Center Of Curvature Research Articles

Discrete Dynamics of Balls in Cageless Ball Bearings

Cageless ball bearings are often preferred as a back-up bearing for active magnetic bearings to support a falling rotor, but the contact between the balls of the cageless ball bearing may lead to the deterioration of the bearing performance and affect the dynamic stability of the rotor system. Thus, we studied the discrete dynamics of cageless ball bearings. First, a model is proposed to change the groove curvature center of the local outer raceway to control the ball velocity to achieve dispersion. Combined with the spatial geometry theory, the mathematical model of the discrete raceway is established, the collision between the balls is considered as an abruptly added constraint, and the non-smooth dynamics equation of the cageless ball bearing with a local discrete raceway is established. Then, the fourth-order Adams prediction correction algorithm is used to numerically solve the dynamic discretization of the ball, and the structural parameters of the discrete raceway are preferably selected, according to the phase diagram of the ball and the change in the angular spacing. The results show that the structure of the discrete raceway has a strong influence on the discrete dynamics of the ball.

Sectional Model Wind Tunnel Test and Research on the Wind-Induced Vibration Response of a Curved Beam Unilateral Stayed Bridge

The linear curve distribution of the beam and the asymmetrical layout of the stay cables may have beneficial or adverse influences on cable-stayed bridges. Sectional model wind tunnel tests and numerical simulations were used to analyze the influence of these two factors on the wind-induced vibration characteristics of a curved beam unilateral stayed bridges (CBUSB) and the interaction between its stay cables and curved beams. According to the basic similarity law, the sectional models of a CBUSB example were designed and manufactured. The aerodynamic force and wind-induced vibration of the models were measured in an atmospheric boundary wind tunnel laboratory to obtain the aerodynamic coefficient and displacement, respectively. Based on the wind tunnel test results, the verified finite element model was used to determine the displacement, acceleration, and cable tension of the CBUSB excited by the buffeting force under 5 curvature cases and 4 cable layout cases. Then, band-pass filter technology and fast Fourier transform technology were used to analyze the influence of these two parameters on the wind-induced vibration characteristics of the CBUSB. Results show that the CBUSB had good aerodynamic stability in the wind tunnel at low and high wind speeds. With increasing curvature, the high-order modal vibration and modal coupling vibration of the CBUSB may be generated. The frequency, the proportion of wind-induced vibration response components, and the distribution characteristics of spectrum energy of CBUSB will be affected by 4 cable layout schemes. Cables arranged on both sides of the bridge and near the center of curvature can improve pedestrian comfort and reduce wind-induced vibration, respectively. Affected by the interaction between cable and bridge, the cable and bridge transmit their own vibration to each other, both of which contain the response components of each other.

Radial and Tangential Retinal Magnifications as Functions of Visual Field Angle Across Spherical, Oblate, and Prolate Retinal Profiles.

PurposeTo provide a tool for calculating radial and tangential retinal magnifications as functions of field angle and retinal shape and to articulate patterns of magnification across the retina for monocular and binocular combinations of prolate-, oblate-, and spherical-shaped retinas.MethodsFormulae were derived to calculate radial and tangential retinal magnifications (mm/deg) from field angle (degrees), retinal asphericity (unitless conic constant), retinal vertex radius of curvature (mm), and nodal point position (mm). Monocular retinal magnifications were determined for eyes with prolate, spherical, and oblate retinas as functions of field angle. Bilateral differences in magnifications were examined for combinations of those eyes.ResultsRetinal shape substantially affects magnification profiles even for eyes with the same axial length. Greatest magnification changes across a retina and between eyes, as well as greatest increase in radial–tangential differences (distortion), occur with prolate retinas. Binocular magnification differences were smallest for oblate retinas. Nodal points anterior to the vertex center of curvature and oblate asphericity both cause field-dependent reductions in magnification relative to the fovea (barrel distortion), whereas nodal points posterior to vertex center of curvature and prolate asphericity cause the opposite (pincushion distortion). Retinal magnification differences due to eye shape are much greater than aniseikonia thresholds and chromatic differences in magnification. A spreadsheet tool implements the magnification calculations.ConclusionsLocal retinal magnifications as functions of field angle have substantial effects on objective applications (imaging retinal anatomy) and subjective experiences (aniseikonia) and quantify an ocular property that differs across eye shapes and refractive errors.Translational RelevanceMethods are provided to customize the calculation of radial and tangential magnifications across the retina for individual eyes, which will bolster the multifactorial study of the effects of foveal and peripheral optics across eye shapes and refractive errors.

