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Active vibration control of spindle in ultra-precision turning machine
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作者 WANG Jia-chun, LI Dan (Precision Engineering Research Institute, Harbin Institute of Technology, Harbin, 150001, China) 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2000年第S1期48-50,共3页
In order to minimize vibration and improve rotary precision of spindle, we apply active vibration control technique to ultra-precision turning machine based on the analysis of vibration characteristic of aerostatic be... In order to minimize vibration and improve rotary precision of spindle, we apply active vibration control technique to ultra-precision turning machine based on the analysis of vibration characteristic of aerostatic bearing spindle. Using aerostatic bearing itself as actuator, the vibration of spindle is controlled by adjusting admission pressure respectively and by changing pressure distribution in the bearing. The experiments and simulations prove that this method can minimize the vibration of spindle effectively. 展开更多
关键词 ultra-precision turning machine SPINDLE VIBRATION ROTARY PRECISION active VIBRATION control
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Study on 6-DOF active vibration-isolation system of the ultra-precision turning lathe based on GA-BP-PID control for dynamic loads
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作者 Bo Wang Zhong Jiang Pei-Da Hu 《Advances in Manufacturing》 SCIE EI CAS CSCD 2024年第1期33-60,共28页
The vibration disturbance from an external environment affects the machining accuracy of ultra-precision machining equipment.Most active vibration-isolation systems(AVIS)have been developed based on static loads.When ... The vibration disturbance from an external environment affects the machining accuracy of ultra-precision machining equipment.Most active vibration-isolation systems(AVIS)have been developed based on static loads.When a vibration-isolation load changes dynamically during ultra-precision turning lathe machining,the system parameters change,and the efficiency of the active vibration-isolation system based on the traditional control strategy deteriorates.To solve this problem,this paper proposes a vibration-isolation control strategy based on a genetic algorithm-back propagation neural network-PID control(GA-BP-PID),which can automatically adjust the control parameters according to the machining conditions.Vibration-isolation simulations and experiments based on passive vibration isolation,a PID algorithm,and the GA-BP-PID algorithm under dynamic load machining conditions were conducted.The experimental results demonstrated that the active vibration-isolation control strategy designed in this study could effectively attenuate vibration disturbances in the external environment under dynamic load conditions.This design is reasonable and feasible. 展开更多
关键词 ultra-precision diamond turning lathe Active vibration isolation Six degrees of freedom Dynamic load Genetic algorithm-back propagation neural network-PID(GA-BP-PID)control
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Weakening of the anisotropy of surface roughness in ultra-precision turning of single-crystal silicon 被引量:1
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作者 Wang Minghai Wang Ben Zheng Yaohui 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2015年第4期1273-1280,共8页
Ultra-precision machining causes materials to undergo a greatly strained deformation process in a short period of time.The effect of shear strain rates on machining quality, in particular on surface anisotropy, is a t... Ultra-precision machining causes materials to undergo a greatly strained deformation process in a short period of time.The effect of shear strain rates on machining quality, in particular on surface anisotropy, is a topic deserving of research that has thus far been overlooked.This study analyzes the impact of the strain rate during the ultra-precision turning of single-crystal silicon on the anisotropy of surface roughness.Focusing on the establishment of cutting models considering the tool rake angle and the edge radius, this is the first research that takes into account the strain rate dislocation emission criteria in studying the effects of the edge radius, the cutting speed, and the cutting thickness on the plastic deformation of single-crystal silicon.The results of this study show that the uses of a smaller edge radius, faster cutting speeds, and a reduced cutting thickness can result in optimally uniform surface roughness, while the use of a very sharp cutting tool is essential when operating with smaller cutting thicknesses.A further finding is that insufficient plastic deformation is the major cause of increased surface roughness in the ultra-precision turning of brittle materials.On this basis, we propose that the capacity of single-crystal silicon to emit dislocations be improved as much as possible before brittle fracture occurs, thereby promoting plastic deformation and minimizing the anisotropy of surface roughness in the machined workpiece. 展开更多
