scholarly journals Dynamics of a vibration system, taking into account the hereditary type friction and the mobility of a vibration limiter

2018 ◽  
Vol 226 ◽  
pp. 03022
Author(s):  
Vladimir S. Metrikin ◽  
Leonid A. Igumnov ◽  
Mikhail V. Zaitsev ◽  
Aleksandr V. Boev
Keyword(s):  
Classical Method ◽  
Functional Dependence ◽  
Variable Structure ◽  
Mapping Method ◽  
Research Approach ◽  
Vibration System ◽  
Friction Forces ◽  
Periodic Action ◽  
Point Mapping ◽  
The Coefficient Of Friction

The paper investigates the dynamics of some vibration systems taking into account the hereditary-type dry friction and mobility of a vibration limiter. The interaction of the vibration limiter and the vibration system occurs either according to Newton’s hypothesis (an absolutely rigid limiter) or softly (the limiter is mobile). A general mathematical model (MM) of systems has been developed, which is highly non-linear nonautonomous system with variable structure. A numerical-analytical approach using the mathematical apparatus of the point mapping method is implemented to study the dynamics of the MM. The peculiarity in the research approach is that the point mapping is not formed by the classical method (mappings of the Poincaré surface into itself), but by the duration of relative rest of the vibration system, which greatly facilitated the process of point mapping and its detailed study. The presence of floating boundaries of slip-motion plates required the creation of an original approach in constructing point mapping and interpreting the results obtained. The structure of the phase portrait of the MM as a function of the characteristics of the sliding and state friction forces, as well as on the type and position of the limiter was studied using the developed research methodology and the created software product. Based on the character of changes in bifurcation diagrams, it was possible to determine the main laws of changes in the motion regimes (occurrence of random complexity via the period possible transfer to chaos doubling process) when changing the parameters of the vibration system (amplitude and frequency of periodic action, the form of the functional dependence describing the change in the coefficient of friction of relative rest. Analytical results with and without a vibration limiter are compared.

Vibration and Analysis of Multi-Disk Friction Systems

1998 ◽  
Author(s):  
Henric Larsson ◽  
Kambiz Farhang
Keyword(s):  
Frictional Contact ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Lumped Parameter ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction ◽  
Slip Region ◽  
Stiffness And Damping

Abstract The paper presents a lumped parameter model of multiple disks in frictional contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping parameters in the axial as well as the torsional directions. The formulation accounts for the coupling betwen the axial and angular motions by viewing the contact normal force to be the result of axial behavior of the system. The frictional contact of two disks in contact is modeled in two dynamic states (i.e. sticking and slipping state) having individual lumped parameter models and the conditions that control the switching between the two states are established. The friction forces are represented by assuming the coefficient of friction to be a function of the sliding velocity, varying exponentially from its static value at zero relative velocity to its kinetic value at high velocities. A computer simulation of an eight-rotor disk assembly is presented. The torsional vibration characteristics and how it is liked to the axial modes of vibration is analyzed. The vibration characteristics in the transient, steady-state and stick-slip region is compared. In the stick-slip region, the angular velocity of the interfaces in frictional contact is depicted and the sticking and slipping states are defined. It is shown that the duration of slip is approximately constant and the duration of stick increases almost exponentially until a final sticking is achieved.

Direct and Indirect Approaches at the Plasto-Hydrodynamic Lubrication Problem. Application to an Industrial Ironing Process

1999 ◽  
Vol 121 (3) ◽  
pp. 523-528 ◽  
Author(s):  
V. Cahouet ◽  
L. Baillet ◽  
M. H. Meurisse ◽  
B. Bou-Sai¨d
Keyword(s):  
Optimal Control Theory ◽  
Indirect Method ◽  
Classical Method ◽  
Hydrodynamic Lubrication ◽  
Direct Solution ◽  
Hydrodynamic Problem ◽  
Forming Process ◽  
Contact Conditions ◽  
Friction Forces ◽  
Tangential Contact

