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Improving fatigue properties of normal direction ultrasonic vibration assisted face grinding Inconel 718 by regulating machined surface integrity
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作者 Nianwei Xu Renke Kang +4 位作者 Bi Zhang Yuan Zhang Chenxu Wang Yan Bao Zhigang Dong 《International Journal of Extreme Manufacturing》 SCIE EI CAS CSCD 2024年第3期458-475,共18页
Fatigue properties are crucial for critical aero-engine components in extreme serviceenvironments,which are significantly affected by surface integrity(SI)indexes(especially surface topography,residual stressσ_(res),... Fatigue properties are crucial for critical aero-engine components in extreme serviceenvironments,which are significantly affected by surface integrity(SI)indexes(especially surface topography,residual stressσ_(res),and microhardness)after machining processes.Normal-direction ultrasonic vibration-assisted face grinding(ND-UVAFG)has advantages in improving the machinability of Inconel 718,but there is a competitive relationship between higher compressiveσ_(res)and higher surface roughness R_(a)in affecting fatigue strength.The lack of a quantitative relationship between multiple SI indexes and fatigue strength makes theindeterminacy of a regulatory strategy for improving fatigue properties.In this work,a model of fatigue strength(σ_f)_(sur)considering multiple SI indexes was developed.Then,high-cycle fatigue tests were carried out on Inconel 718 samples with different SI characteristics,and the influence of ND-UVAFG process parameters on SI was analyzed.Based on SI indexes data,the(σ_f)_(sur)distribution in the grinding surface layer for ND-UVAFG Inconel 718 samples was determined using the developed model,and then the fatigue crack initiation(FCI)sites were furtherpredicted.The predicted FCI sites corresponded well with the experimental results,therebyverifying this model.A strategy for improving the fatigue life was proposed in this work,which was to transfer the fatigue source from the machined surface to the bulk material by controlling the SI indexes.Finally,a critical condition of SI indexes that FCI sites appeared on the surface or in bulk material was given by fitting the predicted results.According to the critical condition,an SI field where FCI sites appeared in the bulk material could be obtained.In this field,thefatigue life of Inconel 718 samples could be improved by approximately 140%. 展开更多
关键词 surface integrity fatigue strength Inconel 718 ultrasonic assisted grinding
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Boosting rate performance of layered lithium-rich cathode materials by oxygen vacancy induced surface multicomponent integration
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作者 Youyou Fang Yuefeng Su +7 位作者 Jinyang Dong Jiayu Zhao Haoyu Wang Yun Lu Bin Zhang Hua Yan Feng Wu Lai Chen 《Journal of Energy Chemistry》 SCIE EI CAS CSCD 2024年第5期250-262,共13页
The rapid development of electric vehicles and portable energy storage systems demands improvements in the energy density and cost-effectiveness of lithium-ion batteries,a domain in which Lithium-rich layered cathode(... The rapid development of electric vehicles and portable energy storage systems demands improvements in the energy density and cost-effectiveness of lithium-ion batteries,a domain in which Lithium-rich layered cathode(LLO)materials inherently excel.However,these materials face practical challenges,such as low initial Coulombic efficiency,inferior cycle/rate performance,and voltage decline during cycling,which limit practical application.Our study introduces a surface multi-component integration strategy that incorporates oxygen vacancies into the pristine LLO material Li1.2Mn_(0.6)Ni_(0.2)O_(2).This process involves a brief citric acid treatment followed by calcination,aiming to explore rate-dependent degradation behavior.The induced surface oxygen vacancies can reduce surface oxygen partial pressure and diminish the generation of O_(2)and other highly reactive oxygen species on the surface,thereby facilitating the activation of Li ions trapped in tetrahedral sites while overcoming transport barriers.Additionally,the formation of a spinel-like phase with 3D Li+diffusion channels significantly improves Li^(+)diffusion kinetics and stabilizes the surface structure.The optimally modified sample boasts a discharge capacity of 299.5 mA h g^(-1)at a 0.1 C and 251.6 mA h g^(-1)at a 1 C during the initial activation cycle,with an impressive capacity of 222.1 mA h g^(-1)at a 5 C.Most notably,it retained nearly 70%of its capacity after 300 cycles at this elevated rate.This straightforward,effective,and highly viable modification strategy provides a crucial resolution for overcoming challenges associated with LLO materials,making them more suitable for practical application. 展开更多
关键词 Lithium-ion battery Layered lithium rich cathode surface multicomponent integration Rate-dependent degradation and Li^(+) diffusion kinetics
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Average Secrecy Capacity of the Reconfigurable Intelligent Surface-Assisted Integrated Satellite Unmanned Aerial Vehicle Relay Networks
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作者 Ping Li Kefeng Guo +2 位作者 Feng Zhou XuelingWang Yuzhen Huang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第2期1849-1864,共16页
