Grinding Process Research Articles

Research on the generation mechanism of surface and subsurface damage in loose abrasive lapping of RB-SiC ceramics

Reaction-bonded silicon carbide ceramics (RB-SiC) are extensively utilized in aerospace, space optics, and other fields due to their superior physical and chemical properties. Loose abrasive lapping plays a crucial role in the optical manufacturing of large-diameter RB-SiC mirrors. Previous research predominantly focused on grinding processes and overlooked the removal mechanism during lapping and their impact on surface and subsurface damage. In this study, a three-body brittle fracture removal model was established to explore the removal mechanisms of RB-SiC. Additionally, experiments were carried out to investigate the influence of abrasive particle size on the surface and subsurface damage. Experimental results confirm the theoretical model and indicate that for RB-SiC, different particle sizes correspond to distinct removal mechanisms, causing abrupt changes in surface roughness, while the layer under SiC acts as a buffer against the propagation of subsurface damage. These findings help optimize the manufacturing process, improve lapping efficiency, and enhance mirror performance.

The capability of Acoustic Emission features to monitor diamond-coated burr grinding wear and effectiveness

Within manufacturing there is a growing need for autonomous Tool Condition Monitoring (TCM) systems, with the ability to predict tool wear and failure. This need is increased, when using specialised tools such as Diamond-Coated Burrs (DCBs) for grinding high strength ceramics or glass, in which the random nature of the tool, inconsistent manufacturing methods and high wear rates create large variance in tool life. This unpredictable nature leads to a significant fraction of a DCB tool's life being underutilised due to premature replacement. Workpiece surface damage, increased grinding forces and large-scale diamond grain pullout could all be the result of high levels of runout and in-circularity common within electroplated DCBs. As such it is important to not only monitor the overall tool wear but also tool condition. Acoustic Emission (AE) presents as an indirect on-machine sensing method highly suited to grinding applications. The high frequency range of AE, >20 kHz, prevents machine noise from dominating the acquired signals, isolating the micro-scale machining processes within noises machine environments. AE resulting from the grinding process has the potential to monitor not only tool wear but also runout and circularity. A series of DCB wear tests have been conducted, each consisting of the continuous acquisition of AE during grinding and frequent tool surface measurements. Preliminary results demonstrate AE kurtosis can be seen as an indicator of each tool’s runout, representing the fraction of time the tool and workpiece are in contact during a revolution. As a result, an indirect monitoring system capable of monitoring wear and tool state with AE could be utilised within the manufacturing sector.

Insight into the effect of ultrasonic treatment on surface properties and flotation behavior of chalcopyrite after galvanic corrosion of grinding media and chalcopyrite

Ultrasonic treatment is an effective means to promote chalcopyrite flotation. Chalcopyrite needs to be grinded before flotation production. During the grinding process, galvanic corrosion occurs between chalcopyrite and iron grinding media. Galvanic corrosion significantly affects the efficacy of ultrasonic treatment on chalcopyrite flotation. Nonetheless, there is still a lack of research on ultrasonic treatment of chalcopyrite after galvanic corrosion. In this study, micro-flotation tests, SEM-EDS, TOF-SIMS, XPS, ICP-OES and electrochemical tests were used to study the effects of ultrasonic treatment on the surface properties and flotation behavior of chalcopyrite before and after galvanic corrosion under different ultrasonic conditions and galvanic corrosion conditions. The results show that in the absence of galvanic corrosion, short time and low power ultrasonic treatment can improve chalcopyrite floatability. However, when the chalcopyrite after strong galvanic corrosion is subjected to ultrasonic treatment, the increase of galvanic corrosion temperature, galvanic corrosion time, ultrasound power and ultrasound time result in a marked reduction of the flotation recovery of chalcopyrite. The synergistic effect of ultrasonic and galvanic corrosion significantly inhibits the flotation recovery of chalcopyrite, which may provide a new potential way for the inhibition of sulfide ore in flotation production. The research results are helpful to expand the use range of ultrasonic processing for sulfide mineral pretreatment and flotation, and provide a theoretical reference for the application of ultrasonic treatment in sulfide minerals with galvanic corrosion.