A finite element fluid-structure coupling is developed in order to simulate a lubricated forming process, A dynamic explicit code is used for elasto-plastic deformation calculations and normal and tangential contact conditions are handled using a dynamic projection method. Two complementary approaches to the hydrodynamic lubrication problem are proposed: a classical method using the direct solution of the inverse hydrodynamic problem and an original indirect method based on the so called “optimal control theory.” The applicability of the code developed is proved by the numerical simulation of an industrial ironing process. Results of the two methods are compared in terms of friction forces and film thickness profiles. The distribution of local friction coefficients is also obtained.

Discrete Variable Structure Control for an Active Anti-Vibration System

1990 ◽  
Vol 23 (1) ◽  
pp. 147-152
Author(s):  
A. Parvinmehr ◽  
R.D. Greenough ◽  
A.J. Wilkinson ◽  
A. Jenner
Keyword(s):  
Variable Structure Control ◽  
Variable Structure ◽  
Vibration System ◽  
Discrete Variable ◽  
Structure Control

Experimental Studies of Deformation and Temperature Processes Mandrelling in the Deform-3D System

2021 ◽  
Vol 1037 ◽  
pp. 357-368
Author(s):  
Mikhail F. Selemenev ◽  
Arkady A. Cherepenko ◽  
Elena A. Zvyagina ◽  
Artem N. Tkachenko ◽  
Elena M. Selemeneva
Keyword(s):  
Heat Transfer ◽  
Coefficient Of Friction ◽  
Experimental Studies ◽  
Contact Stresses ◽  
Temperature Analysis ◽  
Friction Forces ◽  
The Coefficient Of Friction ◽  
Cutting Zone ◽  
Deform 3D

The article discusses the effect of epilamated coatings during mandrelling. The picture of the change in contact stresses in the DEFORM-3D system is presented. It was established that a decrease in the coefficient of friction from 0.9 to 0.6 leads to a decrease in the number of foci and areas of contact stresses, as well as temperature analysis showed that a decrease in the friction forces reduces heat transfer in the cutting zone by about 40 ° C.

Point mapping method in investigating the dynamics of relay stabilization with account for nonlinearity of the speed sensor, delays, and time-independent perturbation

2021 ◽  
Author(s):  
R.P. Simonyants ◽  
V.N. Bulavkin
Keyword(s):  
Limit Cycles ◽  
Dead Zone ◽  
Mapping Method ◽  
General Purpose ◽  
Point Mapping ◽  
Speed Sensor ◽  
Literary Sources ◽  
The Dead ◽  
Phase Surface ◽  
Analytical Expressions

Using the point mapping method, we obtained analytical expressions for the first return functions for determining simple and complex attractors in the stabilization mode by a general-purpose relay controller with the linear formation of the control signal. We investigated self-oscillations with account for the operating members’ aftereffect, the dead zone of the speed sensor, and the time-independent perturbation action. The study shows that the dead zone of the speed sensor introduces significant changes in the behavior of the system, giving it new properties. The analysis of dynamic processes on a three-sheet phase surface revealed a wide variety of limit cycles and their dependence on the system’s parameters. Complex limit cycles are represented by combining simple cycles of two types, which allowed for a simplifying approach to their search based on the theory of multidimensional transformations of Yu.I. Neymark. A more complete result was obtained in comparison with the well-known literary sources.

