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齿圈布置是牙轮钻头设计的一个重要内容，对牙轮钻头的工作性能和破岩效率有很大影响。本文在牙轮钻头运动学基础上研究了齿圈布置与井底破碎之间的关系，建立了系统地进行齿圈布置设计分析的新方法。根据牙齿在井底的运动分析，对钻头各圈牙齿在井底的滑移进行了定量的分析计算和各圈牙齿在井底径向平面内的运动轨迹所形成的包络线，作出了井底径向破碎图，它改进了传统的井底击碎图，可直观地反映移轴距和牙齿径向滑移对井底径向破碎的影响；建立了井底破碎环带划分和各齿圈单齿破岩量计算的新方法，指出齿圈布置设计，应尽可能均衡钻头各齿圈的单齿破岩量。这对牙轮钻头布齿设计具有重要指导意义。
The ring gear arrangement is an important part of cone bit design, which has a great influence on the working performance and rock breaking efficiency of roller cone bit. Based on the kinematics of roller cone bit, this paper studies the relationship between gear ring arrangement and bottom hole crushing, and establishes a new method to systematically design and analyze ring gear arrangement. According to the movement analysis of the teeth in the bottom of the hole, the slip of the tooth at the bottom of the bit was quantitatively analyzed and calculated and the envelope formed by the movement trajectories of the teeth in the radial plane of the bottom hole was made. Bottom radial crushing map, which improves the traditional bottomhole crushing map, which can directly reflect the influence of the axial distance and the tooth radial slip on the bottomhole radial crushing. The wellbore crushing zone division and each tooth It is pointed out that the arrangement of ring gear should be balanced with the single tooth breaking amount of each ring gear of the bit as much as possible. This is of great importance to the design of roller cone bits.