Active compliance control of grinding process for stripping enameled copper wire

The hairpin motor is among the motors used in eco-friendly automobiles. Unlike the random-winding method, this method features a square cross-sectional enamel coil formed into several hundred hairpins inserted into the stator. This offers an increased space factor, which leads to enhanced motor power. With the growing use of hairpin motors, there is an increasing demand for automated equipment in their production. With an aim to improve the manufacturing quality of hairpin motors, many countries are conducting research and development. The process of enamel removal is one of the key steps in hairpin-forming equipment and can significantly affect the performance of the motor. A precise machining process technology is required to improve the enamel removal process, achieve higher enamel removal rates, and reduce wire loss rates. Grinding is a technique used for enamel removal. In this study, an adaptive control algorithm was applied to the grinding process to enhance the enamel removal machining performance. During the machining process, the vertical position of the spindle was controlled to maintain a consistent machining depth for tracking the target grinding force. An experimental setup, which included a system for measuring the spindle torque to calculate the grinding force in real time, was created. To validate the performance of the adaptive control technology, experiments were conducted using this setup. Furthermore, experiments were conducted to observe the changes in the grinding force ratio based on the conditions of the grinding wheel. The correlation between the grinding force ratio and tool condition was analyzed, and based on this, the feasibility of assessing tool condition and determining the timing for tool replacement through real-time monitoring of the grinding force ratio was confirmed.

Chatter stability analysis for non-circular high-speed grinding process with dynamic force modelling

To avoid instability and resulting chatter during the non-circular grinding process, it is necessary to elucidate the potential occurrence of periodic chatter behavior when high-speed grinding loses stability and to define the stability boundary of the grinding system. Building upon an analysis of the geometric kinematic characteristics of non-circular profiled components, a dynamic grinding force model for non-circular high-speed grinding was derived by considering both the delay effect and the elastic yielding mechanism between the grinding wheel and workpiece. Then, A multi-factor coupled dynamic model of non-circular grinding was established. By employing a multi-scale approach, bifurcation analysis and classification of the instability process in the grinding system were conducted, using a typical non-circular profiled shaft component, such as a camshaft, for theoretical analysis and experimental validation. The research determined the stability boundary of the high-speed grinding process for non-circular profile components, validated the possibility of the existence of a conditionally stable chatter region in the non-circular high-speed grinding process, and identified differences in grinding chatter characteristics among different segments of the cam profile, with a greater propensity for chatter at the juncture of the cam fall and base circle.

Rotary ultrasonic surface machining of silicon: Effects of ultrasonic power and tool rotational speed

The surging demand for monocrystalline silicon materials in the production of microelectronic components highlights its crucial role in the semiconductor and optic industries. Hence it is inevitable to produce a silicon workpiece with high quality finish to meet the demand in semiconductor industries. Due to high brittleness, controlling the quality of silicon in surface machining is quite difficult. Traditional manufacturing processes induce issues like rough surfaces and edge chipping. It was reported that rotary ultrasonic surface machining (RUSM) can effectively reduce cutting force, roughness, and edge chipping in machining of brittle materials. There have been several studies on drilling and sliding silicon materials using rotary ultrasonic machining investigating the effects of machining parameters on the output variables such as cutting force, torque, edge chipping, surface roughness etc. However, to the best of the authors’ knowledge, there are no reported investigations on effects of machining variables (ultrasonic power and tool rotation speed) in surface machining of silicon materials using the rotary ultrasonic machining. This study aimed to investigate the impacts of ultrasonic power and tool rotation speed on the cutting force, edge chipping, and surface roughness. Experimental results show that the ultrasonic vibration and tool rotation speed had a notable impact on edge chipping and cutting forces. Lastly, the current research has paved the way for widening the research on investigating grinding of the silicon wafer in semiconductor manufacturing with ultrasonic vibration and high rotation speed. In semiconductor wafer manufacturing, grinding process is used to reduce the flatness but generate surface and subsurface damage. With further investigations, RUSM can contribute to reducing these damages.