关键词 Anisotropy of surface roughness Cutting speed Edge radius Single-crystal silicon Strain rate ultra-precision turning WEAKENING
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Case Retrieval Strategy of Turning Process Based on Grey Relational Analysis
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作者 Jianfeng Zhao Yunliang Huo +3 位作者 Ji Xiong Junbo Liu Zhixing Guo Qingxian Li 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第2期1663-1678,共16页
To solve the problem of long response time when users obtain suitable cutting parameters through the Internet based platform,a case-based reasoning framework is proposed.Specifically,a Hamming distance and Euclidean d... To solve the problem of long response time when users obtain suitable cutting parameters through the Internet based platform,a case-based reasoning framework is proposed.Specifically,a Hamming distance and Euclidean distance combined method is designed to measure the similarity of case features which have both numeric and category properties.In addition,AHP(Analytic Hierarchy Process)and entropy weight method are integrated to provide features weight,where both user preferences and comprehensive impact of the index have been concerned.Grey relation analysis is used to obtain the similarity of a new problem and alternative cases.Finally,a platform is also developed on Visual Studio 2015,and a case study is demonstrated to verify the practicality and efficiency of the proposed method.This method can obtain cutting parameters which is suitable without iterative calculation.Compared with the traditional PSO(Particle swarm optimization algorithm)and GA(Genetic algorithm),it can obtain faster response speed.This method can provide ideas for selecting processing parameters in industrial production.While guaranteeing the characteristic information is similar,this approach can select processing parameters which is the most appropriate for the production process and a lot of time can be saved. 展开更多
关键词 CBR turning process grey relation AHP entropy weight
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Analysis on the turning point of dynamic in-plane compressive strength for a plain weave composite
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作者 Xiaoyu Wang Zhixing Li +2 位作者 Licheng Guo Zhenxin Wang Jiuzhou Zhao 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第2期485-495,共11页
Experimental investigations on dynamic in-plane compressive behavior of a plain weave composite were performed using the split Hopkinson pressure bar. A quantitative criterion for calculating the constant strain rate ... Experimental investigations on dynamic in-plane compressive behavior of a plain weave composite were performed using the split Hopkinson pressure bar. A quantitative criterion for calculating the constant strain rate of composites was established. Then the upper limit of strain rate, restricted by stress equilibrium and constant loading rate, was rationally estimated and confirmed by tests. Within the achievable range of 0.001/s-895/s, it was found that the strength increased first and subsequently decreased as the strain rate increased. This feature was also reflected by the turning point(579/s) of the bilinear model for strength prediction. The transition in failure mechanism, from local opening damage to completely splitting destruction, was mainly responsible for such strain rate effects. And three major failure modes were summarized under microscopic observations: fiber fracture, inter-fiber fracture, and interface delamination. Finally, by introducing a nonlinear damage variable, a simplified ZWT model was developed to characterize the dynamic mechanical response. Excellent agreement was shown between the experimental and simulated results. 展开更多
关键词 Plain weave composite Dynamic strength Quantitative criterion turning point Failure mechanism
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Tool path generation of ultra-precision diamond turning: A state-of-the-art review
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作者 Hu Gong Shengjun Ao +2 位作者 Kuntao Huang Yi Wang Changya Yan 《Nanotechnology and Precision Engineering》 EI CAS CSCD 2019年第3期118-124,共7页
With the increasing market demand for optical complex surface parts,the application of multi-axis ultraprecision single-point diamond turning is increasing.A tool path generation method is very important to decrease m... With the increasing market demand for optical complex surface parts,the application of multi-axis ultraprecision single-point diamond turning is increasing.A tool path generation method is very important to decrease manufacturing time,enhance surface quality,and reduce cost.Compared with the tool path generation of the traditional multi-axis milling,that of the ultra-precision single-point diamond turning requires higher calculation accuracy and efficiency.This paper reviews the tool path generation of ultra-precision diamond turning,considering several key issues:cutter location(CL)points calculation,the topological form of tool path,interpolation mode,and G code optimization. 展开更多