Area law for magnetic domain walls in bent cylindrical nanowires

The dynamics of several systems in nature occurs under some constraints and symmetries that ensure the appearance of constants of motion. In this work, we discuss the dynamics of the magnetic domain wall (DW) under the Walker regime (i.e., when its position oscillates as a function of time) in bent cylindrical magnetic nanowires (NWs) with constant curvatures. It is shown that the DW position sweeps, in relation to the curvature center, the same area for different NW curvatures. This phenomenon appears due to an exchange-driven curvature-induced interaction. The translational DW motion is accompanied by its rotation around the NW axis, leading to a periodic curvature-independent angular momentum, from which one obtains an area's law for the DW motion.

Spatiotemporal Identification of Cell Divisions Using Symmetry Properties in Time-Lapse Phase Contrast Microscopy

A variety of biological and pharmaceutical studies, such as for anti-cancer drugs, require the quantification of cell responses over long periods of time. This is performed with time-lapse video microscopy that gives a long sequence of frames. For this purpose, phase contrast imaging is commonly used since it is minimally invasive. The cell responses of interest in this study are the mitotic cell divisions. Their manual measurements are tedious, subjective, and restrictive. This study introduces an automated method for these measurements. The method starts with preprocessing for restoration and reconstruction of the phase contrast time-lapse sequences. The data are first restored from intensity non-uniformities. Subsequently, the circular symmetry of the contour of the mitotic cells in phase contrast images is used by applying a Circle Hough Transform (CHT) to reconstruct the entire cells. The CHT is also enhanced with the ability to “vote” exclusively towards the center of curvature. The CHT image sequence is then registered for misplacements between successive frames. The sequence is subsequently processed to detect cell centroids in individual frames and use them as starting points to form spatiotemporal trajectories of cells along the positive as well as along the negative time directions, that is, anti-causally. The connectivities of different trajectories enhanced by the symmetry of the trajectories of the daughter cells provide as topological by-products the events of cell divisions together with the corresponding entries into mitoses as well as exits from cytokineses. The experiments use several experimental video sequences from three different cell lines with many cells undergoing mitoses and divisions. The quantitative validations of the results of the processing demonstrate the high performance and efficiency of the method.

Effect of Mutual Interference of Bridge Piers on Scouring in Meandering Channel

Local scour is the reduction of original bed level around any hydraulicstructure. Bridge failure due to scouring has made researchers study thecause of scouring and predict the scour depth and pattern around bridgepiers and foundations. Several investigators have extensively studiedlocal scour around isolated bridge pier, but modern designs of the bridgescomprise of wide span and thus group of piers rather than a single pier. Theflow and scour pattern around group of piers are different from the case of asingle pier due to the interaction effect. The objective of present study is toinvestigate the effect of mutual interference of bridge piers on local scourexperimentally around two piers in non-cohesive bed. Experiments werecarried out on model bridge piers of circular cross section in a meanderingchannel. It was observed that when front and rear piers were placed at anangular displacement of θ = 40° and 80° respectively, maximum depth ofscour is maximum. Here θ is the angle the line drawn at the inlet of bend tothe line joining the centre of curvature and any point on the outer portion ofthe bend.

