三块平板对研的理论探讨

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中图分类号：TH161

DOI：10.3969/j.issn.1004-132X.2025.07.002 开放科学（资源服务）标识码（OSID）：

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

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 flatened 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

0 引言

1830年，英国机械学家约瑟夫·惠特沃斯发明了三块平板对研、刮削加工精密平面的方法，促进了精密工程的发展。（剩余12602字）