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Development of an Automatic Precision Sheet Resistance Measurement System Using the four-point Probe method

JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2025年第4期20卷 2799-2808页

作者： Kang, Jeon-Hong Lee, Sang Hwa Yu, Kwang Min Joo, Sungjung KRISS Grp Quantum Elect & Magnetism Metrol Daejeon 34113 South Korea

This paper presents the development of an automated system for precise measurement of sheet resistance in conductive thin-film materials, including ITO, carbon nanotubes, graphene, and silicon wafers. The system integrates a sheet resistance meter utilizing the four-point probe (FPP) method in both single and dual configuration modes. Key components include a motorized probe station for vertical movement of the FPP, a C# software interface enabling automated measurement, and a temperature chamber for controlled testing environments. Additionally, a custom-designed wafer thickness gauge and a thermometer for chamber temperature monitoring were implemented. The sheet resistance meter achieved measurement ranges of 4.532 m ohm/square to 45.32 M ohm/square in single configuration, and 2.605 m ohm/square to 26.05 M ohm/square in dual configuration. The instrument supported measurement of resistance, sheet resistance, and specific resistance, demonstrating high repeatability and reproducibility with less than 0.1% full-scale error in resistance measurements.

关键词： four-point method Sheet resistance Precision measurement Single and dual configuration Uncertainty

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four-point method in the Measurement and Separation of Spindle Rotation Error

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IEEE-ASME TRANSACTIONS ON MECHATRONICS 2021年第1期26卷 113-123页

作者： Liu, Fei Liang, Lin Xu, Guanghua Hou, Chenggang Liu, Dan Xi An Jiao Tong Univ Sch Mech Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Key Lab Educ Minist Modern Design & Rotor Bearing Syst Xian 710049 Peoples R China Xi An Jiao Tong Univ State Key Lab Mfg Syst Engn Xian 710054 Peoples R China

For the spindle of machine tool, rotation error is a main factor affecting the machining quality, so many investigations have been focused on the measurement of the rotation error. In this article, a measurement and separation method of the rotation error is proposed to extract the orbit of spindle section center and to quantize the rotation error with a special measurement system. Thereinto, systematic measurement strategy has been especially designed to achieve the measurement and analysis of the rotation error. When the measurement does not conform to the small error conditions, the method can reduce the noise level from sensors and improve measurement accuracy in measuring the orbit of spindle section center. When it is necessary to accurately quantify the rotation error and the roundness error, the method also can effectively separate them with independent coordinate system and sensor bracket. Additionally, considering the effect of high temperature on spindle, the method can reduce the form error caused by thermal expansion in the measurement process, which is very important in industrial online measurement. Finally, the theoretical analyses are shown good agreement with experimental results, and these also reveal that it is an effective measurement method for the rotation error.

关键词： Extraterrestrial measurements Measurement uncertainty Rotation measurement Coordinate measuring machines Sensor systems Displacement measurement Dynamic error detection four-point method machine tool spindle rotation error roundness error

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A new development of four-point method to measure the electrical resistivity in situ during plastic deformation

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MEASUREMENT 2021年 180卷

作者： Saberi, Saeid Stockinger, Martin Stoeckl, Christian Buchmayr, Bruno Weiss, Helmut Afsharnia, Reza Hartl, Karin Univ Leoben Chair Met Forming A-8700 Leoben Austria Univ Leoben Inst Elect Engn A-8700 Leoben Austria Islamic Azad Univ Dept Mech Engn Najafabad Branch Najafabad Iran

The presented study introduces a new test method to measure the change of the electrical resistivity in situ during plastic deformation to characterize the deformation behaviour of metals. This investigation is based on a specially developed four- point method, which determines the change in electrical resistance of sheet samples of an aluminium alloy 6062, a copper alloy CW024A and steel DC04 in situ during deformation in a tensile test. Results show that the strain path, the deformation history, the plastic anisotropy as well as the plastic deformation have a significant influence on the electrical resistivity of all investigated materials. Therefore, this technique is universally applicable for all sheet metals, independent of the crystal structure, the electrical and mechanical properties to characterize structural changes during forming. The obtained data can be used for simulations of metal forming processes, e. g. to predict forming limit curves and damage monitoring under service loading.

关键词： Plastic deformation Plastic anisotropy Plane strain test Uniaxial tensile test Electrical resistivity four-point method

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An Experimental Electrothermomechanical Characterization of Pipe Steels within Elastic-Plastic Range Based on Resistivity Measurement for Oil Country Tubular Goods

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JOURNAL OF MATERIALS ENGINEERING AND PERFORMANCE 2025年第5期34卷 4477-4485页

作者： Saberi, Saeid Weiss, Helmut Winter, Gerald Klarner, Juergen Stockinger, Martin Univ Leoben Leoben Austria Univ Leoben Inst Elect Engn Leoben Austria Voestalpine Tubulars GmbH & Co KG Kindberg Austria

The complex geometry of thread and difficult access to the thread surface make conventional methods for residual stress measurement impossible. Therefore, an in situ measurement of electrothermomechanical properties of quenched-tempered martensitic pipe steel P110 based on the four-point method was developed in this research. Electrical resistivity and thermomechanical properties of investigated pipe steel P110 due to plastic deformation were determined. The average value of the temperature change, the plastic work per volume, the relative resistance and the relative resistivity of samples up to 3% uniform plastic strain were obtained as 2.2 degrees C, 30.01 MPa, 0.1 and 0.01, respectively.

