Rigid Disk Research Articles

Investigation of the interaction between a viscous incompressible fluid layer and walls of a channel formed by coaxial vibrating discs

The interaction between a viscous incompressible fluid layer and walls of a channel formed by two concentric discs moving perpendicularly to their planes due to vibration of the base on which the channel is mounted is investigated. The case of two absolutely rigid discs with elastic suspension and the case in which one of the discs is an elastic plate with the rigid restrain on the edges are considered. The velocity and pressure distributions over the fluid and the laws of motion of the walls and their frequency characteristics which make it possible to determine the resonance vibration frequencies of the mechanical system considered are found.

Haemodynamic effects of negative pressure wound therapy when using a rigid barrier to prevent heart rupture

Right ventricular heart rupture is a devastating complication associated with negative pressure wound therapy (NPWT) in cardiac surgery. The use of a rigid barrier has been suggested to offer protection against this lethal complication by preventing the heart from being drawn up and damaged by the sharp sternum bone edges. The aim of this study was to investigate the haemodynamic effects of placing a rigid barrier over the heart to protect it from rupture during NPWT. Eight pigs underwent median sternotomy followed by NPWT at --70 and --120 mmHg, using foam, with or without a rigid plastic disc between the heart and the sternal edges. The heart frequency, cardiac output, mean systemic arterial pressure, mean pulmonary artery pressure, central venous pressure and left atrial pressure were recorded. Cardiac output was not affected by NPWT, regardless of whether a rigid barrier was used. Heart frequency decreased during NPWT without a disc, and showed a tendency towards a decrease when using a rigid disc. The blood pressure decreased during NPWT without a disc, and showed only a tendency towards a decrease when a disc was inserted between the heart and the sternum. In conclusion, the results of this haemodynamic study show that a rigid disc can safely be placed over the heart during NPWT, to prevent heart rupture. The haemodynamic effects of NPWT in sternotomy wounds are slightly reduced by the presence of the rigid disc.

The influence on wound contraction and fluid evacuation of a rigid disc inserted to protect exposed organs during negative pressure wound therapy

The use of a rigid disc as a barrier between the wound bed and the wound filler during negative pressure wound therapy (NPWT) has been suggested to prevent damage to exposed organs. However, it is important to determine that the effects of NPWT, such as wound contraction and fluid removal, are maintained during treatment despite the use of a barrier. This study was performed to examine the effect of NPWT on wound contraction and fluid evacuation in the presence of a rigid disc. Peripheral wounds were created on the backs of eight pigs. The wounds were filled with foam, and rigid discs of different designs were inserted between the wound bed and the foam. Wound contraction and fluid evacuation were measured after application of continuous NPWT at -80 mmHg. Wound contraction was similar in the presence and the absence of a rigid disc (84 ± 4% and 83 ± 3%, respectively, compared with baseline). Furthermore, the rigid disc did not affect wound fluid removal compared with ordinary NPWT (e.g. after 120 seconds, 71 ± 4 ml was removed in the presence and 73 ± 3 ml was removed in the absence of a disc). This study shows that a rigid barrier may be placed under the wound filler to protect exposed structures during NPWT without affecting wound contraction and fluid removal, which are two crucial features of NPWT.

Disk model for wheels moving over highway bridges with rough surfaces

In most previous analyses of vehicle–bridge interaction (VBI) problems in highways involving surface roughness, the wheels of vehicles have been treated as points, referred to as the point model, and the tracks as a series of hills and valleys. The point model is unrealistic for wheels, as they are of finite size and cannot touch the bottom of valleys. In this study, each wheel will be modeled instead as a rigid disk of finite size, referred to as the disk model, neglecting the tire deformations. The VBI element will be modified accordingly for computing the vehicle and bridge responses. Numerical examples are prepared to illustrate the effect of wheel size on the dynamic responses of the bridge and passing vehicles. It is concluded that the point model tends to introduce some unrealistic high-frequency vibrations on the system responses, while underestimating the amplitude of vehicle frequency in the vehicle response. The disk model should be adopted, if the velocity and acceleration responses of the bridge and the dynamic responses of the moving vehicle are of major concern.