A note on determination of center of disk-cam curvature

A note on determination of center of disk-cam curvature

Structural optimization of ball bearings with three-point contact at high-speed

Three-point contact state is a common state for four-point contact ball bearings (FPCBB), significantly improving the performance in high-speed and light-load conditions. However, in this case, the internal contact state is in a dynamic transition between two-point and three-point contact, with substantial frictional losses. To this end, a nonlinear dynamic model of FPCBB, considering the lubrication traction and the bearing assemblies’ dynamic features, is proposed to optimize the FPCBB's performance for three-point contact state. The dynamic changes of contact states under high-speed and light-load conditions are revealed, and four sets of conditions are picked as optimization conditions. Beside, groove curvature coefficient and curvature center eccentricity, depending on outer ring structure, are selected as optimized structural parameters. On this basis, the behavior performance in three-point contact state is optimized for specific operating conditions. The results show that with the gradual growth of eccentricity, the bearing fatigue life first extends slowly and then reduces rapidly, where an optimum value exists; for bearings possibly serving in skidding condition, it is better to prefer a larger eccentricity or a smaller curvature coefficient to reduce sliding damage.

Point diffraction interferometer based on a silicon nitride waveguide spherical wave source.

A point diffraction interferometer based on silicon nitride waveguide (WG-PDI), adopting a silicon nitride waveguide spherical wave source (WG-SWS) with Si substrate and SiO2 cladding, is proposed for spherical surface testing. The WG-SWS is used to overcome the drawbacks of the existing spherical wave sources, which can generate high accuracy and high numerical aperture spherical reference wave. In this paper, the theory of the WG-PDI is described, and the possible errors introduced by the device are analyzed. In addition, the lateral deviation between the curvature center of the test wave and the curvature center of the reference wave cannot be eliminated in the reflected configuration of the pinhole diffraction interferometer. After analyzing the influence of the systematic error introduced by the lateral deviation, the semi-reflective film was coated on the output facet of the waveguide spherical wave source to realize point diffraction interference without lateral deviation. Finally, the surface error of a spherical surface was measured by WG-PDI. The experimental results agree well with those measured by the ZYGO interferometer.

Magnetic proximity induced valley-contrasting quantum anomalous Hall effect in a graphene- CrBr3 van der Waals heterostructure

The magnetic proximity effect is an imperative tool to comprehend the valley contrasting quantum anomalous Hall (QAH) effect in van der Waals (vdW) heterostructure. The introduction of magnetic exchange and spin orbit interaction together enables to realize topological phases, with a particular emphasis on an interface can be envisioned towards dissipationless electronics. Herein, the proximity coupled valley contrasting QAH effect is predicted in vdW heterostructure consisting of graphene and a ferromagnetic (FM) semiconductor ${\mathrm{CrBr}}_{3}$ with the implication of relativistic effect, from the ab initio density functional theory (DFT) simulation. The valley contrasting QAH effect is observed with a nonzero Chern number at a high-symmetry point stemming from Berry curvature and Wannier charge center (WCC), leading to a topologically nontrivial state. The occurrence of strong magnetic proximity coupling between graphene and ${\mathrm{CrBr}}_{3}$ monolayer is realized intrinsically, from shifting of Hall coefficient value near Fermi level. The opening of the global band gap (178 meV) is observed with the inclusion of spin orbit coupling (SOC). The anomalous Hall conductivity (AHC) demonstrates the presence of two maxima peaked at valley ${K}^{\ensuremath{'}}$ and $K$. The observation of AHC is mainly dominated by nonzero surface charge and localized potential at the heterointerface due to proximity interaction. The Fermi level is found to be located exactly inside the nontrivial global band gap, which can be tuned effectively by applying the external electric field or by introducing a staggered sublattice potential. This robustness makes experimental fabrication highly favorable for developing a valley contrasting QAH device prototype.

