Edge Geometry Research Articles

Edge and skin effects in rhombus reciprocal photonic crystals.

With the development of non-Hermitian physics, the non-Hermitian skin effect (NHSE) has attracted much attention. Existing research highlights the critical roles of the periodic boundary condition (PBC) spectrum, lattice symmetry, and macroscopic symmetry of the lattice in relation to the geometry-dependent skin effect (GDSE). However, the impact of macroscopic edge geometry is frequently neglected. We find that the GDSE is highly sensitive to the edge and cannot be simply determined by the symmetries. Specifically, the GDSE can emerge at trivial interfaces of rhombus photonic crystals (PhCs) with zigzag edge and bearded edge. Furthermore, we analyze the underlying mechanisms from the perspective of point-gap topology. This work underscores important, yet frequently overlooked, aspects in two-dimensional (2D) reciprocal PhC systems and can be used to enhance design flexibility, allowing the NHSE to have better applications in areas such as lasers and highly sensitive sensors.

Analytical and Experimental Study of the Start of the Chip Removal in Rotational Turning

The present challenges in the automotive industry require the development and practical implication of novel machining procedures, which will provide appropriate solutions. These procedures should still meet the requirements of productivity, surface quality and energy efficiency. The further development of novel machining procedures introduces new problems that did not occur (or occurred to a lesser extent) with traditionally applied procedures. Rotational turning has come to the attention of production engineers in the previous decade since it can be used to machine ground-like surfaces in an ecologically friendly and highly productive manner. However, the chip removal characteristic is slightly different from traditional turning due to the applied special kinematic relation and complex tool edge geometry. The run-in phase will take longer, which is the time period between the first contact of the tool and the formation of a constant chip cross-sectional area. The clarification of the chip formation is important in any machining procedure. To achieve this goal, the geometric parameters of the chip must be determined. Since the start of the chip removal is a crucial stage in rotational turning due to its length, the chip height, chip width and the cross-sectional area of the chip should be separately defined in the initial stage. Therefore, in this paper, the initial phase of chip removal in rotational turning is studied. The increasing cross-sectional area of the chip is determined analytically by the application of the previously elaborated equation of the cut surface. Calculating formulas are defined for the different stages of the start of the chip removal, which could be used in the forthcoming studies to analyze the chip formation. The effects of different determining parameters are analyzed theoretically by the deduced formulas of the run-in phase and practical experiments are also carried out. The analytical and experimental analyses showed that increasing feed also increases the dynamic load on the cutting edge, while the depth of cut lowers the growth of the characteristic parameters of the chip, which results in a lower dynamic load on the tool.

An Investigation of the Effects of Cutting Edge Geometry and Cooling/Lubrication on Surface Integrity in Machining of Ti-6Al-4V Alloy

This investigation sought to characterize the combined influence of cutting-edge microgeometry and cooling/lubricating strategies on process thermo-mechanics and the resultant surface integrity in orthogonal machining of the Ti-6Al-4V alloy. Reverse waterfall cutting inserts were prepared with varying cutting-edge geometries, and machining experiments were conducted under cryogenic cooling with liquid nitrogen (LN2), minimum quantity lubrication (MQL), and dry machining conditions, using constant machining parameters. The induced surface integrity was characterized in terms of the developed cutting forces and through-thickness microhardness, grain morphology, dislocation generation, and residual stress formation. The experimental results revealed that the governing process physics are strongly influenced by variation in the implemented machining parameters. As a greater proportion of the cutting edge is distributed on the flank face, competing mechanical ploughing and thermal-based frictional effects both become more pronounced. Utilization of advanced cooling strategies to control cutting interface thermal gradients thus provides a processing route to generate tailored microstructures and surface integrity during the machining of this alloy.

Digital dynamic modeling and topology optimized design of shell face mills

This paper presents digital modeling of shell face mills in milling cylinder heads. The cutter's structural dynamics and its mode shapes are predicted using a Finite Element system. The geometries of the cutter body and inserts are imported from their Computer Aided Design (CAD) models. The insert edge is discretized into small segments to model its varying normal rake and inclination angles, which affect the cutting mechanics. The cutter is dynamically assembled with the target machine tool spindle using the receptance coupling method. A general dynamic cutting force model, which considers the varying edge geometry and inserts’ run-outs, is developed and used to predict cutting forces and chatter stability diagrams. The proposed model is experimentally verified to demonstrate the feasibility of the systematic application of physics-based digital design and analysis of tools for the mass machining of specific parts. The cutter body shape is optimized to increase the stiffness of the bending mode shape that caused chatter via topology optimization, which led to five-fold increase in the absolute stable depth of cut.

