A complete analysis of axial piston pump leakage and output flow ripples

The paper is focused on understanding the flow losses and the resulting flow/pressure dynamics in a piston pump. Initially, equations to evaluate leakages in all piston pump gaps will be presented and tested against numerical models, later the equations will be linked to determine the general pressure/flow pump dynamic characteristics. The model will also provide the temporal pressure in each piston/cylinder chamber and the temporal leakage in all pump clearances. A test rig able to measure the dynamic pressure inside a piston chamber was build and employed to evaluate pressure ripple dynamics as a function of turning speed, outlet pressure and swash plate angle. The comparison between experimental and simulated results is very good, giving confidence to the model presented. The advantage of using the analytical approach is that explicit equations allow a more direct understanding of the effect of dimension changes and operating conditions on pump dynamics. Fluid used hydraulic oil ISO 32.     

双缸单作用活塞泵中活塞匀速运动的探讨

通常双缸单作用活塞泵的恒转速运行会导致管路流量波动,使之在恒流量场合较少应用.对双缸单作用活塞泵的运动建立微分方程,给出了MATLAB7的仿真结果,提出了活塞近似匀速运动的条件,并对电动机转轴的角速度的计算方法作了讨论,得出了在中、低速运行时采用变角速度控制能近似实现恒流量的结论.     

A revisit of spinning disk models. Part I: derivation of equations of motion

Previous models of spinning disks have focused on modelling the disk as a spinning membrane. The effect of bending stiffness was then incorporated by adding the appropriate term to the previously derived spinning membrane equation. A pure spinning plate model does not exist in the literature. Furthermore, in both existing linear and nonlinear models of spinning disks, the in-plane inertia and rotary inertia of the disk have been ignored. This paper revisits the derivation of the equations of motion of a spinning plate. The derivation focuses on the use of Hamilton's principle with linear Kirchhoff and nonlinear von Karman strain expressions. In-plane and rotary inertias of the plate are automatically taken into account. The use of Hamilton's principle guarantees the correct derivation of the corresponding boundary conditions. The resulting equations and boundary conditions are discussed.     

Analysis of the adiabatic piston problem via methods of continuum mechanics

We consider a system modelling the motion of a piston in a cylinder filled by a viscous heat conducting gas. The piston is moving longitudinally without friction under the influence of the forces exerted by the gas. In addition, the piston is supposed to be thermally insulating (adiabatic piston). This fact raises several challenges which received a considerable attention, essentially in the statistical physics literature. We study the problem via the methods of continuum mechanics, specifically, the motion of the gas is described by means of the Navier–Stokes–Fourier system in one space dimension, coupled with Newton's second law governing the motion of the piston. We establish global in time existence of strong solutions and show that the system stabilizes to an equilibrium state for $t\to \infty$.     

Vibration and stability analysis of a simply-supported Rayleigh beam with spinning and axial motions

The vibration and stability of a simply supported beam are analyzed when the beam has an axially moving motion as well as a spinning motion. When a beam has spinning and axial motions, rotary inertia plays an important role on the lateral vibration. Compared to previous studies, the present study adopts the Rayleigh beam theory and derives more exact kinetic energy and equations of motion. The rotary inertia terms derived by the present study are compared to those of the previous studies. We investigate the natural frequencies between the present and previous studies. In addition, the critical speed and stability boundary for the spinning and moving speeds are also analyzed. It can be observed from the computed natural frequencies and dynamic responses that the present equations of motion are more reliable than the previous equations because the present equations fully consider the rotary inertia terms.     

