Nonlinear Free Dynamic Response of a One Degree-of-Freedom Oscillator Induced by a Quadratic Velocity Dependent Model of Friction

2012 ◽  
Author(s):  
Fida Majdoub ◽  
Joël Perret-Liaudet ◽  
Michel Belin ◽  
Jean-Michel Martin
Keyword(s):  
Dynamic Response ◽  
Quadratic Function ◽  
Force Transducer ◽  
Friction Model ◽  
Degree Of Freedom ◽  
Quadratic Term ◽  
Friction Behavior ◽  
Dimensionless Equation ◽  
Model Of Friction ◽  
Free Dynamic

In this paper, we study a kinematic friction model of a single degree-of-freedom oscillating system. This model has the following dimensionless equation of motion: y″+2ζy′+y=-μky′ in which the kinematic friction is described by a quadratic function of the velocity as the following: μky′=μ0+μ2y′2sgny′+μ1y′ The sign function preserves the asymmetry of the friction force. The model captures most of the friction behavior that has been observed experimentally using a recent apparatus known as “dynamic oscillating tribometer”. This experimental setup is based on the non-linear free dynamic response of this kind of oscillator. However, this technique is able to carefully determine, with no need for any force transducer, the velocity-independent and velocity-dependent friction coefficients, μ0 and μ1 respectively, for a linear description of the kinematic friction, μk, around y′ = 0 where: μky′=μ0sgny′+μ1y′ In this context, the principal aim is to investigate numerically and analytically the effect of the additional quadratic term. To analyze the free dynamic response and their corresponding envelops, different numerical methods are performed. New characteristics of the envelops are discussed in detail with respect to the form of the kinematic friction coefficient. This allows a better comprehension of the results observed experimentally.

scholarly journals DYNAMIC FRICTION BEHAVIOR IN PRE-SLIDING REGIME OF PNEUMATIC ACTUATORS

2017 ◽  
Vol 7 (1) ◽  
pp. 50-68
Author(s):  
Tran Xuan Bo ◽  
Do Viet Long ◽  
Hideki Yanada
Keyword(s):  
Mathematical Model ◽  
Friction Model ◽  
Experimental Setup ◽  
Lugre Model ◽  
Friction Behavior ◽  
Pneumatic Actuators ◽  
Simulation Results ◽  
Model Of Friction ◽  
Force Displacement ◽  
Pneumatic Cylinders

This paper focuses on investigating friction behavior in pre-sliding regime and developing a new mathematical model of friction for fluid power actuators. Using pneumatic cylinders with different sizes, an experimental setup is built to measure friction force-displacement characteristics in presliding regime under various conditions of pressures in the cylinder chambers. A new mathematical model of friction for the pneumatic cylinders is proposed by incorporating a hysteresis function into the new modified LuGre model. The experimental results show that when the pressures are varied, friction of the pneumatic cylinders in pre-sliding regime is represented by behavior of a nonlinear spring. In addition, hysteresis behavior with nonlocal memory is obtained in the friction forcedisplacement characteristics and that the size of the hysteresis loop is increased with increasing pressures in the cylinder chambers. The simulation results show that the new friction model can accurately simulate the friction behavior of the pneumatic cylinders in pre-sliding regime as well as sliding regime.

scholarly journals Investigation of X and Y Configuration Modal and Dynamic Response to Velocity Excitation of the Nanometer Resolution Linear Servo Motor Stage with Quasi-Industrial Guiding System in Quasi-Stable State

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 951
Author(s):  
Artur Piščalov ◽  
Edgaras Urbonas ◽  
Darius Vainorius ◽  
Jonas Matijošius ◽  
Artūras Kilikevičius
Keyword(s):  
Dynamic Response ◽  
System Analysis ◽  
Operating Time ◽  
Stable State ◽  
Degree Of Freedom ◽  
Diagnostic Tools ◽  
Nanometer Scale ◽  
Positioning Systems ◽  
Industrial Enterprises ◽  
Guiding System

Research institutions and industrial enterprises demand high accuracy and precision positioning systems to fulfil cutting edge requirements of up-to-date technological processes in the field of metrology and optical fabrication. Linear motor system design with high performance mechanical guiding system and optical encoder ensures nanometer scale precision and constant static error, which can be calibrated by optical instruments. Mechanical guiding systems has its benefits in case of control theory and its stability; unfortunately, on the other hand, there exists high influence of structure geometry and tribological effects such as friction and modal response. The aforementioned effect cannot be straightforwardly identified during the assembly process. Degradation of dynamic units can be detected only after certain operating time. Single degree of freedom systems are well investigated and the effect of degradation can be predicted, but there exists a gap in the analysis of nanometer scale multi degree of freedom dynamic systems; therefore, novel diagnostic tools need to be proposed. In this particular paper, dual axes dynamic system analysis will be presented. The main idea is to decouple standard stacked XY stage and analyse X and Y configuration as two different configurations of the same object, while imitators of corresponding axes are absolutely solid and stationary. As storage and analysis of time domain data is not efficient, main attention will be concentrated on frequency domain data, while, of course, statistical and graphical representation of dynamic response will be presented. Transfer function, dynamic response, spectral analysis of dynamic response, and modal analysis will be presented and discussed. Based on the collected data and its analysis, comparison of X and Y responses to different velocity excitation will be presented. Finally, conclusions and recommendations of novel diagnostic way will be presented.