关键词 ultra-precision machining Tool path generation Diamond turning Optical surface
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3-Turns教学法在实践共同体促进深度学习中的应用
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作者 陈东毅 王武 +2 位作者 林建新 黄捷 陈建国 《实验室研究与探索》 CAS 北大核心 2024年第4期151-154,共4页
在电气工程专业实践教学过程中凝练出由Turn up、Turn away、Turn back等环节组成的3-Turns教学法。经过多轮的实践应用,3-Turns教学法在实践共同体中提供了一个兼具解释性与可操作性的教学样例。研究发现,3-Turns教学法对实践共同体促... 在电气工程专业实践教学过程中凝练出由Turn up、Turn away、Turn back等环节组成的3-Turns教学法。经过多轮的实践应用,3-Turns教学法在实践共同体中提供了一个兼具解释性与可操作性的教学样例。研究发现,3-Turns教学法对实践共同体促进工科生深度学习起到了提质增效的作用;3-Turns教学法为工程实践学习情境的强化设计提供了理论依据与经验支持。该研究验证了基于3-Turns教学法的实践共同体促进工科生深度学习的有效性,为助力工科人才培养质量的持续提升做出了积极的探索与实践。 展开更多
关键词 实践共同体 深度学习 3-turns教学法 实践教学
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Integral Event-Triggered Attack-Resilient Control of Aircraft-on-Ground Synergistic Turning System With Uncertain Tire Cornering Stiffness 被引量:1
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作者 Chenglong Du Fanbiao Li +2 位作者 Yang Shi Chunhua Yang Weihua Gui 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第5期1276-1287,共12页
This article proposes an integral-based event-triggered attack-resilient control method for the aircraft-on-ground(AoG) synergistic turning system with uncertain tire cornering stiffness under stochastic deception att... This article proposes an integral-based event-triggered attack-resilient control method for the aircraft-on-ground(AoG) synergistic turning system with uncertain tire cornering stiffness under stochastic deception attacks. First, a novel AoG synergistic turning model is established with synergistic reverse steering of the front and main wheels to decrease the steering angle of the AoG fuselage, thus reducing the steady-state error when it follows a path with some large curvature. Considering that the tire cornering stiffness of the front and main wheels vary during steering, a dynamical observer is designed to adaptively identify them and estimate the system state at the same time.Then, an integral-based event-triggered mechanism(I-ETM) is synthesized to reduce the transmission frequency at the observerto-controller end, where stochastic deception attacks may occur at any time with a stochastic probability. Moreover, an attackresilient controller is designed to guarantee that the closed-loop system is robust L2-stable under stochastic attacks and external disturbances. A co-design method is provided to get feasible solutions for the observer, controller, and I-ETM simultaneously. An optimization program is further presented to make a tradeoff between the robustness of the control scheme and the saving of communication resources. Finally, the low-and high-probability stochastic deception attacks are considered in the simulations. The results have illustrated that the AoG synergistic turning system with the proposed control method follows a path with some large curvature well under stochastic deception attacks. Furthermore,compared with the static event-triggered mechanisms, the proposed I-ETM has demonstrated its superiority in saving communication resources. 展开更多
关键词 Adaptive observer aircraft-on-ground(AoG)synergistic turning attack-resilient controller integral-based event-triggered mechanism L_2-stability
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The summer solstice is the turning point when light and temperature affect the growth of trees
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作者 Tao Xu 《Journal of Forestry Research》 SCIE CAS CSCD 2023年第6期1657-1657,共1页
The interaction between light and temperature is known to influence the seasonal growth of trees.Traditional studies on"light"primarily focus on day length,specifically short day(SD)or long day(LD)conditions... The interaction between light and temperature is known to influence the seasonal growth of trees.Traditional studies on"light"primarily focus on day length,specifically short day(SD)or long day(LD)conditions.However,little research has been conducted on the process of transitioning between SD and LD conditions. 展开更多
关键词 turning primarily specifically
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Technique for Multi-Pass Turning Optimization Based on Gaussian Quantum-Behaved Bat Algorithm
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作者 Shutong Xie Zongbao He Xingwang Huang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第8期1575-1602,共28页