Sternum wound contraction and distension during negative pressure wound therapy when using a rigid disc to prevent heart and lung rupture

BackgroundThere are increasing reports of deaths and serious complications associated with the use of negative pressure wound therapy (NPWT), of which right ventricular heart rupture is the most devastating. The use of a rigid barrier has been suggested to offer protection against this lethal complication by preventing the heart from being drawn up against the sharp edges of the sternum. The aim of the present study was to determine whether a rigid barrier can be safely inserted over the heart with regard to the sternum wound edge movement.MethodsSternotomy wounds were created in eight pigs. The wounds were treated with NPWT at -40, -70, -120 and -170 mmHg in the presence and absence of a rigid barrier between the heart and the edges of the sternum. Wound contraction upon NPWT application, and wound distension under mechanical traction to draw apart the edges of the sternotomy were evaluated.ResultsWound contraction resulting from NPWT was similar with and without the rigid barrier. When mechanical traction was applied to a NPWT treated sternum wound, the sternal edges were pulled apart. Wound distension upon traction was similar in the presence and absence of a the rigid barrier during NPWT.ConclusionsA rigid barrier can safely be inserted between the heart and the edges of the sternum to protect the heart and lungs from rupture during NPWT. The sternum wound edge is stabilized equally well with as without the rigid barrier during NPWT.

Analytical Solution for the Consolidation around a Laterally Loaded Pile

This paper presents a closed-form analytical solution for the consolidation of soil around a laterally loaded pile, assuming the soil skeleton deforms elastically and under plane strain conditions. The problem is idealized as a circular rigid disk surrounded by a deformable soil zone. Drainage is assumed to occur at the boundary of the assumed zone of deformable soil around the pile. The response around the pile is obtained using an uncoupled consolidation analysis. The solution for the governing equation of excess pore water pressure is found by using the separation of variables technique. Expressions for the initial excess pore water pressure distribution are derived from the mean total stress changes given by the elastic solution. Curves showing decay of the excess pore water pressure with time, and also the variation of pile displacement, are plotted in nondimensional form. The parameters that affect the displacement prediction are illustrated and discussed. Comparison with three-dimensional analysis of a laterally loaded pile shows that the two-dimensional analysis can reasonably predict the consolidation process along the shaft of the pile.

The Motion of a Fluid–Rigid Disc System at the Zero Limit of the Rigid Disc Radius

We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier-Stokes equations and the motion of the rigid body by conservation laws of linear and angular momentum. We show that, assuming that the rigid disc is not allowed to rotate, as the radius of the disc goes to zero, the solution of this system converges, in an appropriate sense, to the solution of the Navier-Stokes equations describing the motion of only fluid in the whole plane. We also prove that the trajectory of the centre of the disc, at the zero limit of its radius, coincides with a fluid particle trajectory.

BioVyon Protein A, an alternative solid-phase affinity matrix for chromatin immunoprecipitation

Chromatin immunoprecipitation (ChIP) is an important technique in the study of DNA/protein interactions. The ChIP procedure, however, has limitations in that it is lengthy, can be inconsistent, and is prone to nonspecific binding of DNA and proteins to the bead-based solid-phase matrices that are often used for the immunoprecipitation step. In this investigation, we examined the utility of a new matrix for ChIP assays, BioVyon Protein A, a solid support based on porous polyethylene. In ChIP experiments carried out using two antibodies and seven DNA loci, the performance of BioVyon Protein A was significantly better, with a greater percentage of DNA pull-down in all of the assays tested compared with bead-based matrices, Protein A Sepharose, and Dynabeads Protein A. Furthermore, the rigid porous disc format within a column made the BioVyon matrix much easier to use with fewer steps and less equipment requirements, resulting in a significant reduction in the time taken to process the ChIP samples. In summary, BioVyon Protein A provides a column-based assay method for ChIP and other immunoprecipitation-based procedures; the rigid porous structure of BioVyon enables a fast and robust protocol with higher ChIP enrichment ratios.

