Search Results (17)

To address path deviation and efficiency reduction issues in traditional interpolation optimization algorithms for complex path machining, this paper proposes a chord error-priority bilevel interpolation optimization method (CPBI). First, arc length parametric modeling of the machining path is performed within the Frenet–Serret framework, yielding curvature and torsion information. After introducing geometric-based multi-machining constraints in the outer layer, the velocity upper limit is established by controlling chord error to dynamically adjust regions with curvature mutation. In the inner layer, combining the velocity limit with bidirectional scanning achieves adaptive optimization of interpolation step size and optimal velocity planning that balances precision and smoothness. Simulation results demonstrate that CPBI effectively reduces the number of interpolation points by 30–50% while ensuring the chord error. Compared with the reference method, the CPBI improved efficiency by 14.31% and 34.72% in machining experiments on S-shaped and wave-shaped paths, respectively. The results validated the CPBI’s high precision and efficiency advantages in complex path machining, providing an effective solution for CNC path optimization in high-end manufacturing. Full article

Real-time parametric interpolation plays a crucial role in achieving high-speed and high-precision multi-axis CNC machining. In the interpolation cycle, the position of the next interpolation point is required to be calculated in real-time to guide the action of the machining process. Due to the existence of the positioning error of the interpolation point, it is extremely difficult to eliminate the feedrate fluctuation, which may lead to dramatic decreases in machining quality and the driving capabilities’ saturation of each axis. A computationally efficient and precise feedrate fluctuation minimization method is proposed for the NURBS tool path interpolation in the CNC milling process. The model for the arc length and curvature, with respect to the parameter of the NURBS tool path, is established to reduce the calculation amount required by interpolation points determination. The deviation between the theoretical and actual interpolation step length is decreased by the proposed arc length compensation method to minimize the feedrate fluctuation. In addition, the interpolation points derived from the arc length compensation process are further corrected by performing the Newton iteration to restrict the feedrate fluctuation within the preset accuracy threshold. The effectiveness and superiorities of the proposed feedrate fluctuation minimization method are verified by simulation and milling experiments. Full article

This paper presents a practice-oriented numerical modelling procedure to assess the loadbearing capacity of reinforced concrete (RC) columns under axial compression loading. A simplified procedure was incorporated to analyse the performance of RC columns with corroded stirrups, a prevalent deterioration phenomenon in corroded RC columns. The modelling framework incorporates material and geometric nonlinearities caused by material and buckling failure under axial compression, utilising the Arc-length algorithm with integrated geometric imperfections. Stirrup corrosion scenarios were incorporated by removing stirrups and modifying core concrete confinement properties, providing a practice-oriented approach to assess the loadbearing capacity of corroded columns. The study focused on square RC columns that are commonly used in low-rise buildings with nominal reinforcement detailing. The modelling method was validated against experimental data, and it showed a good agreement. A comprehensive parametric analysis was then conducted to examine the effects of critical design parameters, including (1) slenderness, (2) eccentricity, (3) stirrup corrosion, and (4) material properties, on axial compression performance. Parametric analyses demonstrated that the developed modelling technique appropriately predicted the axial compression behaviour of un-corroded RC columns in alignment with analytical design rules. For stirrup-corroded RC columns, the absence of confinement for up to 300 mm length near the base, due to stirrup corrosion, led to premature buckling. Based on the analysed cases, the reduction in bearing capacity of the stirrup-corroded RC columns could range between 4.9 and 18.6% (higher for slender columns) as compared to corresponding un-corroded RC columns. Full article

Inertial loads induced by base motion excitation introduce significant complexities in equilibrium point determination and linearization of systems incorporating squeeze film dampers (SFDs). The coupled effects of base motion excitation and SFD characteristics on periodic stability have received limited attention in previous investigations. This study investigates the dynamic characteristics and periodic stability of a rotor system with SFD subjected to base motion excitation. A finite element model of the rotor-SFD-support system under non-inertial motion is established. The periodic responses are solved using the harmonic balance method with alternating frequency/time technique (HB-AFT) and the arc-length continuation algorithm incorporating the predictor–corrector method, while system stability is analyzed using Floquet theory and the Newmark method. A systematic parametric study is conducted to investigate the effects of base motion parameters, mass unbalance, and SFD parameters on the system’s periodic response. Results demonstrate that base pitching motion enhances system stability, suppresses bistable responses and jump phenomena, and reduces unstable vibration regions. However, under specific parameter combinations, pitching motion can trigger secondary Hopf bifurcations, leading to quasi-periodic and chaotic motions, among other complex nonlinear behaviors. This research provides theoretical foundations for stability-oriented design optimization of rotor systems with SFDs under base motion excitation. Full article

