Abstract: On analyzing the arrangement of cutters in a PDC bit,two coordinate systems are built which are bit's space circular cylindrical coordinate system(OREH) and outter's space position coordinate system(OXYZ),three outter's angles(φ,β,γ) are defined.On this basis,the PDC bit's five-point survey theory is developed,and a series of formulas are derived,applying PDC bits' geometry and analytic space geometry.The five-point survey theory is used to calculate PDC cutter's position parameter and direction parameter in arbitrary five survey points' coordinate.Arbitrary three points of them are not collinear for the goal of examining and surveying PDC bit and testing the situation software.

Key words: PDC bit, theoretical study, quality check, survey, mathematical model

摘要： 通过分析PDC钻头的布齿情况,建立了钻头圆柱坐标系O1RθH和切削齿位置坐标系O2XYZ,定义了三个切削齿的空间角度(,β,γ).在此基础上,运用PDC钻头几何学和空间解析几何学中的四点共面、行列式、坐标变换的知识,提出并推导出了PDC钻头的五点测绘理论及系列公式.五点测绘理论用于利用复合片上的任意五个测绘点(其中任意三点都不共线)坐标求出复合片的空间位置参数和空间方向参数;达到检验和测绘PDC钻头、检验模拟软件的目的.

关键词: PDC钻头, 理论研究, 质量检验, 测绘, 数学模型