In this research, geometric parameters were given in dimensionless form by the Buckingham pi dimensional analysis method, and a series of dimensionless groups were found for deep drawing of the round cup. To find the best group of dimensionless geometric parameters, three scales are evaluated by commercial FE software. After analyzing all effective geometric parameters, a fittest relational model of dimensionless parameters is found. St12 sheet metals were used for experimental validation, which were formed at room temperature. In addition, results and response parameters were compared in the simulation process, experimental tests, and proposed dimensionless models. By looking at the results, it very well may be inferred that geometric qualities of a large scale can be predicted with a small scale by utilizing the proposed dimensionless model. Comparison of the outcomes for dimensionless models and experimental tests shows that the proposed dimensionless models have fine precision in determining geometrical parameters and drawing force estimation. Moreover, generalizing proposed dimensionless model was applied to ensure the estimating precision of geometric values in larger scales by smaller scales.

中文翻译：

---

关于无量纲分析的一种用于深拉伸过程中拉伸力预测的新方法的研究

在这项研究中，通过白金汉pi尺寸分析方法以无量纲形式给出几何参数，并找到了一系列无量纲组来深冲圆杯。为了找到最佳的无量纲几何参数组，可通过商业有限元软件评估三个比例。在分析了所有有效的几何参数之后，找到了无因次参数的最适合的关系模型。St12薄板用于在室温下形成的实验验证。此外，在仿真过程，实验测试和提出的无量纲模型中比较了结果和响应参数。通过观察结果，可以很好地推断出，通过利用所提出的无量纲模型，可以以小规模预测大尺度的几何质量。无量纲模型和实验测试结果的比较表明，所提出的无量纲模型在确定几何参数和拉伸力估计方面具有良好的精度。此外，应用广义的无量纲模型来确保以较小的比例尺在较大的比例尺上估计几何值的精度。