Material removal mechanism of TiCp/Fe composite by multi-diamond-abrasive-grinding considering the random distribution characteristics of particles

The TiC ceramics reinforced Fe matrix composite (TiCp/Fe) exhibits exceptional properties, including high hardness, strength, wear, and heat resistance. This study focuses on investigating the material removal mechanism to achieve high-quality and low-damage surfaces. A three-dimensional particle random distribution algorithm is proposed based on the random distribution characteristics of TiC particles. Furthermore, a multi-diamond-abrasive grinding finite element model is established using the Rayleigh probability distribution model to account for the randomness of undeformed chip thickness during the grinding process. This study combines experimental and simulation analyses to investigate the variations in grinding forces, stress field distributions, and surface and subsurface quality. The results reveal that the material removal process can be categorized into five stages: ploughing of the Fe matrix and TiC particle, TiC particle crack initiation, TiC particle crack extension, and TiC particle fracture. Moreover, the process of removing TiC particles can be further grouped into ductile removal, ductile-brittle removal, and brittle removal, depending on the undeformed chip thickness. This study improves the comprehension of the mechanism of TiCp/Fe composite material and establishes a significant practical guidance for the diamond grinding processing of metal matrix composites.

Enhancement of capacitance retention of ZnCo2S4@Metal organic framework composite electrodes by hydrothermal process

Metal organic framework-derived materials are promising electrodes for electrochemical supercapacitors due to their surface area, porosity, and excellent redox behaviors. In the present study the fabrication of ZnCo2S4 and ZnCo2S4@ZIF-67 composites synthesized by solid-state grinding and hydrothermal processing for supercapacitor utilization. Studies using XRD, XPS, FTIR, BET, FE-SEM, and HR-TEM are employed to validate the morphological, surface, and structural characteristics. Highly conductive ZnCo2S4 nanostructured materials are intercalated with MOF surfaces to enhance electron transport. The high number of active sites involved in the rapid electrochemical phase fluctuation using 1 M KOH electrolyte may be the cause of this. ZnCo2S4 and ZnCo2S4@ZIF-67 composites are used to create the working electrode, while a 1 M KOH electrolyte is used for the supercapacitor. By employing a three-electrode design, the created composite electrodes improve cyclic retention with specific capacitances of 245 and 447.14F/g at 1 A/g, respectively. Two electrode configurations are used to build ZnCo2S4@ZIF-67/1M KOH/SSC, which produced results of 151.42F/g at 1 A/g, 85.2 % capacitance retention at 7 A g−1 of 6000 cycles, and 18.93 Wh kg−1 energy density at 642.85 W kg−1 power density. Thus, the fabricated composite electrodes may find application in electrochemical symmetric supercapacitor via two electrode configuration systems.

Experimental model of crushing coriander seeds

Seed crushing is one of the main technological operations [1] in the process of obtaining essential and fatty oils, on which their yield and quality depend [2]. Improving the process of preparation for the extraction of coriander seeds by selective cryodesintegration and creating technological lines of various productivity is of significant importance and relevance. However, modern methods and means of cryodesintegration of coriander seeds require research and improvement. The process of seed grinding is divided into three phases [3]: elastic deformation, which occurs from the beginning of the action of the applied force on the material being ground until the elastic limit is reached and is accompanied by compaction and compression of the structural aggregates of the seeds; plastic deformation, which occurs from the moment of the beginning of the shift of individual elements of the material relative to each other and is characterized by the relative displacement of the structural aggregates of the seed kernel, as a result of which the material is compacted and flattened; destruction of the material with the formation of a free surface of particles. The main parameter of the process of cryodesintegration of coriander seeds is subject to theoretical justification - normal pressure, leading to deformation, where the pressure on the seeds exceeds their tensile strength, but there is no appearance of oil on the surface of the opened seeds. This prevents oil loss and contamination of the working parts, especially with essential oils. Monitoring theoretical studies of the grinding process allows us to talk about the need to develop a mathematical description of this process.

Unveiling the temperature-dependent deformation mechanisms of single crystal gallium nitride in nanoscratching

The surface grinding process of single crystal gallium nitride (GaN) is intricate, and localized high temperature generated during interactions between the workpiece and the abrasives on grinding wheel is inevitable. Elevated temperatures significantly affect the deformation mechanisms of GaN, which remains inadequately elucidated. In this study, nanoscratching experiments were systematically conducted on the (0001) plane of GaN single crystal across a temperature range up to 500 ℃, and the resultant deformation patterns were thoroughly characterized. The results indicate that temperature elevation delays the brittle-to-ductile transitions in GaN and enhance its anisotropy. Additionally, GaN exhibits increased plasticity as temperature rises, leading to distinct scratch-induced subsurface deformation patterns at varying temperatures: at room temperature, the thickness of the subsurface damaged layer is primarily influenced by the penetration depth of cross slips, whereas at 500 ℃, basal slipping predominantly defines the thickness of the subsurface damaged layer. The plastic deformation patterns at both room temperature and 500 ℃ mainly involve phase transition, polycrystal formation, slips, stacking faults, dislocations and lattice distortions. The discrepancies in deformations at varying temperatures were thoroughly investigated by transmission electron microscopy and molecular dynamics simulations, and the underlying mechanisms were elucidated.

