scholarly journals Nonlinear Dynamics Analysis of a Rolling Bearing

2021 ◽  
Vol 54 (1) ◽  
pp. 21-26
Author(s):  
Arkadiusz Smagala ◽  
Krzysztof Kecik
Keyword(s):  
Degrees Of Freedom ◽  
Rolling Bearing ◽  
Point Of View ◽  
Shaft Speed ◽  
Response Mechanism ◽  
Vibration Direction ◽  
Hertz Theory ◽  
Ball Number ◽  
Clearance Level ◽  
Bearing Dynamics

A numerical analysis of the nonlinear bearing model about two degrees of freedom has been presented in this paper. The contact between a ball and ring by Hertz theory is described. Influence of the number of balls, shaft rotation and clearance on the acceleration were investigated in detail. Three numbers of balls from 11 to 16 were analyzed. The clearance level in the range of 0-71μm has been studied. It has been shown that the acceleration responses are different, depending on the vibration direction and are usually higher when the radial internal clearance and the shaft speed are increased. The higher ball number caused that the accelerations decreased in both directions. Moreover, two dynamic indicators that can be used for comparison bearing dynamics have been proposed. These obtained results are useful for understanding the vibration response mechanism from a practical point of view.

scholarly journals From Loschmidt daemons to time-reversed waves

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150156 ◽  
Author(s):  
Mathias Fink
Keyword(s):  
Wave Propagation ◽  
Time Reversal ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Propagation Time ◽  
Reversal Invariance ◽  
Spatial Boundary ◽  
Dual Approaches ◽  
Spatio Temporal

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses ‘time-reversal mirrors’ with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that ‘instantaneous time mirrors’, mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

DARK GEOMETRY

2004 ◽  
Vol 13 (10) ◽  
pp. 2275-2279 ◽  
Author(s):  
J. A. R. CEMBRANOS ◽  
A. DOBADO ◽  
A. L. MAROTO
Keyword(s):  
Dark Matter ◽  
Extra Dimensions ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
Point Of View ◽  
Missing Mass ◽  
Brane Worlds ◽  
Mass Problem ◽  
Extra Space ◽  
The Universe

Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space–time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES

2010 ◽  
Vol 02 (03n04) ◽  
pp. 217-234
Author(s):  
IOANNIS STEFANOU ◽  
JEAN SULEM
Keyword(s):  
Mechanical Properties ◽  
Discrete System ◽  
Degrees Of Freedom ◽  
Fractured Rock ◽  
Three Dimensional ◽  
Cosserat Continuum ◽  
Point Of View ◽  
Rock Masses ◽  
Homogenization Technique ◽  
Rock Structure

The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

KINEMATICS FEATURES OF HAMMER PERFORATED TILLAGE ROLL

2020 ◽  
pp. 13-19
Author(s):  
I. А. Sharonov ◽  
◽  
Yu. М. Isaev ◽  
V. I. Kurdyumov ◽  
◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Soil Layer ◽  
Point Of View ◽  
Lagrange Equations ◽  
Middle Volga Region ◽  
Perforated Cylinder ◽  
Winter Crops ◽  
Combined Impact ◽  
The Impact

The task of improving the quality of agricultural tools by improving the technological processes of their functioning, taking into account the kinematic features of the combined impact of working elements of tools on the soil environment is important from a scientific and technical point of view. To form the required structure and density of the soil layer at the depth of sowing, a hammer perforated tillage roller (HPTR) has been developed. The study aim is to improve the quality of post-sowing compaction and structuring of the soil layer in the seed location zone based on the development of an innovative design of HPTR that combines different effects on the treated environment. The object of research is the kinematic mode of operation of the HPTR, equipped with cylindrical hammers installed at the ends of the rod, which, in turn, are radially and pivotally installed on the axis of the gunFeature of offered HPTR is the excitation of hammer vibrations, which changes the kinematic parameters of the tillage tool as a whole. Lagrange equations of the second kind are used to describe the process of HPTR operation, which is represented as a system of material objects with several degrees of freedom. The conducted studies revealed the periodic nature of changes in the strength of the impact of HPTR on the soil. The obtained equations allow us to determine the features of the HPTR movement at different masses of a hollow perforated cylinder and cylindrical hammers. This is of great importance for increasing the efficiency of soil bolster destruction and creating the soil structure recommended for winter crops sown in the Middle Volga region.

