scholarly journals The Nonsmooth Vibration of a Relative Rotation System with Backlash and Dry Friction

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Minjia He ◽  
Shuo Li ◽  
Jinjin Wang ◽  
Zhenjun Lin ◽  
Shuang Liu
Keyword(s):  
Dry Friction ◽  
Time History ◽  
Static Friction ◽  
Friction Torque ◽  
Relative Rotation ◽  
Rotation System ◽  
Inclusion Theory ◽  
Nonsmooth Dynamical Systems ◽  
Driving Torque ◽  
Function Time

We investigate a relative rotation system with backlash and dry friction. Firstly, the corresponding nonsmooth characters are discussed by the differential inclusion theory, and the analytic conditions for stick and nonstick motions are developed to understand the motion switching mechanism. Based on such analytic conditions of motion switching, the influence of the maximal static friction torque and the driving torque on the stick motion is studied. Moreover, the sliding time bifurcation diagrams, duty cycle figures, time history diagrams, and the K-function time history diagram are also presented, which confirm the analytic results. The methodology presented in this paper can be applied to predictions of motions in nonsmooth dynamical systems.

Clearance and Dry Friction Study in a Nonlinear Torsional Vibration of a Rotating Machinery

1999 ◽  
Author(s):  
Kazuki Mizutani ◽  
Hossain Md. Zahid
Keyword(s):  
Torsional Vibration ◽  
Dry Friction ◽  
Friction Torque ◽  
Frictional Property ◽  
Behavioral Characteristics ◽  
Spring Stiffness ◽  
Response Curves ◽  
Friction Models ◽  
The Difference ◽  
Friction Study

Abstract Clearance problem in coupling is often experienced in a rotary torsional vibration system. We tried to analyze the qualitative and quantitative characteristics of torsional vibration by modeling the bilinear spring stiffness with changing friction torque. Symmetric and asymmetric spring stiffness with friction models are developed to investigate the behavioral characteristics of the system for simulations and experiments. The frequency response curves and time response curves with external sinusoidal excitation are observed by several non-dimensional numerical simulations. The thoroughly experiments are done to understand the actual phenomena of torsional vibration, verification of models and adjustability of simulations. The frictional property considered as dry friction in coupling is found very significant parameter to reduce the vibration within a tolerable range in both of the simulations and experiments. The difference between the results getting from simulations and experiments are also demonstrated in this paper elaborately.

LMI Based Control of Stick-Slip Oscillations in Drilling

2014 ◽  
Author(s):  
Matthew W. Harris ◽  
Behçet Açıkmeşe ◽  
Eric van Oort
Keyword(s):  
Linear Matrix Inequality ◽  
Convex Sets ◽  
Static Friction ◽  
Friction Torque ◽  
Angular Motion ◽  
Linear Matrix ◽  
Model Parameters ◽  
Matrix Inequality ◽  
Stick Slip ◽  
Linear Matrix Inequality Approach

This paper investigates control of stick-slip oscillations in drilling from a linear matrix inequality perspective. Stick-slip oscillations include a period of no angular motion at the bit caused by a large static friction torque followed by a period of rapid angular motion at the bit caused by a build up of torque in the drilling pipe. Many of the model parameters are uncertain but belong to convex sets, and the friction torques are not easily modeled. The linear matrix inequality approach facilitates design of state feedback controllers in the presence of polytopic uncertainties and can be optimized to reject disturbance effects relative to outputs. Results indicate that the linear matrix inequality approach leads to a simple controller, successfully alleviates the stick-slip problem, and is robust to uncertainties.

scholarly journals TWO MODELS OF NONSMOOTH DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (10) ◽  
pp. 2853-2860 ◽  
Author(s):  
MADELEINE PASCAL
Keyword(s):  
Dry Friction ◽  
Coupled Oscillators ◽  
Degrees Of Freedom ◽  
Analytical Form ◽  
Critical Value ◽  
Form Solution ◽  
Nonsmooth Systems ◽  
The Stability ◽  
Close Form ◽  
Nonsmooth Dynamical Systems

Two examples of nonsmooth systems are considered. The first one is a two degrees of freedom oscillator in the presence of a stop. A discontinuity appears when the system position reaches a critical value. The second example consists of coupled oscillators excited by dry friction. In this case, the discontinuity occurs when the system's velocities take a critical value. For both examples, the dynamical system can be partitioned into different configurations limited by a set of boundaries. Within each configuration, the dynamical model is linear and the close form solution is known. Periodic orbits, including several transitions between the various configurations of the system, are found in analytical form. The stability of these orbits is investigated by using the Poincaré map modeling.

scholarly journals Hopf Bifurcation Characteristics of Dual-Front Axle Self-Excited Shimmy System for Heavy Truck considering Dry Friction

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
Daogao Wei ◽  
Ke Xu ◽  
Yibin Jiang ◽  
Changhe Chen ◽  
Wenjing Zhao ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Dry Friction ◽  
Steering System ◽  
Front Axle ◽  
Friction Torque ◽  
The Self ◽  
Lagrange’S Equation ◽  
Excited Vibration ◽  
Heavy Truck ◽  
Manifold Theory

Multiaxle steering is widely used in commercial vehicles. However, the mechanism of the self-excited shimmy produced by the multiaxle steering system is not clear until now. This study takes a dual-front axle heavy truck as sample vehicle and considers the influences of mid-shift transmission and dry friction to develop a 9 DOF dynamics model based on Lagrange’s equation. Based on the Hopf bifurcation theorem and center manifold theory, the study shows that dual-front axle shimmy is a self-excited vibration produced from Hopf bifurcation. The numerical method is adopted to determine how the size of dry friction torque influences the Hopf bifurcation characteristics of the system and to analyze the speed range of limit cycles and numerical characteristics of the shimmy system. The consistency of results of the qualitative and numerical methods shows that qualitative methods can predict the bifurcation characteristics of shimmy systems. The influences of the main system parameters on the shimmy system are also discussed. Improving the steering transition rod stiffness and dry friction torque and selecting a smaller pneumatic trail and caster angle can reduce the self-excited shimmy, reduce tire wear, and improve the driving stability of vehicles.

Torque Analysis and Shape Optimization of Electromagnetic Clutch

2010 ◽  
Vol 426-427 ◽  
pp. 122-126
Author(s):  
Chang Hao Piao ◽  
Z.Y. Huang ◽  
J. Wang ◽  
Chong Du Cho
Keyword(s):  
Static Friction ◽  
Friction Torque ◽  
Geometrical Shape ◽  
Fem Model ◽  
Torque Analysis ◽  
Numerical Process ◽  
Analytical Result ◽  
Electromagnetic Clutch ◽  
Static Torque ◽  
Mathematical Process

This paper is devoted to the static friction torque of electromagnetic clutch. The torque maximization is also investigated by optimizing the geometrical shape of armature. For the purpose of designing and optimizing electromagnetic clutch, torque prediction is a very important factor. We construct an axi-symmetric FEM model to analyze static friction torque and use a torque tester to evaluate real torque. In this work, analytically predicted torque is compared with the experimental one to discuss the rationality of numerical process. The analytical result agrees well with experimental data, which proves the validity of the mathematical process. Through optimization of the shape of armature, we also improve the static torque of electromagnetic clutch about 30%.

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