Justification of design-mode parameters separating device

In Kazakhstan, the basis of the country's food security is livestock products. Increasing the production of livestock products is impossible without creating a strong feed base, high-quality preparation of feed, rational use and reduction of feed losses. Preparation of coarse stem feed for feeding requires grinding with feed grinding and mixing machines to obtain balanced feed mixtures. The grinding process is complicated by the fact that, along with coarse stem feed, foreign solid impurities enter, which damage the cutting organs of machines and cause a long shutdown of the entire feed preparation line, disruption of the feeding schedule, and reduction in animal weight gain and milk yield. These problems are of particular relevance in the development of small farms with a low level of mechanization. The authors have developed a device for separating foreign solid impurities from coarse stem feeds, the novelty of which is confirmed by a patent for an invention of the Republic of Kazakhstan. The article theoretically substantiates the influence of the design and operating parameters of the separating device for cleaning stem feed from foreign solid impurities. To separate foreign solid impurities from bound materials, such as stem feed, the most effective are separators with working bodies in the form of an air flow. In separators of this type, differences in the totality of physical and mechanical properties are used to separate foreign impurities from stem feeds. This approach makes it possible to achieve better separation by mechanical devices and expect their development towards the use of as many combinations of the distinctive properties of the separated components as possible.

Comparison of polishing methods for two types of monolithic all-ceramic crowns after occlusal adjustments: Polishing paste versus glazed porcelain.

This study compared the effects of two surface preparation methods on two types of zirconia. Immediately prior to the placement of a monolithic zirconia crown, its morphology may be modified using a rotary cutting instrument for occlusal adjustments. The crown surface is scratched during the grinding process and, thus, requires polishing. Simplified zirconia crowns of 3Y and 5Y were fabricated and used as specimens. The surface roughness and gloss of the occlusal surfaces of specimens were measured and compared when a polishing compound was used after polishing points and when a silica-based coating was sintered. No significant differences were observed in surface roughness between 3Y and 5Y zirconia. The use of polishing compounds was effective because polishing points alone only resulted in a level of surface roughness that may cause wear on antagonist teeth. Although the silica-based coating improved surface properties, the polishing compound more effectively improved surface roughness.

Impact of axial segregation characteristics on the particle collision energy in rotating drums

The particle mixture in rotating drums is not always in a completely mixed state, resulting in a complex relationship between the particle mixing and segregation characteristics and the overall collision energy. Based on existing experimental validation, the rotary drums with axial adjacent segments are numerically simulated via the discrete element method to investigate the axial segregation mechanism of the particle mixtures in rotary drums. The results show that the rotational direction of the adjacent axial segments changes the axial flow configuration, resulting in a transformation of the overall particle mixing and segregation characteristics. Based on the proposed novel relative regional total energy (RRTE) index, this work further evaluates the impact of the axial segregation characteristics on the collision energy of binary and ternary particle mixtures within rotary drums. The axial segregation phenomenon makes the RRTE of each radial surface inconsistent, resulting in difficultly reflecting the particle collision energy through the individual radial surface. Compared with the radial drum surface, the RRTE represented by the axial surface can better reflect the particle collision energy in rotating drums. In summary, the more obvious the presence of axial segregation characteristics in rotary drums, the lower the total collision energy used for overall grinding process of the media and abrasive particles.