Dynamic Modeling and Analysis of the Large-Scale Rotary Machine with Multi-Supporting

The large-scale rotary machine with multi-supporting, such as rotary kiln and rope laying machine, is the key equipment in the architectural, chemistry, and agriculture industries. The body, rollers, wheels, and bearings constitute a chain multibody system. Axis line deflection is a vital parameter to determine mechanics state of rotary machine, thus body axial vibration needs to be studied for dynamic monitoring and adjusting of rotary machine. By using the Riccati transfer matrix method, the body system of rotary machine is divided into many subsystems composed of three elements, namely, rigid disk, elastic shaft, and linear spring. Multiple wheel-bearing structures are simplified as springs. The transfer matrices of the body system and overall transfer equation are developed, as well as the response overall motion equation. Taken a rotary kiln as an instance, natural frequencies, modal shape, and response vibration with certain exciting axis line deflection are obtained by numerical computing. The body vibration modal curves illustrate the cause of dynamical errors in the common axis line measurement methods. The displacement response can be used for further measurement dynamical error analysis and compensation. The response overall motion equation could be applied to predict the body motion under abnormal mechanics condition, and provide theory guidance for machine failure diagnosis.

A Simplified Method for Seismic Analysis of Tanks with Floating Roof by using Finite Element Method: Case Study of Kharg (Southern Iran) Island Tanks

Tanks with floating roof have shown high vulnerability subjected to past earthquakes, such as Kobe, and Izmit. The main cause of damage is believed to be the interaction between the floating roof and the tank wall. In this paper a simplified method is presented for modeling the floating roof and its interaction with the tank wall, making it possible to use Finite Element Analysis (FEA) for calculating the seismic response of tank-floating roof system. In the proposed method, assuming that the sloshing phenomenon is mainly suppressed by the floating roof, the seal between the roof and the tank's wall is modeled by introducing some radial pre-compressed ‘only-compression elements’ all around the roof, itself substituted by a rigid disk, and the tank's wall is modeled by 3-dimensional shell elements. The dynamic effect of the impounded oil in the tank is taken into account by the use of added mass concept. If during the time history analysis the maximum relative displacement between the roof disk and the tank's wall in any radial direction exceeds the initial length of the pre-compressed only-compression springs the tank is considered to be vulnerable. The proposed method has been applied to a tank sample in Kharg (southern Iran) island.

Dynamic Modeling and Analysis of the Large-Scale Rotary Machine with Multi-Supporting

The large-scale rotary machine with multi-supporting, such as rotary kiln and rope laying machine, is the key equipment in the architectural, chemistry, and agriculture industri es. The body, rollers, wheels, and bearings constitute a chain multibody system. Axis line deflection is a vital parameter to determin e mechanics state of rotary machine, thus body axial vibration needs to be studied for dynamic monitoring and adjusting of rotary machine. By using the Riccati transfer matrix method, the body system of rotary machine is divided into many subsystems composed of three elements, namely, rigid disk, elastic shaft, and linear spring. Multiple wheel-bearing structures are simplified as springs. The transfer matrices of the body system an d overall transfer equation are developed, as well as the response overall motion equation. Taken a rotary kiln as an instance, natural frequencies, modal shape, and response vibration with certain exciting axis line deflection are obtained by numerical c omputing. The body vibration modal curves illustrate the cause of dynamical errors in the common axis line measurement methods. The displacement response can be used for further measurement dynamical error analysis and compensation. The response overall motion equation could be applied to predict the body motion under abnormal mechanics condition, and provide theory guidance for machine failure diagnosis.

