Elliptical Trajectory Research Articles

Research on quality and performance of FRM laser welded joints with different shaft length ratios elliptical trajectory

The emerging Flexible Ring Mode(FRM) laser technology has shown great potential for welding copper and its alloys with high reflectivity and has been widely used. The design of the welding trajectory significantly affects the porosity and performance of welded joints. This paper first selects the ellipse and its parameters from the three trajectories by numerical simulation method, then studies the appearance forming and counts the weld porosity through the longitudinal and cross-section developing quality, and finally uses a high-speed camera to monitor the copper Behavior of molten pool and spot oscillation process at the front of the plate. It is found that the trajectory of circular motion has a more stable heating process and has a preheating function for the center of the weld. Compared with linear welding, orbital welding achieves penetration of weld seam and forms better weld seam. Laser confocal tests show that S4(a1b0.5) has the most negligible variation in weld appearance and the best formability. S3(a0.5b0.5) has the lowest porosity, which also explains the mechanism of laser welding trajectory stirring the molten pool and pooling of pores under hydrostatic pressure. The tensile test shows that: S3 has the highest tensile strength (215.35 MPa), 89.79% of the base material. But its strain is only 50% of that of the S4 sample with almost the same tensile strength (215.03 MPa). Therefore, this paper proposes that an elliptical welding trajectory can be adopted to obtain welded joints with better tensile strength and plasticity, with the long axis along the welding direction and the short axis perpendicular to the welding direction. This study provides theoretical guidance for the optimal oscillation mode selection for tunable ring mode laser welding of highly reflective materials.

Enhancing cotton harvesting efficiency through elliptical drum design: a comparative analysis of spindle performance in the working area

This article describes improving the working conditions of the vertical spindle cotton harvester in the cotton collection zone (working area). A comparative analysis of the performance of spindles in standard and elliptical drums in the working area was conducted. A significant increase in the gripping capacity of the spindles was observed due to their elliptical trajectory, resulting in an increase in the contact surface of the spindles with the cotton plants and the number of spindles participating in the collection process. The main criteria for evaluating the gripping capacity of spindles were the simultaneous activity of the spindles and the compressive forces exerted by the drums on the cotton bolls during their presence in the working area. The boundary positions of the spindles, within which they have gripping capacity, were determined, allowing the development of a methodology for determining the time of spindle presence in the working area for both elliptical and standard drums in an actively oriented state. The results of a numerical experiment comparing the time of spindle presence in the collection zone on elliptical and standard drums showed the ability to control the contact time of the spindles with the cotton bolls by varying the geometric parameters of the elliptical drum.

Shaped vibration cutting: A novel fabrication method for mid-infrared relief gratings with controllable profiles

Relief gratings are a particular group of diffractive gratings with a controlled profile, which can precisely modulate the intensity distribution of diffractive lights through its surface structure of depressions and elevations. The mechanical ruling is still one of the most dominant methods for fabricating relief gratings due to its accuracy and capacity to texture free-formed surfaces. However, the ruling has the drawbacks of low material adaptability and inflexible profile adjustability that restrict its wider application. This study invents a novel ruling process, i.e., shaped vibration cutting (SVC), which uses a controllable special-shaped vibration locus of a diamond cutting tool. The tool moves perpendicularly to the cutting plane, enabling the ruling-based fabrication of relief grating on difficult-to-cut materials with flexible control of the grating profile. Slope grooving tests with elliptical and triangular trajectories were performed on aluminum and silicon materials to explore the surface generation and defect formation mechanism comprehensively. The defect-less process window regarding the vibration trajectory, crossfeed, depth of cut, and ruling velocity was identified. Finally, mid-infrared relief gratings were successfully fabricated using the SVC process on aluminum without burrs and silicon in a ductile regime with a maximum depth of 2.3 µm, which outperforms the existing cutting-based texturing technique. To further demonstrate the process capacity of SVC in high material adaptability and flexible profile adjustability, multi-blaze gratings that have spatially varying groove profiles have been fabricated on bulk metallic glass.

Characteristics of Elliptical Vibration-Assisted Cutting with Variations in Tilt Angle of Elliptical Locus.