Integrated satellite unmanned aerial vehicle relay networks(ISUAVRNs)have become a prominent topic in recent years.This paper investigates the average secrecy capacity(ASC)for reconfigurable intelligent surface(RIS)-e... Integrated satellite unmanned aerial vehicle relay networks(ISUAVRNs)have become a prominent topic in recent years.This paper investigates the average secrecy capacity(ASC)for reconfigurable intelligent surface(RIS)-enabled ISUAVRNs.Especially,an eve is considered to intercept the legitimate information from the considered secrecy system.Besides,we get detailed expressions for the ASC of the regarded secrecy system with the aid of the reconfigurable intelligent.Furthermore,to gain insightful results of the major parameters on the ASC in high signalto-noise ratio regime,the approximate investigations are further gotten,which give an efficient method to value the secrecy analysis.At last,some representative computer results are obtained to prove the theoretical findings. 展开更多
关键词 integrated satellite unmanned aerial vehicle relay networks reconfigurable intelligent surface average secrecy capacity(ASC) asymptotic ASC
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Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material
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作者 Yali ZHANG Yueting ZHOU Shenghu DING 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第1期179-196,共18页
Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical... Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads. 展开更多
关键词 wavy surface periodic contact thermoelectric(TE)material Hilbert integral kernel
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Hierarchically wood-derived integrated electrode with tunable superhydrophilic/superaerophobic surface for efficient urea electrolysis 被引量:1
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作者 Yu Liao Songlin Deng +3 位作者 Yan Qing Han Xu Cuihua Tian Yiqiang Wu 《Journal of Energy Chemistry》 SCIE EI CAS CSCD 2023年第1期566-575,I0014,共11页
Conferring surfaces with superhydrophilic/superaerophobic characteristics is desirable for synthesizing efficient gas reaction catalysts.However,complicated procedures,high costs,and poor interfaces hinder commerciali... Conferring surfaces with superhydrophilic/superaerophobic characteristics is desirable for synthesizing efficient gas reaction catalysts.However,complicated procedures,high costs,and poor interfaces hinder commercialization.Here,an integrated electrode with tunable wettability derived from a hierarchically porous wood scaffold was well designed for urea oxidation reaction(UOR).Interestingly,the outer surface of the wood lumen was optimized to the preferred wettability via stoichiometry to promote electrolyte permeation and gas escape.This catalyst exhibits outstanding activity and durability for UOR in alkaline media,requiring only a potential of 1.36 V(vs.RHE)to deliver 10 m A cm^(-2)and maintain its activity without significant decay for 60 h.These experiments and theoretical calculations demonstrate that the nickel(oxy)hydroxide layer formed through surface reconstruction of nickel nanoparticles improves the active sites and intrinsic activity.Moreover,the superwetting properties of the electrode promote mass transfer by guaranteeing substantial contact with the electrolyte and accelerating the separation of gaseous products during electrocatalysis.These findings provide the understanding needed to manipulate the surface wettability through rational design and fabrication of efficient electrocatalysts for gas-evolving processes. 展开更多
关键词 integrated electrode Wood scaffold Superhydrophilic/Superaerophobic surface Urea oxidation reaction
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Surface Integrity of Inconel 738LC Parts Manufactured by Selective Laser Melting Followed by High-speed Milling
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作者 Guanhui Ren Sai Guo Bi Zhang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2023年第1期65-79,共15页
This study is concerned with the surface integrity of Inconel 738LC parts manufactured by selective laser melting(SLM)followed by high-speed milling(HSM).In the investigation process of surface integrity,the study emp... This study is concerned with the surface integrity of Inconel 738LC parts manufactured by selective laser melting(SLM)followed by high-speed milling(HSM).In the investigation process of surface integrity,the study employs ultradepth three-dimensional microscopy,laser scanning confocal microscopy,scanning electron microscopy,electron backscatter diffractometry,and energy dispersive spectroscopy to characterize the evolution of material microstructure,work hardening,residual stress coupling,and anisotropic effect of the building direction on surface integrity of the samples.The results show that SLM/HSM hybrid manufacturing can be an effective method to obtain better surface quality with a thinner machining metamorphic layer.High-speed machining is adopted to reduce cutting force and suppress machining heat,which is an effective way to produce better surface mechanical properties during the SLM/HSM hybrid manufacturing process.In general,high-speed milling of the SLM-built Inconel 738LC samples offers better surface integrity,compared to simplex additive manufacturing or casting. 展开更多
