An Effective Method for Modeling Stiction in Multibody Dynamic Systems

1996 ◽  
Vol 118 (1) ◽  
pp. 172-176 ◽  
Author(s):  
R. G. Synnestvedt
Keyword(s):  
Complex Systems ◽  
Dynamic Systems ◽  
Degrees Of Freedom ◽  
Dynamic Equations ◽  
Stick Slip ◽  
System A ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Spring System ◽  
Mass Spring

This paper presents an effective method for developing dynamic equations which realistically model dynamics of multibody mechanical systems with stiction, or stick-slip friction. This method is used in three examples—a mass-spring system, a top, and a robot linkage—to illustrate the facility with which the method is implemented. The method dynamically partitions sets of dynamic equations to model a system through discontinuities, changes in degrees of freedom and changes in states. Comparisons of this method with others is presented for simple and complex systems.

Investigation of a Friction-Induced Source of Excitation in Disc Brake Systems

2002 ◽  
Author(s):  
V. N. Pilipchuk ◽  
C. A. Tan
Keyword(s):  
Degrees Of Freedom ◽  
Resonance Condition ◽  
Bending Moment ◽  
Flexural Vibration ◽  
Stick Slip ◽  
Short Period ◽  
Disc Brakes ◽  
Spring System ◽  
Mass Spring ◽  
Friction Induced Vibration

Friction-induced vibration of a two-degrees-of-freedom mass-spring system interacting with a decelerating rigid strip is considered. The friction law is approximated by an analytic function to facilitate the numerical integration, whereas the truncated Taylor expansion of this function gives good qualitative results. It was shown that after a quasi-harmonic transient period, accompanied by viscous energy dissipation, a relatively short period of intensive stick-slip vibration occurs, with its out-of-phase component generating a series of micro-impacts on the strip. It was further shown that, because of the impulsive character of such kind of loading, its Fourier spectrum is sufficiently rich. Based on the simplified ‘normal form’ equations, it was shown that the out-of-phase vibration mode of the block system absorbs more energy from the decelerating strip if the corresponding natural frequencies satisfy the resonance condition. The out-of-phase stick-slip vibration of the blocks creates an impulsive bending moment applied to the strip, and therefore can be considered as a possible source of flexural vibration. In particular, the results are applied to explanation of squeal generation in automotive disc brakes, although the technique can be extended on other ‘squealing systems’ including geophysical fault (earthquake) models.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Nonstationary Vibrations of a String With Time-Varying Length and a Mass-Spring System Attached at the Lower End

1993 ◽  
Author(s):  
Y. Terumichi ◽  
M. Ohtsuka ◽  
Y. Fukawa ◽  
M. Yoshizawa ◽  
Y. Tsujioka
Keyword(s):  
Degrees Of Freedom ◽  
Horizontal Displacement ◽  
Experimental Setup ◽  
Time Varying ◽  
Nonstationary Vibrations ◽  
String Vibration ◽  
Varying Length ◽  
Spring System ◽  
Mass Spring ◽  
Theoretical Results

Abstract The purpose of this paper is to study the nonstationary vibrations of a string with time-varying length, and a mass-spring system attached at the lower end. The string is excited sinusoidally by the horizontal displacement at its upper end and the mass-spring system has two-degrees-of-freedom vertically and horizontally. It is clarified analytically that the moving velocity of the string influences the peak amplitude of the string vibration at the passage through resonances. Moreover it is shown numerically that the amplitudes of both the string and the mass vibrations depend on the sign of the moving velocity, in the case where the natural frequency of the mass-spring system is close to the frequency of the excitation. The above two theoretical results are confirmed experimentally with a simple experimental setup.

Linearization of Multibody Dynamic Systems Using Automatic Differentiation (AD) Tools

1993 ◽  
Author(s):  
Tsung-Chieh Lin
Keyword(s):  
Dynamic Systems ◽  
Degrees Of Freedom ◽  
Automatic Differentiation ◽  
Robot Manipulator ◽  
Order Approximation ◽  
General Purpose ◽  
Dynamics Of Multibody Systems ◽  
Closed Chain ◽  
Multibody Dynamic ◽  
First Order Approximation

Abstract This paper presents an automatic method to linearize the dynamics of multibody systems that are modeled through a recursive approach. The first-order approximation of the nonlinear dynamic systems is obtained by the use of an automatic differentiation (AD) tool (GRESS) and a 9,700 lines Fortran model for the dynamics. The efficiency and accuracy of this AD implementation is shown by two examples: a five-bar closed-chain robot manipulator and a 18 degrees of freedom tractor-trailer. This study successfully demonstrates how to create a general-purpose numerical tool that can provide accurate solutions and derivatives for multibody dynamic systems.

scholarly journals Complex-Damped Dynamic Systems in the Time and Frequency Domains

2004 ◽  
Vol 11 (3-4) ◽  
pp. 209-225 ◽  
Author(s):  
Elvio Bonisoli ◽  
John E. Mottershead
Keyword(s):  
Frequency Response ◽  
Structural Dynamics ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Root Locus ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Domains ◽  
Spring System ◽  
Mass Spring

The fact that a complex-damped model may represent the dynamic behaviour of elasto-mechanical systems when acted upon by a magnetic field was brought to the attention of the structural dynamics community very recently by Professor Bruno A. D. Piombo and his colleagues at the Politecnico di Torino. In this paper a thorough analysis of the single degree-of-freedom complex-damped mass-spring system is presented. The analysis includes the root locus, the (non-causal) impulse response, the frequency response and the transmissibility. Regions of different behaviour in the frequency response and transmissibility are described in detail. The stiffening behaviour observed in Prof. Piombo's experiments and known as the "phantom effect" is demonstrated by the complex-damped model.