Effect of the water erosion on the non-equilibrium condensation in steam turbine cascade

In the final stage of steam turbines, droplets formed by non-equilibrium condensation continuously impact and erode the blades, leading to changes in surface roughness and leading edge erosion. This study investigates the effects of roughness changes and leading edge erosion, induced by water erosion, on non-equilibrium condensation in steam turbine cascades using numerical simulation methods. In a Moses-Stein nozzle, the mechanism of roughness influencing non-equilibrium condensation is analyzed. Subsequently, entropy generation theory is applied to assess the loss distribution caused by roughness variations in a Dykas cascade. Furthermore, flow field analysis and entropy generation theory are utilized to examine the loss distribution pattern resulting from leading edge erosion. Results show that increased roughness delays non-equilibrium condensation, reducing average outlet humidity (from 0.05351 to 0.04361 as roughness rises from 0 to 500 µm). The effect of roughness on thermodynamic entropy generation exhibits a non-linear relationship, balancing steam flow losses with mitigated phase-change-related losses at a roughness of 896 µm. Significant blade erosion (>3 mm) alters leading edge geometry, causing local flow separation and a substantial increase in airfoil losses.

Edge-state-mediated RKKY coupling in graphene nanoflakes

We investigate the long-range behavior and size dependence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in hexagonal and triangular graphene nanoflakes with zigzag and armchair edges. We employ the tight-binding model with exact diagonalization to calculate the RKKY interaction as a function of the distance between magnetic impurities, nanoflake size, and edge geometry. Our findings demonstrate a strong dependency of the RKKY interaction on edge geometry and flake size, with notable changes in the RKKY interaction strength. We further analyze the influence of structural defects on the interaction strength of exchange interactions.

Effect of edge distance-diameter ratio on pin-bearing strength of TC18 by laser melting deposition

Abstract This paper presents an experimental study on the pin-bearing characteristics of TC18 titanium alloy produced by laser melting deposition. Two types of specimens with edge distance-to-diameter ratios (e/D) were manufactured for pin-bearing tests. The S-Basis values of bearing strength are calculated based on statistical analysis of experimental data. The results indicate that the S-Basis value of bearing ultimate stress with e/D =1.5 specimens is 1648.12 MPa, and the S-Basis value of bearing ultimate stress is 1967.89 MPa for e/D =2.0 specimens. The S-Basis value of bearing ultimate stress for e/D=2.0 specimens is higher by 19.4% than that of e/D=1.5. The test result showed three different failure modes: shear-out, cleavage, and bearing. Each failure mode depends on the specific hole edge geometry adopted. The proportion of shear-out failure for e/D=1.5 samples is more than for e/D=2.0 specimens.

Arc-enhanced glow discharge ion etching of WC-Co cemented carbide for improved PVD thin film adhesion and asymmetric cutting edge preparation of micro milling tools

Wear-resistant thin films on cutting tools require effective ion etching to enhance adhesion and thus extended tool service life. Arc enhanced glow discharge (AEGD) ion etching, characterized by high ionization degrees and high etch rates, was applied to ultrafine-grained WC-Co cemented carbide, commonly used for micromilling cutters. The effect of AEGD ion etching on the surface integrity of WC-Co and the resulting adhesion behavior of a TiAlSiN thin film was investigated by varying the etching time in comparison with conventional glow discharge (GD) ion etching. In addition, the impact of intensive etching on the cutting edge geometry of micro end cutters and, in turn, on the cutting performance in micromilling of hardened and annealed high-speed steel was evaluated.AEGD achieves remarkable etch rates of 12 nm/min at extended etching times, which are 100 times greater than conventional glow discharge (GD) ion etching. Prolonged AEGD ion etching for ≥30 min removes entire near-surface WC grains and exposes carbides beneath, resulting in increased surface roughness. After the etching process, polished WC-Co substrates exhibit a slight reduction in residual compressive stresses, which steadily decrease with increasing AEGD ion etching time. Furthermore, a TiAlSiN thin film demonstrates high adhesion on AEGD-etched surfaces compared to GD ion etching. Even a brief 5 min AEGD ion etching ensures the highest adhesion class according to the Rockwell C indentation test. Moreover, the intensive material removal results in significant changes in cutting edge geometry of micro end cutters, yielding substantial cutting edge rounding and an asymmetrical shape with form-factors Κ ≥ 2. In cutting tests, the resulting cutting edge geometries effectively reduce the wear formation and the associated wear-related increase in process forces during micromilling hardened and tempered powder metallurgical high-speed steel. In summary, AEGD ion etching emerges as a highly effective method for both enhancing thin film adhesion and preparing adapted asymmetrical cutting edge geometries for micromilling tools.