关键词 surface integrity Inconel 738LC Selective laser melting High-speed milling
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Machining the Integral Impeller and Blisk of Aero-Engines:A Review of Surface Finishing and Strengthening Technologies 被引量:19
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作者 Youzhi Fu Hang Gao +1 位作者 Xuanping Wang Dongming Guo 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2017年第3期528-543,共16页
The integral impeller and blisk of an aero-engine are high performance parts with complex structure and made of difficult-to-cut materials. The blade surfaces of the integral impeller and blisk are functional surfaces... The integral impeller and blisk of an aero-engine are high performance parts with complex structure and made of difficult-to-cut materials. The blade surfaces of the integral impeller and blisk are functional surfaces for power transmission, and their surface integrity has signif- icant effects on the aerodynamic efficiency and service life of an aero-engine. Thus, it is indispensable to finish and strengthen the blades before use. This paper presents a comprehensive literature review of studies on finishing and strengthening technologies for the impeller and blisk of aero-engines. The review includes independent and inte- grated finishing and strengthening technologies and dis- cusses advanced rotational abrasive flow machining with back-pressure used for finishing the integral impeller and blisk. A brief assessment of future research problems and directions is also presented. 展开更多
关键词 integral impeller and blisk AERO-ENGINE surface integrity surface finishing surface strengthening
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Optimize Multiple Peening Effects on Surface Integrity and Microhardness of Aluminum Alloy Induced by LSP
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作者 Enoch Asuako Larson Samuel Adu-Gyamfi +7 位作者 Milku Augustine Philip Yamba Jamal-Deen Kukurah Karimu Abdulai Joseph Sekyi-Ansah Osman Abdul-Razak Emmanuel A. Akurugu Aston Kuzmin 《Materials Sciences and Applications》 2023年第3期208-221,共14页
Laser shock peening is a modernized surface enhancement performed methodically to improve fatigue life, enhance the hardness of the material and make coarse grains flat under the superficial layer. In this current stu... Laser shock peening is a modernized surface enhancement performed methodically to improve fatigue life, enhance the hardness of the material and make coarse grains flat under the superficial layer. In this current study, the effect of varying optimized multiple laser shock peening (LSP) is studied on the surface integrity, microhardness, and mechanical properties. The results show that the LSP-treated specimens have visible signs of valleys, wavy and varying height distribution as well as dimples. However, the presence of non-uniformity and sharp protrusions was detected from the superficiality of the as-received specimen and this was so because of the SiC abrasive material used to polish the superficial layer of the specimen before the test experiment. Prior to LSP, the surface roughness was 2 μm, however, after LSP the roughness increased to 4 μm, 6 μm and 17 μm for 1, 2, and 4 impacts, respectively. High-density dislocation can also be observed close to the grain boundary because the grain boundary prevents the migration of dislocation which could lead to dislocation walls and dislocation tangles. The increase in impacts decrease the average grain size, nevertheless, the micro-strain increased after multiple impacts. Furthermore, coarse grains after LSP were transformed into finer grains. The increase in the number of impacts increases the micro-strain likewise the full-width half maximum (FWHM). Finally, the increase in microhardness increases as the LSP impacts increase. 展开更多
关键词 surface integrity MICROHARDNESS Sharp Protrusions SiC Abrasive Material FWHM
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ROUGH MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS 被引量:6
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作者 伍火熊 许建开 《Acta Mathematica Scientia》 SCIE CSCD 2009年第2期294-304,共11页
In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions ... In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results. 展开更多
关键词 Marcinkiewicz integral product domain surfaces of revolution rough kernel
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Boundedness of singular integrals along surfaces on Lebesgue spaces 被引量:2
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作者 ZHANG Yan-dan CHEN Jie-cheng ZHANG Chun-jie 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第2期192-198,共7页
In the paper, we establish the LP(Rn+1)-boundedness for a class of singular integral operators associated to surfaces of revolution {(y,γ(|y|), y ∈ Rn} with rough kernels. We also give several applications o... In the paper, we establish the LP(Rn+1)-boundedness for a class of singular integral operators associated to surfaces of revolution {(y,γ(|y|), y ∈ Rn} with rough kernels. We also give several applications of this inequality. 展开更多
关键词 Singular integrals surfaceS rough kernels Plancherel's theorem oscillatory singular integrals.