Elliptical vibration-assisted cutting (EVAC), one of the advanced micromachining methods, enables results not possible with traditional ultra-precision machining. It is considered to be one of the most viable options for manufacturing micro/nanostructured surfaces. However, it is difficult to control the elliptical locus with different tilt angles; therefore, previous studies have primarily focused on fixed locus and investigated the effects of the amplitude and frequency on machining performance. In addition, tilt angle is an important factor affecting the characteristics of EVAC. To maximize the cutting performance of EVAC, the cutting characteristics of EVAC with variations in tilt angle of elliptical locus are investigated. The mathematical model of elliptical trajectory based on different tilt angles is established via geometric analysis. The effects of the different tilt angle (0-180°) on cutting forces, chip formation, defect generation and surface roughness are observed and theoretically analyzed in microgroove experiments. The experimental results show that the tilt angle has a significant effect on the cutting force, chip formation, defects and surface roughness. The best cutting performance can be obtained at the tilt angle of 30°, while the worst is recorded at 90°. The results can provide a valuable reference for further comprehensive studies to maximize the cutting performance of EVAC.

Kinematic Analysis of a Spatial Cable-Driven Mechanism and Its Equivalent Hybrid Mechanism for Elliptical Trajectory

In this paper, a spatial cable-driven parallel mechanism in a V-shaped cable arrangement is proposed. It is further simplified as a planar hybrid cable-driven parallel mechanism to analyze its kinematics, which consists of two identical active cable chains and a passive cross-slide mechanism. In order to investigate the degrees of freedom (DoFs) of the hybrid mechanism using screw theory, cable chains are represented as rotational–prismatic–rotational (RPR) chains. The motion pairs of all the chains are denoted according to screw theory. Firstly, the number and the types of DoFs of each chain are determined. Then, the number and the types of DoFs for the hybrid mechanism are calculated. Furthermore, the theoretical result is verified using the modified Grübler–Kutzbach (G-K) formula. It shows that the unique DoF of the equivalent mechanism is a rotation with a continuously changing axis, which is consistent with the V-type cable-driven mechanism with elliptical trajectories. Finally, the kinematics analysis of the cross-slider mechanism driven by two cables is carried out. The length, velocity and acceleration of the cables are obtained from numerical calculation in MATLAB, and the results are demonstrated using ADAMS simulation.

Memory Maps with Elliptical Trajectories

A family of maps with memory, parameterized by [Formula: see text], is shown to have either periodic trajectories or dense trajectories on ellipses which support absolutely continuous invariant measures. Furthermore, for [Formula: see text], i.e. [Formula: see text] with [Formula: see text] and [Formula: see text], all points except [Formula: see text] either go into a polygonal region centered at [Formula: see text] if [Formula: see text] is rational, or are attracted to an elliptical region having the same center, if [Formula: see text] is irrational. In the polygonal case, we examine a mechanism for the appearance of islands supporting absolutely continuous invariant measures.

Wave propulsion for surface vehicle by foils with active angle of attack adjustment

Extracting wave energy as propulsion for surface vehicles saves non-renewable energy. The fluid moves in a circular or elliptical trajectory in the wave, and its direction of motion varies regularly by 360°. The angle of attack of fixed-angle wave foil cannot be controlled as the direction of incoming flow changes, so the propulsion obtained from the wave is limited. This paper discusses a wave propulsion method by actively controlling the foil to follow the changing incoming current direction, thereby increasing the propulsion extracted by the foil. The wave phase at the foil position is obtained by measuring the free surface level, so as to estimate the direction of the incoming flow and adjust the foil rotation angle accordingly. The wave propulsion system was modeled and simulated in Matlab/Simulink to analyze the incoming flow and the corresponding foil angle. To take into account the foil wave interaction, STAR-CCM+ is used for numerical study. Simulation results show that the active wave foil can provide wave propulsion and has better performance than the fixed-angle wave foil.

Outage probability optimization of UAV relay system based on elliptical trajectory

Outage probability optimization of UAV relay system based on elliptical trajectory

Development of a novel piezoelectric-driven non-resonant elliptical vibrator with adjustable characteristics.

