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8th International Conference on Electronic Measurement and Instruments

作者： Jiang Fan Chen Weiping Li Yuanyuan Chen Min S China Univ Technol Mech Engn Coll Guangzhou 510640 Peoples R China Guangzhou Univ Informat & Mech Elect Engn Guangzhou 510006 Guangdong Peoples R China Environmental Protect Bur Guangzhou 510630 Guangdong Peoples R China

ISBN: (纸本)1424411351

The oxygen content in bio-reactors is an important parameter to judge the status of bio-reactor operation, but the oxygen content data is finite in experiment. In order to find the distribution of oxygen content in bio-reactors, the interpolation algorithm is introduced in this paper. At first, according to the characteristic of experimental data field, the bio-reactor domain is grided to hexahedron, the space of bio-reactor is reconstructed through the hexahedron element mesh of the scattered data field, and the region mapping algorithm is used to interpolation calculation. This integrate algorithm is good for the data field reconstruction and interpolation, which the field is belongs to the three dimensional space of bio-reactor.

关键词： oxygen content measurement data interpolation algorithm hexahedron element meshing isoparametric transformation region mapping

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A MODIFIED Z-MAP COMPUTATIONAL interpolation algorithm FOR SURFACE MACHINING SIMULATION

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TRANSACTIONS OF THE CANADIAN SOCIETY FOR MECHANICAL ENGINEERING 2013年第3期37卷 515-527页

作者： Tsai, Jo-Peng Far East Univ Dept Comp Sci & Informat Engn Tainan Taiwan Natl Sun Yat Sen Univ Dept Informat Management Kaohsiung 80424 Taiwan

The Z-Map algorithm is one of the most simplistic methods for NC code simulation in obtaining the machined working surface information;therefore, it is often being applied in NC simulation. In this paper, a modified Z-Map computational algorithm was proposed to calculate mesh position and Z coordinates of tool scanning surface according to tool path and initial tool scanning boundary in reducing the long computation time. The proposed algorithm not only can be used to derive straight line and arc machining tool path, but also, can be adopted for helical and spline curves. There is no need to simplify the non-linear curves beforehand. The method proposed in this paper provides a feasible reference for decision about the reliability and suitability of each machining step.

关键词： NC simulation Z-Map interpolation algorithm

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A real-time corner smoothing and interpolation algorithm for short line segments to realize continuous motion of tool axis jerk

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE 2023年第4期237卷 542-560页

作者： Zhang, Liqiang Xie, Jian Yan, Yecui Liu, Gang Shanghai Univ Engn Sci Sch Mech & Automot Engn 333 Longteng Rd Shanghai 201620 Peoples R China

Aiming at the problem of acceleration and jerk fluctuation caused by the discontinuity at the corner of the tool path in the continuous short-line machining process, a real-time corner smoothing and interpolation algorithm for realizing the continuous motion of the tool axis jerk is proposed. In the corner smoothing process, the C-3 continuity of tool path is realized by constructing a symmetrical PH transition curve satisfying the maximum approximation error constraint between adjacent short lines. In the interpolation process, based on the flexible acceleration and deceleration control method, the feed rate, chord error, acceleration, and jerk constraints are considered. For the smooth C-3 continuous path, the acceleration and deceleration profile with jerk-continuous is used for velocity planning and interpolation, and the continuous motion of the tool axis jerk is realized. In this paper, the proposed method is compared and analyzed with the C-2 continuous algorithm and the traditional point-to-point interpolation algorithm through simulation and experiment for the same tool path. The results show that the jerk fluctuation of the proposed algorithm is reduced by 60.36% on average compared with the C-2 continuous algorithm, and the processing time is reduced by 19.5% compared with the point-to-point interpolation algorithm. It proves that the proposed algorithm can effectively reduce the vibration of the machine tool and improve the processing efficiency.