We define a family of special functions (the CSI ones), which can be used to write any parameterized plane curve with polynomial curvature explicitly. These special functions generalize the Fresnel integrals, and may have an interest in their own right. We prove that any plane curve with polynomial curvature is asymptotically a pseudo-spiral. Using the CSI functions, we can approximate, locally, any plane curve; this approach provides a useful criterion for a (local) classification of plane curves. In addition, we present a new algorithm for finding an arc-length parametrization for any curve, within a prescribed degree of approximation. Full article

In linear elastic fracture mechanics, the stress intensity factor describes the magnitude of the stress singularity near a crack tip caused by remote stress and is related to the rate of fatigue crack growth. The literature lacks SIF solutions for cracks emanating from a three-dimensional semi-ellipsoidal pit. This study undertakes a comprehensive parametric investigation of the Mode I stress intensity factor ${(K}_I)$ concerning cracks originating from a semi-ellipsoidal pit in a plate. This work utilizes finite element analysis, controlled by Python scripts, to conduct an extensive study on the effect of various pit dimensions and crack lengths on $K_I$. Two cracks in the shape of a circular arc are introduced at the pit mouth perpendicular to the loading direction. The $K_I$ values are calculated using the displacement extrapolation method. The effect of normalized geometric parameters pit-depth-to-pit-width $(a/2c$), pit-depth-to-plate-thickness $(a/t)$, and crack-radius-to-pit-depth $(R/a)$ are investigated. The crack-radius-to-pit-depth $(R/a)$ is found to be the dominating parameter based on correlation analysis. The data obtained from 216 FEA simulations are incorporated into a predictive model using a k-dimensional (k-d) tree and k-Nearest Neighbour (k-NN) algorithm. Full article

Background: To evaluate the corneal biomechanics of stable keratoconus suspects (Stable-KCS) at 1-year follow-up and compare them with those of subclinical keratoconus (SKC). Methods: This prospective case-control study included the eyes of 144 patients. Biomechanical and tomographic parameters were recorded (Corvis ST and Pentacam). Patients without clinical signs of keratoconus in both eyes but suspicious tomography findings were included in the Stable-KCS group (n = 72). Longitudinal follow-up was used to evaluate Stable-KCS changes. Unilateral keratoconus contralateral eyes with suspicious tomography were included in the SKC group (n = 72). T-tests and non-parametric tests were used for comparison. Multivariate general linear models were used to adjust for confounding factors for further analysis. Receiver operating characteristic (ROC) curves were used to analyze the distinguishability. Results: The biomechanical and tomographic parameters of Stable-KCS showed no progression during the follow-up time (13.19 ± 2.41 months, p > 0.05). Fifteen biomechanical parameters and the Stress–Strain Index (SSI) differed between the two groups (p < 0.016). The A1 dArc length showed the strongest distinguishing ability (area under the ROC = 0.888) between Stable-KCS and SKC, with 90.28% sensitivity and 77.78% specificity at the cut-off value of −0.0175. Conclusions: The A1 dArc length could distinguish between Stable-KCS and SKC, indicating the need to focus on changes in the A1 dArc length for keratoconus suspects during the follow-up period. Although both have abnormalities on tomography, the corneal biomechanics and SSI of Stable-KCS were stronger than those of SKC, which may explain the lack of progression of Stable-KCS. Full article

