Constant Angular Speed Research Articles

Stability of the forced vibrational motion of a vehicular body supported by rubber shear mountings with quadratic response

The stability of the harmonic solution of the forced Duffing equation governing the relative motion of a load on an inclined plate rotating at a constant angular speed about an arbitrary axis is studied. The load is supported by two identical simple shear springs made of a quadratic rubber-like material. It is found that the stability of motion about the center points is governed by the solutions of Hill's equation with three parameter. For certain values of the design parameters, Hill's equation reduces to the Mathieu equation and stability of the motion is studied following the standard procedure. In the general case, an intermediate bifurcation of the response amplitude occurs for motions about the negative center points. It is shown that the position of the center of mass of the load with respect to the plate center in the undisturbed state affects the nature of the response to a great extent. Without extensive analysis, the stability of motion in the general case is predicted for a specific range of the values of the angular speed of the plate.

Some numerical experiments with a linearized model of a synchronous machine with rectifier

After changing a recently developed model of a synchronous machine with diode rectifier into a model of a synchronous machine with controllable thyristor rectifier, the new model is linearized. Fisrt, this linearized model is used to investigate the dynamic behaviour of the synchronous machine with rectifier rotating at a constant angular speed, with special attention to the influence of parameter deviations on the behaviour of the machine with a diode rectifier. Next, after introducing a simple model of a wind turbine, the dynamic behaviour of a wind turbine equipped with a synchronous machine with rectifier is considered.

Finite Element Analysis of Freely Rotating Tires

Abstract Axisymmetric analysis of an inflated tire rotating with constant angular speed can be used to simulate two loading conditions of a tire during its service life: (1) a freely rotating tire on an automobile that is stuck in snow or mud and (2) the top region of a rolling loaded tire, where footprint loading has little influence on the distribution of its stresses and strains. The equations of motion for a freely rotating deformable body with constant angular speed have been derived and implemented into a finite element code developed in-house. The rotation of a thin disk was used to check the validity of the implemented formulation and coding. Excellent agreement between the numerical and the analytical results was obtained. A cast tire, a radial automobile tire, and a radial truck tire, were then analyzed by the new finite element procedure. The tires were inflated and rotated at speeds up to 241 km/h (150 mph). The elastomers in these tires were simulated by incompressible elements for which the nonlinear mechanical properties were described by the Mooney-Rivlin model. Each ply was simulated by its equivalent orthotropic material model. The finite element predictions agreed well with the available experimental measurements. Significant changes in interply shear strain at the belt edge, the bead load, and the crown cord loads of plies were observed in the finite element analysis. These phenomena suggest three possible failure modes in freely rotating tires, i.e. belt edge separation, bead breakage, and belt failure at crown region.

Frictional heat generated in the early stages of an orbital friction welding process

In all types of friction welding the joining process is started by the generation at the rubbing interface of frictional heat arising from the relative motion of the components. In one form of orbital friction welding the two components to be joined are rotated about their longitudinal axes in the same sense with the same constant angular speed: the two longitudinal axes being parallel but offset by a small distance. The interfacial rubbing velocity so created is particularly simple and in this paper a general expression for the rate of heat generation at the rubbing interface during the early stages of the orbital friction welding process is presented. The particular cases of a pair of rods of circular cross-section and two rods of square cross-section are considered in some detail.

Confined Flow in a Partially-Filled Rotating Horizontal Cylinder

Experimental and analytical studies are reported for a Newtonian fluid in a partially-filled cylinder rotating about its centerline axis at constant angular speeds. Two fluids, glycerin and water, are used in this study. The analytical results are in good agreement with the experimental data. This comparison is based on the profiles of the free surfaces and the streamlines experimentally obtained using a flow visualization technique and as predicted by the analytical model. When the rotational speed is not high enough to cause solid body rotation of the fluid, due to excessive centrifugal force, a recirculation region forms at the lower portion of the cylinder. The profile of the free surface in this region depends on the relative magnitude of the body force and the viscous force. In general, two distinct flow regions can be recognized for a cylinder of infinite extent; a recirculating flow and a boundary-layer-type flow along the cylindrical wall. In addition to the volume of the fluid in the cylinder, there are two other parameters governing this problem; the Reynolds number and the ratio, G, of the Reynolds number to the Froude number.

Vortex shedding in rotating flows

Abstract A rotating tow facility whose principle element is a long acrylic channel of rectangular cross-section has been developed. A smooth flexible belt, which can be translated along the channel axis, serves as a false horizontal floor. The system is mounted on a turntable which rotates at a constant angular speed about a vertical axis. The working fluid is bounded above by a sheet of acrylic plastic which can be tilted to simulate the beta effect. Topographic features are mounted on the belt and the flow past these obstacles is made visible by utilizing the electrolytic precipitation technique and recorded by a video tape camera system which translates with the belt. A series of fplane experiments on the flow past a right circular cylinder extending from the belt to the upper bounding surface is investigated in the Reynolds number range 65 < Re < 2,300. It is shown that rotation and the cylinder aspect ratio have a strong influence on the resulting flow characteristics including the Strouhal number. F...