关键词： Jerk-continuous corner smoothing PH curve acceleration and deceleration control interpolation algorithm

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Correcting and compressing interpolation algorithm for free-form surface machining

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2012年第9-12期62卷 1179-1189页

作者： Zhang, Xiaohui Yu, Dong Song, Taotao Shanghai Sany Precis Machinery Co LTD Numer Control Res Inst Shanghai 201200 Peoples R China Chinese Acad Sci Natl Engn Res Ctr High End CNC Shenyang Inst Comp Technol Shenyang 110171 Peoples R China

The existing interpolation algorithm cannot meet the need of high-speed and high-accuracy machining of a free-form surface. So this paper proposed a correcting and compressing interpolation algorithm. Depending on the distance and angle evaluated from the adjacent command points, the machining path of free form can be divided into two machining types. For those regions where the accurate figure is critical such as corners, the convention linear interpolation is performed exactly between the adjacent command points. For those regions having a large radius of curvature where the smooth figure is critical, firstly, the interior point selection method based on circle transition is derived to reduce the tolerance between the machining path and the original surface;secondly, the interior point correction method based on the least-square method is proposed to reduce the calculation error and round-off error in the interior point and estimate the first- and second-order derivative vectors of the interior point;thirdly, the shape-defining point is selected by the bend direction of the machining path and fitted to a quintic spline curve which has the C2 continuity;fourthly, the fitting accuracy controlling method is proposed to ensure the machining accuracy;lastly, the curve interpolation is performed on the fitted smooth curve. Machining tests carried out on a vertical machining center show that the proposed algorithm can improve the machining efficiency and machining quality of a free-form surface.

关键词： High-speed machining interpolation algorithm Free-form surface

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An accurate NURBS curve interpolation algorithm with short spline interpolation capacity

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2012年第9-12期63卷 1257-1270页

作者： Dong, Haitao Chen, Bing Chen, Youping Xie, Jingming Zhou, Zude Huazhong Univ Sci & Technol Natl NC Syst Engn Res Ctr Wuhan 430074 Peoples R China Wuhan Univ Technol Hubei Digital Mfg Key Lab Wuhan 430070 Peoples R China

In this paper, a novel and accurate real-time non-uniform rational B-spline curve interpolation algorithm is proposed. This algorithm not only considers chord errors, feedrate fluctuations, jerk-limited, and acceleration/deceleration (Acc/Dec) capabilities of the machine, but also optimizes the look-ahead process. In the meanwhile, it improves machining efficiency by adding the circular buffer and pre-interpolation (non-off-line) and enhances the real-time performance by removing the time-consuming calculation from the interrupt service routine. Furthermore, the proposed interpolation algorithm can interpolate both the long spline and the short spline with uniform method. The advantages of the proposed method were confirmed by the simulation results.

关键词： CNC NURBS interpolation algorithm Look-ahead S curve accelerationdeceleration

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Timing jitter characterization for mixed-signal production test using the interpolation algorithm

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2007年第2期54卷 1014-1023页

作者： Xia, Tian Zheng, Hao Univ Vermont Sch Engn Burlington VT 05405 USA Univ S Florida Dept Comp Sci & Engn Tampa FL 33620 USA

In this paper, a jitter measurement circuit for mixed-signal production test based on the interpolation algorithm is presented. By utilizing the limited sampling points per cycle, the original signal under test is reconstructed with a high accuracy. From the reconstructed signal, most timing jitter features can be characterized. To validate the design effectiveness, comparative studies have been performed between this jitter measurement method and other standard jitter characterization instruments.

关键词： interpolation algorithm mixed signal production test timing jitter

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An interpolation algorithm with jerk continuity for six-axis machine tools

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CIRP JOURNAL OF MANUFACTURING SCIENCE AND TECHNOLOGY 2023年 45卷 240-252页

作者： Cheng, Liang Wu, Jianbo Guo, Yingjie Li, Jiangxiong Ke, Yinglin Zhejiang Univ State Key Lab Fluid Power Transmiss & Mechatron Sy Hangzhou 310027 Peoples R China Zhejiang Univ Sch Mech Engn Key Lab Adv Mfg Technol Zhejiang Prov Hangzhou 310027 Peoples R China Zhejiang Univ Sch Mech Engn 38 Zheda Rd Hangzhou 310027 Peoples R China

interpolation algorithm is the critical algorithm to achieve good dynamic performance of machine tools. However, due to complex kinematic constraints and calculation conditions, high-order continuous inter-polation algorithms for six-axis machine tools are relatively rare in the literature, although they can greatly improve motion stability, reduce motion impact, and inspire motion performance. This paper develops an interpolation algorithm with jerk continuity for six-axis machine tools. A C3 continuity corner smoothing method of six-axis path is achieved by locally inserting two specially designed symmetrical quintic Bezier curves into the transition corners of linear commands. The pose in the six-axis path is converted to Euler angle with three parameters, and the synchronization of the position and pose are mathematically guar-anteed at the junctions of the linear and curve segments. The proposed corner smoothing method can calculate all control points of Bezier curves under the constraints of approximation error and path curvature analytically, which makes it suitable for online calculation. A quintic-polynomial feedrate schedule is uti-lized to meet the jerk continuity of the motion, and the concept of equivalent jerk is proposed to simplify the schedule calculation and smooth the velocity curve. In this way, the jerk continuity of the algorithm is achieved both at the geometric level and the feedrate level. The developed algorithm is verified to have more advantages than low-order continuous algorithms by simulation and comparison, and can improve the motion continuity of six-axis machine tools.& COPY;2023 CIRP.

