Polarity Free Magnetic Repulsion and Magnetic Bound State

This is a report on a dynamic autonomous magnetic interaction which does not depend on polarities resulting in short ranged repulsion involving one or more inertial bodies and a new class of bound state based on this interaction. Both effects are new to the literature, found so far. Experimental results are generalized and reported qualitatively. Working principles of these effects are provided within classical mechanics and found consistent with observations and simulations. The effects are based on the interaction of a rigid and finite inertial body (an object having mass and moment of inertia) endowed with a magnetic moment with a cyclic inhomogeneous magnetic field which does not require to have a local minimum. Such a body having some degrees of freedom involved in driven harmonic motion by this interaction can experience a net force in the direction of the weak field regardless of its position and orientation or can find stable equilibrium with the field itself autonomously. The former is called polarity free magnetic repulsion and the latter is classified as a magnetic bound state. Experiments show that a bound state can be obtained between two free bodies having magnetic dipole moment as a solution of two-body problem. Various schemes of trapping bodies having magnetic moments by rotating fields are realized as well as rotating bodies trapped by a static dipole field in presence of gravity. Additionally, a special case of bound state called bipolar bound state between free dipole bodies is investigated.

THE GRINDING MECHANISM ON A KNIFE CENTRIFUGAL GRINDING MACHINE

The article presents a methodology for calculating the force effect on a fibrous suspension of working bodies in a centrifugal grinding apparatus. The aim of the research is to calculate the force per tooth of an inertial body at different speeds of rotation of the rotor, to determine the effect of the circumferential speed of movement of inertial bodies on the grinding process of fibrous semi-finished products. The article discusses the mechanism of grinding on a centrifugal knife grinding apparatus, determines the tangential shear forces at the contact of the grinding satellite knives with the grinding bowl knives, determines the effect on the fiber of rolling friction forces and sliding friction forces when the grinding satellite knives come into contact with the grinding bowl knives, as well as the effect of specific pressure at the point of contact of the satellite knives with the grinding bowl knives under the influence of inertial forces. Based on the research results, it is scientifically substantiated that the forces arising at the minimum of the considered values of the rotation speed of inertial bodies are sufficient to break the fiber when using this installation for grinding fibrous semi-finished products. An increase in the speed of rotation of the satellites causes a positive change in the physical and mechanical characteristics of the finished castings.

Polarity Free Magnetic Repulsion and Magnetic Bound State

This is a report on a dynamic autonomous magnetic interaction which does not depend on polarities resulting in short ranged repulsion involving one or more inertial bodies and a new class of bound state based on this interaction. Both effects are new to the literature, found so far. Experimental results are generalized and reported qualitatively. Working principles of these effects are provided within classical mechanics and found consistent with observations and simulations. The effects are based on the interaction of a rigid and finite inertial body (an object having mass and moment of inertia) endowed with a magnetic moment with a cyclic inhomogeneous magnetic field which does not require to have a local minimum. Such a body having some DoF involved in driven harmonic motion by this interaction can experience a net force in the direction of the weak field regardless of its position and orientation or can find stable equilibrium with the field itself autonomously. The former is called polarity free magnetic repulsion and the latter magnetic bound state. Experiments show that a bound state can be obtained between two free bodies having magnetic dipole moment. Various schemes of trapping bodies having magnetic moments by rotating fields are realized as well as rotating bodies trapped by a static dipole field in presence of gravity. Also, a special case of bound state called bipolar bound state between free dipole bodies is investigated.

Modeling of Boring Mandrel Working Process with Vibration Damper

The article considers the issue of modeling the oscillations of a boring mandrel with vibration damper connected to the mandrel with a viscoelastic coupling. A mathematical model of the boring mandrel oscillations, machine support and inertial body (damper) is developed in the form of a differential equations system. The model is made in the form of a four-mass system of connected bodies. The solution to the differential equations system was found using the finite difference method, as well as the operator method with the use of the Laplace transform. As the simulation result, it was found that the use of vibration damper can significantly reduce the amplitude of the boring mandrel natural vibrations when pulsed, and also significantly reduce the forced vibrations amplitude when exposed to periodic disturbing forces. The developed mathematical model and algorithms for the numerical solution to the differential equations allowed us to choose the optimal parameters of the boring mandrel damping element. The obtained data will be used to create a prototype boring mandrel and conduct field tests.

Mechanical analysis of viscoelastic models for Earth media

SUMMARY Linear and non-linear viscoelastic (VE) models such as the standard linear solid (SLS) and the generalized SLS (GSLS) are broadly used to represent the anelasticity of materials and Earth's media. However, although the VE approach is often satisfactory for any given observation, the inferred physical causes of anelasticity may be significantly misrepresented by this paradigm, and its predictions may be wrong or inaccurate in other cases. This problem is particularly important in heterogeneous media, including most cases of interest for seismology. For example, in homogenous media, VE and mechanics-based models predict identical quality-factor Q(f) and phase velocity c(f) spectra, but in heterogenous media, these models yield different time-stepping equations and interactions with material–property boundaries. The commonly used VE algorithms for modelling seismic waves rely on postulated convolutional integrals in time, whereas physically, models of rock rheologies should still be based on spatial interactions. To understand how VE models relate to mechanics, it is instructive to consider which physical properties of the medium are constrained reliably and which of them remain unconstrained by a pair of Q(f) and c(f) spectra, that is by VE properties. Despite its popular association with ‘attenuation,’ the peak value of Q−1(f) is actually a purely elastic property representing the existence of two (for SLS) or multiple (for GSLS) elastic moduli. These moduli are analogous to the drained and undrained moduli in poroelasticity or isothermal and adiabatic moduli in thermodynamics. By virtue of the Kramers–Krönig relations, the peak Q−1 is related to the total velocity dispersion, which is also caused by the difference between elastic moduli. By contrast, true anelasticity-related physical properties like viscosity are represented not by Q−1 values but by the frequencies of Q−1(f) peaks in the data. However, these frequencies also depend on multiple material properties that are not recognized or arbitrarily selected in the SLS and GSLS models. Inertial, body-force friction and the corresponding boundary effects are also ignored in VE models, which may again be improper for layered media. Thus, for physically accurate interpretation of laboratory experiments and numerical modelling of seismic waves, first-principle equations of mechanics should be used instead of VE models.