The elastodynamic field of N interacting vibrators (two‐dimensional theory)

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1229-1252 ◽  
Author(s):  
T. H. Tan
Keyword(s):  
Integral Representation ◽  
Effective Mass ◽  
Half Space ◽  
Unit Length ◽  
Elastic Half Space ◽  
Dynamic Equations ◽  
Mass Unit ◽  
Radiated Power ◽  
Spring System ◽  
Mass Spring

The elastodynamic field of N rigid strips, lying parallel on the surface of an elastic half‐space and harmonically excited in time by vertical forces, was calculated. It is assumed (1) the contact between the rigid strips and the surface of the half‐space is maintained during the motion of the strips, and (2) the horizontal component of the traction is zero on the surface of the half‐space. Calculation of the elastodynamic field is based on the integral representation of the particle displacement in the half‐space, together with the dynamic equations for the strip. From the integral representation and the dynamic equations, a set of coupled integral equations for the vertical component of the traction under the strips can be derived. This set of integral equations was solved numerically by the method of moments. The influence of the hold‐down mass and its spring system is also investigated. It is shown that its action can be accounted for by introducing a frequency‐dependent effective mass of the strips. At the resonance frequency of the hold‐down mass/spring system, the power radiated into the half‐space, is shown to be zero. Numerical results show that for a fixed strip width and fixed parameters of the elastic half‐space, the frequency at which the peak in the radiated power occurs decreases as the mass/unit length of the strip increases, whereas the ratio of the radiated P‐, S‐, and Rayleigh waves does not change at all. Since the frequency at which the peak in the radiated power occurs depends upon the mass/unit length of the strip, and since the influence of the hold‐down mass/spring is actually a frequency‐dependent effective mass of the strip, theoretically it is possible to optimize the radiated power of a vibrator for a frequency band of interest. Such a vibrator, if ever constructed, will most likely depend upon a feedback and control system. I show that the phase difference between the driving force and the velocity of the strip is a suitable feedback signal.

Cableless Magnetic Actuator Capable of High-Speed Movement in Pipe by New Type Propulsion Module

2012 ◽  
Vol 452-453 ◽  
pp. 1252-1256 ◽  
Author(s):  
Tomohiro Izumikawa ◽  
Hiroyuki Yaguchi
Keyword(s):  
High Speed ◽  
Resonance Energy ◽  
Magnetic Actuator ◽  
System A ◽  
New Type ◽  
Spring System ◽  
Inspection And Maintenance ◽  
Mass Spring ◽  
Button Batteries ◽  
Very High

The present paper proposes a novel cableless magnetic actuator that exhibits a very high thrusting force and is capable of high speed locomotion in a thin pipe by using new type propulsion module. The magnetic actuator is moved according to the vibration amplitude and elastic energy of a mass-spring system due to mechanical resonance energy. The proposed actuator contains an electrical inverter that directly transforms DC from button batteries into AC. The electrical DC-AC inverter incorporates a mass-spring system, a reed switch and a curved permanent magnet that switches under an electromagnetic force. Experimental results indicate that the proposed actuator is able to move upward at a speed of 51 mm/s by the power provided by 8 button batteries when pulling a 10 g load mass. This cableless magnetic actuator has several possible applications, including small pipe inspection and maintenance.

The Windup Phenomenon and Anti-windup Illustrated

2011 ◽  
Author(s):  
Luca Zaccarian ◽  
Andrew R. Teel
Keyword(s):  
Disturbance Rejection ◽  
Feedback Loop ◽  
Robot Manipulator ◽  
Input Saturation ◽  
Positioning System ◽  
System A ◽  
Highly Oscillatory ◽  
Oscillatory Response ◽  
Spring System ◽  
Mass Spring

This chapter uses examples where windup occurs to motivate anti-windup synthesis. In particular, it discusses a SISO academic example, a MIMO academic example, the longitudinal dynamics of an F8 aircraft, a servo-positioning system, the damped mass-spring system, the experimental spring-gantry system, a robot manipulator, and a disturbance rejection problem. The examples illustrate the windup phenomenon, which may arise due to input saturation in a feedback loop, and the capabilities of anti-windup synthesis in mitigating the windup phenomenon. They show that windup can manifest itself as a sluggish response, a highly oscillatory response, or a diverging response. In each example, alternatives to anti-windup synthesis include investing in actuators with more capabilities, or redesigning the controller from scratch to account for input saturation directly. These strategies should be considered when the control system's actuators are continuously trying to act beyond their limits.

Numerical Simulation of Two-Part Underwater Towing System: A Lumped Mass-Spring System Approach

2007 ◽  
Author(s):  
P. P. Lalu
Keyword(s):  
System Approach ◽  
Two Dimensional ◽  
Lumped Mass ◽  
System A ◽  
Submerged Body ◽  
Induced Motion ◽  
Spring System ◽  
Experimental Values ◽  
Mass Spring ◽  
Wave Induced

The altitude and position of a submerged body being towed by a vessel is affected by wave induced motion of the latter. To reduce this disturbance, a two-part towing system is used. In this study a two-dimensional dynamic model of the two-part underwater towing system is described. Numerical modeling of the problem was attempted. The finite difference algorithm was used to formulate the problem. A lumped mass-spring system was used for modeling the cable. The formulation for the towed body was based on Kirchhoff’s equations for motion of a rigid body. For the demonstration of the model, a numerical example of the tow-ship traveling in a wave field is described. Subsequently, response of the towed body was simulated and is compared with the experimental values obtained from the literature.

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