回転・伸展を伴う異方性構造物の動的挙動・安定領域解析に関する研究

This study is to propose a useful simple method in the case of initial design for analyzing beam — like anisotropy structures with rotation and/or extension. The anisotropic beam like structure with rotation and extension is modeled as following simplified structures; the mass-less beam which can only change length over time, and the rigid disk which can only change weight according to the length of beam. Using this model, the equation of motion is formulated to consider bending, extension and rotation. In this formulation, the follower force by inertia during extension is also considered. The stable region and the equation of motion are given which describe the dynamic behavior of beam's tip. To evaluate the validity of the numerical simulation results, the experimental apparatus is developed, which can change the length of anisotropic beams during rotation, and the displacement of beam's tip motion are measured. By the comparison of the displacement of beam's tip from rotation center, the analytical results become bigger than the experimental ones just after the extension. That displacement difference just after extension depends on the quantification of the eccentricity, which value changes correspond to the length. But considering about the internal damping, the simulation results get the qualitative tendency of the dynamic behavior of during extension and after extension.

Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

A lagrangian formulation is presented for the total dynamic stiffness and damping matrices of a rigid rotor carrying noncentral rigid disk and supported on angular contact ball bearings (ACBBs). The bearing dynamic stiffness/damping marix is derived in terms of the bearing motions (displacements/rotations) and then the principal of virtual work is used to transfer it from the bearing location to the rotor mass center to obtain the total dynamic stiffness/damping matrix. The bearing analyses take into account the bearing nonlinearities, cage rotation and bearing axial preload. The coefficients of these time-dependent matrices are presented analytically. The equations of motion of a rigid rotor-ACBBs assembly are derived using Lagrange's equation. The proposed analyses on deriving the bearing stiffness matrix are verified against existing bearing analyses of SKF researchers that, in turn, were verified using both SKF softwares/experiments and we obtained typical agreements. The presented total stiffness matrix is applied to a typical grinding machine spindle studied experimentally by other researchers and excellent agreements are obtained between our analytical eigenvalues and the experimental ones. The effect of using the total full stiffness matrix versus using the total diagonal stiffness matrix on the natural frequencies and dynamic response of the rigid rotor-bearings system is studied. It is found that using the diagonal matrix affects natural frequencies values (except the axial frequency) and response amplitudes and pattern and causes important vibration tones to be missig from the response spectrum. Therefore it is recommended to use the full total stiffness matrix and not the diagonal matrix in the design/vibration analysis of these rotating machines. For a machine spindle-ACBBs assembly under mass unbalnce and a horizontal force at the spindle cutting nose when the bearing time-varying stiffness matrix (bearing cage rotation is considered) is used, the peak-to-valley variation in time domain of the stiffness matrix elements becomes significant compared to its counterpart when the bearing standard stiffness matrix (bearing cage rotation is neglected) is used. The vibration spectrum of the time-varying matrix case is marked by tones at bearing outer ring ball passing frequency, rotating unbalnce frequency and combination compared to spectrum of the standard stiffness matrix case which is marked by only the rotating unbalnce frequency. Therfore, it is highly recomended to model bearing stiffness matrix to be a time-dependent.

Analytical study of the dynamic behavior of geometrically nonlinear shaft-disk rotor systems

This paper explores analytically the nonlinear dynamic behavior of rotors. Coupled nonlinear equations of motion are formulated using Hamilton’s principle. The rotor model is composed of a rigid disk and a flexible shaft which is characterized as a beam of circular cross section. Various influences are taken into account like the effect of higher order large deformations, rotary inertia, gyroscopic effect, rotor unbalance and the effect of a dynamic axial force. Forced response due to a mass unbalance is presented first for the linear analysis and then perturbation techniques are used to solve the complete equations of motion including nonlinear terms. Method of multiple scales is applied to examine the nonlinear behaviour of the rotor system. Resonant curves are plotted for different possible resonance conditions. It is concluded that the higher order large deformations and axial force acting dynamically on the rotor have a significant effect on its nonlinear response. This response varies for different parameters of the rotor like an unbalance mass and diameter of the shaft.

Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

A lagrangian formulation is presented for the total dynamic stiffness and damping matrices of a rigid rotor carrying noncentral rigid disk and supported on angular contact ball bearings (ACBBs). The bearing dynamic stiffness/damping marix is derived in terms of the bearing motions (displacements/rotations) and then the principal of virtual work is used to transfer it from the bearing location to the rotor mass center to obtain the total dynamic stiffness/damping matrix. The bearing analyses take into account the bearing nonlinearities, cage rotation and bearing axial preload. The coefficients of these time-dependent matrices are presented analytically. The equations of motion of a rigid rotor-ACBBs assembly are derived using Lagrange's equation. The proposed analyses on deriving the bearing stiffness matrix are verified against existing bearing analyses of SKF researchers that, in turn, were verified using both SKF softwares/experiments and we obtained typical agreements. The presented total stiffness matrix is applied to a typical grinding machine spindle studied experimentally by other researchers and excellent agreements are obtained between our analytical eigenvalues and the experimental ones. The effect of using the total full stiffness matrix versus using the total diagonal stiffness matrix on the natural frequencies and dynamic response of the rigid rotor-bearings system is studied. It is found that using the diagonal matrix affects natural frequencies values (except the axial frequency) and response amplitudes and pattern and causes important vibration tones to be missig from the response spectrum. Therefore it is recommended to use the full total stiffness matrix and not the diagonal matrix in the design/vibration analysis of these rotating machines. For a machine spindle-ACBBs assembly under mass unbalnce and a horizontal force at the spindle cutting nose when the bearing time-varying stiffness matrix (bearing cage rotation is considered) is used, the peak-to-valley variation in time domain of the stiffness matrix elements becomes significant compared to its counterpart when the bearing standard stiffness matrix (bearing cage rotation is neglected) is used. The vibration spectrum of the time-varying matrix case is marked by tones at bearing outer ring ball passing frequency, rotating unbalnce frequency and combination compared to spectrum of the standard stiffness matrix case which is marked by only the rotating unbalnce frequency. Therfore, it is highly recomended to model bearing stiffness matrix to be a time-dependent.

Lanx Corporation

Lanx was the first manufacturer of vacuum-deposited rigid disks. The technology was based on a Co–Cr perpendicular magnetic recording medium that was compatible with commercially available ferrite ring heads. Performance data for the Lanx perpendicular disk, a description of the manufacturing equipment and some comments on the times are given.

Движение плоских твердых дисков в поле тяжести, соударяющихся с гладкой горизонтальной плоскостью

Движение плоских твердых дисков в поле тяжести, соударяющихся с гладкой горизонтальной плоскостью

Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

A mathematical model incorporating the higher order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. The rotor system considered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (deformation) energies of the rotor system are derived and the Rayleigh–Ritz method is used to discretize these energy expressions. Hamilton’s principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed.

Contact with break-off under bending of an elastic strip with a rigid disk

We consider the problem of the theory of elasticity of the contact interaction of a rigid circular disk and an elastic strip, which rests upon two supports with disturbance of contact in the middle part of the contact region. On the basis of the Wiener–Hopf method, an integral equation of the problem is reduced to an infinite system of algebraic equations. The size of the zone of break-off of the boundary of the strip from the disk and the distribution of contact stresses are determined.

Rocking vibration of a rigid circular disc in a transversely isotropic full‐space

AbstractIn this paper, forced rocking vibration of a rigid circular disc placed in a transversely isotropic full‐space, where the axis of material symmetry of the full‐space is normal to the surface of the plate, is analytically investigated. Because of using the Fourier series and Hankel integral transforms, the mixed boundary‐value problem is transformed into two separate pairs of integral equations called dual integral equations. The dual integral equations involved in this paper are reduced to Fredholm integral equations of the second kind. With the aid of contour integration, the governing integral equation is numerically evaluated in the general dynamic case. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure and the static impedance/compliance function are explicitly determined, and it is shown that the pressure in between the plate and the full‐space and the compliance function reduced for isotropic half‐space are identical to the previously published solutions. The dynamic contact pressure in between the disc and the space and also the related impedance function are numerically evaluated in general dynamic case and illustrated. It is shown that the singularity exists in the contact pressure at the edge of the disc is the same as the static case. To show the effect of material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared. Copyright © 2010 John Wiley & Sons, Ltd.