Constraints and/or Passive Degree of Freedom

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Yi Lu ◽  
Nijia Ye ◽  
Yang Lu ◽  
Bingyi Mao ◽  
Xu Zhai ◽  
...  
Keyword(s):  
Degree Of Freedom ◽  
Type Synthesis ◽  
Single Degree Of Freedom ◽  
Redundant Constraints ◽  
Single Degree ◽  
Redundant Constraint ◽  
In Series ◽  
Associated Linkage

The relations among the associated linkages (ALs), the redundant constraints, the passive degree of freedom (DoF), and the degree of freedom are studied systematically for the type synthesis of the closed mechanisms in this paper. First, the kinematic pairs with multidegree of freedoms are formed by combination of the basic joints with single degree of freedom in series, and the formulae are derived for the calculation of the degree of freedoms of the associated linkages, the number of the basic joints, and the valid numbers of the basic links in the associated linkages. Second, many different associated linkages and the number of basic links are derived, and the relations among the associated linkages, the redundant constraints, the passive degree of freedom, and the degree of freedoms of the closed mechanisms are analyzed. Third, some topology graphs are derived and the relative closed mechanisms with the redundant constraints and the passive degree of freedom are synthesized. Finally, the redundant constraints and the degree of freedoms of the closed mechanisms are determined.

Transients in Simple Undamped Oscillators Under Inertial Disturbances

1959 ◽  
Vol 26 (2) ◽  
pp. 217-223
Author(s):  
Antongiulio Dornig
Keyword(s):  
Exact Solution ◽  
Maximum Amplitude ◽  
Degree Of Freedom ◽  
Inertial Forces ◽  
Constant Acceleration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Approximate Formulas

Abstract Single-degree-of-freedom systems acted upon inertial forces are often found in technical applications. In this paper we shall study the transients in the vibrations of the system due to a change in speed in the machine in which the inertial forces are generated. We shall state the problem in the most general case, and then study the starting and the stopping with constant acceleration. After giving the exact solution of the problem we shall derive very simple approximate formulas for the determination of the maximum amplitude reached in these transients.

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