scholarly journals Four-dimensional Integral Model of Dry Friction on the Example of Wheel Movement

2021 ◽  
Vol 2096 (1) ◽  
pp. 012043
Author(s):  
M S Salimov ◽  
G R Saypulaev ◽  
I V Merkuriev
Keyword(s):  
Dry Friction ◽  
Rolling Friction ◽  
Equation Of Motion ◽  
Friction Model ◽  
The Body ◽  
Integral Model ◽  
Control Torque ◽  
Padé Approximations ◽  
Pade Approximations ◽  
Dimensional Integral

Abstract A four-dimensional model of dry friction in the interaction of a solid wheel and a horizontal rough surface is investigated. It is assumed that there is no separation between the wheel and the horizontal surface. The movement of the body occurs in conditions of combined dynamics, when in addition to the sliding movement, the body participates in spinning and rolling. The equation of motion of the wheel is compiled using the Appel equation. The resulting model of sliding, spinning, and rolling friction is given for the case where the contact area is a circle. The cumbersome integral expressions were replaced by fractional-linear Pade approximations. Pade approximations accurately describe the behavior of the components of the friction model. A mathematical model is proposed that describes the simultaneous sliding, spinning and rolling of a solid wheel. The dependences of the parallel and perpendicular components of the friction force and the torque of the spinning friction were ploted with respect to the parameter that characterizes the movement of the wheel. Comparisons of the integral friction model and the model based on Pade approximations are presented. The results of the comparison showed a qualitative correspondence of the models. After obtaining the equation of motion, the simulation of motion at a constant control torque of the wheel is carried out. The graphs allow you to match the logical behavior of the wheel movement.

scholarly journals Three-dimensional integral dry friction model for the motion of a rectangular body

2021 ◽  
Vol 21 (1) ◽  
pp. 14-21
Author(s):  
M. S. Salimov ◽  
I. V. Merkuriev
Keyword(s):  
Angular Velocity ◽  
Dry Friction ◽  
Three Dimensional ◽  
Friction Model ◽  
The Body ◽  
Horizontal Surface ◽  
Padé Approximations ◽  
Pade Approximations ◽  
Analytical Expressions ◽  
Rectangular Body

Introduction. A three-dimensional dry friction model in the interaction of a rectangular body and a horizontal rough surface is considered. It is assumed that there is no separation of the body from the horizontal surface. The body motion occurs under the conditions of combined dynamics when, in addition to the longitudinal movement, the body participates in twisting.Materials and Methods. Linear fractional Pade approximations are proposed, which replaced the cumbersome analytical expressions that most accurately describe the motion of bodies on rough surfaces. New mathematical models describing sliding and twisting of bodies with a rectangular base are proposed.Results. Analytical expressions of the principal vector and moment of friction for rectangular contact areas are developed and scientifically established. A friction model that takes into account the relationship between sliding and twisting speeds, which provides finding solutions for Pade dependences, is developed. After numerical solution to the equations of motion, the dependences of the sliding speed and angular velocity on time were obtained and constructed. Graphs of the dependences of the friction forces and their moment on two parameters (angular velocity and slip velocity) were constructed, which enabled to compare the integral and normalized models of friction. The comparison results showed good agreement of the integral model and the model based on Pade approximations.Discussion and Conclusions. The results obtained provide considering the dynamic coupling of components, which determines the force interaction of a rectangular body and a horizontal surface. These results can be used in mobile robotics. The analyzed motion of the body occurs through the motion control of a material point inside the body. Such mobile robots can be used when solving a wide class of problems: when creating autonomous robots for the exploration of outer space and planets; in the diagnosis and treatment in case of passing through complex structures of veins and arteries; in research under water, in places of large differential temperature; in underground operations.

scholarly journals A study on the vibration dissipation mechanism of the rotating blade with dovetail joint

2021 ◽  
pp. 146134842098533
Author(s):  
Chaofeng Li ◽  
Zengchuang Shen ◽  
Zilin Chen ◽  
Houxin She
Keyword(s):  
Dry Friction ◽  
Vibration Reduction ◽  
Friction Model ◽  
Rotating Speed ◽  
System Parameters ◽  
Tangential Stiffness ◽  
Damping Characteristics ◽  
Rotating Blade ◽  
Spatial Beam ◽  
Dissipation Mechanism

The vibration dissipation mechanism of the rotating blade with a dovetail joint is studied in this paper. Dry friction damping plays an indispensable role in the direction of vibration reduction. The vibration level is reduced by consuming the total energy of the turbine blade with the dry friction device on the blade-root in the paper. The mechanism of the vibration reduction is revealed by the variation of the friction force and the energy dissipation ratio of dry friction. In this paper, the flexible blade with a dovetail interface feature is discretized by using the spatial beam element based on the finite element theory. Then the classical Coulomb-spring friction model is introduced to obtain the dry friction model on the contact interfaces of the tenon-mortise structure. What is more, the effects of the system parameters (such as the rotating speed, the friction coefficient, the installation angle of the tenon) and the excitation level on blade damping characteristics are discussed, respectively. The results show that the variation of the system parameters leads to a significant change of damping characteristics of the blade. The variation of the tangential stiffness and the position of the external excitation will affect the nonlinear characteristics and vibration damping characteristics.

scholarly journals Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽  
2021 ◽  
Author(s):  
Gábor Csernák ◽  
Gábor Licskó
Keyword(s):  
Dry Friction ◽  
Continuation Method ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Kinetic Coefficients ◽  
Friction Oscillator ◽  
Lugre Friction ◽  
Friction Parameters ◽  
Two Parameter ◽  
Parameter Bifurcation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation

2006 ◽  
Vol 11 (2) ◽  
pp. 139-158 ◽  
Author(s):  
Kathy Driver ◽  
Helmut Prodinger ◽  
Carsten Schneider ◽  
J. A. C. Weideman
Keyword(s):  
Symbolic Computation ◽  
Padé Approximations ◽  
Pade Approximations

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.

scholarly journals On rolling friction

2019 ◽  
Vol 485 (3) ◽  
pp. 295-299
Author(s):  
A. P. Ivanov
Keyword(s):  
Friction Coefficient ◽  
Angular Velocity ◽  
Viscous Friction ◽  
Rolling Friction ◽  
The Body ◽  
Normal Velocity ◽  
Contact Conditions ◽  
Combined Motion ◽  
Pure Rolling ◽  
Over Time

The dependence of rolling friction on velocity for various contact conditions is discussed. The principal difference between rolling and other types of relative motion (sliding and spinning) is that the points of the body in contact with the support change over time. Due to deformations, there is a small contact area and, entering into contact, the body points have a normal velocity proportional to the diameter of this area. For describing the dependence of the friction coefficient on the angular velocity in the case of “pure” rolling, a linear dependence is proposed that admits a logical explanation and experimental verification. Under the combined motion, the rolling friction retains its properties, the sliding and spinning friction acquiring the properties of viscous friction.

Sign in / Sign up

Export Citation Format

Share Document