The Application of Cell Mapping Method to High-Dimensional Nonlinear System

2005 ◽  
Author(s):  
Xiang Yu ◽  
Shi-Jian Zhu ◽  
Shu-Yong Liu
Keyword(s):  
Global Analysis ◽  
Mapping Method ◽  
High Dimensional ◽  
Dimensional System ◽  
Cell Mapping ◽  
Chaotic Motions ◽  
Point Mapping ◽  
Modified Method ◽  
Conventional Cell ◽  
Selection Of

After analyzing the inefficiency of the conventional Cell Mapping Methods in global analysis for high-dimensional nonlinear systems, several principles should be followed for these methods’ implementations in high-dimensional systems are proposed in this paper. Those are: appropriate selection of investigating plane, reduction of data size, and projection of attractors to the investigating plane. According to these, the idea of dynamic array is introduced to the method of Point Mapping Under Cell Reference (PMUCR) to improve computing efficiency. The comparison of the CPU time between the applications of this modified method to a 2-dimensional system and to a 4-dimensional one is carried out, and the results confirm this modified method can be utilized to analyze high-dimensional systems effectively. Finally, as examples, the periodic and chaotic motions of a coupled Duffing system are investigated through this method and some diagrams of global characteristics are presented.

On the Mechanics of Crack Initiation and Propagation in Elasto-Plastic Materials in Impact Fretting Wear

2004 ◽  
Vol 126 (2) ◽  
pp. 395-403 ◽  
Author(s):  
Y. B. Gessesse ◽  
M. H. Attia
Keyword(s):  
Crack Initiation ◽  
Contact Pressure ◽  
Coefficient Of Friction ◽  
Contact Area ◽  
Plastic Material ◽  
Oblique Impact ◽  
Fretting Wear ◽  
Isotropic Hardening ◽  
Friction Forces ◽  
The Coefficient Of Friction

Normal and oblique impact wear processes are characterized by unique features, which include the development of some residual stress components that vanish in unidirectional sliding. Parametric finite element analyses were conducted to estimate the likelihood locations for crack initiation, and the subsequent direction and rate of crack propagation in an elasto-plastic material with bi-linear isotropic hardening properties. The results showed that the increase in contact pressure can cause a significant increase in the size of the plastically deformed crack initiation zone and allows it to reach the surface. Such behavior is not predicted under continuous sliding conditions. The presence of surface friction forces in oblique impact, can also result in the development of a secondary region of high tensile stresses at the contact area. Using the crack tip slip displacement CTSD method, the rate of crack growth was found to be linearly proportional to the crack length, and significantly dependent on the contact pressure and the coefficient of friction at the crack surface. The small effect of the coefficient of friction at the micro-contact area on wear suggests that the effect of shear traction is mainly due to the increase in the depth of the crack nucleation zone. As expected, the increase of the material flow stress with strain-hardening has a wear reducing effect.

scholarly journals Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics

1997 ◽  
Vol 3 (4) ◽  
pp. 329-371
Author(s):  
Henryk Flashner ◽  
Ramesh S. Guttalu
Keyword(s):  
Stability Analysis ◽  
Degrees Of Freedom ◽  
Mapping Method ◽  
Periodic Systems ◽  
Resonance Problem ◽  
Point Mapping ◽  
Analytical Stability ◽  
Functional Relations ◽  
Ground Resonance ◽  
The Stability

Apoint mappinganalysis is employed to investigate the stability of periodic systems. The method is applied to simplified rotorcraft models. The proposed approach is based on a procedure to obtain an analytical expression for the period-to-period mapping description of system's dynamics, and its dependence on system's parameters. Analytical stability and bifurcation conditions are then determined and expressed as functional relations between important system parameters. The method is applied to investigate the parametric stability of flapping motion of a rotor and the ground resonance problem encountered in rotorcraft dynamics. It is shown that the proposed approach provides very accurate results when compared with direct numerical results which are assumed to be an “exact solution” for the purpose of this study. It is also demonstrated that the point mapping method yields more accurate results than the widely used classical perturbation analysis. The ability to perform analytical stability studies of systems with multiple degrees-of-freedom is an important feature of the proposed approach since most existing analysis methods are applicable to single degree-of-freedom systems. Stability analysis of higher dimensional systems, such as the ground resonance problems, by perturbation methods is not straightforward, and is usually very cumbersome.

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