Steerable drops on heated concentric microgroove arrays

Guided drop transport is of great importance in various water and thermal management technologies. Unidirectional drop transport on a hot surface has been widely developed, but a bidirectional reversal is still challenging. Here, we report a steerable transport of drop impinging on heated concentric microgroove arrays, on which the directionality of drop transport is dictated by the drop boiling modes. In the transition boiling state, the driving force originated from the Laplace pressure difference rendered by the microgrooves, which enables the drop rebounding towards the center of curvature. While in the film boiling state, a net force towards the opposite side is generated between the grooves and the penetrated liquid, that drives the drop far away from the center of curvature. Our experimental and theoretical results uncover that the lateral displacement is controlled by both the Weber number and off-center distance. These findings strengthen our fundamental understanding of drop impact dynamics at high temperatures and are essential for effective cooling of hot-spot cores and drop sieving.

Vector spherical harmonic analysis and experimental validation of spherical shells illuminated with broadband, millimeter wave Gaussian beams: applications to corneal sensing.

Coupling to longitudinal modes of thin spherical shells, under Gaussian-beam illumination, was explored with a theoretical method based on Fourier-optics analysis and vector spherical harmonics and was scrutinized with an experimental setup. For the theory part, the illumination frequency band was fixed between 100-600 GHz and the outer spherical shell radius of curvature and thickness are 7.5 mm and 0.5 mm, respectively. The shell material was either the lossless cornea or an aqueous effective media representing the cornea. Six different beam-target strategies were introduced being potential candidates for maximum coupling. Two dispersion-tuned beam ensembles with strongly frequency-dependent phase center location have been created with a fixed incident beam 1/e radius and radius of curvature called forward strategies. These computations of different alignments were continued with four beam ensembles of frequency-invariant phase center, constructed from fits to experimental data, oriented at four different axial locations with respect to the spherical shell center of curvature, they are called reverse strategies. Coupling efficiency for all strategies was calculated for different targets including perfect electrical conductor (PEC) sphere, PEC core covered by a cornea loss-free layer and cornea. All scattering strategies contrasted to scattering from equivalent planar targets as a reference with maximum coupling. The results show that, under an ideal calibration, forward strategies are a closer approximation to the plane-wave condition for the cornea. An experimental setup was assembled to explore the simulation approach in a frequency range between 220 GHz to 330 GHz. Two different quartz samples with permittivity of 4.1 were mounted on a water core, acting for a cornea. The first and second quartz radius and thickness were 7.5 mm and 0.5 mm and 8 mm and 1 mm, respectively. An adequate agreement between theory and experiment was confirmed. A particle optimisation swarm algorithm was applied to extract the thickness and permittivity of quartz from the measured back-scattered field for reverse strategies.

Effect of NaOCl and EDTA irrigating solutions on the cyclic fatigue resistance of EdgeTaper Platinum instruments

BackgroundTo compare the solution on the cyclic fatigue resistance of EdgeTaper Platinum (ETP) instruments with that of ProTaper Gold (PTG) in the presence of ethylenediaminetetraacetic acid (EDTA) or sodium hypochlorite (NaOCl) irrigating solutions.MethodsSixty PTG and 60 ETP instruments with the same size (#25) and taper (8%) were tested under 17% EDTA, 5.25% NaOCl, or distilled water (n = 20 each). Cyclic fatigue was tested using artificial canals that were milled in stainless steel blocks using a laser micromachining technique. The canals had a curvature angle of 60 and a curvature radius of 5 mm. The center of maximum curvature was set at 5 mm from the instrument tip. The block of artificial canals was stabilized inside a container that was filled with one of the tested solutions. The temperature was fixed at 37 °C with a tolerance limit of 1 °C. The number of cycles to fracture (NCF) was calculated and the fractured surfaces were examined using a scanning electron microscope. All statistical analyses were performed using SPSS software Version 20 (IBM-SPSS Inc., Chicago, IL) at a confidence level of 95%.ResultsETP showed higher NCF than PTG in any of the tested solutions (P < 0.05). Within each group, NaOCl drastically decreased the NCF compared to water and EDTA (P < 0.05) and changing the solution from distilled water to EDTA did not affect the fatigue resistance (P > 0.05).ConclusionsETP showed improved cyclic fatigue performance compared to PTG in all tested irrigating solutions. EDTA can be used in combination with NiTi instruments during canal instrumentation without compromising the cyclic fatigue resistance of PTG and ETP instruments. However, NaOCl drastically decreased the NCF.