Boundary-layer transition on a rotating cone in still fluid

A linear stability analysis and experiments were carried out for the laminar–turbulent transition of three-dimensional incompressible boundary layers induced on the surface of a cone rotating around the axis of symmetry with constant angular speed in still fluid. Five cones having total angle of 30°–150° were tested. The results show that the critical and transition Reynolds numbers, the direction of spiral vortices appearing in the transition region and their number on a cone increase as the cone angle is increased, and they tend to the values for the case of a rotating disk. Flow visualizations were made for the transitional process and also for cross-sectional flows of spiral vortices.

Stability and vibrations of spinning tubes subjected to uniform radial pressure

The theory of small motions superposed on large, elastic, static deformations is used to investigate the stability and small vibrations of circular cylindrical tubes of arbitrary wall thickness. The tube is assumed to rotate about its axis with constant angular speed and be simultaneously subjected to a uniform radial pressure. The material of the tube is of Mooney-Rivlin type which is elastic, isotropic, homogeneous and incompressible. The effect of angular speed on the frequency of small vibrations and the buckling pressure is illustrated with several examples.

Biomechanical measurement of spastic plantarflexors.

A study was conducted to determine the feasibility of quantifying spasticity in plantarflexors by measuring the resistance to passive dorsiflexion of the ankle joint at several constant angular speeds. Repeated testing was conducted on normal subjects and spastic patients. Good repeatability was found for both groups and both groups were found to differ significantly from each other with respect to the measurement variable. The method will provide a useful tool for quantifying alterations in plantarflexor spasticity which result from various surgical and non-surgical treatments.

How to place a Knudsen source to obtain optimal uniformity of film thickness on a spherical substrate holder

Knudsen sources are placed in na offset position on the surface of the same sphere on which the substates are located. Geometric positions for uniform film thickness are shown, i.e. favourable places for locating a thickness monitor. It is demostrated that if the sphere rotates on its diameter parallel to the axis of symmetry of the Knudsen source with constant angular speed the film thickness at any point of the surface of the sphere (over the source) is identical after each complete turn. This leads to a simple relation between film thickness and quantity of material evaporated. Some considerations are given to the design of planetary systems.

Motility of basal fragments of sea urchin sperm flagella.

Both live and reactivated sea urchin sperm flagella were broken by passage through a pipette. Distal fragments stopped, but basal fragments continued to beat. Intact flagella were about 48 micrometer long; basal fragments were about 4-20 micrometer long. Beat periods of tritonated fragments were 11% shorter than those of unbroken controls, possibly reflecting decreased viscous loading; beat periods of live fragments were 18% shorter than those of unbroken controls, possibly reflecting reduced rates of ATP consumption as well as decreased viscous loading. The undulations of basal fragments were compared with those of the basal regions of unbroken flagella, using the patterns of development of the radii and angles of basal bends. Fragments closely resembled basal regions of unbroken flagella, except that bends tended to open as they approached the distal end of a fragment, so that their radii increased more rapidly than those unbroken flagella. Fragments about 4 micrometer long contained only one bend during part of the cycle, and appeared to be straight during part of the cycle. They flipped back and forth with fairly constant angular speeds and abrupt changes in direction, so that plots of angle between their distal end and base often resembled triangular waves, although the peaks of the waveforms were often rounded. This behaviour suggests a mechanism in which sliding switches between 2 modes. Both the speed of sliding and the maximum angles attained in one direction of bending were greater than those attained in the other direction, suggesting differences between the doublets on the 2 sides of the axoneme. Sliding of the doublets continued as fast speeds as the fragments straightened, in contrast to the characteristics of some curvature-sensitive models. These flagellar fragments provide a simplified system for the study of flagellar oscillations.

Linear Stability Theory of Boundary Layer along a Cone Rotating in Axial Flow

A linear stability theory is treated for an incompressible laminar boundary layer along a cone rotating about its axis of symmetry with a constant angular speed in an external forced flow field. Small perturbations are assumed to be of spiral vortices. This leads to one set of perturbation equations including an order of magnitude (δ1/R0), where δ1 denotes a displacement thickness of the boundary layer, calculated from a velocity component in the meridional section, and R0 is a local radius of the cone at instability. A numerical procedure for solving the eigenvalue problem is shown. As an example, calculations are carried out for a cone having a total included angle of 30° at a rotating speed ratio 3, where the rotating speed ratio is defined as the ratio of the circumferential velocity at the cone surface to the external flow velocity at the outer edge of the boundary layer. From stability diagrams obtained herein, critical Reynolds number, spiral angle and the associated eigenvalues are determined. The critical Reynolds number is compared with an experiment.

