Compressed packer rubber is large deformation material, which endures biaxial contact friction between oil-pipe and casing-pipe in sitting and sealing process. Large-deformation theory analysis of rubber brings huge difficulties to solve, this is due to the material, geometry and contact non-linearity should be considered. In this article, the deformation of compressed packer rubber tube (CPRT) is divided into free deformation, unidirectional and bidirectional constrained deformations. Based on the theory of thick-wall-cylinder and the linear constitutive of rubber material segment, the CPRT mathematical model in different deformation processes is established and the influences of axial load, axial height of CPRT and contact friction coefficient of casing inner wall etc are considered. Based on incremental calculated approach, the mathematical model is solved. By comparing the results of the theoretical model with the results of finite element method and experimental results, it is found that the theoretical maximum contact stress is more conservative than the FEM and experimental solutions, so the sealing reliability of packer effectively predicted under the premise of allowable contact stress and the theoretical results can provide a lower limit reference value for the contact stress of the packer in the actual seal process. Meanwhile, the deviation of contact stress in FEM and theoretical value at z150 height of CPRT is among 1.13%∼4.90%, which can predict the contact stress in the compressed area near the stress concentration upper end-face of CPRT under the low friction factor, the results provide a reference for the compressed packer design.

压缩封隔器橡胶是一种大变形材料，在坐封过程中承受油管和套管之间的双向接触摩擦。橡胶的大变形理论分析给解决带来了巨大的困难，这是由于应考虑材料、几何形状和接触非线性。本文将压缩封隔器胶管（CPRT）的变形分为自由变形、单向和双向受约束变形。基于厚壁圆柱体理论和橡胶材料段的线性本构，建立了不同变形过程中的CPRT数学模型，分析了轴向载荷、CPRT轴向高度和套管内壁接触摩擦系数等因素的影响。经过考虑的。基于增量计算的方法，数学模型求解。通过将理论模型的结果与有限元法的结果和实验结果进行比较，发现理论最大接触应力比有限元法和实验解更保守，因此有效预测了封隔器密封可靠性的前提下允许接触应力和理论结果可为封隔器在实际密封过程中的接触应力提供下限参考值。同时，有限元法的接触应力与CPRTz150高度处的理论值偏差在1.13%～4.90%之间，可以预测低摩擦系数下CPRT应力集中上端面附近受压区域的接触应力，结果为压缩封隔器设计提供参考。通过将理论模型的结果与有限元法的结果和实验结果进行比较，发现理论最大接触应力比有限元法和实验解更保守，因此有效预测了封隔器密封可靠性的前提下允许接触应力和理论结果可为封隔器在实际密封过程中的接触应力提供下限参考值。同时，有限元法的接触应力与CPRTz150高度处的理论值偏差在1.13%～4.90%之间，可以预测低摩擦系数下CPRT应力集中上端面附近受压区域的接触应力，结果为压缩封隔器设计提供参考。通过将理论模型的结果与有限元法的结果和实验结果进行比较，发现理论最大接触应力比有限元法和实验解更保守，因此有效预测了封隔器密封可靠性的前提下允许接触应力和理论结果可为封隔器在实际密封过程中的接触应力提供下限参考值。同时，有限元法的接触应力与CPRTz150高度处的理论值偏差在1.13%～4.90%之间，可以预测低摩擦系数下CPRT应力集中上端面附近受压区域的接触应力，结果为压缩封隔器设计提供参考。