Dry Friction and Mechanical System Motion Implicit Equations

2021 ◽  
pp. 4-16
Author(s):  
V.V. Lapshin
Keyword(s):  
Mechanical System ◽  
Sliding Friction ◽  
Single Point ◽  
Mechanical Systems ◽  
Equation System ◽  
Rolling Friction ◽  
Body Motion ◽  
Motion Equations ◽  
Differential Motion ◽  
Implicit Equations

It is shown that forces acting on the mechanical system points could depend on accelerations of the system points. Differential equation system of the mechanical system motion appears to be implicit. It is not resolved with respect to senior derivatives. Fundamental mathematical problems appear associated with possibility and uniqueness of these equations' solution with respect to the senior derivatives. Such problems are common in mechanical systems with dry sliding friction and rolling friction. Such problems are missing in the point dynamics. However, such problems are rather typical in more complex mechanical systems appearing in the study of a rigid body motion, which entire mass is concentrated in a single point, as well as in systems with one degree of freedom. Four fairly simple examples of mechanical systems are considered, and their motion is described by implicit differential motion equations. Situations could appear in these systems, when motion equations are not solvable with respect to the senior derivatives (motion equations are missing), as well as situations, when there are several solutions with respect to senior derivatives (there are several different systems of the mechanical system motion equations). At the same time, one of the fundamental principles of mechanics is not fulfilled, i.e., the principle of determinism

New Formulations on Motion Equations in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 49-54 ◽  
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Higher Order ◽  
Analytical Dynamics ◽  
Lagrange Principle ◽  
Motion Equations ◽  
Differential Motion

Using the main author's researches on the energies of acceleration and higher order equations of motion, this paper is devoted to new formulations in analytical dynamics of mechanical multibody systems (MBS). Integral parts of these systems are the mechanical robot structures, serial, parallel or mobile on which an application will be presented in order to highlight the importance of the differential motion equations in dynamics behavior. When the components of multibody mechanical systems or in its entirety presents rapid movements or is in transitory motion, are developed higher order variations in respect to time of linear and angular accelerations. According to research of the main author, they are integrated into higher order energies and these in differential equations of motion in higher order, which will lead to variations in time of generalized forces which dominate these types of mechanical systems. The establishing of these differential equations of motion, it is based on a generalization of a principle of analytical differential mechanics, known as the D`Alembert – Lagrange Principle.

scholarly journals Design procedure of first-order perturbations for collisions trajectories with a perturbing body

2019 ◽  
Vol 138 ◽  
pp. 01034
Author(s):  
Vera Petelina
Keyword(s):  
Design Procedure ◽  
Equation System ◽  
Body Motion ◽  
Differential Equation System ◽  
Motion Equations ◽  
Rectangular Coordinates ◽  
The Right ◽  
Approximating Polynomials ◽  
Disturbed Motion

The article is devoted to the determination of firstand secondorder perturbations in rectangular coordinates and velocity components of body motion. Special differential equation system of perturbed motion is constructed. The right-hand sides of this system are finitesimal polynomials in powers of an independent regularizing variate. This allows constructing a single algorithm to determine firstand second-order perturbations in the form of finitesimal polynomials in powers of regularizing variates that are chosen at each approximation step. Following the calculations results with the developed method use, the coefficients of approximating polynomials representing rectangular coordinates and components of the regularized body speed were obtained. Comparison with the numerical results of the disturbed motion equations shows their close agreement. The developed method make it possible to calculate any visa point of body motion by the approximating polynomials.

