Industries such as 3C are increasingly incorporating titanium alloy structural components, leading to a significant demand for machining tools. The geometric parameters of these tools are crucial for their lifespan. However, the current reliance on manual design and iterative processes hampers rapid and high-quality tool design, adversely affecting product quality, production speed, and costs. To tackle this industrial challenge, it is essential to explore intelligent prediction paradigms for geometric parameter design. Achieving end-to-end prediction of multiple geometric parameters for cutting tools remains a complex task, with limited research on small-sample multi-task tabular data. This article proposes a novel deep transfer learning framework (Phy-MTDTL) for multi-task tabular data, integrating two pre-training and transfer paradigms while incorporating physical knowledge. This approach addresses challenges in multi-task prediction, small sample sizes, and the interpretability of industrial tabular data modeling. The framework introduces an innovative paradigm for high-precision and high-qualification-rate intelligent prediction of multiple geometric parameters, paving the way for new research directions in cutting tool design. The integration of physical knowledge is reflected in three aspects: dataset, model structure, and evaluation indicators, enhancing the interpretability and credibility of the proposed method. Experimental results demonstrate the framework's effectiveness, showing significantly superior prediction accuracy and physical pass rates exceeding 90 % across five different geometric parameter prediction tasks compared to current transfer learning models. Additionally, the incorporation of physical knowledge enhances transfer prediction performance for small-sample tabular data. These results indicate that the study has significant industrial applicability and value.