中径公式与特雷斯卡公式应用范围拓展的研究

Research on Application Range Extension of Mid-diameter and Tresca Formula

为拓展承压容器爆破压力计算公式的应用范围,基于承压容器实测爆破压力与中径公式或特雷斯卡公式计算值之比是基本符合正态分布随机变量的研究,应用数理统计与概率论知识,建立了随机变量分布参数取值区间的优化方法,以及公式精度和稳定性的比较方法。研究表明:(1)当承压圆筒实测爆破压力不超过105.5MPa,位于91.0MPa与329.6MPa之间,以及不超过329.6MPa时,中径公式或特雷斯卡公式对应随机变量的分布参数分别无显著差异,可视为同一个随机变量;双侧置信度为98%时,分布参数均值不小于0.9800且不大于0.9932,标准差不小于0.0413且不大于0.0578,均值取值区间的波动范围为0.0132,标准差取值区间的波动范围为0.0165。(2)在保持公式精度与稳定性不降低的条件下,中径公式的应用范围可从实测爆破压力不超过105.5MPa拓展至不超过329.6MPa;特雷斯卡公式的应用范围可从实测爆破压力位于91.0MPa与329.6MPa之间拓展至不超过329.6MPa。

In order to extend the applied range of pressure vessel burst pressure calculation formula,based on the study that the ratio of actual burst pressure to the Mid-diameter or Tresca formula calculated value was basically in accordance with the normal distribution random variables,application of the knowledge of mathematical statistics and probability theory,the optimization method of the interval of random variable distribution parameters and the comparison method of formula precision and stability were established.Research shows that:(1)When the measured burst pressure of the vessel does not exceed 105.5MPa,between 91.0MPa and 329.6MPa,and below 329.6MPa,there was no significant difference in the distribution parameters of random variables corresponding to the Mid-diameter formula or Tresca formula,which can be regarded as the same random variable.When the bilateral confidence was 98%,the mean value of distribution parameter is not less than 0.9800 and not greater than 0.9932.standard deviation not less than 0.0413 and not greater than 0.0578,the fluctuation range of the mean value range is equal to 0.0132,and the fluctuation range of standard deviation value range is equal to 0.0165.(2)Under the condition that the formula precision and stability were not reduced,the mid-diameter formula applied range can be extended from the burst pressure measured values not exceeding 105.5MPa to not exceeding 329.6MPa,the Tresca formula applied range can be extended from the burst pressure measured values located between 91.0MPa and 329.6MPa.