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Reynolds Equation
In fluid mechanics (specifically lubrication theory), the Reynolds equation is a partial differential equation governing the pressure distribution of thin viscous fluid films. It was first derived by Osborne Reynolds in 1886. The classical Reynolds Equation can be used to describe the pressure distribution in nearly any type of fluid film bearing; a bearing type in which the bounding bodies are fully separated by a thin layer of liquid or gas. General usage The general Reynolds equation is: \frac\left(\frac\frac\right)+\frac\left(\frac \frac\right) = \frac \left(\frac\right)+\frac \left(\frac\right)+\rho\left(w_a-w_b\right) - \rho u_a\frac - \rho v_a \frac + h\frac Where: *p is fluid film pressure. *x and y are the bearing width and length coordinates. *z is fluid film thickness coordinate. *h is fluid film thickness. *\mu is fluid viscosity. *\rho is fluid density. *u, v, w are the bounding body velocities in x, y, z respectively. *a, b are subscripts denoting the top and bot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of disciplines, including mechanical engineering, mechanical, aerospace engineering, aerospace, civil engineering, civil, chemical engineering, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into ''fluid statics'', the study of various fluids at rest; and ''fluid dynamics'', the study of the effect of forces on fluid motion. It is a branch of ''continuum mechanics'', a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a macroscopic viewpoint rather than from microscopic. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Difference Method
In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating Derivative, derivatives with Finite difference approximation, finite differences. Both the spatial domain and time domain (if applicable) are Discretization, discretized, or broken into a finite number of intervals, and the values of the solution at the end points of the intervals are approximated by solving algebraic equations containing finite differences and values from nearby points. Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be Nonlinear partial differential equation, nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently, and this, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Bearings
Plain bearing on a 1906 S-Motor locomotive showing the axle, bearing, oil supply and oiling pad A sliding table with four cylindrical bearings A wheelset from a Great Western Railway (GWR) wagon showing a plain, or journal, bearing end A plain bearing, or more commonly sliding contact bearing and slide bearing (in railroading sometimes called a solid bearing, journal bearing, or friction bearing), is the simplest type of bearing, comprising just a bearing surface and no rolling elements. Therefore, the part of the shaft in contact with the bearing slides over the bearing surface. The simplest example of a plain bearing is a shaft rotating in a hole. A simple linear bearing can be a pair of flat surfaces designed to allow motion; e.g., a drawer and the slides it rests on or the ways on the bed of a lathe. Plain bearings, in general, are the least expensive type of bearing. They are also compact and lightweight, and they have a high load-carrying capacity. Design T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Air Bearings
Air bearings (also known as aerostatic or aerodynamic bearings) are bearings that use a thin film of pressurized gas to provide a low friction load-bearing interface between surfaces. The two surfaces do not touch, thus avoiding the problems of friction, wear, particulates, and lubricant handling associated with conventional bearings, and air bearings offer distinct advantages in precision positioning, such as lacking backlash and static friction, as well as in high-speed applications. Spacecraft simulators now most often use air bearings, and 3-D printers are now used to make air-bearing–based attitude simulators for CubeSat satellites.Nemanja Jovanovic, et al. Design and Testing of a Low-Cost, Open Source, 3-D Printed Air-Bearing-Based Attitude Simulator for CubeSat Satellites. ''Journal of Small Satellites'' Vol. 8, No. 2, pp. 859–880 (2019). https://jossonline.com/letters/design-and-testing-of-a-low-cost-open-source-3-d-printed-air-bearing-based-attitude-simulator-for-cub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ball Bearings
A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races. The purpose of a ball bearing is to reduce rotational friction and support radial and axial loads. It achieves this by using at least two races to contain the balls and transmit the loads through the balls. In most applications, one race is stationary and the other is attached to the rotating assembly (e.g., a hub or shaft). As one of the bearing races rotates it causes the balls to rotate as well. Because the balls are rolling, they have a much lower coefficient of friction than if two flat surfaces were sliding against each other. Ball bearings tend to have lower load capacity for their size than other kinds of rolling-element bearings due to the smaller contact area between the balls and races. However, they can tolerate some misalignment of the inner and outer races. Common ball bearing designs include ''angular contact, axial, deep-groove,'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Mechanics
Contact mechanics is the study of the Deformation (mechanics), deformation of solids that touch each other at one or more points. A central distinction in contact mechanics is between Stress (mechanics), stresses acting perpendicular to the contacting bodies' surfaces (known as normal stress) and frictional stresses acting Tangential and normal components, tangentially between the surfaces (shear stress). Normal contact mechanics or frictionless contact mechanics focuses on normal stresses caused by applied normal forces and by the adhesion present on surfaces in close contact, even if they are clean and dry. ''Frictional contact mechanics'' emphasizes the effect of friction forces. Contact mechanics is part of mechanical engineering. The physical and mathematical formulation of the subject is built upon the mechanics of materials and continuum mechanics and focuses on computations involving Elasticity (physics), elastic, viscoelasticity, viscoelastic, and Plastic Deformation, p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pyotr Kapitsa
Pyotr Leonidovich Kapitsa or Peter Kapitza (, ; – 8 April 1984) was a leading Soviet physicist and Nobel laureate, whose research focused on low-temperature physics. Biography Kapitsa was born in Kronstadt, Russian Empire, to the Bessarabian Leonid Petrovich Kapitsa (), a military engineer who constructed fortifications, and to the Volhynian Olga Ieronimovna Kapitsa, from a noble Polish Stebnicki family. Besides Russian, the Kapitsa family also spoke Romanian. Kapitsa's studies were interrupted by the First World War, in which he served as an ambulance driver for two years on the Polish front. He graduated from the Petrograd Polytechnical Institute in 1918. His wife and two children died in the flu epidemic of 1918–19. He subsequently studied in Britain, working for over ten years with Ernest Rutherford in the Cavendish Laboratory at the University of Cambridge, and founding the influential Kapitza club. He was the first director (1930–34) of the Mond Laborat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. Computers are usually used to perform the calculations required. With high-speed supercomputers, better solutions can be achieved and are often required to solve the largest and most complex problems. FEM is a general numerical method for solving partial differential equations in two- or three-space variables (i.e., some boundary value problems). There are also studies about using FEM to solve high-dimensional problems. To solve a problem, FEM subdivides a large system into smaller, simpler parts called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Volume Method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages. "Finite volume" refers to the small volume surrounding each node point on a mesh. Finite volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations of a so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lubrication Theory
In fluid dynamics, lubrication theory describes the flow of fluids (liquids or gases) in a geometry in which one dimension is significantly smaller than the others. An example is the flow above air hockey tables, where the thickness of the air layer beneath the puck is much smaller than the dimensions of the puck itself. Internal flows are those where the fluid is fully bounded. Internal flow lubrication theory has many industrial applications because of its role in the design of fluid bearings. Here a key goal of lubrication theory is to determine the pressure distribution in the fluid volume, and hence the forces on the bearing components. The working fluid in this case is often termed a lubricant. Free film lubrication theory is concerned with the case in which one of the surfaces containing the fluid is a free surface. In that case, the position of the free surface is itself unknown, and one goal of lubrication theory is then to determine this. Examples include the flow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
