Angular Velocity Ratio Research Articles

Closed form analytical solution and scan pattern shaping theory of three-element Risley prism for LiDAR systems

Three-element Risley prism are emerging technologies in LiDAR. It can convert the FoV into a rectangular shape with high coverage rates in specific conditions, making it suitable for applications in autonomous driving scenarios. The addition of a third prism has been proven effective in eliminating blind spots and singularity problems. One challenge facing the use of three-element scanners in autonomous driving is the accurate positioning control of light beams during high-speed motion, especially in specific scan patterns such as near rectangles. This work introduces a closed-form analytical solution and parameters for the scan patterns of the three-element scanner through a non-paraxial tracing method. The closed-form solution includes two groups of coefficients representing all possible configurations of the three-element scanner. The parameters consist of ten degrees of freedom: angular velocity ratio, M1, M2, deflection angle ratio, k1, k1, initial phases, θ0q(q=1,2,3), distance between the two prisms dair1, dair2, and distance from the screen, P. To our knowledge, this is the first study to discuss these degrees of freedom in the context of the closed-form solution. We obtain its scan patterns by MATLAB 2019a and explore a configuration of three-element Risley prism in near-rectangular scan patterns, achieving a wide FoV and high point cloud density while avoiding blind spots and singularity issues. To validate the simulation results, a three-element Risley prism scanner system based on brushless motor is developed. Our study suggests that the three-element rotating prism scanner holds potential superiority in forward-looking LiDAR solutions.

Influence of heat source/sink on a rotating cone in a rotating nanofluid with magnetic field impact: Application of Hosoya polynomial‐based collocation method

AbstractThe present analysis considers the angular velocities of the free flow and the arbitrarily fluctuating cone over time, leading to an unsteady stream over a rotating cone in a rotating nanofluid. The effects of heat source/sink and magnetic field on an unsteady flow past a rotating cone in a rotating nanoliquid are considered in this examination. The dimensional governing equations are transformed into nondimensional ordinary differential equations (ODEs) using the similarity variables. The nonlinear system of ODEs has been solved using the Hosoya polynomial‐based collocation method (HPBCM), and the obtained values are compared with the numerical method Runge Kutta Fehlberg's fourth‐fifth order (RKF‐45) scheme. The effects of numerous factors on the momentum and thermal distributions are shown graphically. Results reveal that the ratio of the cone angular velocity to the free stream angular velocity increases the velocity profile but converse trend is seen for the thermal profile. The upsurge in the values of the magnetic parameter intensifies the velocity profile. The rise in the values of the heat source/sink parameter upsurges the thermal profile. As the unsteady parameter increases temperature profile declines.

Kinematics analysis of planetary roller screw mechanism with misalignment

The misalignment is unavoidable for planetary roller screw mechanism (PRSM) in practical application due to many uncertainties. The misalignment has a strong effect on the kinematic characteristics of PRSM. However, the relevant research has been rarely reported in the past. In order to clearly present the motion characteristics, a novel kinematics model of PRSM with misalignment is established in this article. The rotational tensor theory is introduced to obtain the coordinate transformation equations. The position vectors of PRSM with misalignment are acquired to calculate the position of the contact point. The motion model of PRSM with misalignment is derived by analyzing the velocity of the contact point. Compared with some published literature, the kinematic model of PRSM is verified. Moreover, a relationship between the misalignment variates, which are the misalignment angle, the misalignment azimuth angle, and the offset distance of the nut's ending point, respectively, and the kinematic characteristics of PRSM are investigated. The results indicate that those misalignment variates have a great influence on the kinematics of PRSM and lead to fluctuations in the PRSM's transmission velocity and angular velocity ratio. The fluctuation amplitude of transmission velocity is positively correlated with misalignment angle.