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SURFACE INTEGRAL OF THREE-DIMENSIONAL VELOCITY FIELD FOR SQUARE BAR DRAWING THROUGH CONICAL DIE 被引量:2
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作者 Zhao, DW Guo, CW +1 位作者 Liu, XH Fang, YK 《中国有色金属学会会刊:英文版》 CSCD 1996年第3期131-135,共5页
SURFACEINTEGRALOFTHREE-DIMENSIONALVELOCITYFIELDFORSQUAREBARDRAWINGTHROUGHCONICALDIE¥ZhaoDewen;GuoChangwu;Liu... SURFACEINTEGRALOFTHREE-DIMENSIONALVELOCITYFIELDFORSQUAREBARDRAWINGTHROUGHCONICALDIE¥ZhaoDewen;GuoChangwu;LiuXianghua(RollingT... 展开更多
关键词 SQUARE BAR DRAWING three dimensional VELOCITY FIELD surface integral
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Adaptive integral dynamic surface control based on fully tuned radial basis function neural network 被引量:2
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作者 Li Zhou Shumin Fei Changsheng Jiang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第6期1072-1078,共7页
An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network (FTRBFNN) is presented for a general class of strict-feedback nonlinear systems,which may possess a wid... An adaptive integral dynamic surface control approach based on fully tuned radial basis function neural network (FTRBFNN) is presented for a general class of strict-feedback nonlinear systems,which may possess a wide class of uncertainties that are not linearly parameterized and do not have any prior knowledge of the bounding functions.FTRBFNN is employed to approximate the uncertainty online,and a systematic framework for adaptive controller design is given by dynamic surface control. The control algorithm has two outstanding features,namely,the neural network regulates the weights,width and center of Gaussian function simultaneously,which ensures the control system has perfect ability of restraining different unknown uncertainties and the integral term of tracking error introduced in the control law can eliminate the static error of the closed loop system effectively. As a result,high control precision can be achieved.All signals in the closed loop system can be guaranteed bounded by Lyapunov approach.Finally,simulation results demonstrate the validity of the control approach. 展开更多
关键词 adaptive control integral dynamic surface control fully tuned radial basis function neural network.
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Rough singular integrals associated with surfaces of Van der Corput type 被引量:2
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作者 LIU Feng WU Huo-xiong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2014年第1期86-100,共15页
In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф(lul)u' : u ε ]t^n} as well as the related maimal operators provided that the f... In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф(lul)u' : u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ(R+) for γ 〉 1 and the sphere function ΩεFβ(S^n-1) for someβ 〉 0 which is distinct from HI(Sn-1). 展开更多
关键词 42B20 42B25 42B30 Singular integrals surfaces of Van der Corput type maximal operators Littlewood-Paley theory Fourier transform estimates
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Surface integral analogy approaches for predicting noise from 3D high-lift low-noise wings 被引量:1
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作者 Hua-Dong Yao Lars Davidson +3 位作者 Lars-Erik Eriksson Shia-Hui Peng Olof Grundestam Peter E.Eliasson 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2014年第3期326-338,共13页
Three surface integral approaches of the acoustic analogies are studied to predict the noise from three concep- tual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff... Three surface integral approaches of the acoustic analogies are studied to predict the noise from three concep- tual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings (FW-H) method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to con- struct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object-the actual wing with high-lift devices-the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill's stress tensors on the noise pre-diction are then evaluated by comparing the results of the Curle method with the other two methods. 展开更多
关键词 AERO-ACOUSTICS High-lift facilities surface integral approaches of acoustic analogy
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Simplified permeable surface correction for frequency-domain Ffowcs Williams and Hawkings integrals 被引量:1
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作者 Zhiteng Zhou Hongping Wang Shizhao Wang 《Theoretical & Applied Mechanics Letters》 CSCD 2021年第4期192-196,共5页
A simplified surface correction formulation is proposed to diminish the far-field spurious sound generated by the quadrupole source term in Ffowcs Williams and Hawkings(FW-H)integrals.The proposed formulation utilizes... A simplified surface correction formulation is proposed to diminish the far-field spurious sound generated by the quadrupole source term in Ffowcs Williams and Hawkings(FW-H)integrals.The proposed formulation utilizes the far-field asymptotics of the Green’s function to simplify the computation of its high-order derivatives,which circumvents the difficulties reported in the original frequency-domain surface correction formulation.The proposed formulation has been validated by investigating the benchmark case of sound generated by a convecting vortex.The results show that the proposed formulation successfully eliminates the spurious sound.The applications of the proposed formulation to flows with some special parameters are also discussed. 展开更多