Thermal-fluid-structure coupling analysis for valve plate friction pair of axial piston pump in electrohydrostatic actuator (EHA) of aircraft

This paper deals with thermal-fluid-structure coupling analysis for valve plate friction pair of axial piston pump in electrohydrostatic actuator (EHA) of aircraft. The axial piston pump with high pressure and high rotational speed to be widely applied in EHA of more electric aircraft can increase the power density, but it also deteriorates thermal-fluid-structure coupling of the friction pairs. In order to reveal its interior multiphysics field coupling mechanism, taking the valve plate friction pair in three key friction pairs for example, this study carries out the research on multiphysics field coupling. Firstly, Navier–Stokes equations and energy equation of the incompressible fluid considering the influence of temperature and pressure on the oil properties, heat conduction governing equation with many boundary conditions including heat flux, heat convection, heat radiation and considering the influence of the structure deformation on the temperature and the influence of the temperature on the material properties, the elastic mechanics model of the structure exerted together by temperature, fluid pressure and mechanical load, are established. On this basis, a complete set of fast and effective thermal-fluid-structure coupling method is originally presented, and the numerical analysis is conducted using it for the valve plate friction pair. By the calculation results, the evolution laws with time and space are revealed regarding to the pressure and temperature of the fluid in the chambers, and the temperature, stress and deformation of the valve plate friction pair, the wedge-shaped clearance forms between them, even mixed friction occurs, and the corresponding improving measures aimed at the discovered problems are discussed. These results can provide the theoretical evidence for the design and development of the pump of EHA.     

Invariant sets in the Goryachev–Chaplygin problem: existence,stability and branching

The existence, stability and branching of invariant sets in the problem of the motion of a heavy rigid body with a fixed point, which satisfies the Goryachev–Chaplygin conditions, are discussed. Both trivial invariant sets, in which the pendulum-like motions of a Goryachev–Chaplygin spinning top lie, as well as non-trivial invariant sets, in which the motion of the top is described by elliptic functions of time, are investigated.     

Nonlinear reynolds equation for lubrication of a rapidly rotating shaft

Using the homogenization theory, we derive the nonlinear Reynolds equation governing the process of lubrication of a slipper bearing with rapidly rotating shaft. We prove that this nonliner lubrication law is an approximation of the full Navier-Stokes equations in a thin cylinder with periodic roughness. The analyticity of the nonlinear function giving the relation between the velocity and the pressure drop is proved. The first term in its Taylor's expansion is the classical linear Reynolds law. Boundary layer correctors are computed.     

Free vibrations and stability of hydraulic cylinder fixed elastically on both ends

The boundary value problem of the stability and free vibration of a hydraulic cylinder has been formulated and solved in this paper. The considered hydraulic cylinder has been elastically fixed at both ends and loaded by Euler force. An elastical fixation has been modelled by rotational springs. The mentioned above hydraulic cylinder consists of a piston rod and cylinder replaced by rods. There are conditions of continuity between the rods. The boundary value problem has been formulated on the basis of minimum potential energy (static problem) and on the basis of Hamilton's principle (free vibration problem). In this paper example results of numerical calculations of the stability and free vibration have been presented. Experimental research has been performed in order to verify the correctness of the assumed mathematical model. Professional measuring apparatus and special stand for research into the slender systems have been used in experiment. Natural frequencies have been measured in dependence on the values of an external load. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-magneto-dynamic stresses and perturbation of magnetic field vector in a non-homogeneous hollow cylinder

An analytical method is presented to investigate thermo-magneto-elastic stresses and perturbation of the magnetic field vector in a conducting non-homogeneous hollow cylinder under thermal shock. The interaction between the deformation and the magnetic field vector in a non-homogeneous hollow cylinder is considered by adding a Lorentz’s electro-magneto-force into the equation of thermo-elastic motion of the non-homogeneous hollow cylinder in an axial magnetic field. The exact solution for magneto-thermo-dynamic stresses and perturbation responses of an axial magnetic field vector in a conducting non-homogeneous hollow cylinder was obtained by using finite integral transforms. From numerical calculations, the dynamic characteristics on both thermo-magneto-stresses and perturbation of the axial magnetic field vector in the conducting non-homogeneous hollow cylinder is revealed and discussed.     

The stabilization of program motions of controlled nonlinear mechanical systems

We consider a controlled nonlinear mechanical system described by the Lagrange equations. We determine the control forcesQ ₁ and the restrictions for the perturbationsQ ₂ acting on the mechanical system which allow to guarantee the asymptotic stability of the program motion of the system. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having nonpositive derivatives. The following examples are considered: stabilization of program motions of mathematical pendulum with moving point of suspension and stabilization of program motions of rigid body with fixed point.     