Reduced-dimensional prediction method for the axial aerodynamic forces in the off-design operation of near-critical CO2 centrifugal compressors

In the high-load centrifugal compressor of near-critical CO2 (NcCO2) power-generation cycle, the overload of axial aerodynamic force causes significant harms to the structural safety and operational stability of turbomachinery components. Based on a transcritical CO2 compressor of a MWt-class simple recuperated cycle, we numerically studied the aero-thermodynamic characteristics of back-cavity leakage, and discussed the physical model of the axial aerodynamic forces in off-design operation of NcCO2 compressors. Finally, reduced-dimensional prediction method for the axial aerodynamic forces in the near-critical CO2 compressor was developed. Wherein, the Japikse's method was used to estimate the primary aerodynamic loads of centrifugal impeller, and a 1-D radial equilibrium equation with angular velocity ratio was derived to predict the thrust force acting on the impeller back disk. Furtherly, based on the near-wall distribution pattern of angular velocities and physical property of Rankine vortex, a semi-empirical model of angular velocity ratio was introduced and completed the model of back-disk force. In validation, the reduced-dimensional prediction method exhibited satisfactory accuracy with perfectly acceptable errors compared to the refined CFD simulations. Thereby, a reduced-dimensional prediction method for the axial aerodynamic forces was developed for the economical and agile analysis of NcCO2 compressors in engineering practices.

Impact of slippage on the wall correction rotation factor of MHD couple stress fluid between two concentric spheres

The creeping rotational motion of a magnetohydrodynamic couple stress fluid between two concentric spheres under the impact of slippages. The slippage conditions are applied on the surface of the inside sphere. In addition, the couple stresses on the boundary are assumed to vanish. The analytical solution to the problem is used to obtain the field functions of velocity, tangential stress, and couple stresses. The wall correction factor experienced by the fluid on the inner solid sphere is evaluated and plotted. However, in the presence of a magnetic field, the eddy current caused by rotating particles produces a torque that tends to rise because the assumption of the torque direction is the opposite direction of magnetic induction. Also, the first couple stress parameter, the angular velocity ratio, and slip condition did an improvement in the torque. On the other side, the wall correction factor slows down with slippage on the inner sphere and the size parameter. All results give limiting cases with no slippage and viscous fluid.

Digital Twin for Diagnosis of Belt Looseness in HVAC Systems using multi-body dynamics simulation

Most heating, ventilation, and air conditioning (HVAC) systems operate using a belt pulley system that provides high efficiency at a low cost. To monitor the health of the HVAC system, it is essential to detect looseness, which is one of the primary failure modes of belt-pulley systems. The main feature used to identify looseness is belt slip, which can be computed using the ratio of angular velocity and diameter between the drive pulley and driven pulley. However, accurately diagnosing the condition of the HVAC system based on the slip distribution calculated by measuring the rotational speed can be based on empirical criteria. To overcome this problem, this paper proposes constructing a digital twin model for accurate diagnosis of belt loosening in HVAC systems. The proposed approach involves performing multi-body dynamics (MBD) based time-domain analysis considering uncertainty. To validate the proposed model, belt looseness is applied to the HVAC system, and the slip distribution is calculated and compared with the results computed by the digital twin model. Through this comparison, it was demonstrated that the proposed model can be utilized to diagnose belt looseness in the HVAC system.

Modelling the wall friction coefficient for a simple shear granular flow in view of the degradation mechanism

A steady granular flow experiment was performed in a confined annular shear cell to examine how the wall friction coefficient $\mu _w$ degrades from the intrinsic sliding friction coefficient $f$ between the grains and the container wall. Two existing models are invoked to examine the decay trend of $\mu _w/f$ in view of the ratio of shear velocity to the square root of granular temperature $\chi$ (Artoni & Richard, Phys. Rev. Lett., vol. 115, 2015, 158001) and the ratio of grain angular and slip velocities $\varOmega$ (Yang & Huang, Granul. Matt., vol. 18, issue 4, 2016, p. 77), respectively. As both models correlate $\mu _w/f$ to different flow properties, a hidden relation is speculated between $\chi$ and $\varOmega$ , or equivalently, between the granular temperature and the grain rotation speed. We used experiment data to confirm and reveal this hidden relation. From there, a unified $\mu _w/f-\chi$ model is proposed with physical meanings for the model coefficients and to show general agreement with the measured trend. Hence we may conclude that both the fluctuations in grain translations and their mean rotation are the crucial yet equivalent mechanisms to degrade $\mu _w/f$ .

