**5. Conclusions**

A tolerance design method based on SkinModel Shapes considering processing feature degradation is proposed in this paper. To include the geometric form deviation and degrading processing feature, the machined surface model was constructed in the form of 3D point clouds based on Skin Model Shapes. A uniform sampling was implemented on the grid nodes of the assembly surface. Using machine part samples in mass production, the point dataset was acquired by a high-precision coordinate measuring machine. Then, a continuous-time multi-dimensional Markov process was trained to model the feature degradation process; it was also used in further numerical experiments. To improve the reliability and rationality of the numerical experiments, the assembly force constraints and assembly entity constraints were applied to the assembly simulation. Then, the static and dynamic tolerance indices were analyzed and synthesized. The values of the to-be-designed tolerance terms were designed with the aim of conforming to the assembly tolerance requirement, guaranteeing the assembling probability and reducing the manufacturing cost as much as possible.

The tolerance design method in this paper was applied to an example assembly tolerance design problem regarding a five-axis machine tool rotary feed system. Data analysis indicated that the predictive machined surface model is more accurate than that employed in common Skin Model Shape

methods. The designed tolerance scheme has a larger tolerance interval and lower manufacturing costs. That is, the generation of the feature degradation model comprises an in-depth profile and dynamic investigation for production systems based on sampling machining data, which improved the ability of self-configuration of the designed tolerance scheme. Also, the designing reliability and robustness was improved through the improved assembly simulation considering multiple assembling constraints. In addition, the collection and analysis of the manufacturing information and the process of virtual simulation is closely related to the deployment of Internet of Things (IoT) systems and Cyber-Physical Production Systems (CPPS), especially manufacturing equipment with sensors, automation, and information flow. As a result, the proposed method helps to promote the design capability and production flexibility, and improves competence in an increasingly competitive business environment. It provides a new way to design with digitality and intelligence to help fill in the gaps between virtual engineering processes and virtual engineering factories, which would contribute to completing the structure of Industry 4.0. However, evenly distributed sampling points on the assembly surface may cause model distortion when local geometric features are complicated. Boundary treatment in point cloud combination, advanced sampling methods, and dimensionality reduction in solution space also need attention in further research.

**Author Contributions:** Conceptualization, C.H. and L.Q.; methodology, C.H.; software, C.H.; validation, C.H., S.Z. and L.Q.; formal analysis, S.Z.; investigation, C.H.; resources, C.H.; data curation, C.H.; writing—original draft preparation, C.H.; writing—review and editing, C.H., S.Z., L.Q., Z.W. and X.L.; visualization, C.H.; supervision, L.Q., S.Z., Z.W. and X.L.; project administration, L.Q.; funding acquisition, L.Q.

**Funding:** The work is supported by the National Science Foundation of China under gran<sup>t</sup> No. 51675478.

**Conflicts of Interest:** The authors declare no conflict of interest.
