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研究了硬质合金内衬的多层组合超高压筒体的强度优化设计。以等强度理论为设计原则,建立了以各外层径比(外径与内径的比值)为变量,容器总径比为约束,弹性承压能力最大为目标的优化设计数学模型。应用Lagrange乘子法进行优化,得到了各层最优径比公式及最大内压公式。在此基础上,从叠加原理出发,推导了不同材料多层容器的层间缩套压力及过盈量的最优精确解。最后通过实际算例与分析表明,硬质合金内衬的组合容器需要更大的缩套压力,对于三层容器,中间层和内衬主要承担径向压应力,而外层主要承担周向拉应力。
The strength optimization design of cemented carbide lined multilayer composite ultrahigh pressure cylinder was studied. Based on the principle of isosceles theory, an optimized design mathematical model was established with the outer diameter ratio (the ratio of outer diameter to inner diameter) as the variable, the container diameter ratio as the constraint and the maximum elastic bearing capacity as the goal. Lagrange multiplier method was used to optimize the optimal ratio formula of each layer and the maximum internal pressure formula. Based on this, based on the principle of superposition, the optimal and exact solution of interlayer shrinkage pressure and interference of multi-layer containers with different materials is deduced. Finally, the practical examples and analysis show that the composite container with cemented carbide lining needs more shrinkage pressure. For the three-layer container, the intermediate layer and the lining mainly bear the radial compressive stress, while the outer layer mainly takes the circumferential pull stress.