Measurement of Rolling and Sliding Friction Coefficients of Tread Compounds

1968 ◽  
Vol 41 (4) ◽  
pp. 908-942 ◽  
Author(s):  
E. Clamroth ◽  
W. Heidemann
Keyword(s):  
Friction Surface ◽  
Sliding Friction ◽  
Water Drop ◽  
Single Point ◽  
Water Layer ◽  
Rolling Friction ◽  
Skid Resistance ◽  
Friction Coefficients ◽  
Friction Forces ◽  
Rubber Surface

Abstract We have described two methods to measure friction forces arising from sliding and rolling on a wet surface. In rolling friction we showed that energy of deformation of a braked rubber specimen could be estimated and separated from friction energy. Rolling friction shows a characteristic slip dependence for various compounds. The rise at low slip values can be quantitatively explained. Especially with polybutadiene vulcanizates, at higher slips the friction coefficient decreases; this is attributable to thickness of the water layer between specimen and friction surface and depends on ease of wetting with water. Wetting can be altered by addition of a wetting agent like Pril, and measured by the contact angle of a water drop on the rubber surface. In wet friction, the changes in the water layer outweigh the temperature and velocity dependent shifts expected for adhesion and deformation friction components. A sort of mixed friction occurs on wet surfaces. The true contact surface, that is, surface not covered with water, has a strong effect on the magnitude of friction forces. In general only the highest asperities of the friction surface extend above the water and are in direct contact with the rubber surface. It is therefore understandable that surface asperity has a strong effect on friction coefficients. Finally we have compared friction coefficients determined with our apparatus with those obtained using the Portable Skid Resistance Tester and with results of road tests. The Portable Skid Resistance Tester provides a single point method, which has good reproducibility and whose results correlate well with those on the road at a speed of about 48 km/hr. Our apparatus has the advantage that test conditions such as velocity, temperature, and load can be widely varied. In this way, various actual driving conditions can be approximated and one may seek to determine the mechanism of friction from dependence of friction coefficients on these parameters.

The Simulation of Mechanical Systems Kinematics and Dynamics

2002 ◽  
Author(s):  
Q. K. Yuan
Keyword(s):  
Mechanical System ◽  
Mechanical Systems ◽  
Dynamics Simulation ◽  
Simulation Program ◽  
Kinematics And Dynamics ◽  
Software System ◽  
Motion Equations

The Kinematics and dynamics is the important properties of a mechanical system or a mechanical product. In this paper, a describing method by the symbol sets, motion equations auto-building method and auto-solving method are discussed, a software system MSKDSP (Mechanical System Kinematics and Dynamics Simulation Program) is developed, and an example is given.

The Brake Device Design for Children Two-Wheel Dynamic Scooter

2011 ◽  
Vol 421 ◽  
pp. 724-727
Author(s):  
Xue Feng Yi ◽  
Li Jun He
Keyword(s):  
Sliding Friction ◽  
Rolling Friction ◽  
Safety Performance ◽  
Device Design ◽  
Emergency Braking ◽  
Design For Children ◽  
Brake Device

Children scooter safety performance is not good enough in the market, the cause of the majority of injuries to children is difficult to control the speed or emergency braking. According to the phenomenon, this paper focuses on designing dynamic scooter brake device for 8-10 child, we conceive that the brake device is given the force of the rolling friction and the sliding friction, so it can play a dual brake effect. It will enhance the security and stability of children dynamic scooter.

The Control of Vibration Transmissibility Using an Electrodynamic Actuator –Close-Loop Solution

2013 ◽  
Vol 436 ◽  
pp. 166-173
Author(s):  
A. Mihaela Mîţiu ◽  
Daniel Constantin Comeagă ◽  
Octavian G. Donţu
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mechanical System ◽  
Closed Loop ◽  
Mechanical Systems ◽  
Vibration Transmissibility ◽  
Technical Solutions ◽  
The Mathematical Model

In this paper are presented some aspects of transmissibility control of mechanical systems with 1 DOF so that the effects of vibration on their action to be minimized. Some technical solutions that can be used for this purpose is analyzed. Starting from the mathematical model of an electro-mechanical system with 1 DOF, are identified the parameters which influence the effectiveness of the transmissibility control system using an electrodynamic actuator who work in "closed loop".

