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描述垂直井中螺旋弯曲管柱轴力分布和变形行为的力学方程是一组高阶非线性常微分方程组。求得了这组非线性 方程在对称性条件下的渐近螺线解；分析了摩擦系数对整个管柱上的轴力分布、“中性点”位置、“自锁点”位置以及“自锁 力”等的影响；导出了“中性点”、“自锁点”以及“自锁力”的计算公式；并绘制出对应不同摩擦系数的轴力分布曲线以及“中 性点”、“自锁点”随端部轴压变化的曲线。本文研究的结果对于高温、高压深井井下作业管柱的合理设计和作业参数的合 理选择等具有较大的实用价值。
The mechanical equation describing the axial force distribution and deformation behavior of a helical tube in a vertical well is a set of higher order nonlinear ordinary differential equations. The asymptotic spiral solutions of this set of nonlinear equations under symmetrical conditions are obtained. The influence of friction coefficient on axial force distribution, “neutral” position, “self-locking point” position and “self-locking Force ”and so on. The calculation formulas of“ neutral point ”,“ self-locking point ”and“ self-locking force ”are deduced. And the axial force distribution curves corresponding to different friction coefficients are drawn, Lock point "with the end of the axial pressure curve. The results of this paper have great practical value for the reasonable design of the downhole work string and the reasonable choice of operating parameters for the deep well in high temperature and high pressure.