Experimental Investigations to Study the Effectiveness of Cepstral Features to Detect Surface Fatigue Wear Development in a FZG Spur Geared System Subjected to Accelerated Tests

Gears are essential machine elements used to transmit power and motion from one unit to another under desired angular velocity ratio. Various types of gears have been developed to fulfill power transmission requirements in industrial applications. Under normal or fluctuating operating conditions, increase in fatigue load cycles, transition in lubrication regimes, fluctuating loads and speeds, etc., result in various surface fatigue wear modes which affect the performance of geared system. The severity of wear anomalies developed on gear tooth surfaces can be assessed by using vibration signals acquired from the gear box. On the other hand, reliable wear assessment is very important to perform maintenance action which depends on the sensors, data acquisition procedure, vibration signal analysis and interpretation. This paper presents results of the experimental investigations carried out to assess initiation and propagation of surface fatigue failure wear modes developed on gear tooth contact surfaces. A FZG back to back power recirculation type spur gearbox was used to conduct fatigue test experiments on spur gears under accelerated test conditions. Accelerated test conditions resulted in a rapid transition of lubrication regimes, i.e., hydrodynamic lubrication regime to boundary lubrication regime which triggered surface fatigue faults on gear tooth surfaces. A cepstral analysis method was used to assess fault severity in the geared system. The results obtained from the cepstral features were correlated to various surface fatigue faults and reduction in gear tooth stiffness. Results obtained from the experimental investigations highlighted the suitability of cepstral features to assess incipient faults developed on spur gear tooth surfaces.

Rotationally symmetric hybrid-nanofluid flow over a stretchable rotating disk

Owing to the advanced thermophysical properties of hybrid nanofluids and stabilizing nature of surface stretching, the problem of rotationally symmetric flow and heat transfer induced over a rotating disk is extended to the case of a stretchable disk, considering Cu and TiO2 nanoparticles suspended in water. In addition, this study deals with four distinct shapes (sphere, brick, cylinder, platelet) of Cu and platelet-shaped TiO2 nanoparticles to elucidate the shape effects. Different from the traditionally applied external vertical magnetic field, the flow is investigated under the influence of a horizontal magnetic field. Moreover, the impact of solar radiation parameters is taken into account to inspect the radiated hybrid nanoparticles. For the same sense and weak & opposite sense (−0.161≤β≤0, here β signify the angular velocity ratio of fluid to disk ) of fluid and disk rotation, solutions are obtained in all cases. However, in the case of strong and opposite sense of rotation, physically acceptable solutions exist after a critical value of the stretching parameter (for example, when β=−0.8,Scr≈0.6). These numerical results have significant engineering applications to fluid flows in rotating machineries such as rotating heat exchangers, rotating disk air cleaners and gas turbine engines.

Absolute Mueller Polarimeters Based on Dual-Rotating Imperfect Retarders and Arbitrary Ratio of Angular Velocities

Dual-rotating retarder polarimeters constitute a family of well-known instruments that are used today in a great variety of scientific and industrial contexts. In this work, the periodic intensity signal containing the information of all sixteen Mueller elements of depolarizing or nondepolarizing samples is determined for different ratios of angular velocities and non-ideal retarders, which are mathematically modeled with arbitrary retardances and take into account the possible diattenuating effect exhibited by both retarders. The alternative choices for generating a sufficient number of Fourier harmonics as well as their discriminating power are discussed. A general self-calibration procedure, which provides the effective values of the retardances and diattenuations of the retarders, the relative angles of the retarders and the analyzer, and the overall scale coefficient introduced by the detection and processing device are also described, leading to the absolute measurement of the Mueller matrix of the sample.

Numerical and experimental analyses of the performance of a vertical axis turbine with controllable-blades for ocean current energy