A novel method to correct the bias of curvilinear light stripe center

Light stripe center extraction is an important operation for the line-structured light measurement system. Common methods use Gaussian kernels to smooth the image before extracting, but it changes the grayscale distribution of curvilinear light stripe, which causes the bias towards the center of curvature. A novel method is proposed to correct the bias of curvilinear light stripe center. The method involves two steps: first, the new images similar in nature to the linear light stripe are formed by the gray values of the light stripe center before correction and its surrounding pixels. Second, the first derivative zero-crossing detection is applied to the new images to obtain the corrected center points. Simulations and experiments show that the bias of curvilinear light stripe center caused by the Gaussian smoothing can be effectively corrected by this method.

Effects of Locations of Spur Dyke on Bed and Scour around Bridge Piers in Meandering Channel

Spur dykes are the structures which are used to protect the eroding bank of rivers. They are sometimes also used to safeguard the life of many structures such as bridge piers, abutments etc. The efficiency of spur dykes has been checked in straight channels by conducting model tests in laboratories by many investigators. Very few studies were done in curved channels. In present work an attempt has been made to study the effect of location of spur dyke on bed and scour around bridge pier in curved open channel (bend angle = 80o ) with time. Experiment has been carried out in 80o channel bend at constant discharge (3.5×10–3 m3 /s) and bridge pier is located at angular displacement ϴ = 60o . Here ϴ is the angle the line drawn at the inlet of any bend to the line joining the centre of curvature and any point on the outer portion of the bend. It is found that maximum scouring occurs at ϴ = 0o and 20o along inner wall and at ϴ = 60o and 80o along outer wall. It is also found that scouring around bridge pier is more in the vicinity of pier and decreases with increase in distance from pier. The most suitable location for spur dyke to protect bridge pier is at angular displacement ϴ = 20o . Scour developed rapidly during initial time and then rate of scouring decreases with elapse of time.

A dynamic approach for evaluating the moment rigidity and rotation precision of a bearing-planetary frame rotor system used in RV reducer

The rotating vector reducer (RV reducer) is widely used in joint transmission of industrial robots. The moment rigidity and rotation precision of the non-standard angular contact ball bearings-planetary frame rotor system (BPFRS) in the RV reducer have a significant impact on the service performance of industrial robots. This paper presents an improved dynamic model to study the moment rigidity and rotation precision of the BPFRS. The proposed model optimizes the theoretical method for calculating balls-races contact deflection and contact angle, which can more precisely describe the locus of the inner race groove curvature center. Furthermore, a moment rigidity test experiment is designed to verify the accuracy of the proposed model. On the basis, effects of different load conditions, axial preload displacement, numbers of balls, and combinations of inner and outer race groove curvature radius coefficients on moment rigidity and rotation precision of the BPFRS are analyzed, respectively. The results show that these factors have a significant effect on moment rigidity and rotation precision. Besides, dynamic characteristics of the spatial rotation trajectory of the reducer center are obtained.

Free vibration analysis of a circular cylindrical shell using a new four-variable refined shell theory

A theory is proposed to study the vibrations of homogenous isotropic circular cylindrical shells based on a developed plate vibration theory. By proposing a novel distribution of the shear stress and strain across the thickness of the shell, the arguments are adjusted such that the transverse shear strains and stresses equal zero at the shell surfaces. Due to the existing curvature in the circumferential direction, the defined shear stress and strain distributions consider a change in the position of the neutral plane toward the center of curvature. In the presented Two-Separated Lateral Displacement (TSLD) theory, the lateral displacement is defined by two bending and shear parts to provide an analytical model, referred to as the four-variable refined plate theory. The similarity to classical theory and involving only four unknowns are significant features of the introduced theory. The TSLD theory is verified against the available data in the literature. It is shown that the provided stress and stress distributions lead to more accurate results, especially in moderately thick cylinders. The proposed theory is remarkably more precise than classical shell theory and First-order Shear Deformation Theory (FSDT). Results of the TSLD theory are as accurate as the Higher-Order Shear Deformation Theory (HOST12) for the higher frequency parameters and more thick shells, while the TSLD theory implementation is much simpler than the HOST12.