Tool-edge geometry effects in semi-to-finish cut machining operations on subsurface integrity and tool thermo-mechanical loadings: A coupled damage-fracture energy based finite element approach

Present work put forwards a numerical approach to quantify the effects of honed-edge and chamfered-edge tools on residual stresses and end-burr generation while performing semi-to-finish cut machining operations. Maximum stresses and temperatures experienced by tools are computed to predict tool wear intensity at its various sections. Furthermore, the impact of tool edge geometry on fracture and the size of the material damage zone ahead of the tool tip has also been detailed. Chip formation, its evolution and separation have been realized using a coupled damage-fracture energy model considering coupled temperature-displacement simulations in two steps modeling strategy: cutting step and stress relaxation and cooling step. A numerical model has been validated with previous experimental results of chip morphology and cutting forces when machining was performed under similar cutting conditions and tool geometrical profile.

Effects of Failure Criteria on Quantitatively Determining the Machining Mechanics for CFRP with Different Tool Rake Angles

Abstract The machining mechanics of carbon fiber reinforced polymer (CFRP) materials is influenced by the coupled effects of the workpiece anisotropy, tool edge geometry, and cutting parameters. Predicting the chip formation mechanism is crucial for optimizing cutting parameters, reducing tool wear, and improving efficiency and surface quality. This study quantitatively evaluates the effect of main CFRP failure criteria on the chip formation mechanism in modeling the machining mechanics of CFRP. The results show that the Hashin-Puck and Davila criteria excel at capturing chip formation across all fiber orientations because of the incorporation of ‘internal friction’ concept, while others only achieve accurate predictions in specific fiber orientation ranges due to improper shear strength consideration. The sources of the prediction similarities, differences, and limitations of failure criteria are experimentally validated. Sensitivity analyses quantitatively determine the effect of the tool rake angle on the machining energy consumption and cutting forces across the fiber orientation range. This research can be used to select the optimal failure criteria, design proper cutting tool geometry, and inform the cutting parameter choices for CFRP machining operations.

Wafer Edge Metrology and Inspection Technique Using Curved-Edge Diffractive Fringe Pattern Analysis

Abstract This paper introduces a novel wafer-edge quality inspection method based on analysis of curved-edge diffractive fringe patterns, which occur when light is incident and diffracts around the wafer edge. The proposed method aims to identify various defect modes at the wafer edges, including particles, chipping, scratches, thin-film deposition, and hybrid defect cases. The diffraction patterns formed behind the wafer edge are influenced by various factors, including the edge geometry, topography, and the presence of defects. In this study, edge diffractive fringe patterns were obtained from two approaches: (1) a single photodiode collected curved-edge interferometric fringe patterns by scanning the wafer edge and (2) an imaging device coupled with an objective lens captured the fringe image. The first approach allowed the wafer apex characterization, while the second approach enabled simultaneous localization and characterization of wafer quality along two bevels and apex directions. The collected fringe patterns were analyzed by both statistical feature extraction and wavelet transform; corresponding features were also evaluated through logarithm approximation. In sum, both proposed wafer-edge inspection methods can effectively characterize various wafer-edge defect modes. Their potential lies in their applicability to online wafer metrology and inspection applications, thereby contributing to the advancement of wafer manufacturing processes.

Hole Edge Metrology and Inspection by Edge Diffractometry

Abstract This article introduces a novel hole edge inspection and metrology technology by edge diffractometry, which occurs when light interacts with the hole edge. The proposed method allows for simultaneous characterization of hole part error and edge roughness conditions. Edge diffraction occurs as light bends at a sharp edge. Such a diffractive fringe pattern, the so-called interferogram, is directly related to edge geometry and roughness. Image-based diffractometry inspection technology was developed to capture the diffractive fringe patterns. The collected fringe patterns were analyzed through statistical feature extraction methods, and numerical results such as roundness index, concentricity, and via edge roughness (VER) were obtained. The results indicated that hole 1 had an average VER of 0.665 μm and a roundness index of 0.95, while hole 2 was measured an average VER of 0.753 μm and a roundness index of 0.96. Through-focus scanning optical microscopy (TSOM) was also utilized to perform three-dimensional characterization of hole features along the depth direction. As a result, the proposed method could characterize hole part error and evaluate its roughness conditions. This study showed the potential to be adapted for automatic optical inspection for advancing microelectronics and semiconductor packaging technology.