The multi-pass turning operation is one of the most commonly used machining methods in manufacturing field.The main objective of this operation is to minimize the unit production cost.This paper proposes a Gaussian qu... The multi-pass turning operation is one of the most commonly used machining methods in manufacturing field.The main objective of this operation is to minimize the unit production cost.This paper proposes a Gaussian quantum-behaved bat algorithm(GQBA)to solve the problem of multi-pass turning operation.The proposed algorithm mainly includes the following two improvements.The first improvement is to incorporate the current optimal positions of quantum bats and the global best position into the stochastic attractor to facilitate population diversification.The second improvement is to use a Gaussian distribution instead of the uniform distribution to update the positions of the quantum-behaved bats,thus performing a more accurate search and avoiding premature convergence.The performance of the presented GQBA is demonstrated through numerical benchmark functions and amulti-pass turning operation problem.Thirteen classical benchmark functions are utilized in the comparison experiments,and the experimental results for accuracy and convergence speed demonstrate that,in most cases,the GQBA can provide a better search capability than other algorithms.Furthermore,GQBA is applied to an optimization problem formulti-pass turning,which is designed tominimize the production cost while considering many practical machining constraints in the machining process.The experimental results indicate that the GQBA outperforms other comparison algorithms in terms of cost reduction,which proves the effectiveness of the GQBA. 展开更多
关键词 Bat algorithm quantum behavior gaussian distribution numerical optimization multi-pass turning
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Status of research on non-conventional technology assisted single-point diamond turning
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作者 Zhuang Chen Guangjun Chen +2 位作者 Zhiwei Yu Jiashuai Huang Hong Wei 《Nanotechnology and Precision Engineering》 EI CAS CSCD 2023年第3期79-92,共14页
With the increasing use of difficult-to-machine materials in aerospace applications,machining requirements are becoming ever more rigorous.However,traditional single-point diamond turning(SPDT)can cause surface damage... With the increasing use of difficult-to-machine materials in aerospace applications,machining requirements are becoming ever more rigorous.However,traditional single-point diamond turning(SPDT)can cause surface damage and tool wear.Thus,it is difficult for SPDT to meet the processing requirements,and it has significant limitations.Research indicates that supplementing SPDT with unconventional techniques can,importantly,solve problems due to the high cutting forces and poor surface quality for difficult-to-machine materials.This paper first introduces SPDT and reviews research into unconventional techniques for use with SPDT.The machining mechanism is discussed,and the main advantages and disadvantages of various methods are investigated.Second,hybrid SPDT is briefly described,which encompasses ultrasonic-vibration magnetic-field SPDT,ultrasonic-vibration laser SPDT,and ultrasonic-vibration cold-plasma SPDT.Compared with the traditional SPDT method,hybrid SPDT produces a better optical surface quality.The current status of research into unconventional techniques to supplement SPDT is then summarized.Finally,future development trends and the application prospects of unconventional assisted SPDT are discussed. 展开更多
关键词 Single-point diamond turning Machined surface quality Tool wear Unconventional auxiliary technique
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Development and Evaluation of Intersection-Based Turning Movement Counts Framework Using Two Channel LiDAR Sensors
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作者 Ravi Jagirdar Joyoung Lee +2 位作者 Dejan Besenski Min-Wook Kang Chaitanya Pathak 《Journal of Transportation Technologies》 2023年第4期524-544,共21页
This paper presents vehicle localization and tracking methodology to utilize two-channel LiDAR data for turning movement counts. The proposed methodology uniquely integrates a K-means clustering technique, an inverse ... This paper presents vehicle localization and tracking methodology to utilize two-channel LiDAR data for turning movement counts. The proposed methodology uniquely integrates a K-means clustering technique, an inverse sensor model, and a Kalman filter to obtain the final trajectories of an individual vehicle. The objective of applying K-means clustering is to robustly differentiate LiDAR data generated by pedestrians and multiple vehicles to identify their presence in the LiDAR’s field of view (FOV). To localize the detected vehicle, an inverse sensor model was used to calculate the accurate location of the vehicles in the LiDAR’s FOV with a known LiDAR position. A constant velocity model based Kalman filter is defined to utilize the localized vehicle information to construct its trajectory by combining LiDAR data from the consecutive scanning cycles. To test the accuracy of the proposed methodology, the turning movement data was collected from busy intersections located in Newark, NJ. The results show that the proposed method can effectively develop the trajectories of the turning vehicles at the intersections and has an average accuracy of 83.8%. Obtained R-squared value for localizing the vehicles ranges from 0.87 to 0.89. To measure the accuracy of the proposed method, it is compared with previously developed methods that focused on the application of multiple-channel LiDARs. The comparison shows that the proposed methodology utilizes two-channel LiDAR data effectively which has a low resolution of data cluster and can achieve acceptable accuracy compared to multiple-channel LiDARs and therefore can be used as a cost-effective measure for large-scale data collection of smart cities. 展开更多
