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offset approximation based on reparameterizing the path of a moving point along the base circle

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Applied Mathematics(A Journal of Chinese Universities) 2009年第4期24卷 431-442页

作者： ZHAO Hong-yan WANG Guo-jin Department of Mathematics Zhejiang University Zhejiang 310027 China State Key Laboratory of CAD & CG Zhejiang University Zhejiang 310027 China College of Fundamental Studies Shanghai University of Engineering Science Shanghai 201620 China

This paper presents a novel algorithm for planar curve offsetting. The basic idea is to regard the locus relative to initial base circle, which is formed by moving the unit normal vectors of the base curve, as a unit circular arc first, then accurately to represent it as a rational curve, and finally to reparameterize it in a particular way to approximate the offset. Examples illustrated that the algorithm yields fewer curve segments and control points as well as C^1 continuity, and so has much significance in terms of saving computing time, reducing the data storage and smoothing curves entirely.

关键词： CAD/CAM offset circle convolution Bezier/B-spline curve rational curve

Influence of Pin offset on Microstructure and Mechanical Properties of Friction Stir Welded Mg/Ti Dissimilar Alloys

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Acta Metallurgica Sinica(English Letters) 2019年第10期32卷 1261-1268页

作者： Qi Song Zhong-Wei Ma Shu-De Ji Qing-Hua Li Liu-Fang Wang Rui Li School of Aerospace Engineering Shenyang Aerospace University

The influences of pin offset on the formation, microstructure and mechanical properties of friction stir welded joint of Ti6 Al4 V and AZ31 B Mg dissimilar alloys were investigated. The results show that sound joints are obtained at different offsets. With the offset decreasing from 2.5 to 2.1 mm, the number of Ti alloy fragments is increased, and the stir zone(SZ) is enlarged and the grains in SZ become coarser. A hook-like structure is formed at the Mg/Ti interface and its length is increased with the decrease in pin offset. The Al element has an enrichment trend at the Ti alloy side near the Mg/Ti interface when the offset is decreased, which is beneficial to the bonding of the interface. An Al-rich layer with a thickness of 3–5μm forms at the offset of 2.1 mm. All the joints fracture at the interface and present a mixed ductile-and-brittle fracture mode. The joint tensile strength is increased with the offset decreasing from 2.5 to 2.1 mm, and the maximum tensile strength of 175 MPa is acquired at the offset of 2.1 mm.

关键词： Mg/Ti dissimilar alloys Friction stir welding Pin offset Mechanical properties Microstructure

An offset-insensitive switched-capacitor bandgap reference with continuous output

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Journal of Semiconductors 2009年第8期30卷 132-135页

作者：郑鹏严伟张科李文宏 State Key Laboratory of ASIC & System Fudan University

An improved switched-capacitor bandgap reference with a continuous output voltage of 1.26 V has been implemented with Chartered 0.35-μm 5-V CMOS process. The output offset voltage, induced by non-ideal characteristics of operational amplifier and bias current generator, is suppressed by the proposed sample-and-hold circuit and self-bias technique. Experimental results show that the proposed circuit operates properly under a supply voltage varying from 3 to 5 V. The measured temperature coefficient is 112 ppm/℃ and the power supply rejection ratio of output voltage without any filtering capacitor is -40 dB and -33 dB at 100 Hz and 10 MHz, respectively.

关键词： bandgap reference switched-capacitor offset self-bias continuous output

Effects of offset Blade on Aerodynamic Characteristics of Small-Scale Vertical Axis Wind Turbine

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Journal of Thermal Science 2019年第2期28卷 326-339页

作者： LI Yan ZHAO Shouyang QU Chunming FENG Fang KOTARO Tagawa Heilongjiang Provincial Key Laboratory of Technology and Equipment for the Utilization of Agricultural Renewable Resources in Cold Regions Northeast Agricultural University College of Engineering Northeast Agricultural University College of Science Northeast Agricultural University Faculty of Agriculture Tottori University

A new way of connecting blade to rotor shaft named offset blade method was proposed for straightbladed vertical axis wind turbine(SB-VAWT) in this study. In order to invest the efficiency of this method and effects of main parameters including offset length and blade airfoil on improving the output power performance and static starting characteristics, numerical simulations and wind tunnel tests were carried out. Four kinds of blade airfoil including NACA0012, NACA0018, NACA0024 and S809 were selected to analyze the influence of blade thickness and symmetry on SB-VAWT with offset blade. Numerical simulations were firstly carried out on output power for the rotor with 6 kinds of offset length for each airfoil. Wind tunnel tests were also carried out to compare with the results of simulations. The flow fields of rotor with different offset lengths were simulated and the effects of offset blade were analyzed. The optimum offset length among all studied for output power performance was found. Furthermore, the static starting torque and aerodynamic force characteristics of the rotor with optimum offset length were researched. According to the results, appropriate offset length can improve the output power characteristics and smooth the fluctuations of the static torque during one rotational period. The best offset length varies with the airfoil.

