Constant Angular Speed Research Articles

Elastic analysis of rotating functionally graded polar orthotropic disks

This paper investigates an elastic problem of rotating functionally graded hollow polar orthotropic circular disks. Emphasis is placed on the influence of orthotropy and gradient on the elastic field in particular the hoop stress distribution in hollow annular plates rotating at constant angular speed about its axis. For the gradient of power-law profile, we obtain explicit expressions for the elastic field. For arbitrarily variable gradient, we present a method for transforming the problem into solving a Fredholm integral equation. Numerical results are presented for two particular cases: free boundaries and clamped-free boundaries. A comparison of numerical results with exact ones for power-law material properties is made, indicating the effectiveness of our proposed method. For material properties varying in any way according to the Voigt rule, numerical results are presented to show the effects of gradient parameter and orthotropy degree on the distribution of elastic field.

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angular speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form velocity equations. Making use of this solution, analytical formulas for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condition of suction or injection imposed on the wall.

Investigation of Vibration Mitigation of Flexibly Support Rigid Rotors Equipped with Controlled Elements

Abstract The subject of investigations presented in this article is achieving the optimum attenuation of lateral vibration of rotors by means of two design variants of constraint elements: semiactive magnetorheological squeeze film dampers and actively controlled hydrodynamic bearings. The damping effect of magnetorheological dampers is controlled by the change of magnetic flux generated in electric coils and of the hydrodynamic bearings by the change of magnitude of the proportional gain of a feedback controller exciting movement of the bearing housings. In the developed mathematical models the rotor is considered as absolutely rigid and the controllable constraint elements are represented by force couplings. The rotor turns at constant angular speed, is loaded by its weight and in addition it is excited by a centrifugal force caused by the disc unbalance. In both design cases its lateral vibration is governed by a nonlinear equation of motion. The pressure distribution in the lubricating film in the magnetorheological squeeze film damper is described by a Reynolds equation modified for Bingham fluid whose yield shear stress depends on magnetic induction. The hydraulic forces acting in the hydrodynamic bearings are determined for the case of π-film cavitation and position of the bearing housings is adjusted by actuators activated by a proportional feedback controller. The aim of the analysis is to deal with approaches leading to minimizing amplitude of the rotor steady state vibration and magnitude of the force transmitted into the rotor casing and to compare efficiency of both design variants. The performed computer simulations show that the arrangement with the magnetorheological squeeze film damper gives better results in reducing magnitude of the transmitted force than those when the rotor is supported by hydrodynamic bearings with actively controlled position of the bearing housings.

Computing Center Conditions for Non-analytic Vector Fields with Constant Angular Speed

Computing Center Conditions for Non-analytic Vector Fields with Constant Angular Speed

Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

Vibration Analysis of a Rotating Disk with a Crack

This paper studies the vibrational behaviour of a rotating disk with a radially or circumferentially oriented crack. The disk rotates with a constant angular speed. To treat this problem, the finite element method is employed. The disk is discretised into finite elements, and the crack is considered as nonpropagating and always open. The solutions to this problem's governing equations yield the natural frequencies and mode shapes. The frequency response due to dynamic loading is also yielded to determine the crack's effect on the frequency domain. For both crack orientations, parametric studies are conducted to investigate the sensitivity of the vibrational behaviour to the disk's angular speed and radial crack length or circumferential crack angle and distance from the disk's centre. The accuracy of the results is validated through comparisons with results available from the literature.

Zero-g Simulation of Space Manipulator in Furled Status

The zero-g simulation device is designed by using suspender spring and counter weight,and the static gravity compensation formulas of space manipulator's detached body are deduced with gravity compensation theory.Based on the least minimum square theory,an optimization program of suspension force is developed,through which the optimization of multiple torques is transformed into the optimization of a whole target,and the numerical value of each suspension force can be obtained.The model of the zero-g simulation device of space manipulator is built in ADAMS when the length of suspender spring is 1 000 mm.Under the condition that the space manipulator is in stationary state,the relative errors between the optimization results and the simulation results are around 10%.And the bending torque and counter torque generated by the zero-g simulation device can meet the technical requirements when each joint of space manipulator moves at the constant angular speed of 0.5°/s and 1°/s.Therefore,this approach is suitable for zero-g simulation of space manipulator.