Aiming at the fabrication of a micro-textured surface, a novel piezoelectric-driven non-resonant elliptical vibrator is proposed in this paper; the output characteristics could be adjusted by the length change of the tool holder. The flexible mechanism is the primary structure of the vibrator, which includes a lever type mechanism, an enhanced Scott-Russell mechanism, and a T-shaped mechanism. The former two mechanisms are used to enlarge the output of the piezoelectric actuator, and the T-shaped mechanism is applied to transfer the parallel movements to the elliptical trajectory. The theoretical models including the elliptical trajectory, output stiffness, and resonant frequencies are established to investigate the impacts of the tool holder and controlling signals on the output characteristics of the vibrator, which are further validated using the finite element analysis method. A prototype is developed by integrating the non-resonant elliptical vibrator assembly and controlling system. Some experiments are carried out to verify the basic performance and the adjustable properties of the vibrator.

An analytical cutting force model for elliptical vibration texturing of nano-grating surfaces

Although the direct texturing processes using dynamic cutting depth modulation have been widely demonstrated for generating micro/nano-structured surfaces, the material shearing removal dominates the surface topography generation that inevitably inhibits the machining feasibility of high-aspect textures. This paper proposes a novel nano-grating generation mechanism governed by the combined effect of shearing-based material removal and compressive forming-based deformation in elliptical vibration texturing. A newly dynamic cutting force model is established to reveal its transient cutting mechanics that incorporating the process elastic rebounding behaviors and essential local cutting characteristics in three deformation zones. The model fully considers the complex transient shear angle variation, friction reversal phenomenon on tool-chip interface as well as the unique flank-waviness interaction. A series of texturing experiments are delicately designed to modulate the contribution of material shearing removal and flank compressive forming on nano-grating generation mechanism. The measured dynamic cutting force show good agreements with the simulated results, based on which the model accuracy and main process assumptions are well validated. Furthermore, the relationship between the cutting force characteristics and nano-grating topography is analyzed to guide the optimal elliptical trajectory designs for simultaneously achieving high-quality nano-gratings and smaller dynamic cutting forces. The outcomes of this paper not only lay the scientific foundations for machining capability extension of direct texturing processes, but also contribute to the understandings of combined surface generation mechanisms of other intermittent cutting processes in nano-scale domain.

A novel hollow-type XY piezoelectric positioning platform

To enhance space efficiency and reduce the planar dimensions of the piezoelectric platform, propose an innovative three-stage flexible lever hollow XY piezoelectric platform powered by piezoelectric stack. This paper details the platform's design configuration and operational principles. Analyze and optimize the platform's static and dynamic characteristics using matrix-based compliance modeling and finite element methods. The platform measures 39 mm × 39 mm × 40 mm with a hollow diameter of 29 mm × 29 mm × 40 mm and weighs 60.12 g. An array of experiments was performed to evaluate the prototype platform's performance. Experimental results revealed that the platform's motion ranges are 30.76 μm and 29.79 μm, the cross-coupling ratios are 2.02% and 2.26%, the hysteresis ratios are approximately 5.48% and 5.56%, the displacement resolution are less than 29.3 nm and 31.4 nm, and the carrying load exceeds 1 kg, all measured in the X-axis and Y-axis respectively. Moreover, after installing a simulated laser generator load, achieved square and elliptical motion trajectories by exciting different signals. The study further highlights the successful application of the novel piezoelectric positioning platform for precise motion positioning and inspection of minute electronic components under an optical microscope, signifying its potential to enhance detection and sorting processes in the electronics industry. When compared with earlier piezoelectric positioning platforms, proposed platform not only provides a superior space utilization rate but also exhibits enhanced performance. In the future, the platform will be used for high performance scanning and optical system tracking for atomic force microscopes.