关键词 Vehicle Trajectory Construction Two Channel LiDAR turning Movement Counts RTMS Smart Cities LIDAR
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Design of a coated thinly clad chalcogenide long-period fiber grating refractive index sensor based on dual-peak resonance near the phase matching turning point
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作者 齐倩玉 李耀威 +3 位作者 刘婷 张培晴 戴世勋 徐铁峰 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第1期327-333,共7页
A novel method for designing chalcogenide long-period fiber grating(LPFG) sensors based on the dual-peak resonance effect of the LPFG near the phase matching turning point(PMTP) is presented. Refractive index sensing ... A novel method for designing chalcogenide long-period fiber grating(LPFG) sensors based on the dual-peak resonance effect of the LPFG near the phase matching turning point(PMTP) is presented. Refractive index sensing in a high-refractive-index chalcogenide fiber is achieved with a coated thinly clad film. The dual-peak resonant characteristics near the PMTP and the refractive index sensing properties of the LPFG are analyzed first by the phase-matching condition of the LPFG. The effects of film parameters and cladding radius on the sensitivity of refractive index sensing are further discussed. The sensor is optimized by selecting the appropriate film parameters and cladding radius. Simulation results show that the ambient refractive index sensitivity of a dual-peak coated thinly clad chalcogenide LPFG at the PMTP can be 2400 nm/RIU, which is significantly higher than that of non-optimized gratings. It has great application potential in the field of chemical sensing and biosensors. 展开更多
关键词 chalcogenide longperiod fiber grating dual-peak resonance phase matching turning point refractive index sensor
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DE-DOLLARIZATION IS TRENDING AND THERE'S NO TURNING BACK
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作者 Thomas W.Pauken II 《China Report ASEAN》 2023年第5期62-63,共2页
The U.S.dollar has long stood tall as the pre-eminent global currency for international cross-border trade settlements and foreign exchange reserves ever since the launch of the Bretton Woods institutions-Internationa... The U.S.dollar has long stood tall as the pre-eminent global currency for international cross-border trade settlements and foreign exchange reserves ever since the launch of the Bretton Woods institutions-International Monetary Fund(IMF)and World Bank(WB). 展开更多
关键词 DOLLAR turn ING
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Analysis and Prediction of Effect of Turning Marks Diffraction on Image Quality of Optical System
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作者 Haokun Ye Jianping Zhang +3 位作者 Shuanglong Tan Shangnan Zhao Mingxin Liu Xin Zhang 《Optics and Photonics Journal》 2023年第6期97-108,共12页
Single-point diamond turning (SPDT) is widely used in the machining of infrared materials and metal-based mirrors. Diamond tips can scratch material, replicate the shape of the tip, and create annular turning marks on... Single-point diamond turning (SPDT) is widely used in the machining of infrared materials and metal-based mirrors. Diamond tips can scratch material, replicate the shape of the tip, and create annular turning marks on optical surfaces, which can have unpredictable adverse effects on imaging. In order to predict the effect of turning marks diffraction on the degradation of imaging quality, a model of the influence of SPDT processing parameters on the reduction of system imaging MTF under the influence of ideal grating turning marks diffraction was established. The results show that the depth of the turning mark will lead to the decline of MTF, especially the low frequency information. Finally, a method is proposed to reduce the effect of turning marks diffraction through changing the processing parameters. . 展开更多
关键词 Single-Point Diamond turning DIFFRACTION MTF Blaze Grating
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Analyzing the Effects of Tool Holder Stiffness on Chatter Vibration Reduction in Turning
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作者 Kadir Gok Erol Turkes +1 位作者 Özler Karakas Arif Gok 《Journal of Metallic Material Research》 2023年第1期16-24,共9页