关键词： electrical resistance four-point method oil country tubular goods pipe steel plastic deformation thermal properties uniaxial tensile test

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Fracture toughness of seven resin composites evaluated by three methods of mode I fracture toughness (K_Ic)

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DENTAL MATERIALS JOURNAL 2016年第6期35卷 893-899页

作者： Mese, Ayse Palamara, Joseph E. A. Bagheri, Rafat Fani, Mehdi Burrow, Michael F. Dicle Univ Sch Dent Dept Prosthodont Diyarbakir Turkey Univ Melbourne Melbourne Dent Sch Restorat Sect 720 Swanston St Melbourne Vic Australia Shiraz Univ Med Sci Sch Dent Dept Dent Mat Ghasrodasht St Shiraz Iran Shiraz Univ Med Sci Sch Dent Biomat Res Ctr Ghasrodasht St Shiraz Iran

This study compared the fracture toughness values of seven resin composites and analyzed the consistency of data values using three methods: compact tension, three point and four point bending for Mode I failure. Seven resin composites were selected: Estellite Sigma Quick, Esthet X HD, Filtek Supreme XTE, Heliomolar, Ice, Rok, and Vit-l-escence. For each material, 18 specimens (n=6 for each test) were prepared. Maximum load to failure was recorded using a universal testing machine and fracture toughness was calculated. There was a direct significant correlation among all tested methods. Rok showed the highest and Estelite the lowest K-Ic values. SEM of the fractured surface of compact tension method showed propagation of the cracks from stresses concentrating at the corner of the notch and the surface of the sample. four-point test gave the largest range in K-Ic, and was a simple method to discriminate between the resin composite values of K-Ic.

关键词： Fracture toughness four-point method Three-point method Compact tension method Resin composite

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Research on Earth Resistivity Measuring and Modeling of HVDC Deep-Well Grounding Electrode Sites

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IEEE ACCESS 2020年 8卷 23776-23786页

作者： Jing, Maoheng Wen, Xishan Cai, Hansheng Teng, Yun Hu, Shangmao Zhang, Yi Lan, Lei Lu, Hailiang Wuhan Univ Sch Elect Engn & Automat Wuhan 430072 Peoples R China CSG Elect Power Res Inst Guangzhou 510670 Peoples R China

HVDC Deep-well grounding electrode covers a small area, which effectively alleviates the problem of difficulty in selecting the site of grounding electrode. Due to the small number of electrodes, each sub-electrode has to bear tens of times the current of conventional electrodes. In order to reduce the current density on the electrode, it is usually necessary to use long vertical electrodes to extend into low resistivity layers' hundreds of meters underground. Because it involves a wide range of underground depths, it is particularly important to accurately evaluate the distribution of resistivity at the electrode site for calculating the electrical parameters of deep-well grounding electrodes. In this paper, four-point method (FP), controllable source audio magnetotelluric method (CSAMT) and magnetotelluric method (MT) are proposed to analyze the conductivity structure of the shallow layer, deep layer and the vicinity of the electrode, and the earth resistivity model of deep-well grounding electrode is obtained. By comparing the on-site grounding resistance measurements of practical engineering application, it is found that the absolute error of the earth resistivity model obtained in this paper is 0.064 Omega when calculating the grounding resistance of the deep-well grounding electrode. Engineering examples show that the exploration method in this paper has strong adaptability to the site, and the earth resistivity modeling method has good reliability.

关键词： HVDC deep-well grounding electrode earth resistivity four-point method controlled source audio magnetotelluric method magnetotelluric method grounding resistance

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Uncertainty analysis of phase and amplitude of harmonic components of bearing inner ring four-point roundness measurement

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PRECISION ENGINEERING-JOURNAL OF THE INTERNATIONAL SOCIETIES FOR PRECISION ENGINEERING AND NANOTECHNOLOGY 2018年 54卷 118-130页

作者： Viitala, Raine Widmaier, Thomas Hemming, Bjorn Tammi, Kari Kuosmanen, Petri Aalto Univ Sch Engn Dept Mech Engn Helsinki Finland VTT Tech Res Ctr Finland Ltd MIKES Metrol Espoo Finland