Mathematical Physics of Time Dilation through Curved Trajectories with Applications

In special relativity, the time dilation formula has been obtained by particles propagation in a straight line trajectory relative to an observer in motion. Up to now, there are no available formulas for other possible trajectories of particles. However, this paper obtains formulas of time dilation for several trajectories of particle such as parabolic, elliptic, and circular and finds a relatively accurate trajectory. The obtained formulas are employed in order to analyze the time dilation of the muon particles decay. In this paper, it is found that the time dilation of the parabolic and the elliptical trajectories exceed the corresponding results utilizing the standard Lorentz-Einstein time dilation formula. Consequently, if we are able to control the trajectory of unstable particles by some external forces, then their life-times might be increased. Probably, the increase in lifetime via a curved trajectory occurs at lower relative velocity & acceleration energy if compared to the straight line trajectory. In addition, the circular trajectory leads to multiple values of time dilation at certain velocities of an observer in motion, which may give an interpretation of fluctuations of time dilation in quantum mechanics. The result arises from the present relatively accurate formula of time dilation that is very close to the experimental data of muon decay (CERN experiment) when it is compared to the result obtained by the Lorentz-Einstein formula. Finally, it may be concluded that the time dilation not only depends on relative velocity and acceleration energy of particles but also on curved trajectories. The present work may attract other researchers to study different trajectories.

Theoretical and experimental study for implementation of the elliptical trajectory in dual-motor vibration system

In the petroleum drilling industry, the smoothly functioning vibrating screens play a critical role in control of solid–liquid and recovery of drilling fluid. Due to the mechanical coupling, the surface of the vibrating screen tends to produce unbalanced swings, which makes the motion trajectory inconsistent with the situation at the center of mass, thus affecting the screening efficiency. In order to reveal the reasons for the unbalanced swings of the vibration system and the principle of the trajectory equilibrium characteristics (TECs), the self-synchronization characteristics of two eccentric rotors (ERs) driven by elliptical trajectory dual-motor vibrating system are investigated. The kinematic differential equations of the vibration system are determined by the Lagrange method. Then, the conditions of synchronization and stability of the vibration system are determined, respectively, by the small parameter average approach and the Routh–Hurwitz criterion. Subsequently, the impact of the structural parameters about the synchronization stability is examined by numerical discussion. Furthermore, the effectiveness of the theoretical research is confirmed by comparing the results between dynamics simulation and experiment under different structural parameters. Finally, by focusing on the analysis of the trajectories of different measuring points in the experiment, the relevant conclusions on how to reduce the unbalanced swings and maintain the TECs of the vibration system are obtained. The elliptical trajectory form of the system is most affected by the motor installation angle and installation distance in vibrating body, while less affected by the installation deflection angle and installation offset distance between the motors. In addition, the elliptical trajectories of the oscillating body are in a good equilibrium when reducing the swing angle of the vibration system, in other words, increasing the installation angle and reducing the installation distance of the exciters in the stable state.

A novel bonded-type 3-degree-of-freedom ultrasonic motor: design, simulation, and experimental investigation

Most of 3-degree-of-freedom (3-DOF) ultrasonic motors generally have the problems of low positioning accuracy, difficulty to apply preload, and excessive longitudinal dimension, leading to the limitation in industrial application. To address these issues, a novel bonded-type 3-DOF ultrasonic motor, consists of a convex cylindrical stator, a pre-tightening force structure, and a hemispherical rotor, is proposed in this study. A quadratically polarized toroidal piezoelectric ceramic is bonded to the upper surface of the stator. Three vibration modes of the stator are excited by applying different excitation signals on the piezoelectric ceramic. By coupling any two of the three vibration modes, the elliptical motion of the driving feet of the convex cylindrical stator around the x, y, and z axes are excited, respectively. A novel pre-tightening force application method is proposed to adjust the contact between the stator and rotor. Under the action of friction, the elliptical motion of the driving feet in three directions drives the rotor to rotate around three axes, respectively. The vibration modes of the stator are first simulated by using the finite element method. In addition, the optimal structural dimensions of the stator and the elliptical motion trajectories of the driving feet are calculated. Finally, a prototype of the proposed 3-DOF ultrasonic motor is fabricated and experimentally investigated. The experimental results show that the no-load rotary velocities of the motor prototype in the three rotation directions are 25 r min−1, 22 r min−1, and 380 r min−1, respectively, its start/stop response time are 4.1 ms/3.9 ms, 6.3 ms/7.5 ms, and 6.1 ms/7.9 ms, respectively, and its angular displacement resolutions are 4.3 μrad, 5.1 μrad, and 10.2 μrad, respectively, when the excitation voltage is 250 VPP. The proposed motor holds the advantages of compact structure, adjustable preload, and high positioning accuracy, and presents a broad application prospect in the fields of robot joint technology, optical tracking system, and laser communication.