In recent times, there has been a significant focus on electromagnetic resonant shunt damping (ERSD) and quasi-zero-stiffness vibration isolators (QZS VI) as prominent solutions for vibration mitigation or energy harvesting. In this paper, an innovative retrofittable model is proposed for dual-functional energy harvesting and low-frequency vibration attenuation by combining the ERSD and two-stage quasi-zero-stiffness vibration isolator (TQZS VI). The viscous dissipative element between the TQZS VI upper and lower layers is implemented using an electromagnetic shunt transducer that is connected in parallel with a resonant RLC (resistor–inductor–capacitor) circuit. Firstly, the mathematical model of the electromagnetic resonant shunt series quasi-zero-stiffness isolator (ERS-TQZS VI) is developed. Then, the magnitude-frequency response equations of the ERS-TQZS VI system are approximately solved using the harmonic balance method (HBM) in combination with the pseudo-arc-length method (PLM). The analytical approach is validated using numerical simulations. Moreover, the force transmissibility and output power of the ERS-TQZS VI are defined, and detailed parametric analysis for energy harvesting and low-frequency vibration attenuation is performed to assess the critical design parameters that result in optimal performance of the ERS-TQZS VI. The results demonstrate that the ERS-TQZS VI exhibits a significant reduction in resonance peaks of low-frequency vibration while simultaneously enabling effective vibration energy harvesting. Full article

In this paper, we present a new reference model that approximates the actual shape of the Earth, based on the concept of the deformed spheres with the deformation parameter $\lambda$. These surfaces, which are called $\lambda$-spheres, were introduced in another setting by Faridi and Schucking as an alternative to the spheroids (i.e., ellipsoids of revolution). Using their explicit parametrizations that we have derived in our previous papers, here we have defined the corresponding isothermal (conformal) coordinates as well as obtained and solved the differential equation describing the loxodromes (or rhumb lines) on such surfaces. Next, the direct and inverse problems for loxodromes have been formulated and the explicit solutions for azimuths and arc lengths have been presented. Using these explicit solutions, we have assessed the value of the deformation parameter $\lambda$ for our reference model on the basis of the values for the semi-major axis of the Earth a and the quarter-meridian $m_p$ (i.e., the distance between the Equator and the North or South Pole) for the current best ellipsoidal reference model for the geoid, i.e., WGS 84 (World Geodetic System 1984). The latter is designed for use as the reference system for the GPS (Global Positioning System). Finally, we have compared the results obtained with the use of the newly proposed reference model for the geoid with the corresponding results for the ellipsoidal (WGS 84) and spherical reference models used in the literature. Full article

The impetus of writing this paper is to propose an efficient detection mechanism to scan the surface profile of a micro-sample using cantilever-based atomic force microscopy (AFM), operating in non-contact mode. In order to implement this scheme, the principal parametric resonance characteristics of the resonator are employed, benefiting from the bifurcation-based sensing mechanism. It is assumed that the microcantilever is made from a hyperelastic material, providing large deformation under small excitation amplitude. A nonlinear strain energy function is proposed to capture the elastic energy stored in the flexible component of the device. The tip–sample interaction is modeled based on the van der Waals non-contact force. The nonlinear equation governing the AFM’s dynamics is established using the extended Hamilton’s principle, obeying the Euler–Bernoulli beam theory. As a result, the vibration behavior of the system is introduced by a nonlinear equation having a time-dependent boundary condition. To capture the steady-state numerical response of the system, a developed Galerkin method is utilized to discretize the partial differential equation to a set of nonlinear ordinary differential equations (ODE) that are solved by the combination of shooting and arc-length continuation method. The output reveals that while the resonator is set to be operating near twice the fundamental natural frequency, the response amplitude undergoes a significant drop to the trivial stable branch as the sample’s profile experiences depression in the order of the picometer. According to the performed sensitivity analysis, the proposed working principle based on principal parametric resonance is recommended to design AFMs with ultra-high detection resolution for surface profile scanning. Full article

The Kiepert trefoil is an algebraic curve with remarkable geometric and number theoretic properties. Ludwig Kiepert, generalizing ideas due to Serret and Liouville, determined that it could be parametrized by arc length in terms of elliptic functions. In this note, we observe some other properties of the curve. In particular, the curve is a special example of a buckled ring, and thus a solitary wave solution to the planar filament equation, evolving by rotation. It is also a solitary wave solution to a flow in the (three-dimensional) filament hierarchy, evolving by translation. Full article