Stability of motion of a particle with variable constraints

A mechanical system represented by a particle moving over an arbitrary surface that rotates about a vertical axis with constant angular speed is considered. Sufficient conditions for the parametric asymptotic stability of this system are established

How to twirl a hula hoop

We consider the twirling of a hula hoop when the waist of a gymnast moves along an elliptical trajectory close to a circle. For a circular trajectory, two families of exact solutions are obtained, corresponding to twirling of the hula hoop with a constant angular speed equal to the speed of the excitation. We show that one family of solutions is stable, and the other one is unstable. These exact solutions allow us to obtain approximate solutions for a slightly elliptical trajectory of the waist. We demonstrate that to twirl a hula hoop the waist needs to rotate with a phase difference between π/2 and π. An interesting effect of inverse twirling is described when the waist moves in a direction opposite to the hula hoop rotation. The approximate analytical solutions are compared with the results of a numerical calculation.

SU‐E‐T‐433: VMAT Arc Delivery with Gantry Acceleration Constraints

Purpose: To evaluate the impact of gantry acceleration on the VMAT arc therapy delivery. Methods and Materials: The rapid delivery of VMAT arc therapy requires fast motion of the gantry around the patient. The difficulty is that the large inertia of the accelerator gantry limits rotation speed changes restricting the ability of the accelerator to arc as fast as possible without violating the integrity of the plan (plan delivery requires preserving mutual relations between gantry speed, MLC leaves speeds and beam dose rate). This work examines arc therapy deliveries for static and moving target in presence of acceleration limitation for gantry angular speed. We compute the shortest time of arc therapy delivery, provided different acceleration limitations are imposed. The problem of arc delivery to moving target is a complex optimal control due to dependence of motion constraints on the state of the evolution. As may be expected more stringent limits on the acceleration lead to longer delivery time and the successive decrease of the mechanical strain on the gantry rotation mechanism. Results. The static prostate VMAT arc treatment investigated sets the acceleration limitations for gantry speed from 2deg/sec2 to 1.5deg/sec2 to 1.0deg/sec2 to 0.5deg /dsec2 to 0.0deg sec2. For subsequent deliveries the optimal time of therapy delivery increases appropriately from a just above 1 minute to above 3 minutes. Conclusions. The ultimate limitation imposed on the acceleration of the gantry (constant gantry speed delivery) leads to approximately threefold increase in most efficient delivery times for the example. This time increase is accompanied, by complete removal of mechanical stress on the system of the gantry motion. The constant gantry angular speed delivery is not realistically achievable for moving target when the motion is measured in real time if the planned dose delivery integrity is to be preserved.

A computational investigation on the reducing lateral vibration of rotors with rolling-element bearings passing through critical speeds by means of tuning the stiffness of the system supports

Since there are manufacturing and assembling inaccuracies rotors are always slightly imbalanced. Their rapid angular acceleration leads to an increase in the magnitude of the tangential component of the imbalance forces. The slow acceleration enables the development of an almost steady state vibration. In both cases the amplitude of their oscillation is high. The frequency tuning achieved by changing the stiffness of the rotor supports represents one approach to its attenuation. Stiffness decreases shortly before reaching the critical speed, and after crossover, the stiffness increases again. As almost all publications and computer procedures from the field of rotor dynamics deal only with the case when the rotor turns at a constant angular speed, derivation of the equations of motion of the rotor rotating at variable velocities and investigation of the operating conditions and individual parameters of the supports on the vibration of the rotor passing critical speeds represent the fully new contribution of this paper. The critical revolutions are determined from the Campbell diagram. To solve the equations of motion the Newmark method has been proposed and tested.

Exact Solutions for the Incompressible Viscous Fluid of a Rotating Disk Flow

The present paper is devoted to a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a disk rotating with a constant angular speed. In place of the traditional von Karman's axisymmetric evolution of the flow, the rotational non-axisymmetric stationary flow is taken into account here. As a consequence, the governing equations allow an exact solution to develop over the disk, which is influenced by a fixed point on the disk and also bounded everywhere in the normal direction to the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions, which differ from those of corresponding to the classical von Karman's flow. Making use of this solution, analytical formulas for the wall shear stresses are extracted. The critical peripheral locations at which extrema of the local skin friction occur are also determined. Analytic calculations show that for the specific flow the thicknesses take the same value. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. According to the Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, which is proportional to product of the thermal conduction, Reynolds number and temperature difference. Key Words: Exact Solution; Rotating-Disk Flow; Shear Stresses; Heat Transfer