关键词： Six -axis machine tools Corner smoothing Pose and position synchronization Feedrate schedule interpolation algorithm

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Window function and interpolation algorithm for OFDM frequency-offset correction

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2003年第3期52卷 654-670页

作者： Zhang, R Tjhung, TT Hu, HJ He, P Stanford Univ Dept Elect Engn Stanford CA 94305 USA Inst Commun Res Singapore 117674 Singapore Natl Univ Singapore Dept Elect & Comp Engn Singapore 119260 Singapore

In orthogonal frequency-division multiplexing (OFDM) digital communication systems, an uncorrected frequency offset can lead to a severe degradation of the system performance. This paper describes a technique to mitigate the influence of frequency offset on system performance by applying a weighted discrete Fourier transform (DFT) to a novel OFDM frequency-assignment scheme in which null carriers are regularly inserted among modulated data carriers. This frequency-assignment scheme makes possible the application of a window, function at the demodulator to broaden,the signal spectrum and renders the demodulated signal more immune to the influence of frequency offset. In addition, a variant of this frequency-assignment scheme also leads to a DFT-based measurement technique for, easy and accurate determination of the frequency offset. interpolation algorithms and frequency-assignment schemes suitable for both initial frequency acquisition and subsequent frequency tracking are described in detail. The Rife and Vincent (Class-I) windows are examined and their estimation results are obtained for an additive white Gaussian noise (AWGN) and a multipath fading channel.

关键词： discrete Fourier transform frequency offset correction and tracking interpolation algorithm orthogonal frequency division multiplexing window function

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Calculation of electromagnetic parameter based on interpolation algorithm

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JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 2015年 393卷 24-29页

作者： Zhang, Wenqiang Yuan, Liming Zhang, Deyuan China Agr Univ Coll Engn Beijing 100083 Peoples R China Beihang Univ Bion & Micro Nano Bio Mfg Technol Res Ctr Beijing 100191 Peoples R China

Wave absorbing material is an important functional material of electromagnetic protection. The wave absorbing characteristics depend on the electromagnetic parameter of mixed media. In order to accurately predict the electromagnetic parameter of mixed media and facilitate the design of wave-absorbing material, based on the electromagnetic parameters of spherical and flaky carbonyl iron mixture of paraffin base, this paper studied two different interpolation methods: Lagrange interpolation and Hermite interpolation of electromagnetic parameters. The results showed that Her mite interpolation is more accurate than the Lagrange interpolation, and the reflectance calculated with the electromagnetic parameter obtained by interpolation is consistent with that obtained through experiment on the whole. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Wave-absorbing material Electromagnetic parameter interpolation algorithm Theoretical calculation Experimental verification

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A real-time high-precision interpolation algorithm for general-typed parametric curves in CNC machine tools

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INTERNATIONAL JOURNAL OF COMPUTER INTEGRATED MANUFACTURING 2010年第2期23卷 168-176页

作者： Liu, Q. Jin, X. J. Long, Y. H. Wuhan Univ Technol Sch Informat Engn Wuhan 430070 Peoples R China

The machining accuracy of computer numerical control (CNC) machine tools largely depends on the interpolation algorithms implemented. In this paper, a real-time high-precision interpolation algorithm for a general-typed parametric curve is proposed. As with other time-partition interpolation algorithms, the linear motion trajectory (employed to approximate the real trajectory) in a sampling cycle is determined from the current position of the tool to another point (target point) on the target trajectory. To determine the target point in a sampling cycle, a neighbourhood interval containing the point is first determined, the target point is then iteratively approached by means of the bi-section or secant method for equation resolutions. Simulation results show that the order of magnitude of the maximum feedrate relative errors (the relative deviation of the computed feedrate from the desired one) is -8 or less, while the order of magnitude of the maximum chord errors in the unit of meter is -6 or less. The performance indices can be further improved with more computation iteration in each sampling cycle. The algorithm is general, and applicable to any smooth curve that can be formulated in parametric equations.

关键词： interpolation algorithm motion trajectory numerical control real-time

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