This study illustrates the impact of single discrete arc-shaped ribs (SDASR)-type artificial roughness on the performance of a jet impingement solar thermal collector (JISTC). The impact of parametric variations of SDASR on the Nusselt number $(N{u}_{sdr})$, friction factor $(f_{sdr})$, and thermohydraulic performance $({\eta }_{sdr})$ is examined. The spacer length ($S_{sdr}$) of the SDASR was changed from 0 mm to 300 mm in stages of 100 mm during the experiment. The fixed parameters of the SDASR were a relative discrete distance $\left(D_d/L_v\right)$ of 0.67, relative discrete width $\left(g_w/H_r\right)$ of 0.87, relative rib height $\left(H_r/H\right)$ of 0.047, relative rib pitch $\left(P_r/H\right)$ of 1.7, angle of an arc $\left({\alpha }_{sdr}\right)$ of 60°, jet diameter ratio $\left(D_j/D_{hy}\right)$ of 0.065, streamwise pitch ratio $\left(X/D_{hy}\right)$ of 1.72, and spanwise pitch ratio $\left(Y/D_{hy}\right)$ of 0.82. The Reynolds number $\left(Re\right)$ was altered from 3000 to 19,000. The $N{u}_{sdr}$ and $f_{sdr}$ of a JISTC with a roughened absorber plate was found to be enhanced by 5.25 and 5.98 times as compared to an STC without artificial roughness. The optimal findings of $N{u}_{sdr}$, $f_{sdr},$ and ${\eta }_{sdr}$ were achieved at $S_{sdr}$ = 0 mm. The maximum value of the ${\eta }_{sdr}$ obtained at $S_{sdr}$ = 0 mm was 2.9. Full article

The objective of this paper is to define one class of plane curves with arc-length parametrization. To accomplish this, we constructed a novel class of special polynomials and special functions. These functions form a basis of $L^2\left(\mathbb{R}\right)$ space and some of their interesting properties are discussed. The developed curves are used for the linear static analysis of curved Bernoulli–Euler beam. Due to the parametrization with arc length, the exact analytical solution can be obtained. These closed-form solutions serve as the benchmark results for the development of numerical procedures. One such example is provided in this paper. Full article

Runoff water harvesting (RWH) is considered as an important tool for overcoming water scarcity in arid and semi-arid regions. The present work focuses on identifying potential RWH sites in the Wadi Watir watershed in the south-eastern part of the Sinai Peninsula. This was carried out by means of significant integration of the analytical hierarchy process (AHP), distributed spatial model, geographical information system (GIS), watershed modeling system (WMS), and remote sensing techniques (RS). This integration of modern research tools has its own bearing on the accurate identification of optimum RWH sites, which could be relied upon in developmental planning for arid environments. Eight effective RWH parameters were chosen to apply a multi-parametric decision spatial model (MPDSM), namely the overland flow distance, volume of annual flood, drainage density, maximum flow distance, infiltration number, watershed slope, watershed area and watershed length. These parameters were used within ArcGIS 10.1© as thematic layers to build a distributed hydrological spatial model. The weights and ranks of each model parameter were assigned according to their magnitude of contribution in the RWH potentiality mapping using a pairwise correlation matrix verified by calculating the consistency ratio (CR), which governs the reliability of the model application. The CR value was found to be less than 0.1 (0.069), indicating acceptable consistency and validity for use. The resulting MPDSM map classified the watershed into five categories of RWH potential, ranging from very low to very high. The high and very high classes, which are the most suitable for RWH structures, make up approximately 33.24% of the total watershed area. Accordingly, four retention dams and seven ground cisterns (tanks) were proposed in these areas to collect and store the runoff water, whereby these proposed RWH structures were chosen according to the soil type and current land-use pattern. The resulting MPDSM map was validated using a topographic wetness index (TWI) map, created for the watershed. This integrative and applied approach is an important technique which can be applied in similar arid environments elsewhere. Full article

Root pass manufacturing in automated welding is still a challenge when the backing plate is not feasible. Using the concept of bead formation in an original way, the GMAW (Gas Metal Arc Welding) switchback technique was assessed against linear movement as a means of facing this challenge. Experimental work was applied, keeping the process parametrization and joint configuration, so that only the switchback parameters were modified, i.e., the stroke lengths and speeds. Thermography was used to estimate the effect of the switchback parameters on bead formation. The results showed the potential of the switchback technique as a means of favoring weld pool control. Surprisingly, the operational gap range is not necessarily larger when switchback is applied. The strong influence of stroke lengths and speeds on the process performance was characterized. In general, the results showed that linear movement leads to larger pools and deeper penetrations, more adequate for gaps with no clearances. Shorter stroke lengths and slower stroke speeds (intermediate pool size) better suit root gaps that are not too wide, while longer stroke lengths and faster stroke speeds (smaller pool size, more easily sustainable) are applicable to larger root gaps. Full article