Phasing out high-carbon-emission fossil fuels and using renewable energy have become a global consensus for mitigating climate change. For the application of renewable energy, this study proposes a high-efficiency controllable-blade vertical axis turbine, which has six blades and a cam plate, for ocean current power generation. A novel design for the turbine using cam to control the opening and closing of blades to enhance the performance of vertical axis turbines. The design feature of the drag-type blade is to be active or open quickly in downstream. The effective area of the blade under thrust is increased to enhance the performance. On the other hand, the blade is designed to be inactive or close quickly in upstream and the drag of blade in upstream can be reduced. A commercial software, ANSYS FLUENT is used to simulate the performance of the vertical turbine. The streamline, velocity, and pressure around the turbines are then obtained. The power coefficients and torques are evaluated at various angular velocities and tip speed ratios and are validated by experimental results. The maximum power coefficient of the proposed turbine occurs at an angular velocity ratio of 4 with quick opening of blades and is higher than that of 3, 5, or 6 by 3.4 %, 2.7 %, or 7.4 %, respectively. In addition, performance comparisons among controllable-blade vertical axis turbine, fixed-blade vertical axis turbine, and Savonius turbine are made. The results show that the maximum power coefficient of the presented controllable-blade vertical axis turbine is 143 % and 103 % higher than that of the fixed-blade vertical axis turbine and Savonius turbine at V = 1 m/s, respectively.

Drug-induced symmetry effects on ventricular repolarization dynamics

The detection of proarrhythmic effects of many current drugs has prompted the search for complementary non-invasive markers of cardiotoxicity risk. Indices based on studies of cardiac vector dynamics have emerged. We use quaternions to quantify symmetry changes in cardiac vector velocity during ventricular repolarization, which could signal the arrhythmia risk. Principal component analysis is used to homogenize the information and reduce the space to three dimensions. A comparison with the ratio of normalized areas of the repolarization loop (T-wave) and two standard measurements was made: QT and T peak-end intervals. Assessment was conducted by comparing 52 healthy subjects with patients undergoing treatment with Sotalol: 7 recordings with Torsade de Pointes events and 15 without arrhythmic effects. Significant differences (p ¡ 5E-4) were found in both phases of repolarization in terms of absolute velocities and areas. The ratio between the maximums of each parameter in both halves of the T-wave showed a trend towards 1 in the proximity of an arrhythmic event. Angular velocity ratios reached a sensitivity/specificity pair of 100 (95%CI: 59–100)/90 (95%CI: 79–97) with an AUC of 98.6 (95%CI: 95.7–100) in the comparison of healthy population with at-risk patients. Linear discriminant analysis improved the classification by reaching sensitivity and specificity values of 100 (95%CI: 59–100) and 96 (5%CI: 87–100), respectively. The high performance of the method exceeded the diagnostic power of standard measurements, thus showing its potential to contribute to drug evaluation methods. Further research with a larger number of events is required to generalize the method.

Study on output characteristics of Offset Twist-roller Frictional Transmission Mechanism

According to the requirements of high resolution and compact space of a rotational-double-prism system, combined with its practical application characteristics of small load and low speed, an offset twist-roller frictional transmission mechanism is proposed. Compared with the clearance elimination gear transmission mechanism, it has the advantages of high output resolution, adjustable reduction ratio, simple structure and low cost. The influence of twist angle on the output characteristics of offset twist-roller frictional transmission mechanism is studied by experiment. The results show that the larger the twist angle, the smaller the driving torque of the driven wheel, the larger the transmission ratio of the mechanism, the larger the fluctuation range of output angular velocity and transmission ratio, and the more unstable the transmission. The transmission ratio of the mechanism in stable transmission is about 30, which is much higher than that in single-stage cylindrical gear drive. The output angular resolution of the mechanism is better than 0.005°, meeting the system requirements. Through the above analysis, it lays a foundation for the application of offset twist-roller frictional transmission mechanism in rotational double prisms system.

A Study on the Dynamic Behavior of a Sieve in an Industrial Sifter

Various vibrating screens are often applied in various industries, e.g., mining, agriculture, and others. The complex shapes of the screen trajectories in the oscillating motion strongly affect the best processing properties of such machines. One of the possible methods for obtaining such complex shapes is the application of double-frequency vibrators on such screens. The goal of the present study was to analyze the dynamical behavior of the prototype sifter sieve elaborated. The simulation model of such a sifter sieve and the research stand for studies on its sifter trajectories were elaborated. Simulations of sifter motion were conducted, and their results were compared with those obtained from measurements on the research stand. The recommendations as to the frequency ratio of vibrators enabling obtaining a high complexity of sieve movement have been formulated and included in the paper. Particularly, the multiple of the value equal to one third for the ratio of angular velocities under their reverse synchronization for two rotary vibrators exciting the screen analyzed was the best among all analyzed values of such a ratio.