Automatic analysis of the continuous edges of stone tools reveals fundamental handaxe variability

The edges of stone tools have significant technological and functional implications. The nature of these edges–their sharpness, whether they are concave or convex, and their asymmetry–reflect how they were made and how they could be used. Similarly, blunt portions of a tool’s perimeter hint at how they could have been grasped or hafted and in which directions force could be applied. However, due to the difficulty in accurately measuring the complex 3D geometry of tool edges with traditional methods, their attributes are often overlooked. When they are analyzed, they have traditionally been assessed with visual qualitative categories or unreliable physical measurements. We introduce new computational 3D methods for automatically and repeatably measuring key attributes of stone tool edges. These methods allow us to automatically identify the 3D perimeter of tools, segment this perimeter according to changes in edge angles, and measure these discrete edge segments with a range of metrics. We test this new computational toolkit on a large sample of 3D models of handaxes from the later Acheulean of the southern Levant. Despite these handaxes being otherwise technologically and morphologically similar, we find marked differences in the amount of knapped outline, edge angle, and the concavity of their edges. We find many handaxes possess blunt portions of perimeter, suitable for grasping, and some handaxes even possess more than one discrete sharp edge. Among our sample, sites with longer occupations and more diverse toolkits possessed handaxes with more diverse edges. Above all, this paper offers new methods for computing the complex 3D geometry of stone tool edges that could be applied to any number of artifact types. These methods are fully automated, allowing the analysis and visualization of entire assemblages.

Cutting edge preparation of micro end mills by PVD-etching technology

Micromilling tools face significant challenges in achieving cutting edge preparation by mechanical processes due to their small size. To address these limitations, a new approach for cutting edge preparation of micro end mills by physical vapor deposition (PVD) etching technology is presented. By adapting the etching strategy, which is conventionally used as pre-treatment process for PVD technology to clean and condition the surface of cemented carbide substrate, cutting edges of micromilling tools were successfully modified. The high-energy process variation by Advanced Arc-Enhanced Glow Discharge (AEGD) offers the possibility of achieving high material removal rates on the tool surfaces and thereby altering the cutting edge geometry. Fundamental investigations on material removal as well as on the effects on surface topography, sub-surface properties, and coating adhesion of a subsequently applied PVD coating are performed. To influence the topography and the cutting edge geometry, the preparation time tp and bias voltage UB were selected. Subsequently, the machining performance of the modified tools is evaluated in a micromilling process of the hardened powder-metallurgical high-speed steel AISI M3:2 with a hardness of 62 ± 1 HRC. For this purpose, micro end mills of cemented carbide with a diameter of D = 1 mm were conditioned, achieving asymmetric geometric properties of cutting edges with varying average cutting edges rounding of S¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\overline S}$$\\end{document}= 5.8 … 14.8 µm and a form-factor of K = 2.0 … 2.7. Based on the application tests a positive influence on the process forces was found. Thus, an efficient approach to cutting edge preparation can be identified by specifically designing ion etching in the PVD coating process.

Exploring Spin Distribution and Electronic Properties in FeN4-Graphene Catalysts with Edge Terminations.

Understanding the spin distribution in FeN4-doped graphene nanoribbons with zigzag and armchair terminations is crucial for tuning the electronic properties of graphene-supported non-platinum catalysts. Since the spin-polarized carbon and iron electronic states may act together to change the electronic properties of the doped graphene, we provide in this work a systematic evaluation using a periodic density-functional theory-based method of the variation of spin-moment distribution and electronic properties with the position and orientation of the FeN4 defects, and the edge terminations of the graphene nanoribbons. Antiferromagnetic and ferromagnetic spin ordering of the zigzag edges were considered. We reveal that the electronic structures in both zigzag and armchair geometries are very sensitive to the location of FeN4 defects, changing from semi-conducting (in-plane defect location) to half-metallic (at-edge defect location). The introduction of FeN4 defects at edge positions cancels the known dependence of the magnetic and electronic proper-ties of undoped graphene nanoribbons on their edge geometries. The implications of the reported results for catalysis are also discussed in view of the presented electronic and magnetic properties.