Gaussian Curvature and Gyroscopes

We relate Gaussian curvature to the gyroscopic force, thus giving a mechanical interpretation of the former and a geometrical interpretation of the latter. We do so by considering the motion of a spinning disk constrained to be tangent to a curved surface. It is shown that the spin gives rise to a force on the disk that is equal to the magnetic force on a point charge moving in a magnetic field normal to the surface, of magnitude equal to the Gaussian curvature, and of charge equal to the disk's axial spin. In a special case, this demonstrates that the precession of Lagrange's top is due to the curvature of a sphere determined by the parameters of the top. © 2017 Wiley Periodicals, Inc.     

The unsteady Reynolds slider bearing

Summary This paper studies the unsteady low Reynolds number flow which results when a two-dimensional slipper slides over a plane guide, the space between the slipper and the guide being occupied by a thin lubricating film the thickness of which is time independent. With axes fixed relative to the slipper, results are presented for a number of possible motions of the guide and special attention is given to the response of the normal force on the slipper following a rapid change in the speed of the guide from one constant value to another.

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Résumé Il s'agit d'une étude de l'écoulement instable, de petit nombre de Reynolds, qui intervient quand un objet à deux dimensions effectue un mouvement de glissement sur un guide plat, l'espace entre le guide et l'objet glissant étant rempli d'un mince film lubrifiant, dont l'épaisseur est supposée être indépendante du temps. Les résultats se rapportent à différents mouvements relatifs possibles du guide, dans un système de référence où l'objet glissant est fixe; en particulier la réponse de la force normale agissant sur l'objet glissant est déterminée quand le guide effectue un rapide changement de vitesse relative, d'une valeur constante à une autre.

     

Vibration and stability of an axially moving Rayleigh beam

In this paper, the vibration and stability of an axially moving beam is investigated. The finite element method with variable-domain elements is used to derive the equations of motion of an axially moving beam based on Rayleigh beam theory. Two kinds of axial motions including constant-speed extension deployment and back-and-forth periodical motion are considered. The vibration and stability of beams with these motions are investigated. For vibration analysis, direct time numerical integration, based on a Runge–Kutta algorithm, is used. For stability analysis of a beam with constant-speed axial extension deployment, eigenvalues of equations of motion are obtained to determine its stability, while Floquet theory is employed to investigate the stability of the beam with back-and-forth periodical axial motion. The effects of oscillation amplitude and frequency of periodical axial movement on the stability of the beam are discussed from the stability chart. Time histories are established to confirm the results from Floquet theory.     

Ground Contact Detection with Shortstroke Buttons for Biped Robots

Robust walking motion of humanoid robots requires a sensor system that can accurately sense the robot's state and its environment. Especially in case the ground is not modeled and uneven, information about the contact state is crucial to initiate an appropriate response. Many humanoid robots use strain gauge-based force/torque sensors to obtain information about the contact state. In this paper, we propose the integration of shortstroke buttons in the foot design to detect ground contact faster and more reliably. Simulation results with our robot Lola suggest that impact forces in case of an unexpected ground contact can be reduced significantly by integrating these sensors. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stability of the plane periodic motions of a symmetrical rigid body with a fixed point

A rigorous non-linear analysis of the orbital stability of plane periodic motions (pendulum oscillations and rotations) of a dynamically symmetrical heavy rigid body with one fixed point is carried out. It is assumed that the principal moments of inertia of the rigid body, calculated for the fixed point, are related by the same equation as in the Kovalevskaya case, but here no limitations are imposed on the position of the mass centre of the body. In the case of oscillations of small amplitude and in the case of rotations with high angular velocities, when it is possible to introduce a small parameter, the orbital stability is investigated analytically. For arbitrary values of the parameters, the non-linear problem of orbital stability is reduced to an analysis of the stability of a fixed point of the simplectic mapping, generated by the system of equations of perturbed motion. The simplectic mapping coefficients are calculated numerically, and from their values, using well-known criteria, conclusions are drawn regarding the orbital stability or instability of the periodic motion. It is shown that, when the mass centre lies on the axis of dynamic symmetry (the case of Lagrange integrability), the well-known stability criteria are inapplicable. In this case, the orbital instability of the periodic motions is proved using Chetayev's theorem. The results of the analysis are presented in the form of stability diagrams in the parameter plane of the problem.     