Controlled Arming of Mechanical Systems Embedded into Embarked Electrical Systems

2014 ◽  
Vol 555 ◽  
pp. 209-216
Author(s):  
Gheorghe Negru
Keyword(s):  
Kalman Filter ◽  
Mechanical System ◽  
High Speed ◽  
Mechanical Systems ◽  
Electrical Systems ◽  
General Motion

The paper presents an application of the Kalman filter to achieve the controlled arming of mechanical system embedded into embarked electrical systems (FMES). The solution of FMES which contain mechanical subsystems electronically controlled could significantly reduce the influence, on their functioning, of the general motion of high speed object (HSO) .

The Method for Determining the Vibration-Damping Elements for the Mechanical System to Obtain the Desired Amplitude Value

2014 ◽  
Vol 657 ◽  
pp. 644-648 ◽  
Author(s):  
Andrzej Dymarek ◽  
Tomasz Dzitkowski
Keyword(s):  
Mechanical System ◽  
Dynamic Characteristics ◽  
Vibration Reduction ◽  
Mechanical Systems ◽  
Vibration Damping ◽  
Displacement Velocity ◽  
Synthesis Methods ◽  
Resonance Frequencies

The paper presents the use of synthesis methods to determine the parameters of passive vibration reduction in mechanical systems. Passive vibration reduction in a system is enabled by units called dampers whose values are determined on the basis of the method formulated and formalized by the authors. The essence of the method are, established at the beginning of a task, dynamic characteristics in the form of the resonance and anti-resonance frequencies, and amplitudes of displacement, velocity or acceleration of vibration.

Some Regularities of Life Time and Damage for the New Structural Material MoNiCa during Sliding Friction and Mechano-Sliding Fatigue

2021 ◽  
Vol 320 ◽  
pp. 90-96
Author(s):  
Aliaksandr Bahdanovich ◽  
Sergei Sherbakov ◽  
Ivan Lis ◽  
Regita Bendikiene ◽  
Ramūnas Česnavičius ◽  
...  
Keyword(s):  
Heat Treatment ◽  
Structural Material ◽  
Mechanical System ◽  
Sliding Friction ◽  
Limit State ◽  
High Strength ◽  
Life Time ◽  
Average Wear ◽  
The Republic ◽  
Number Of Cycles

The results of an experimental study of damage for the structural material MoNiCa (it is high-strength cast iron VCHTG – patent of the Republic of Belarus № 15617) on sliding friction and mechano-sliding fatigue are analyzed in the report. Tests of the mechanical system shaft (a sample with a working part diameter of 10 mm made of 0.45 % carbon steel) - an insert (a prismatic counter sample with a cross section of 10 ´ 10 mm made of MoNiCa) were carried out. The kinetics of the change in average wear at 8 local points along the perimeter of the dangerous area of the sample is given for contact loads FN from 20 to 92 N of the mechanical system under study with MoNiCa inserts without heat treatment and with heat treatment. The test results of the system under study are also presented in the form of sliding friction and mechano-sliding fatigue curves in coordinates of the contact load FN – the number of cycles N until the limit state.

Two Basic Features of Instantaneous Conjugate Motion and Their Importance in Facilitating Motion Analysis

2004 ◽  
Vol 126 (1) ◽  
pp. 119-127 ◽  
Author(s):  
Chih-Hsin Chen ◽  
Janet Hong-Jian Chen
Keyword(s):  
Motion Analysis ◽  
Mechanical Systems ◽  
Body Motion ◽  
Geometrical Constraints ◽  
Free Body ◽  
Basic Features

Two basic features of instantaneous conjugate motion, which distinguishes it from instantaneous free body motion, are pointed out. Their influences on the geometrical constraints requisite for surface/line conjugation are discussed. Their importance in facilitating motion analysis of mechanical systems through linearization of relevant equations is clarified. Two illustrative examples are cited.

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