空间超高速撞击碎片云前端速度的预测模型

文章利用一组二级轻气炮发射2017-T4铝质球形弹丸撞击6061-T6单层铝板的地面试验数据，通过选择适当的函数模型，采用多元函数拟合的方法，得到了碎片云前端速度与靶板厚度、弹丸直径和弹丸速度关系的三元二阶多项式模型。再用另外一组数据对该模型进行检验，验证了其对碎片云前端速度具有较好的预测效果。将以上两组数据同样用于建立“无量纲化”模型进行碎片云前端速度预测，并与前述多项式模型的预测结果进行比较发现，该多项式模型预测的方均根误差及平均相对误差均明显优于“无量纲化”模型。该多项式模型可用于预测空间碎片撞击航天器产生的碎片云的前端速度，有助于航天器的空间碎片防护设计。

A model of velocity for predicting debris clouds produced by hypervelocity impacts in space

Using the data obtained from the ground tests based on 2017-T4 aluminum spheres projected by the two-stage light-gas gun impacting 6061-T6 aluminum sheets, and choosing a proper function model, this paper establishes a 3-variable polynomial model with order 2 for the velocity of the front particle of the debris cloud with respect to the sheet thickness, the impact diameter and the impact velocity, making use of the method of the multivariate data fitting. The model is verified by using another group of data and it is shown that the model can give a good forecast for the velocities of the front particle of the debris cloud. The same group of modeling data and a group of test data are also applied to the normalized model. A comparison between the two models shows that the polynomial model is better than the normalized one distinctly regardless of whether the mean squares error or the mean relative error is used. The model can be used to forecast the velocities of the front element of the debris cloud produced by the impact between the space debris and the spacecraft, and be used in the design to protect the spacecraft against the space debris.