The four-point roundness measurement method enables the measurement of roundness without a requirement for a precise rotating motion of the workpiece or a measurement sensor. The four-point roundness measurement method can separate the roundness profile and the motion of the rotating axis of the workpiece. In the present study, the uncertainty of the four-point roundness measurement of a bearing inner ring was analysed. The bearing inner ring was installed in its operating position on the shaft of a large rotor during the measurement in order to investigate the bearing inner ring roundness profile in operating conditions. Since the measurement evaluation using the four-point method is complex, the uncertainty analysis was conducted through a MonteCarlo simulation, using realistic error sources in typical measurement conditions. The uncertainty of both the amplitude and phase of the harmonic components of the roundness profile was analysed for the 2nd till the 30th harmonic component. Attention was directed especially towards the phase of the harmonic components, since the uncertainty of the phase is analysed very little in existing research studies. In addition, the phase of the harmonic components of the roundness profile is important when considering compensative precision grinding applications of round workpieces. The results show that below the 10th harmonic component, the maximum amplitude standard uncertainty was circa 0.5 mu m, and the maximum phase standard uncertainty was circa 5 degrees. The standard uncertainties of the amplitudes for the complete harmonic component range were below 1.3 mu m for odd components and 0.2 mu m for even components. The maximum standard uncertainties of the phases for the complete harmonic component range were circa 15 degrees for odd components and circa 5 degrees for even components. The measured roundness profile itself did not have an effect on the uncertainty of the method.

关键词： Monte-Carlo simulation Phase uncertainty Harmonic component uncertainty Uncertainty evaluation Bearing excitation Odd and even harmonic components four-point method Three-point method

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Reconstruct unrecoverable data in real-time networks using Bezier curve

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IET COMMUNICATIONS 2015年第5期9卷 596-602页

作者： Nugroho, Dwi Agung Rizal, Syamsul Kim, Dong-Seong Kumoh Natl Inst Technol Dept IT Convergence Engn Sch Elect Engn Gumi Si South Korea

This study proposes a method to handle unrecoverable data using a formula called Bezier curve. The proposed method suggests the possibility to approximate the damaged data, which have been processed by the error correction scheme. The proposed method works on the real-time distributed system which retransmission is considered as unsuitable solution to manage the overall networked system. By using the Bezier curve, the transmitted unrecoverable data are reconstructed again by using the functional approximation. This method provides a smoothing effect on damaged data that usually are normalised on real-time transmission of PROFIBUS. Three differences Bezier curve methods are compared in PROFIBUS data, four-points (FP) method, two-points two-degrees method and four-degrees (FD) method. Simulation results show that all three Bezier curve methods can approximate data in PROFIBUS. FD has higher computation complexity compared with others. However, FD compensates with its data size which is only half of FP method.

关键词： computational geometry function approximation computational complexity data handling transmitted unrecoverable data reconstruction real-time networks Bezier curve unrecoverable data handling damaged data approximation error correction scheme real-time distributed system data retransmission overall networked system management functional approximation smoothing effect normalisation real-time PROFIBUS transmission four-point method two-point-two-degree method four-degree method FD method computation complexity data size FP method

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Subcritical vibrations of a large flexible rotor efficiently reduced by modifying the bearing inner ring roundness profile

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2018年 110卷 42-58页

作者： Viitala, Raine Widmaier, Thomas Kuosmanen, Petri Aalto Univ Sch Engn Dept Mech Engn Aalto Finland

Undesired vibration of a rotor is harmful for industrial processes and decreases the machine lifetime. In industrial processes, large rotors are commonly operated below the critical speed. In the subcritical speed range, the bearings are an important excitation source of vibration. The bearing inner ring based excitation is observed at a frequency, which is the rotor rotating frequency multiplied by the number of undulations in the roundness profile of the roller race of the bearing inner ring. Subcritical resonance occurs, when the bearing excitation frequency equals the natural frequency of the rotor system. The present study investigates the effect of the bearing inner ring roundness profile on the subcritical vibrations of a flexible rotor. The roundness profile of the bearing inner ring was measured, while installed on the rotor shaft. The roundness profile was modified to five different geometries to investigate different excitation cases. Finally, the roundness error of the inner ring was minimized. The rotor subcritical vibration was measured with each bearing inner ring geometry in the horizontal and vertical directions. The analysis was focused on the 2nd, 3rd and 4th harmonic vibration components, occurring at 1/2, 1/3 and 1/4 of the critical rotational speed. The results clearly suggest that the roundness profile of the roller race of the bearing inner ring affects the rotor subcritical vibration significantly. The increased waviness components of the bearing inner ring roundness profile increased the corresponding subcritical vibration amplitude. Minimizing the roundness error decreased the subcritical vibration substantially. (C) 2018 The Author(s). Published by Elsevier Ltd.

关键词： Rotor dynamics Dynamic run-out Low-order bearing waviness four-point method

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Precision of electrical resistivity measurements

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MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 2007年第1-2期462卷 339-342页

作者： Hajek, M. Vesely, J. Cieslar, M. Charles Univ Prague Fac Math & Phys Dept Met Phys CR-12116 Prague Czech Republic

The influence of the specimen shape on the electrical resistivity measurements was investigated both theoretically, by means of finite element method modelling, and experimentally, by measuring electrical resistivity of samples of variable shapes. Precision of electrical resistivity measurements using a four-point method for samples of arbitrary shape was critically reviewed. (C) 2006 Elsevier B.V. All rights reserved.

关键词： electrical resistivity four-point method finite elements

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