A miniature longitudinal-bending hybrid linear ultrasonic motor inspired by the planar hinged five bar mechanism

Inspired by the double crank planar hinged five bar mechanism, a longitudinal-bending hybrid linear ultrasonic motor with compact miniature is proposed and tested. In order to realize miniaturization, it adopts a bonded-type structure. Four lead zirconate titanate (PZT) piezoelectric ceramics are distributed equally into two groups and bonded to the two ends of the metal frame, and then, two voltages with a phase difference of 90° are applied to each of the two groups of PZT ceramics. Subsequently, the first-order longitudinal vibration and second-order bending vibration generated by the motor combine with each other at the tip of the driving foot to form an elliptical motion trajectory. According to the theoretical kinematic analysis of the free beam, the initial structural dimensions of the motor were designed. Then, the initial dimensions of the motor were optimized, and the zero-order optimization algorithm was used to achieve the purpose of longitudinal and bending resonance of the motor, and finally, the optimal dimensions of the motor were obtained. A prototype of the designed motor was made, followed by experimental tests on the performance of the prototype, including mechanical output. The maximum motor speed without load at 69.4kHz is 134.57 mms-1. Under 200 Vpp voltage and 6 N preload, the output thrust of the motor is about 0.4 N at the maximum. The actual mass of the motor is about 1.6g; therefore, the thrust-to-weight ratio was calculated as 25.

Experimental study on the galloping characteristics of single ice-coated transmission lines under oblique flows

Galloping of ice-coated transmission lines is occasionally observed under oblique wind directions. However, most current investigations on the galloping mechanisms are for flow perpendicular to the span of the transmission lines. In order to address this gap, this research studies the galloping characteristics of ice-coated transmission lines under oblique flows based on wind tunnel tests. The wind-induced displacement of an aero-elastic iced-coated transmission line model was measured with a noncontact displacement measurement equipment in a wind tunnel at different wind speeds and directions. The results show that galloping is characterized by elliptical trajectories and negative damping, which is more likely to occur under oblique flows than the direct flow (0°). At 15° wind direction, a galloping in vertical direction was observed at wind speeds above 5 m/s. At 30° wind direction, galloping was observed over the entire range of the tested wind speeds. Moreover, the galloping amplitudes under oblique flows are observed to be larger than that at the direct flows. Consequently, when the wind direction between the major winter monsoon azimuth and the lateral direction of transmission line route is between 15° and 30°, appropriate anti-galloping devices are highly recommended in practice.

On the separation mechanism of high vibration frequency compound dry separator and multi-parameter optimization

ABSTRACT Dry coal separation is the key technology for coal separation in arid and water-scarce areas. The content of −6 + 1 mm coal gradually increases, and the weak gravity affect of this part of coal restricts the separation effect, causing serious resource waste and environmental pollution. In this paper, a process intensification method for compound dry separation based on high-frequency vibration was proposed to improve the separation effect of fine coal. The kinematic characteristics of the bed surface with high-frequency vibration was captured by the three-channels acceleration sensor, and the motion trajectories of different regions on bed surface were reconstructed. The separation area was located at the front end of the vibrating bed, and the elliptical trajectory promoted the material to roll. However, the tail of the bed showed a linear trajectory, the main team to the transport of the material. And then the force characteristics of various density particles were studied by using spherical inertial sensors. Compared with low-density particle swarm, the collision between high-density particles was more obvious, causing serious loss of kinetic energy, which increased the motion difference of particles with different densities. Furthermore, the significance of the effects of vibration frequency, bed inclination and air velocity on the separation effect of −6 + 1 mm coal and the interaction between the factors were investigated. Furthermore, the influence of vibration frequency, inclination, and air velocity on the separation effect and the interaction among various factors were explored. The influence of frequency and inclination was more obvious than that of gas velocity. And then a mathematical model was established to predict the calorific value of clean coal. The results illustrated that at a vibration frequency of 37.52 Hz, a bed inclination angle of 13.69°, and an air velocity of 2.26 m/s, the calorific of product was increased from 4306 kcal/kg to 5868 kcal/kg, and the heat efficiency reached 90.18%. The results provide a referable way to realize the large-scale and high-efficiency dry separation of fine coal.