scholarly journals Partition Function in One, Two, and Three Spatial Dimensions from Effective Lagrangian Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Christoph P. Hofmann
Keyword(s):  
Partition Function ◽  
Degrees Of Freedom ◽  
Spatial Dimension ◽  
Lagrangian Method ◽  
Point Of View ◽  
Low Energy ◽  
Effective Theory ◽  
Goldstone Bosons ◽  
Effective Lagrangian ◽  
Spatial Dimensions

The systematic effective Lagrangian method was first formulated in the context of the strong interaction; chiral perturbation theory (CHPT) is the effective theory of quantum chromodynamics (QCD). It was then pointed out that the method can be transferred to the nonrelativistic domain—in particular, to describe the low-energy properties of ferromagnets. Interestingly, whereas for Lorentz-invariant systems the effective Lagrangian method fails in one spatial dimension (ds=1), it perfectly works for nonrelativistic systems in ds=1. In the present brief review, we give an outline of the method and then focus on the partition function for ferromagnetic spin chains, ferromagnetic films, and ferromagnetic crystals up to three loops in the perturbative expansion—an accuracy never achieved by conventional condensed matter methods. We then compare ferromagnets in ds=1, 2, 3 with the behavior of QCD at low temperatures by considering the pressure and the order parameter. The two apparently very different systems (ferromagnets and QCD) are related from a universal point of view based on the spontaneously broken symmetry. In either case, the low-energy dynamics is described by an effective theory containing Goldstone bosons as basic degrees of freedom.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

Kinematic Design of a Novel Spatial Remote Center-of-Motion Mechanism for Minimally Invasive Surgical Robot

2015 ◽  
Vol 9 (1) ◽  
Author(s):  
Jianmin Li ◽  
Yuan Xing ◽  
Ke Liang ◽  
Shuxin Wang
Keyword(s):  
Minimally Invasive ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Surgical Robot ◽  
Main Body ◽  
Minimally Invasive Surgical ◽  
Surgical Tool ◽  
Movable Platform ◽  
Robotic Wrist

To deliver more value to the healthcare industry, a specialized surgical robot is needed in the minimally invasive surgery (MIS) field. To fill this need, a compact hybrid robotic wrist with four degrees of freedom (DOFs) is developed for assisting physicians to perform MIS. The main body of the wrist is a 2DOF parallel mechanism with a remote center-of-motion (RCM), which is located outside the mechanism. From the mechanical point of view, it is different from existing 2DOF spherical mechanisms, since there is no physical constraint on the RCM. Other DOFs of the wrist are realized by a revolute joint and a prismatic joint, which are serially mounted on the movable platform of the parallel mechanism. The function of these DOFs is to realize the roll motion and the in-out translation of the surgical tool. Special attention is paid to the parallel RCM mechanism. The detailed design is provided and the kinematic equations are obtained in the paper. Further, the Jacobian matrix is derived based on the kinematic equations. Finally, the paper examines the singularity configurations and implements the condition number analysis to identify the kinematic performance of the mechanism.

The role of coupling in intramolecular proton transfer reactions. The hydrogen oxalate anion as an example

1992 ◽  
Vol 70 (1) ◽  
pp. 100-106 ◽  
Author(s):  
Enric Bosch ◽  
Miquel Moreno ◽  
José María Lluch
Keyword(s):  
Proton Transfer ◽  
Degrees Of Freedom ◽  
Normal Mode Analysis ◽  
Intramolecular Proton Transfer ◽  
Point Of View ◽  
Mode Analysis ◽  
Intrinsic Reaction Coordinate ◽  
Isotope Substitution ◽  
Oxalate Anion ◽  
Proton Transfer Reactions

Coupling between the proton motion and the internal degrees of freedom for intramolecular proton transfer in the hydrogen oxalate anion has been studied. A normal mode analysis at a sequence of points along the Intrinsic Reaction Coordinate (IRC) has been performed and the coupling functions Bk.F have been obtained. It is shown that, although for the reactant the IRC direction essentially consists of the motion of oxygen atoms, the coupling changes this IRC direction towards the motion corresponding to proton transfer itself. From a quantum point of view, the curvature that appears as a consequence allows comer-cutting tunneling. Finally, the effect of isotope substitution is considered. Keywords: intramolecular proton transfer, coupling functions, IRC curvature, tunneling splitting, isotope substitution.

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