An improved nonlinear model considering relative velocity for the friction behavior between untwisted glass-fiber tow and roller

2021 ◽  
pp. 004051752110308
Author(s):  
Yang Liu ◽  
Zhong Xiang ◽  
Xiangqin Zhou ◽  
Zhenyu Wu ◽  
Xudong Hu
Keyword(s):  
Friction Coefficient ◽  
Glass Fiber ◽  
Relative Velocity ◽  
Friction Model ◽  
Woven Fabric ◽  
Test Results ◽  
Application Process ◽  
Friction Behavior ◽  
Improved Model

Friction between the tow and tool surface normally happens during the tow production, fabric weaving, and application process and has an important influence on the quality of the woven fabric. Based on this fact, this paper studied the influence of tension and relative velocity on the three kinds of untwisted-glass-fiber tow-on-roller friction with a Capstan-based test setup. Furthermore, an improved nonlinear friction model taking both tension and velocity into account was proposed. According to statistical test results, firstly, the friction coefficient was found to be positively correlated with tension and relative velocity. Secondly, tension and velocity were complementary on the tow-on-roller friction behavior, with neither being superior to the other. Thirdly, an improved model was found to present well the nonlinear characteristics between friction coefficient and tension and velocity, and predicational results of the model were found to agree well with the observations from Capstan tests.

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

Accelerometer correction for the dynamic analysis of damped multi-degree of freedom systems

1969 ◽  
Vol 59 (4) ◽  
pp. 1591-1598
Author(s):  
G. A. McLennan
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Exact Method ◽  
Three Degrees Of Freedom

Abstract An exact method is developed to eliminate the accelerometer error in dynamic response calculations for damped multi-degree of freedom systems. It is shown that the exact responses of a system can be obtained from the approximate responses which are conventionally calculated from an accelerogram. Response calculations were performed for two typical systems with three degrees of freedom for an assumed pseudo-earthquake. The results showed that the approximate responses may contain large errors, and that the correction developed effectively eliminates these errors.

Numerical Investigation of Size Effect on Dry Friction Behavior in Micro Upsetting Process

2014 ◽  
Vol 997 ◽  
pp. 321-324
Author(s):  
Wei Zheng ◽  
Guang Chun Wang ◽  
Bing Tao Tang ◽  
Xiao Juan Lin ◽  
Yan Zhi Sun
Keyword(s):  
Friction Coefficient ◽  
Size Effect ◽  
Dry Friction ◽  
Normal Pressure ◽  
Friction Model ◽  
Strain Hardening Exponent ◽  
Forming Process ◽  
Friction Behavior ◽  
Initial Yield Stress ◽  
Coulomb’S Friction

After modifying the Wahime/Bay friction model, a new friction model suitable for micro-forming process without lubrication is established. In this model, it is shows that the friction coefficient is a function of strain hardening exponent, the normal pressure and the initial yield stress of material. Based on the experimental data, the micro-upsetting process is simulated using the proposed friction model. The simulation results are used to investigate the size effect on the dry friction behavior. It is found that the Coulomb’s friction coefficient is dropping with miniaturization of specimens when the amount of reduction is not too large.

Dynamic response of a two degree of freedom spherical system in a fluid

1967 ◽  
Vol 35 (6) ◽  
pp. 351-361 ◽  
Author(s):  
J. F. Carney ◽  
L. F. Mockros ◽  
S. L. Lee
Keyword(s):  
Dynamic Response ◽  
Degree Of Freedom ◽  
Spherical System ◽  
Two Degree Of Freedom

An Improved Analytical Model of Friction and Ball Motion in Linear Ball Bearings With Application to Ball-to-Ball Contact Prediction

2018 ◽  
Author(s):  
Bo Lin ◽  
Molong Duan ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Analytical Model ◽  
Analytical Formula ◽  
Point Contact ◽  
Friction Model ◽  
Linear Velocity ◽  
Contact Forces ◽  
Ball Bearings ◽  
Friction Behavior ◽  
Rolling Ball ◽  
Ball Contact

The friction behavior of rolling ball machine components like linear ball bearings is very important to their functionality. For instance, differences in linear velocity of balls induces ball-to-ball contact in certain circumstances, resulting in significant increases and variations in friction. In this paper, an improved analytical formula for determining the linear velocity of balls in four-point-contact linear ball bearings is derived as a function of contact angle deviations and contact forces. The analytical formula is validated against a comprehensive friction model in the literature and shown to be in good agreement, while an oversimplified analytical model proposed by the authors in prior work is shown to be inaccurate. A case study is presented where insights gained from the derived analytical formula are used to mitigate velocity difference of balls in a linear ball bearing which otherwise would experience ball-to-ball contact.

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