Investigation of anode shaping process during co-rotating electrochemical machining of convex structure on inner surface

A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part. The electrodes motion and material removal method of co-rotating electrochemical machining are different from traditional electrochemical machining. An equivalent kinematic model is established to analyze the novel electrodes motion, since the anode and cathode rotate in the same direction while the cathode simultaneously feeds along the line of centres. According to the kinematic equations of the electrodes and Faraday’s law, a material removal model is established to simulate the evolution of the anode profile in co-rotating electrochemical machining. The simulation results indicate that the machining accuracy of the convex structure is strongly affected by the angular velocity ratio and the radius of the cathode tool. An increase of the angular velocity ratio can improve the machining accuracy of a convex structure. A small difference in the radius of the cathode tool will cause changes in the shape of the sidewalls of the convex structure. The width of the cathode window affects only the width of the convex structure and the inclination α of the sidewall. A relation between the width of the cathode window and the width of the convex structure was obtained. The formation process for a convex structure under electrochemical dissolution was revealed. Based on the simulation results, the optimal angular velocity ratio and cathode radius were selected for an experimental verification, and 12 convex structures were simultaneously fabricated on the inner surface of a thin-walled revolving part. The experimental results are in good agreement with the simulation results, which verifies the correctness of the theoretical analysis. Therefore, inner surface co-rotating electrochemical machining is an effective method for fabricating convex structures on the inner surface of a revolving part.

Defining movement strategies in soccer instep kicking using the relationship between pelvis and kick leg rotations

ABSTRACT Growing evidence suggests skilled ball kickers use distinct pelvis and kick leg strategies to achieve successful performance. However, since the interaction between different strategies remains unexplored, the aims of this study were to a) examine relationships between pelvis and kick leg rotations in male players performing soccer instep kicks and b) classify different ‘types’ of kickers based on the observed movement strategies. Twenty semi-professional players performed kicks for maximal speed and accuracy, and kick leg and pelvis kinematics were analysed using 3D motion capture (1000 Hz). A strong relationship was found between change in pelvis transverse angular velocity and thigh-knee angular velocity ratio upon ball contact (r = 0.76, p < 0.001), and participants were categorised by their location on kick leg (thigh-knee) and pelvis (maintainer-reverser) continuums. Knowledge of a player’s preferred strategy can inform departure from ‘one size fits all’ technical and conditioning training practices towards more individualised approaches. For example, pelvis maintainer-thigh dominant kickers might benefit from focus towards the concentric capabilities of the hip flexors, whereas reverser-knee dominant kickers might benefit from developing the ability to decelerate the pelvis and thigh to induce motion-dependent angular acceleration of the lower leg towards the ball.

Flow of two immiscible uniformly rotating couple stress fluid layers

In this article, the flow of two uniformly rotating immiscible couple stress fluid layers is examined. In the upper layer, the flow has different velocity u1, density ρ1, viscosity ν1, couple stress viscosity γ1, and pressure p1, rotating with a constant angular velocity ω1 over another immiscible fluid layer with velocity u2, density ρ2, viscosity ν2, couple stress viscosity γ2, and pressure p2, rotating with a constant angular velocity ω2. The considered problem has a curious form, having characteristics of the famous von Karman and Bo¨dewadth flows of couple stress fluid below and above the interface, respectively. The flows are co-rotating at σ(=ω2/ω1)&amp;gt;0 and counter-rotating at σ&amp;lt;0, where σ is the ratio of angular velocities of the fluid layers. The lower layer would counter-rotate as compared to the upper layer. By utilizing similarity variables, the system of governing equations is transformed into an ordinary system. A finite-difference Keller–Box technique is applied to acquire the numerical results. For co-rotating flows (σ&amp;gt;0), the similarity solution exists for 0≤σ≤1, but for counter-rotating flows (σ&amp;lt;0), the solution exists up to some specific values of σ [i.e., σc(μ)≤σ≤1]. In the limiting cases, there are some similarities between the Bo¨dewadt problem (an outflow of fluid) and the upper layer flow and similarities between the von Karman problem (an inflow of fluid) and the lower-layer flow. The lower fluid layer shows a recirculation region of the flow near the interface, where the fluid cannot transfer.