Creep Analysis of Orthotropic Rotating Cylinder

The stress and strain-rate distributions in the wall of a hollow thick-walled circular cylinder, rotating about its own axis with a constant angular speed, have been obtained using Norton’s law for the steady-state creep. The cylinder is assumed to be made of a homogeneous and orthotropic material. The numerical computations, for a number of steels and steel alloys commonly used to manufacture the cylinder, have been carried out for three cases of anisotropy. The effect of anistropy and of exponent n in creep law has been studied. It is observed that the stress and strain-rate distributions are significantly affected by the anisotropy of material and the value of exponent n. It is also noticed that the values of the effective stress for an anisotropic material for which the ratios of axial to tangential strain rate and of radial to tangential strain rate are equal to 1.2, are lower than the corresponding values for an isotropic material for which these ratios are 1.0. And, because of a power law between effective strain rate and effective stress, much lower values of the effective strain rate for the foregoing anisotropic material than those for the isotropic material will be obtained. Thus the use of the aforementioned anisotropic material may be beneficial for the manufacture of the cylinders because (i) it will result in a longer life for the cylinders (because of the lowest strain rate), or (ii) it will allow the cylinder to sustain larger forces without a risk of failure under creep.

Dynamic response of an annular disk to a moving concentrated, in-plane edge load

In-plane dynamic behaviour of a thin annular disk with a clamped inner boundary is analyzed. The frequencies of free in-plane vibration with a free outer boundary are first evaluated, by using Lamé potentials, for various radius ratios ranging from 0.2 to 0.8. The steady state dynamic stresses induced by a concentrated load moving at a constant angular speed at the outer boundary are then evaluated through a Galilean transformation. Results are presented for a radius ratio of 0.5.

Bifurcation and Stability of Convective Flows in a Rotating or not Rotating Spherical Shell

In this paper bifurcation theory and group theoretical methods are applied to the analysis of the stationary convection of a fluid filling a spherical shell which is rotating (or not rotating) about an axis with a constant angular speed. In the case with rotation, an analytical relation is found between the Rayleigh number and the Taylor number, for which a transcritical branch of stationary and axisymmetric (about the axis of rotation) solutions occur. At fixed Taylor number, these solutions are stable supercritically. When the shell doesn’t rotate, a two-parameter family of axisymmetric solutions is found to bifurcate supercritically, these solutions being deduced one from the other by a simple rotation. Under an assumption on the sign of a certain coefficient, these solutions are “orbitally stable.”

The problem of the rotating plate

The problem of determining stresses and displacements in a homogeneous rectangular plate rotating at constant angular speed about the barycentric axis, perpendicular to the plane of the plate, is considered. It is shown that this problem, if one assumes that the material is linear elastic with Poisson's ratio v, exhibits the same mathematical difficulties as the well-known problem of the rectangular plate subjected to parabolically-distributed tensile stress at two opposite sides.

O 4-covariant Hamiltonian formalism for bounded motion in a central field of force

For every bounded trajectory of a particle in an arbitrary central field of force a uniformly rotating reference frame may be chosen in which this trajectory becomes closed. This circumstance makes it meaningful to introduce a nonconserving analog of the Runge-Lenz-Laplace vectorA called the «precession vector» here and to build theSO4 Poisson-bracket algebra with it. The corresponding hidden symmetry is minimally broken in the sense that the vectorA keeps its length constant and rotates with constant angular speed. In the present paper the phase space of the bounded motions in the 3-dimensional central problem is canonically mapped into a product of two three-dimensional spheres in a four-dimensional space each, and theSO4 acts linearly by rotations on them. The Hamiltonian formalism in this curved phase manifold is obtained. The particle moves with a constant speed along a diametral circle, this circle precessing with a constant angular speed.

The torque on a rotating disk in the surface of a liquid with an adsorbed film

In this paper we consider the problem of calculating the resistive torque on a disk rotating slowly with constant angular speed in the surface of a liquid with an adsorbed surface film. Using the method of complementary representations for generalised axially symmetric potential functions, the boundary-value problem for the azimuthal velocity component is reduced to the solution of a Fredholm integral equation of the second kind. This equation is solved numerically and asymptotically for all values of the ratio of the surface shear viscosity of the film to the viscosity of the substrate fluid, and values calculated for the substrate and film torques on the disk. The results are compared with previous work of Goodrich and his co-workers.

Spatial frequency effect on the pulfrich stereophenomenon

The results of two experiments are reported. In the first it was found that the magnitude of the Pulfrich phenomenon is dependent upon the spatial frequency of the moving stimulus pattern: the greater the spatial frequency for a constant filter density and angular speed, the greater the apparent displacement in depth. In the second study, the magnitude of the Pulfrich effect was found to decrease with increasing angular width of moving single stripes up to an angular width of 27°. The data were interpreted as consistent with the view that for the Pulfrich effect the retinal disparity between the moving stimulus and the fixated stationary stimulus is not given by the retinal points actually stimulated at any instant in time, but rather by the registered rate of motion of the stimulus.

Instabilities of an Asymmetric Rotor With Asymmetric Shaft Mounted on Symmetric Elastic Supports

Instabilities of an asymmetric rotor with asymmetric shaft mounted on symmetric elastic supports are considered. The periodic coefficients which appear in the system equations are eliminated by transformation to a rotating coordinate system rotating at the constant angular speed of the rotor. The unstable speed regions are identified by studying the nature of the roots of the characteristic equation. The combined effects of the inertia and shaft asymmetry and the flexible supports are appreciated by representative numerical examples. The results are presented in three-dimensional diagrams to show how the asymmetry parameters affect the unstable speed regions for known values of support stiffness.