A Computational Investigation of the Disk-Housing Impacts of Accelerating Rotors Supported by Hydrodynamic Bearings

As the radial clearance between disks and the casing of rotating machines is usually very narrow, excessive lateral vibration of accelerating rotors passing critical speeds can produce impacts between the disks and the housing. The computer modeling method is an important tool for investigating such events. In the developed procedure, the shaft is flexible and the disks are absolutely rigid. The hydrodynamic bearings and the impacts are implemented in the mathematical model by means of nonlinear force couplings. Most of the publications and computer codes from the field of rotor dynamics are referred only in the case when the rotor turns at a constant angular speed and in simple cases of disk-housing impacts. Moreover, if the disks turning at variable speed are investigated, the resulting form of the equations of motion derived by different authors slightly differs and the differences depend on the method used for their derivation. Therefore, particular emphasis in this article is given to the derivation of the motion equations of a continuous rotor turning with variable revolutions to explain the mentioned differences, to develop a computer algorithm enabling the investigation of cases when impacts between an arbitrary number of disks and the stationary part take place, and to analyze the mutual interaction between the impacts and the fluid film bearings. The Hertz theory is applied to determine the contact forces. Calculation of the hydrodynamic forces acting on the bearings is based on solving the Reynolds equation and taking cavitation into account. Lagrange equations of the second kind and the principle of virtual work are used to derive equations of motion. The Runge–Kutta method with an adaptive time step is applied for their solution. The applicability of the developed procedure was tested by computer simulations. The results show that it can be used for the modeling of complex rotor systems and that the short computational time enables carrying out calculations for a number of design and operation parameters.

Revolving movement of a dynamic cluster of actin filaments during mitosis

The actin cytoskeleton undergoes rapid changes in its architecture during mitosis. Here, we demonstrate novel actin assembly dynamics in M phase. An amorphous cluster of actin filaments appears during prometaphase, revolves horizontally along the cell cortex at a constant angular speed, and fuses into the contractile ring after three to four revolutions. Cdk1 activity is required for the formation of this mitotic actin cluster and its revolving movement. Rapid turnover of actin in the filaments takes place everywhere in the cluster and is also required for its cluster rotation during mitosis. Knockdown of Arp3, a component of the actin filament-nucleating Arp2/3 complex, inhibits the formation of the mitotic actin cluster without affecting other actin structures. These results identify Arp2/3 complex as a key factor in the generation of the dynamic actin cluster during mitosis.

RETRACTED: Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating disk flow

Abstract The main interest of the present investigation is to generate exact solutions to the steady Navier–Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion due to a disk rotating with a constant angular speed. For an external uniform magnetic field applied perpendicular to the plane of the disk, the governing equations allow an exact solution to develop taking into account of the rotational non-axisymmetric stationary conducting flow. Making use of the analytic solution, exact formulas for the angular velocity components as well as for the wall shear stresses are extracted. It is proved analytically that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. According to Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, though decreases for small magnetic fields because of the dominance of Joule heating, it eventually increases for growing magnetic field parameters.

Fundamental properties of the delivery of volumetric modulated arc therapy (VMAT) to static patient anatomy

The primary goal of this article is to formulate volumetric modulated arc therapy (VMAT) delivery problem and study interdependence between several parameters (beam dose rate, gantry angular speed, and MLC leaf speed) in the delivery of VMAT treatment plan. The secondary aim is to provide delivery solution and prove optimality (minimal beam on time) of the solution. An additional goal of this study is to investigate alternative delivery approaches to VMAT (like constant beam dose rate and constant gantry angular speed delivery). The problem of the VMAT delivery is formulated as a control problem with machine constraints. The relationships between parameters of arc therapy delivery are derived under the constraint of treatment plan invariance and limitations on delivery parameters. The nonuniqueness of arc therapy delivery solutions is revealed from these relations. The most efficient delivery of arc therapy is then formulated as optimal control problem and solved by geometrical methods. A computer program is developed to find numerical solutions for deliveries of specific VMAT plan. Explicit examples of VMAT plan deliveries are computed and illustrated with graphical representations of the variability of delivery parameters. Comparison of delivery parameters with that of Varian's delivery are shown and discussed. Alternative delivery strategies such as constant gantry angular speed delivery and constant beam dose rate delivery are formulated and solutions are provided. The treatment times for all the delivery solutions are provided. The investigations derive and prove time optimal VMAT deliveries. The relationships between delivery parameters are determined. The optimal alternative delivery strategies are discussed.