Recycling and optimum utilization of GFRP waste into low-carbon geopolymer paste for sustainable development

To provide an eco-friendlier alternative to traditional ordinary Portland cement (OPC) binder, this study utilized glass fiber reinforced polymer (GFRP) waste powder as a precursor material to prepare geopolymer paste (GP). Through a series of mechanical, thermal, and mineral admixture activation procedures, efforts are made to augment the reactivity of GFRP powder-based geopolymers. The research reveals that subjecting GFRP powder to a 30-min grinding process amplifies the compressive strength of GP by up to 37 %. Moreover, elevating curing temperatures to 60 °C leads to a substantial enhancement in the strength of GFRP powder-based GP, attributable to the formation of more amorphous N-A-S-H and C-(A)-S-H gels. However, prolonged grinding durations yield only marginal alterations in particle size, while curing at 80 °C demonstrates a detrimental effect on strength. The choice of resin exhibits a discernible impact on both workability and strength. Notably, pure glass fiber powder-based GP displays superior compressive strength but exhibits increased brittleness, whereas GFRP powder-based GP excels in flexural strength. Moreover, the inclusion of ground granulated blast furnace slag (GGBS) in the mixture accelerates setting time and reduces flowability of GFRP powder-based GP. Strength shows a positive correlation with GGBS content, although the impact on flexural strength is less pronounced compared to compressive strength. Life cycle assessment (LCA) showed GFRP powder-based GP with 50 % GGBS replacement had a 35 %–48 % lower Global Warming Potential (GWP)/strength ratio compared to OPC pastes. Furthermore, this formulation demonstrates a 15 % decrease relative to GGBS-based GP, and a reduction of 13 %–25 % compared to GGBS/Fly Ash (FA)-based GPs. These results underscore its potential as an environmentally preferable building material.

Mechanism of three-body abrasive grain grinding on GaN textured surfaces under uniform acceleration and variable depth

In this study, molecular dynamics (MD) was used to simulate the three-body grinding process on the textured surfaces of gallium nitride (GaN) and to investigate the effect of the processing parameters during the grinding process on the quality of the process and the removal mechanism of the material. The results show that the friction coefficient, normal force, tangential force, grinding temperature and potential energy increase with the increase of the accelerated interval segment, while the stress, subsurface damage depth and dislocation length decrease. Overall, higher speed value classes in the GaN grinding process are favorable for improving the surface finish quality. In addition, under the conditions of variable depth machining, with the increase of rising speed, the coefficient of friction, the tangential force, the normal force, the potential energy increase, the grinding temperature increases, the stress decreases, and the subsurface damage of the workpiece and the nucleation of dislocations are also significantly reduced, and the surface finish quality and the surface integrity of the workpiece are improved. The textured surfaces is an innovation in GaN processing.

A FACILE METHOD TO PRODUCE HIGH-BULK AND HIGH-STRENGTH ROLLED RECONSTITUTED TOBACCO SHEET WITH REFINED TOBACCO CELLULOSE FIBERS

The rolling method is a pivotal means for reconstituted tobacco sheet (RTS) production due to its cost-effectiveness. However, the traditional rolling method is limited by its raw material grinding processes and yields of rolled RTS (RRTS) with subpar strength and bulk. Therefore, it is a challenge to develop a method to produce high-strength and high-bulk RRTS. Here, by replacing traditional raw materials grinding processes with papermaking refining processes, we present a facile and practical method to produce RRTS with elevated bulk and strength. This method separately refines tobacco leaves and stems into long and coarse leave and stem cellulose fibers. These fibers were subsequently reconstructed into RRTS. The detailed process parameters were optimized. The comparative RRTS with flax fibers instead of stem fibers was investigated. The optimal formula of new RRTS was determined. The updated processes, along with the use of refined cellulose fibers, led the RRTS to a significant improvement in strength and bulk, with a 5.3-fold increase in strength, and a 0.7-fold increase in bulk, while smoking qualities were preserved, which surpassed the smoking experience of RRTS with flax fibers. We anticipate this work will enhance the qualities of RTS and facilitate the transition of traditional tobacco industries toward healthier directions.

Physicochemical and Morphological Changes in Long-Grain Brown Rice Milling: A Study Using Image Visualization Technologies