Experiment on fluid regime under different rotate velocity in physical simulation of titanium vertical centrifugal casting

In this paper, the physical simulation of filling process of vertical centrifugal casting (VCC) of complex titanium alloy casting was studied. Combined with the mature PTV particle tracking technology, the high-speed photography pictures of the filling process of VCC at different rotational speeds were obtained. The trajectory and velocity information of tracer particles in the rotating flow field were obtained by the corresponding analysis software. Then, through the analysis and modeling of quantitative experimental data, the flow behavior characteristics and movement law of titanium alloy melt in the mold cavity under different mold speeds were studied. The results show that: 1. When the mold is still, the front edge of the filling fluid forms a curved surface with the curvature center pointing to the outside of the mold; when the mold rotates, the front edge of the liquid flow forms a curved surface with the curvature center pointing to the inside of the mold; 2. With the increase of the mold rotation speed, the speed of the fluid filling the mold increases significantly; when the rotational speed is greater than 120 rpm, the fluid still has a certain driving force in the mold center far away from the gate; it is good for filling the inner corner of mold with fluid; and 3. When the rotational speed of centrifugal casting of titanium alloy reaches 45 rpm or above, typical turbulent vortices appear in the wake; with the increase of rotating speed to 180 rpm, the average curvature radius of turbulent vortices first increases and then decreases, and reaches the minimum value of 0.67 cm at 120 rpm.

Dynamics analysis on the coordination of velocity and accuracy in baseball pitching.

Speed and accuracy are both critical to sports performance but remains poorly understood. In baseball pitching, both ball speed and accuracy must be constrained by human body and ball dynamics. This study examines the dynamics of pitching control ability that coordinates ball speed and control using the center of curvature of trajectories of ball and shoulder joint. Dynamics analysis based on a variable-length pendulum model with the center of curvature of the ball and shoulder joint trajectories reveals that the control of shoulder acceleration affects the coordination of ball speed and pitch control.

Effects of Rotation on Transient Fluid Flow and Heat Transfer Through a Curved Square Duct: The Case of Negative Rotation

The fluid flow and heat transfer through a rotating curved duct has received much attention in recent years because of vast applications in mechanical devices. It is noticed that there occur two different types of rotations in a rotating curved duct such as positive and negative rotation. The positive rotation through the curved duct is widely investigated while the investigation on the negative rotation is rarely available. The paper investigates the influence of negative rotation for a wide range of Taylor number (&lt;i&gt;−10 ≤ Tr ≤ −2500&lt;/i&gt;) when the duct itself rotates about the center of curvature. Due to the rotation, three types of forces including Coriolis, centrifugal, and buoyancy forces are generated. The study focuses and explains the combined effect of these forces on the fluid flow in details. First, the linear stability of the steady solution is performed. An unsteady solution is then obtained by time-evolution calculation and flow transition is determined by calculating phase space and power spectrum. When &lt;i&gt;Tr&lt;/i&gt; is raised in the negative direction, the flow behavior shows different flow instabilities including steady-state, periodic, multi-periodic, and chaotic oscillations. Furthermore, the pattern variations of axial and secondary flow velocity and isotherms are obtained, and it is found that there is a strong interaction between the flow velocities and the isotherms. Then temperature gradients are calculated which show that the fluid mixing and the acts of secondary flow have a strong influence on heat transfer in the fluid. Diagrams of unsteady flow and vortex structure are further sketched and precisely elucidate the curvature effects on unsteady fluid flow. Finally, a comparison between the numerical and experimental data is discussed which demonstrates that both data coincide with each other.