On coupled transversal and axial motions of two beams with a joint

In this paper we develop and analyze a mathematical model for combined axial and transverse motions of two Euler-Bernoulli beams coupled through a joint composed of two rigid bodies. The motivation for this problem comes from the need to accurately model damping and joints for the next generation of inflatable/rigidizable space structures. We assume Kelvin-Voigt damping in the two beams whose motions are coupled through a joint which includes an internal moment. The resulting equations of motion consist of four, second-order in time, partial differential equations, four second-order ordinary differential equations, and certain compatibility boundary conditions. The system is re-cast as an abstract second-order differential equation in an appropriate Hilbert space, consisting of function spaces describing the distributed beam deflections, and a finite-dimensional space that projects important features at the joint boundary. Semigroup theory is used to prove the system is well posed, and that with positive damping parameters the resulting semigroup is analytic and exponentially stable. The spectrum of the infinitesimal generator is characterized.     

Translated Brownian Motions and Associated Wick Products

Abstract

The concept of Wick product is strongly related to the underlying Brownian motion we have fixed on the probability space. Via the Girsanov's theorem we construct a family of new Brownian motions, obtained as translations of the original one, and to each of them we associate a Wick product. This produces a family of Wick products, named γ-Wick products, parameterized by the performed translations. We aim to describe this family of products. We also define a new family of stochastic integrals, which are related in a natural way to the γ-Wick products.     

Dynamic stability of a porous rectangular plate

The study is devoted to a axial compressed porous-cellular rectangular plate. Mechanical properties of the plate vary across is its thickness which is defined by the non-linear function with dimensionless variable and coefficient of porosity. The material model used in the current paper is as described by Magnucki, Stasiewicz papers. The middle plane of the plate is the symmetry plane. First of all, a displacement field of any cross section of the plane was defined. The geometric and physical (according to Hook's law) relationships are linear. Afterwards, the components of strain and stress states in the plate were found. The Hamilton's principle to the problem of dynamic stability is used. This principle was allowed to formulate a system of five differential equations of dynamic stability of the plate satisfying boundary conditions. This basic system of differential equations was approximately solved with the use of Galerkin's method. The forms of unknown functions were assumed and the system of equations was reduced to a single ordinary differential equation of motion. The critical load determined used numerically processed was solved. Results of solution shown in the Figures for a family of isotropic porous-cellular plates. The effect of porosity on the critical loads is presented. In the particular case of a rectangular plate made of an isotropic homogeneous material, the elasticity coefficients do not depend on the coordinate (thickness direction), giving a classical plate. The results obtained for porous plates are compared to a homogeneous isotropic rectangular plate. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Head Seas Travelling Along a Horizontal Cylinder

Consider a wave train of arbitrary wavelength travelling withoutchange of form along a partially immersed fixed horizontal cylinder,the wave crests being normal to the generators of the cylinder.It is supposed that the cylinder is symmetrical about its longitudinalmid-plane, and that the wave motion is also symmetrical aboutthis plane. At a distance from the cylinder the motion is supposedto approximate to the incident wave train. This wave motionis a limiting form of the motion near a long ship in head seas.It is the purpose of the present work to show that under theusual assumptions of linearized wave theory there can be nosuch wave motion. In other words, according to the linearizedtheory a head sea must deform as it travels along a horizontalcylinder. (The proof fails for those wavelengths, if any, forwhich the Fredholm determinant of a certain integral equationvanishes. There is as yet no general uniqueness theory withoutsuch a limitation.) To illustrate this conclusion a particular problem is treated,corresponding to a head sea travelling along a wall which isslightly inclined to the vertical along part of its length andis exactly vertical elsewhere. For this case the progressivedeformation can be calculated.