This study evaluated the changes in physicochemical properties and appearance quality of long-grain rice during the grinding process using image technologies and aimed to provide reference for future research. The brown rice milling process was divided into three stages, and flatbed scanning, scanning electron microscopy (SEM), X-ray micro-computed tomography (micro-CT), low-field nuclear magic resonance (LF-NMR), and headspace–gas chromatography–ion mobility spectrometry (HS–GC–IMS) were employed to examine the physicochemical and volatile properties of the samples. Results revealed a continuous increase in the degree of milling, with a broken rice rate and a whiteness value increasing by 50.84% and 21.13%, respectively, compared with those during the initial stage; dietary fiber and vitamin B1 contents were reduced by 54.41% and 66.67%, respectively. The image results visualized showed that the cortex of brown rice was gradually peeled off with the increase in milling degree; the cortical thickness was gradually reduced, the endosperm was gradually exposed, and the surface was smoother and shinier. T2 populations exhibited a shift toward longer relaxation times, followed by a decrease in relaxation time during the milling process. Additionally, 31 target compounds impacting rice flavor, mainly ketones, alcohols, and esters, were identified, and the concentration of volatile substances in the B region decreased with the reduction in the bran layer; the concentration of volatile substances in the C region provided rice flavor, which increased with the milling process. This study showed changes in the physicochemical properties and appearance quality of long-grain brown rice during milling. Furthermore, the use of various image processing techniques offers significant insights for optimizing processing parameters and enhancing overall quality and taste.

Experimental Determination and Simulation Validation: Johnson–Cook Model Parameters and Grinding Simulation of 06Cr18Ni11Ti Stainless Steel Welds

Hydrogen permeation resistance in the welded region of 06Cr18Ni11Ti steel is relatively weak due to surface defects, which need high integrity surface machining. The parameters of the welding material for 06Cr18Ni11Ti steel are currently unavailable, which causes some inconvenience for simulation studies. To fill the lack of 06Cr18Ni11Ti steel weld material parameters in the relevant literature at the present stage, the quasi-static tensile test at different strain rates and notch specimen tensile tests were conducted in this paper and determined the Johnson–Cook (J-C) constitutive model parameters and Johnson–Cook failure model parameters. Subsequently, a multi-grain grinding simulation model was built based on W-M fractal dimension theory by using the determined material parameters. The influence of processing parameters on grinding heat was analyzed. Grinding experiments were conducted to analyze the influence of processing parameters on grinding heat and grinding force. By comparing the simulation and experimental results, it is revealed that the average error is 9.37%, indicating relatively small discrepancy. It is demonstrated that the grinding simulation model built in this paper could efficiently simulate the grinding process, and the determined weld material parameters of 06Cr18Ni11Ti steel have been verified to possess high accuracy and reliability.

Improvement of wire marks on the surface of Si3N4 ceramics cut by diamond wire saw

The presence of wavy wire marks on the cut surface of silicon nitride (Si3N4) ceramics reduces the mechanical properties of the slices and increases the workload of subsequent grinding and polishing processes. To improve the wire marks, a workpiece reciprocating movement-assisted diamond wire sawing (RMA-DWS) technology is proposed in this paper. While diamond wire sawing the Si3N4 ceramics, the workpiece is moved back and forth in the direction of the saw wire movement to assist in sawing. Single factor and orthogonal experiments were carried out to analyze the characteristics of the surface created by this sawing technology. The effects of workpiece reciprocating movement distance, workpiece reciprocating movement speed, saw wire speed and feed speed on the sawn surface morphology, surface roughness Ra and wire marks PV value, as well as the primary and secondary relationships of the effects, were investigated. And the optimal parameter combinations were explored. The results show that within the range of process parameters studied in this paper, the surface morphology of Si3N4 ceramics slices shows a comprehensive effect of material ductility and brittleness removal, the RMA-DWS technology can improve wire marks on the slice surface. Surface wire marks PV value can be reduced by increasing the workpiece reciprocating movement distance and saw wire speed, reducing the feed speed, while increasing the reciprocating movement speed of the workpiece, the PV value shows a trend of first decreasing and then increasing. The variation amplitude of surface roughness Ra value is not significant, and the variation trend is roughly similar to the change trend of PV value. It was determined that the experiment with the process parameters combination of 0.1 m/min feed speed, 90 mm workpiece reciprocating distance, 15 mm/s workpiece reciprocating speed and 1400 m/min saw wire speed yielded the optimal result, significantly improving the wire marks of the sliced surface. The results of this paper provide ideas for the development of sawing wire marks improvement technology.

Molecular dynamics investigation of rotation-assisted grinding process for GaN with layered heterostructure of the Wurtzite/Zinc-blende

Molecular dynamics investigation of rotation-assisted grinding process for GaN with layered heterostructure of the Wurtzite/Zinc-blende