At present, most of 3D models generated by deep neural networks are non-parametric and not used for mechanical design and engineering application. To generate parametric CAD models automatically, one of the key problems is that there is no uniform structured representation strategy for parametrical CAD models. In this paper, we introduce a new feature extraction strategy for parametric CAD models and propose a new auto-encoder model, Y-type GAE, to solve the uniform representation problem. In experiments, in order to verify the quality of Y-type GAE, we design a generalization experiment, and an ablation test on some public datasets. Meanwhile, based on the uniform representation of parametric CAD models, we propose three feasible pipelines for 3D model generation, classification and retrieval. The effectiveness of the generation pipeline is evaluated on two public datasets, and the performance of the classification pipeline surpasses other representation methods of parametric CAD models. (The code is available at https://github.com/dishy313/Y-typeGAE ).