三块平板对研的理论探讨

doi:10.3969/j.issn.1004-132X.2025.07.002

中国机械工程 ›› 2025, Vol. 36 ›› Issue (07): 1407-1415.DOI: 10.3969/j.issn.1004-132X.2025.07.002

• 极端制造基础科学与工程前沿专栏（第二十七届中国科协年会学术论文） • 上一篇下一篇

三块平板对研的理论探讨

胡鹏浩¹*;廖进伟¹;石照耀²;管炳良³

1.合肥工业大学仪器科学与光电工程学院，合肥，230009
2.北京工业大学测控技术与仪器工程技术研究中心，北京，100124
3.九江如洋精密科技有限公司，九江，332100

出版日期:2025-07-25 发布日期:2025-08-26
作者简介:胡鹏浩，男，1968年生，教授、博士研究生导师。研究方向为精密仪器设计与制造。发表论文100余篇。E-mail:hupenghao@hfut.edu.cn。
基金资助:
国家自然科学基金(52175505)；第二十七届中国科协年会学术论文

Theoretical Exploration on Whitworth Three Plates Method

HU Penghao¹*;LIAO Jinwei¹;SHI Zhaoyao²;GUAN Bingliang³

1.School of Instrument Science and Opto-electronics Engineering,Hefei University of Technology,
Hefei，230009
2.Beijing Engineering Research Center of Precision Measurement Technology and Instruments,
Beijing University of Technology,Beijing,100124
3.Jiujiang Ruyang Precision Technology Co.,Ltd.,Jiujiang,Jiangxi，332100

Online:2025-07-25 Published:2025-08-26

摘要/Abstract

摘要： 三块平板对研法虽原理表述直观、便于操作，但缺乏理论分析，因此需要从理论上找到三块平板对研一定能获得高精度平面的原因。采用分形理论建立了平板三维模型，通过数学仿真方法模拟了三块平板对研的工艺过程。数据迭代计算揭示了三块平板对研后平面逐渐平整的内在机理。依据实验数据，通过点数和平面度误差评定验证了理论分析的正确性。

关键词: 三平板原理, 高精度平面, 数学仿真, 分形理论

Abstract: The principle of three plates method was expressed intuitively and easy to operate, but lacked theoretical analysis. It was necessary to find the theoretically reasons for three flat plates always obtaining high-accuracy planes. Fractal theory was used to establish a 3D model for flat plates, and a mathematical simulation method was constructed to simulate of three-plate matching and scraping processes. Iteration and convergence analysis revealed the internal mechanism of the surface which was gradually flattened after the scraping. The correctness of the theoretical analysis was verified by point counts and flatness error evaluation based on experiments.

Key words: three-plate principle, high precision plane, mathematical simulation, fractal theory

中图分类号:

TH161

胡鹏浩1, 廖进伟1, 石照耀2, 管炳良3. 三块平板对研的理论探讨[J]. 中国机械工程, 2025, 36(07): 1407-1415.

HU Penghao1, LIAO Jinwei1, SHI Zhaoyao2, GUAN Bingliang3. Theoretical Exploration on Whitworth Three Plates Method[J]. China Mechanical Engineering, 2025, 36(07): 1407-1415.