Flows and Their Stability in Rotating Cylinders With a Porous Lining

Flow fields in an annulus between two rotating cylinders with a porous lining have been numerically examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The effects of porous sleeve thickness and its properties on the flows and their stability in the annulus are numerically investigated. Three-dimensional momentum equations for the porous and fluid layers are formulated separately and solved simultaneously in terms of velocity and vorticity. The solutions have covered a wide range of the governing parameters (10−5≤Da≤10−2, 2000≤Ta≤5000, 0.8≤b¯≤0.95). The results obtained show that the presence of a porous sleeve generally has a stabilizing effect on the flows in the annulus.

Non-uniform temperature gradients and thermal stresses produced by a moving heat flux applied on a hollow sphere

This work presents numerical analyses of transient temperature and thermally-induced stress distributions in a hollow steel sphere heated by a moving uniform heat source applied on a certain zenithal segment (the heated zenithal segment, Θ H ) of its outer surface (the processed surface) under stagnant ambient conditions. Along the process, the moving heat source (MHS) moves angularly from the first zenithal segment to the last zenithal segment on the processed surface with a constant angular speed, ω, and then returns backward to the first zenithal segment with the same speed. It is assumed that the inner surface is heat-isolated and that the outer surface except the heated segment is under stagnant ambient conditions. The numerical calculations are performed individually for a wide range of thermal conductivity, λ, of steel and for the different Θ H s. The maximum effective thermal stress ratio calculated as per the heat flux intensity (q 0) can be reduced in considerable amounts. By increasing λ(∼75%) and ω(∼63%) the maximum effective thermal stress ratio calculated can be significantly reduced.

A CFD approach for modeling the rime-ice accretion process on a horizontal-axis wind turbine

The main objective of this paper is to model the rime-ice accretion process on a horizontal-axis wind turbine (HAWT) operating under icing conditions. The model calculation procedure was divided into two stages. The first stage consists of computing the two-phase flow that is composed of air and water phases. The two-phase flow was solved using the Eulerian–Eulerian approach with the help of Fluent, a commercial CFD code. At the end of the calculations, it is possible to obtain the local volume fraction and local water incidence velocity, which can be used to estimate the local collision coefficient. In the second stage, the thickness of the newly accreted ice layer was calculated and the geometry so obtained was processed with an in-house smoothing algorithm. From the model simulation, it is possible to obtain the 3-D ice shape, as well as the ice load on the HAWT blade, which can then be used to analyze the performance of the HAWT under icing conditions, or to help develop a feasible de-icing solution. The important model input parameters include: air speed, median volume diameter (MVD) of water droplets, liquid water content (LWC) and air temperature. The turbine under consideration is a NREL VI turbine that rotates along its axis at a constant angular speed. In the flow domain, a rotating reference frame was defined to account for the angular movement of the wind turbine. The results reveal, among other things, ice geometry information that can otherwise hardly be obtained by on-site observations.

Irregular spin angular momentum transfer from light to small birefringent particles

The transfer of spin angular momentum from photons to small particles is a key experiment of quantum physics. The particles rotate clockwise or counterclockwise depending on the polarization of the light beam which holds them in an optical trap. We show that even perfectly disk shaped particles will in general not rotate with a constant angular speed. The particles will periodically accelerate and decelerate their rotational motion due to a varying spin angular momentum transfer from the light. Using the Poincar\'e sphere we derive the equation of motion of a birefringent plate and verify the results by measuring the time dependent rotation of small crystals of $\text{Hg}(\text{I})$ iodide and 3,4,9,10-perylene-tetracarboxylic-dianhydride (PTCDA) in the trap of polarized optical tweezers. For small ellipticities of the polarized light in the tweezers the plate stops in a fixed orientation relative to the axes of the light ellipse. We discuss the origin of this halt and propose an application of small birefringent plates as self-adjusting optical retarders in micro-optics.