This paper investigates the effects of tool holder materials on chatter vibration in turning operations.The study uses a complex dynamic turning model with two degrees of freedom for the orthogonal cutting system.Tool... This paper investigates the effects of tool holder materials on chatter vibration in turning operations.The study uses a complex dynamic turning model with two degrees of freedom for the orthogonal cutting system.Tool holders made from different materials,including Al 5083,Al 6082,Al 7012,and a standard 4140 material,were subjected to chatter vibration to investigate their process damping capabilities.The study found that the standard tool holder 4140 allows for higher stable depths of cut and produces similar process damping values compared to the other tool holders.Finite element analyses(FEA)were performed to verify the experimental results,and the modal and FEA analyses produced very similar results.The study concludes that future research should investigate the effects of tool holders made from high alloy steel alloys on process damping.Overall,this paper provides important insights into the effects of tool hold-er materials on chatter vibration and process damping in turning operations,which can help in the design of more effi-cient and effective cutting systems. 展开更多
关键词 turning Tool holder Chatter Process damping Finite element analysis
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High-sensitive state perception method for inverter-fed machine turn insulation based on FrFT-Mel
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作者 Ruitian Fan Xing Lei +3 位作者 Tao Jia Menglong Qin Hao Li Dawei Xiang 《Global Energy Interconnection》 EI CSCD 2024年第2期155-165,共11页
Amidst the swift advancement of new power systems and electric vehicles,inverter-fed machines have progressively materialized as a pivotal apparatus for efficient energy conversion.Stator winding turn insulation failu... Amidst the swift advancement of new power systems and electric vehicles,inverter-fed machines have progressively materialized as a pivotal apparatus for efficient energy conversion.Stator winding turn insulation failure is the root cause of inverter-fed machine breakdown.The online monitoring of turn insulation health can detect potential safety risks promptly,but faces the challenge of weak characteristics of turn insulation degradation.This study proposes an innovative method to evaluate the turn insulation state of inverter-fed machines by utilizing the fractional Fourier transform with a Mel filter(FrFT-Mel).First,the sensitivity of the high-frequency(HF)switching oscillation current to variations in turn insulation was analyzed within the fractional domain.Subsequently,an improved Mel filter is introduced,and its structure and parameters are specifically designed based on the features intrinsic to the common-mode impedance resonance point of the electrical machine.Finally,an evaluation index was proposed for the turn insulation state of inverter-fed machines.Experimental results on a 3kW permanent magnet synchronous machine(PMSM)demonstrate that the proposed FrFT-Mel method significantly enhances the sensitivity of turn insulation state perception by approximately five times,compared to the traditional Fourier transform method. 展开更多
关键词 State perception turn insulation Switching oscillation Fractional Fourier transform Mel filter
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DER SPATIAL TURN IN DEN KLASSISCHEN ALTERTUMSWISSENSCHAFTEN(UND SPEZIELL IN DER EPIGRAPHIK)
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作者 Irene Berti 《Journal of Ancient Civilizations》 2024年第1期99-121,125,共24页
Since the 1990s the so-called spatial turn has brought back space and topography into the discussion within historical studies,particular ancient studies.This survey reviews current trends and developments within the ... Since the 1990s the so-called spatial turn has brought back space and topography into the discussion within historical studies,particular ancient studies.This survey reviews current trends and developments within the field and offers some perspectives on possible future developments related to space,material,objects,their agency,and frames. 展开更多
关键词 AGENCY FRAMES material objects space spatial turn TOPOGRAPHY
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HCB-turn热风干燥器在纸机改造中的应用
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作者 张东生 《中华纸业》 CAS 2024年第1期88-91,共4页
由于市场、成本、车速、纸张品质等原因,需要对背面涂布段进行优化改造,这时候加装HCB-turn热风干燥器则是最佳的选择之一,因为它比常规纸幅运行节省1/3的安装空间,且适用于所有纸种,对纸张和涂层能够有高效的干燥和无污染的转向。
关键词 热风干燥器 涂布 非接触干燥 HCB-turn
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拟共形映射与Turning域
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作者 冯小高 《西华师范大学学报(自然科学版)》 2012年第1期45-47,共3页
讨论了拟共形映射与Turning域及ILC域之间的关系.首先根据拟共形映射与Turning域的性质得到f是拟共形映射的充要条件是f将Rn中的Turning域映成Rn中的Turning域;然后根据Turning域及ILC域的等价性得到f是拟共形映射的充要条件是f将Rn中的... 讨论了拟共形映射与Turning域及ILC域之间的关系.首先根据拟共形映射与Turning域的性质得到f是拟共形映射的充要条件是f将Rn中的Turning域映成Rn中的Turning域;然后根据Turning域及ILC域的等价性得到f是拟共形映射的充要条件是f将Rn中的ILC域映成Rn中的ILC域. 展开更多
关键词 拟共形映射 turning ILC域 同胚
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