Using clinical optical coherence tomography to characterise contact lens edge shape and base curve radius

ABSTRACT Clinical relevance Clinical optical coherence tomography devices are widely used in optometry and ophthalmology and may be used to measure contact lens base curvature radius and visualise contact lens edge shape. Background Knowledge of contact lens geometry facilitates fitting, while optical coherence tomography provides a powerful means of measuring geometrical form. This study evaluates the performance of a clinical optical coherence tomography device (3D OCT-1000) in characterising contact lens edge shape and measuring the back optic zone radius of rigid gas-permeable contact lenses in vitro. Methods First, an opto-mechanical optical coherence tomography contact lens adaptor was designed and 3D-printed to facilitate a contact lens being imaged using a commercial optical coherence tomography device. Second, several image-processing algorithms and a simple calibration method were developed to measure the back optic zone radius in optical coherence tomography B-scans. Finally, based on the findings of two experiments, B-scan performance was evaluated in terms of 1) capacity to differentiate between contact lens edge geometries, and 2) capacity to obtain accurate and repeatable back optic zone radius measurements. Statistical and graphical analyses were performed to characterise reliability and reproducibility. Results The 3D OCT-1000 and adaptor combination was capable of acquiring images of sufficient quality to discriminate between soft and rigid contact lens edge geometries. Additionally, statistical analysis of the rigid contact lens measurements demonstrated satisfactory back optic zone radius measurement accuracy and reproducibility. Conclusion This study demonstrates that a 3D OCT-1000 fitted with an opto-mechanical adaptor combination can be used to assess contact lens edges in vitro and that this clinical optical coherence tomography device, combined with image processing and linear calibration of the B-scans, is capable of obtaining back optic zone radius measurements of rigid gas-permeable contact lenses that are close to the ISO 18,369-2:2018 manufacturing tolerance range (±0.05 mm).

Theoretical and Experimental Investigation of Surface Textures in Vibration-Assisted Micro Milling.

Vibration-assisted micro milling is a promising technique for fabricating engineered mi-cro-scaled surface textures. This paper presents a novel approach for theoretical modeling of three-dimensional (3D) surface textures produced by vibration-assisted micro milling. The proposed model considers the effects of tool edge geometry, minimum uncut chip thickness (MUCT), and material elastic recovery. The surface texture formation under different machining parameters is simulated and analyzed through mathematical modeling. Two typical surface morphologies can be generated: wave-type and fish scale-type textures, depending on the phase difference between tool paths. A 2-degrees-of-freedom (2-DOF) vibration stage is also developed to provide vibration along the feed and cross-feed directions during micro-milling process. Micro-milling experiments on copper were carried out to verify the ability to fabricate controlled surface textures using the vibration stage. The simulated and experimentally generated surfaces show good agreement in geometry and dimensions. This work provides an accurate analytical model for vibration-assisted micro-milling surface generation and demonstrates its feasibility for efficient, flexible texturing.

Robotic Cutting of Fruits and Vegetables: Modeling the Effects of Deformation, Fracture Toughness, Knife Edge Geometry, and Motion

Robotic Cutting of Fruits and Vegetables: Modeling the Effects of Deformation, Fracture Toughness, Knife Edge Geometry, and Motion

Occurrence of catastrophic tool wear patterns through systematic thermomechanical modeling

To achieve optimal tool performance, it is essential to not only comprehend the wear patterns during the steady wear stage but also the final one where catastrophic wear patterns are usually involved. However, previous focus has been put individually into them, thereby the mechanism connections in between have not yet been completely demonstrated. This study aims to bridge this gap by developing an analytical model based on the slip-line theory and imaginary heat source formulations for worn tools with cutting edge geometry extracted from the steady wear stage. The model computes the thermomechanical loads on the tool surface, which are then incorporated into a mechanism-based wear rate model that has been carefully calibrated. Finally, a nodal-displacement algorithm is used to iteratively determine the further tool edge profiles until the final wear stage. The sequential edge profiles demonstrate that the most significant wear increments occur at the rear of the tool flank wear land, resulting in a gradually deepening and widening notched region. These predictions are consistent with experimental findings where a notch belt wear is observed to grow along the tool main cutting edge during the steady wear stage, which ultimately decreases the edge toughness and leads to catastrophic wear patterns.

Analysis of the flange turning of aluminium aerosol cans based on tool edge geometry

In recent years, the cosmetics industry, as the largest user of aerosol packaging, has been growing at an accelerating pace, requiring the production of aerosol cans with an increasing number of design elements. In the production of aluminium aerosol cans, the final shape is formed in several steps from a disc-shaped blank by back-rolling, and a so-called flange cutting (turning) operation is usually carried out after the flange of the can has been formed. Experience has shown that this operation often results in difficult-to-handle flowing chips, which in some cases can lead to a poor-quality product. In this paper, the material and edge geometry of the insert bit used in the flange turning operation are investigated and edge geometry modification recommendations are made to avoid unfavourable machining conditions.