Effects of ultrasonic vibration cutting trajectories on chip formation of tungsten alloys

Chip morphology has a close correlation with machined surface quality and tool wear in turning process. In the current research on ultrasonic vibration cutting, little is known about the effect of different directions of ultrasonic action on chip formation. In this paper, the effect of ultrasonic vibration on chip formation of tungsten alloy when acting in the direction of cutting speed and cutting depth, respectively, was analyzed by splitting the elliptical trajectory. Furthermore, the advantages of elliptical trajectory machining were also explained in terms of strain rate. The results show that ultrasonic vibration in the direction of cutting depth can effectively suppress the serrated chips and promote the formation of smooth and continuous chips. However, ultrasonic vibration in the direction of cutting speed has the opposite effect. When the tool is superimposed with two-way vibration, the chip morphology formed by the elliptical trajectory is smoother and more continuous. Moreover, it achieves the highest strain rate and the lowest cutting force. Finally, as seen from the experiments of conventional cutting and cutting with variable phase difference, the machined surface roughness decreases with the transition of chip from broken and folded shape to smooth shape. Overall, results of cutting experiment are consistent with simulation results demonstrating the effectiveness of the current work.

On the oxidation resistance of sinusoidal microstructure fabricated by elliptical vibration cutting

The sinusoidal microstructure fabricated by the conventional slow tool servo (STS) cutting has low oxidation resistance and large fluctuation of surface roughness, which affects fluid instability in Rayleigh–Taylor experiments. This study is devoted to reducing roughness fluctuation and improving the oxidation resistance of sinusoidal microstructure by adopting the elliptical vibration (EV) of tool in the STS cutting. First, the kinematic principle of EVSTS cutting is demonstrated by highlighting the time-varying orientation of the elliptical tool trajectory relative to instantaneous nominal cutting velocity. Next, the geometric roughness model of sinusoidal surface is developed to analyze the roughness fluctuation along the wavelength direction. Then, flat surface cutting and accelerated oxidation experiments are performed to explore the deterministic effects factors on machined surfaces' surface roughness and oxidation resistance using elliptical vibration cutting (EVC). The experimental results show that the EVC can reduce the oxide thickness of the machined surface after accelerated oxidation by 35 % on average, owing to the reduced roughness and surface strengthening effects. The effects of the vibration trajectory, edge radius, and wavelength-direction nominal cutting velocity on the surface roughness and surface oxidation resistance are established. Finally, the processing parameters for the EVSTS cutting of sinusoidal microstructure are optimized by further considering the time-varying orientation of the elliptical tool trajectory. Surface texturing tests with results demonstrates that the EVSTS can significantly improve the oxidation resistance of the microstructured surface, suppressing the roughness fluctuation along the wavelength direction by 25–60 %.

A time-reversal assisted probabilistic fusion strategy for damage localization in plate-like structures using Lamb waves

Precise damage identification and quantification is of great significance to ensure structural performance and provide early-warning for safety maintenance. In this research, a time-reversal assisted probabilistic strategy is developed to accurately localize damage via baseline-free manner in plate-like structures by fusing damage prediction data obtained from the elliptical trajectory location method (ETLM) and reconstruction algorithm for probabilistic inspection of defects (RAPID) algorithm. Damage features, including time difference for ETLM and correlation coefficient index (CCI) for RAPID algorithm, are extracted from the time-reversal focusing signal using the Hilbert transform (HT). To make full use of the damage-related information contained in the time-reversal focusing signals and improve the localizing accuracy, a decision-level data fusion based on Bayesian inference is proposed to fuse damage features and reconstruct damage information. A series of numerical and experimental studies, including different configurations of damage cases and transducer distributions, were conducted to investigate the performances of the proposed time-reversal assisted probabilistic method on damage localization. Results shows that the proposed method could successfully achieve accurate damage localization via baseline-free manner and significantly reduce the damage artifacts compared to traditional methods.