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参考文献

［1］SCHULZ G, SCHWIDER J. Precise Measurement of Planeness［J］. Applied Optics, 1967, 6(6):1077-1084.
［2］GRZANNA J, SCHULZ G. Absolute Testing of Flatness Standards at Square-grid Points［J］. Optics Communications, 1990, 77(2/3):107-112.
［3］周龙声. 三面互研法［J］. 航空工艺技术, 1983, 26(8):11-14.
ZHOU Longsheng. Three-Sided Mutual Research Method［J］. Aeronautical Manufacturing Technology, 1983, 26(8):11-14.
［4］张美红, 董皓, 赵晓龙, 等.矩形静压推力轴承表面平面度与粗糙度的综合分形模拟［J］. 轴承, 2018(4):55-58.
ZHANG Meihong, DONG Hao, ZHAO Xiaolong, et al. Comprehensive Fractal Simulation for Surface Flatness and Roughness of Rectangular Hydrostatic Thrust Bearings［J］. Bearing, 2018(4):55-58.
［5］JORDAN D L, HOLLINS R C, JAKEMAN E. Measurement and Characterization of Multiscale Surfaces［J］. Wear, 1986, 109(1/4):127-134.
［6］MAJUMDAR A,TIEN C L. Fractal Characterization and Simulation of Rough Surfaces［J］. Wear, 1990, 136(2):313-327.
［7］陈辉, 胡元中, 王慧, 等. 粗糙表面分形特征的模拟及其表征［J］. 机械工程学报, 2006, 42(9):219-223.
CHEN Hui, HU Yuanzhong, WANG Hui, et al. Simulation and Characterization of Fractal Rough Surfaces［J］. Chinese Journal of Mechanical Engineering, 2006, 42(9):219-223.
［8］MAJUMDAR A, BHUSHAN B. FractalModel of Elastic-plastic Contact between Rough Surfaces［J］. Journal of Tribology, 1991, 113(1):1-11.
［9］李成贵, 董申. 三维表面形貌的分形维数计算方法［J］. 航空精密制造技术, 2000, 36(4):36-40.
LI Chenggui, DONG Shen. Counting Methods of Fractal Dimension for 3D Surface Topography［J］. Aviation Precision Manufacturing Technology, 2000, 36(4):36-40.
［10］孙洪泉, 谢和平, 于广明. 分形插值曲面生成方法［J］. 阜新矿业学院学报(自然科学版), 1997, 16(6):662-665．
SUN Hongquan, XIE Heping, YU Guangming. A Practical Way of Fractal Interpolated Surface［J］. Jourmal of Fuxin Mining Institute (Natural Science),1997, 16(6):662-665．
［11］孙洪泉, 谢和平. 分形插值曲面及其维数定理［J］. 中国矿业大学学报, 1998, 27(2):217-220.
SUN Hongquan, XIE Heping. Fractal Interpolation Surface and Its Dimension Theorem［J］. Journal of China University of Mining & Technology, 1998, 27(2):217-220.
［12］焦建利. 分形插值曲面的若干性质［D］. 镇江:江苏大学, 2005.
JIAO Jianli. Some Properties of Fractal Interpolation Surface［D］. Zhenjiang:Jiangsu University, 2005.
［13］孙洪泉. 分形插值曲面的MATLAB程序［J］. 苏州科技学院学报(工程技术版), 2006, 19(4):18-21.
SUN Hongquan. A Practical MATLAB Program of Fractal Interpolated Surface［J］. Journal of University of Science and Technology of Suzhou (Engineering and Technology), 2006, 19(4):18-21.
［14］白承发. 钳工刮削技能与技巧［M］. 北京:中国劳动出版社, 1997.
BAI Chengfa. Clamp Scraping Skills and Techn-iques［M］. Beijing:China Labor Press, 1997.
［15］MOORE W R. The Foundations of Mechanical Accuracy［M］. Bridgeport:Moore Special Tool Company, 1970.
［16］黄富贵. 平面度误差各种评定方法的比较［J］. 工具技术, 2007, 41(8):107-109.
HUANG Fugui. Comparison of Various Evaluating Methods for Flatness Error［J］. Tool Engineering, 2007, 41(8):107-109.
［17］孟凡义. 平板精刮研技术研究［J］. 机车车辆工艺, 2022(4):31-32.
MENG Fanyi. Precise Scraping Techniques for Flat Plate［J］. Locomotive & Rolling Stock Technology, 2022(4):31-32.
［18］张潮. 刮研工艺介绍［J］. 机械制造, 2004, 42(1):16-17.
ZHANG Chao. Introduction of Scraping and Grinding Process［J］. Machinery, 2004, 42(1):16-17.

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三块平板对研的理论探讨

Theoretical Exploration on Whitworth Three Plates Method

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