关键词： vertical axis wind turbine(VAWT) offset blade airfoil numerical simulations wind tunnel tests

Stationary response of stochastic viscoelastic system with the right unilateral nonzero offset barrier impacts

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Chinese Physics B 2019年第1期28卷 195-204页

作者： Deli Wang Wei Xu Xudong Gu Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an 710072China Department of Engineering Mechanics Northwestern Polytechnical UniversityXi’an 710072China

The stationary response of viscoelastic dynamical system with the right unilateral nonzero offset barrier impacts subjected to stochastic excitations is investigated. First, the viscoelastic force is approximately treated as equivalent terms associated with effects. Then, the free vibro-impact(VI) system is absorbed to describe the periodic motion without impacts and quasi-periodic motion with impacts based upon the level of system energy. The stochastic averaging of energy envelope(SAEE) is adopted to seek the stationary probability density functions(PDFs). The detailed theoretical results for Van der Pol viscoelastic VI system with the right unilateral nonzero offset barrier are solved to demonstrate the important effects of the viscoelastic damping and nonzero rigid barrier impacts condition. Monte Carlo(MC) simulation is also performed to verify the reliability of the suggested approach. The stochastic P-bifurcation caused by certain system parameters is further explored. The variation of elastic modulus from negative to zero and then to positive witnesses the evolution process of stochastic P-bifurcation. From the vicinity of the common value to a wider range, the relaxation time induces the stochastic P-bifurcation in the two interval schemes.

关键词： viscoelastic system right unilateral nonzero offset barrier impacts stochastic averaging of energy envelope(SAEE) stochastic P-bifurcation

Lateral wave-field stacking of seismic Fresnel zones for the generalized-offset case

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Applied Geophysics 2015年第2期12卷 235-243,275,276页

作者：田楠范廷恩王宗俊蔡文涛中海油研究总院北京100027

To unify different seismic geometries, the concept of generalized offset is defined and the expressions for Fresnel zones of different order on a plane are presented. Based on wave theory, the equation of the lateral wave-field stacking for generalized-offset Fresnel zones is derived. For zero and nonzero offsets, the lateral stacking amplitude of diffraction bins of different sizes is analyzed by referring to the shape of the Fresnel zones of different order. The results suggest the following. First, the contribution of diffraction bins to wave- field stacking is related to the offset, surface relief, interface dip, the depth of the shot point to the reflection interface, the observational geometry, and the size of the interference stacking region. Second, the first-order Fresnel zone is the main constructive interference, and its contribution to the reflection amplitude is slightly smaller than half the contribution of all Fresnel zones. Finally, when the size of the diffraction bin is smaller than the first- order Fresnel zone, the larger the size of the diffraction bin, the larger is the amplitude of the receiver, even in the nonzero offset-case.

关键词： offset Fresnel zone wave theory stacking amplitude

Self-aligned offset gate poly-Si TFTs using photoresist trimming technology

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Science China(Information Sciences) 2015年第4期58卷 128-133页

作者： WANG LongYan SUN Lei HAN DeDong WANG Yi CHAN ManSun ZHANG ShengDong Institute of Microelectronics Peking University BOE Technology Co. Ltd. Department of Electronic and Computer Engineering Hong Kong University of Science and Technology School of Electronic and Computer Engineering Peking University

This paper reports a simple method of fabricating self-aligned offset gate(SAOG) polycrystalline silicon(poly-Si) thin film transistors(TFTs). The SAOG structure was formed by two key steps, i.e. an isotropic photoresist trimming and an additional gate fringe etching. The fabricated SAOG devices with this proposed method exhibit a significantly suppressed off-current increase with gate bias compared with the non-offset ones,and have identical bi-directional transfer characteristics under reversed source/drain biases. It is also shown that the performances of poly-Si TFTs with metal-induced lateral crystallization can be improved significantly by annealing in forming gas.

关键词： photoresist trimming offset polycrystalline silicon(poly-Si) thin film transistors(TFTs)

Intersections of two offset parametric surfaces based on topology analysis

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2004年第3期5卷 10-19页

作者：欧阳应秀唐敏林军呈董金祥 State Key Laboratory of CAD & CG AI Institute Zhejiang University

Conventional methods for solving intersections between two offset parametric surfaces often include iteratively using computationally expensive SSI (surface/surface intersections) algorithm. In addition, these methods ignore the relations between the intersection curves of parametric surfaces with different offset distances. The algorithm presented in this paper, makes full use of the topological relations between different intersection loops and calculates intersection loops with the help of previously calculated intersection loops. It first pre-processes two parametric surfaces to obtain the characteristic points, called topology transition points (TTPs), which can help in the subsequent finding of the topologies of the intersection curves. Then these points are categorized into several distinct groups, and we can determine the calculation strategy for searching initial points by analyzing the properties of these TTPs on the surfaces. Hence, all intersection curves can be marched from initial points by the tracing algorithm. The proposed algorithm could calculate intersection curves robustly and effectively, and has been tested to be capable of overcoming the degenerate conditions such as loop and singularities leaking that occur frequently in conventional algorithms.

关键词： offset parametric surface Topology transition point Surface intersection

Rational offset approximation of rational Bézier curves

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第9期7卷 1561-1565页

作者： CHENG Min WANG Guo-jin Department of Mathematics Zhejiang University Hangzhou 310027 China Department of Mathematics Zhejiang University of Technology Hangzhou 310032 China

The problem of parametric speed approximation of a rational curve is raised in this paper. offset curves are widely used in various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational approximation algorithm of offset curve, which preserves the direction of normal, is presented.

关键词： Rational Bézier curve Parametric speed offset Rational approximation