作者：甘晓川, 赵子越, 马骊群

作者单位：北京长城计量测试技术研究所，北京 100095

关键词：计量学;球坐标;直角坐标;重复性;空间分布;角度重复性;距离重复性

摘要：

几何量计量中使用直角坐标系统、球坐标系统、关节臂系统等多种不同原理的坐标测量系统。以激光跟踪仪为例，分析球坐标系统的基本测量原理，根据球坐标与直角坐标的相互转换关系，推导计算两坐标系下重复性的传播规律，说明坐标测量重复性表达方式的不同。分别在球坐标系和直角坐标系下，利用Monte Carlo法模拟坐标测量点的空间分布。从理论分析、模拟试验、实际试验3个角度说明球坐标测量系统空间坐标的测量重复性采用角度和距离分别给出更能体现测量点的空间分布，为球坐标测量系统的生产者和使用者提供理论指导。

Coordinate measurement repeatability in spherical coordinate system
GAN Xiaochuan, ZHAO Ziyue, MA Liqun
Changcheng Institute of Metrology & Measurement, Beijing 100095, China
Abstract: The coordinate measurement system based on different measurement principle, such as rectangular coordinate system, spherical coordinate system and articulated arm coordinate measurement system is usually used in geometric metrology. Taking the laser tracker as an example, the basic measurement principle of the spherical coordinate system is analyzed. According to the relationship between the spherical coordinate and the rectangular coordinate, the repeatability propagation law in the two coordinate systems is deduced and calculated. It shows that the repeatability expressed in this two coordinate is different. The Monte Carlo simulation experiment is run in spherical coordinate system and rectangular coordinate system both. The special distribution of the point is simulated, and the difference are compared. From three angles of theoretical analysis, simulation test and actual test, the repeatability of measuring space coordinate of spherical coordinate measuring system is described. The spatial distribution of measuring points can be better expressed by angle and distance respectively. To provide theoretical guidance for the spherical coordinate measuring system as the producer and user.
Keywords: metrology;spherical coordinate;rectangular coordinate;repeatability;spatial distribution;angular repeatability;range repeatability
2020, 46(8):26-33  收稿日期: 2019-12-28;收到修改稿日期: 2020-02-15
基金项目: 国家重点研发计划资助项目（2017YFF0106408）；国防军工技术基础资助项目(JSJL2016205A004)
作者简介: 甘晓川（1979-），男，四川威远县人，高级工程师，硕士，主要从事大尺寸计量理论与技术研究
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