Intermolecular And Surface Forces

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

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Particle Creation by Black Holes

Quality function deployment: A literature review

Annalen der Physik

Nonlinear Oscillations: Exact Solutions and their Approximations

Description of Surfaces Contact Mechanics Dry Contact Friction Lubricant Rheology Principles of Hydrodynamics Thermohydrodynamics Elastohydrodynamics Thrust Bearings Journal Bearings Externally Pressurized Bearings Hydrostatic Bearings Aerostatic Bearings Ball and Rolling Element Bearings Fatigue Wear Adhesion Transient Elastohydrodynamics Valve Trains Pistons Biotribology of Natural Joints Joint Replacements Nanotribology Van Der Waal's Forces Electrostatics Meniscus Action Solvation Hydration MEMS Hard Disk Drives.

Fundamentals of Tribology

This paper presents a detailed model of bearing vibration, including the effect of contact spring non-linearity in balls-to-raceways' contacts. The model incorporates the effect of surface waviness of rolling elements and off-sized balls upon the dynamic internal radial clearance of the bearing. The vibration forces and moments generated are formulated and the significant principal and secondary side-band contributions are highlighted. This model is employed successfully in the recognition of complex real-time vibration spectra of a precision routing spindle, obtained by accurate non-contact sensors.

Bearing induced vibration in precision high speed routing spindles

Vectors and transformations kinematics and dynamics of particles and rigid bodies constraints formulation in multi-body systems multi-body dynamic analysis multi-body analysis - solution methodology engine dynamics power train dynamics optimal control of multi-body systems.

Multi-Body Dynamics: Vehicles, Machines and Mechanisms

This paper presents a theoretical analysis of the vibration response of a rotating rigid shaft supported by two radial deep‐groove lubricated ball bearings. The bearings and their oil films are approximated to a set of non‐linear elastic springs and dampers rotating relative to the shaft when it is subjected to a rotating unbalance or inner race surface waviness. Under gravity load, the shaft's initial vibration is damped down to a limit cycle operating at a quasi‐simple harmonic frequency of small amplitude. Rotating unbalance and surface features introduce further significant frequencies which influence the output response.

/pdf/the-vibrations-of-radial-ball-bearings-4npi0bwvys.pdf

Homer Rahnejat

Papers

Fundamentals of Tribology

Bearing induced vibration in precision high speed routing spindles

Multi-Body Dynamics: Vehicles, Machines and Mechanisms

The Vibrations of Radial Ball Bearings

Tribology of piston compression ring conjunction under transient thermal mixed regime of lubrication