Mass and Heat Transport Assessment and Nanomaterial Liquid Flowing on a Rotating Cone: A Numerical Computing Approach.

In the present study, we explore the time-dependent convectional flow of a rheological nanofluid over a turning cone with the consolidated impacts of warmth and mass exchange. It has been shown that if the angular velocity at the free stream and the cone’s angular velocity differ inversely as a linear time function, a self-similar solution can be obtained. By applying sufficient approximation to the boundary layer, the managed conditions of movement, temperature, and nanoparticles are improved; afterward, the framework is changed to a non-dimensional framework utilizing proper comparability changes. A numerical solution for the obtained system of governing equations is achieved. The effect of different parameters on the velocity, temperature, and concentration profiles are discussed. Tangential velocity is observed to decrease with an increase in the Deborah number, whereas tangential velocity increases with increasing values of the angular velocity ratio, relaxation to the retardation time ratio, and buoyancy parameter. Expansion in the Prandtl number is noted to decrease the boundary layer temperature and thickness. The temperature is seen to decrease with an expansion in the parameters of lightness, thermophoresis parameter, and Brownian movement. It is discovered that the Nusselt number expands by expanding the lightness parameter and Prandtl number, whereas it increases by decreasing the Deborah number. We also noticed that the Sherwood number falls incrementally in Deborah and Prandtl numbers, but it upsurges with an increase in the buoyancy parameter.

Optimal control of growth of instabilities in Taylor–Couette flow

The present work aims to achieve optimal control of instabilities in a standard Taylor–Couette flow. The motivation of the present study is to reduce the disturbance growth and delay the transition process to turbulence. We numerically employ control using a stability modifier, namely, wall transpiration. In the non-modal stability framework, we form a state-space model employing control actuation by means of periodic suction/blowing of fluid from the walls. The study is conducted for two cases of flow rotations: (i) counter-rotating cylinders and (ii) the stationary outer cylinder with inner cylinder rotating. The parametric study was performed with varying radii ratios, Reynolds numbers (Re), axial (α), and azimuthal (n) wavenumbers. The time evolution of governing equation is written in terms of perturbation velocities in radial (r) and azimuthal (θ) directions. The optimal feedback control is obtained using a linear quadratic regulator controller and feed backed to the system to reduce the maximum optimal growth of the instabilities in the flow. The perturbation kinetic energy is taken as the measure of the amplification of disturbances and used as the cost function to be minimized. We use Chebyshev spectral collocation method to discretize the equations and variational method to calculate the optimal growth. We studied four different parametric cases of radii ratios (η=r1r2= 0.1, 0.25, 0.5, 0.75), with angular velocity (Ω2Ω1) ratio fixed as μ=−1 and μ = 0. We choose the subcritical wavenumbers that led to a maximum transient energy growth corresponding to a Reynolds number ≈ 0.65 times the critical Reynolds number for the case of counter-rotation. For the case of the stationary outer cylinder, we showed the effect of the control in the modal analysis framework. The presented control technique resulted in a maximum of 72% reduction in the growth rate and the typical growth of perturbation energy.

Dynamic Analysis of an Enhanced Multi-Frequency Inertial Exciter for Industrial Vibrating Machines

Multi-frequency vibrators have advantages in bulk materials processing but their design is usually complicated. This article presents the synthesis of design parameters of a two-frequency inertial vibrator according to the specified power characteristics. Based on the developed mathematical model, the parameters of variable periodic force is derived for two angular velocities 157, 314 rad/s and their ratios 0.5 and 2. In the case of the 0.5 ratio, the instant angular velocity of the resulting force vector is 2.0–3.5 times greater than for ratio 2. A dynamical model of vibrating screen with the synthesized inertial drive is considered. It was found that at the ratio of angular velocities 0.5, the second harmonic of acceleration prevails at 50 Hz, while at the ratio of 2, the first harmonic has a greater amplitude at 25 Hz. For the first variant, the power does not depend on the initial angle between unbalances, and at the second variant, it can vary. The angle of rotation of unbalances affects the trajectory of the centre of mass and the phases of the harmonics but does not affect their amplitude. Due to such dynamical features, the two-motor inertial drive allows the vibrating machines to operate at a wider range of frequencies and amplitudes.