关键词 FW-H integral surface correction Quadrupole source Aeroacoustics
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Effect of PCBN cutting tools wear on surface integrality in high-speed hard turning 被引量:1
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作者 陈涛 Liu Xian li 《High Technology Letters》 EI CAS 2012年第2期128-131,共4页
In this paper, the effect of of flank wear polycrystalline cubic boron nitride (PCBN) tools on residual stresses, white layer and roughness of machined workpiece surfaces is studied. Experimental results indicate th... In this paper, the effect of of flank wear polycrystalline cubic boron nitride (PCBN) tools on residual stresses, white layer and roughness of machined workpiece surfaces is studied. Experimental results indicate that with the increase of the tool wear, the surface of the machined workpiece tends to generate tensile residual stresses, and white layer becomes clearly thicker and uneven on the workpiece surface. The effect of the flank wear on the surface roughness is less within some range of flank wear value. The results show that it is possible to produce ideal surface integrality levels by controlling the tool flank wear. 展开更多
关键词 polycrystalline cubic boron nitride(PCBN) flank wear high-speed precision hard turning surface integrity
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Formation of integral fins function-surface by extrusion-ploughing process 被引量:5
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作者 陈平 汤勇 +1 位作者 刘小康 刘晓晴 《中国有色金属学会会刊:英文版》 EI CSCD 2006年第5期1029-1034,共6页
An extrusion-ploughing process was presented to fabricate the integral fin function-surface. Cutting edge inclination angle and rake angle can be calculated from the tool’s geometry relationship. The description of f... An extrusion-ploughing process was presented to fabricate the integral fin function-surface. Cutting edge inclination angle and rake angle can be calculated from the tool’s geometry relationship. The description of fins’ geometry characters was standardized. The experiments show that, when the middle cutting edge’s inclination angle η is less than 35°, continuous fin will come out; when η is between 35° and 55°, the fins will be saw-tooth ones, and the fins will be torn when this angle is above 55°; when the extrusion angle θ is between 60° and 150°, the fins will appear, or else, the fins will be torn into chips from the base. Forming angle and clearance angle have little effect on fin’s formation. For continuous fin, its height is close to cutting depth when it is small, but it will become approximately constant as cutting depth grows; for saw-tooth fins, the width, the height, as well as the clearance will increase with the increase of cutting depth, but the increment of clearance is small; neither for continuous fin, nor for saw-tooth ones, cutting velocity has little influence on their structure parameters. 展开更多
关键词 飞边 集成散热片 热焓 挤压
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L^p Bounds for the Commutators of Rough Singular Integrals Associated with Surfaces of Revolution
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作者 Zhendong Niu Kai Zhu Yanping Chen 《Analysis in Theory and Applications》 CSCD 2015年第2期176-183,共8页
In this paper, we establish the L^p (R-n+1) boundedness for the commutators of singular integrals associated to surfaces of revolution, { (t,Ф ( | t| ) ): t ∈R^n }, with rough kernels Ω∈ L(IogL)^2(sn... In this paper, we establish the L^p (R-n+1) boundedness for the commutators of singular integrals associated to surfaces of revolution, { (t,Ф ( | t| ) ): t ∈R^n }, with rough kernels Ω∈ L(IogL)^2(sn^-1), if Ф(|t|) = |t|. 展开更多
关键词 COMMUTATOR singular integral surface of revolution rough kernel.
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L^p BOUNDS FOR SINGULAR INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS
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作者 Huoxiong Wu Shanzhi Yang 《Analysis in Theory and Applications》 2007年第4期389-400,共12页
In this paper, the authors establish Lp boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. The results of the corresponding ... In this paper, the authors establish Lp boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. The results of the corresponding maximal truncated singular integrals are also obtained. The main results essentially improve and extend some known results. 展开更多
关键词 singular integral product domain surfaces of revolution rough kernel
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Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product
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作者 Mirwais Rashid 《Applied Mathematics》 2011年第2期225-229,共5页
Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equati... Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly defined vector products. In a Theorem the surface integral of one of the newly defined vector products is shown to be reduced to a line integral. 展开更多
关键词 ELECTROMAGNETIC FIELD Parallel-Vertical Product surface integral
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