# Assembly Tolerance Design Based on Skin Model Shapes Considering Processing Feature Degradation
## 1 Introduction  
Under the innovative concept of Industry 4.0, automated and digitized systems in smart factories could enable the real-time integration and analysis of massive amounts of data by the use of electronics and information technologies. Moreover, this would finally result in a more flexible and optimized manufacturing process [1; 2; 3]. This theory points to the improvement of intelligent solutions in the tolerance design of mechanical products, including the replacement of empiricism with knowledge-intensive and data-based processes. The general practice of mechanical tolerance design is to treat tolerance design as a combination of tolerance modeling, assembly simulating, tolerance allocation, and optimization. The best combination of part tolerance is assigned through multi-dimensional objective constraints in order to meet environmental clearance, conform to functional requirements, improve product quality, and lower manufacturing costs in the late design stage [4; 5; 6]. To increase the accuracy and robustness of the designed tolerance scheme, the influence of processing feature degradation caused by machining precision deterioration is taken into consideration. In the past few decades, researchers have presented several efficient computer-aided methods for estimating geometry variation and product tolerance. Many models have been developed for geometrical feature representation, deviation accumulation, and tolerance zone estimation [7]. Conventional tolerance modeling methods are mainly categorized into those based on vector loops, Tolerance-Map (T-Map), small displacement torsor (SDT), a Homogeneous Transformation Matrix (HTM), and some other innovative models. Vector loops provide vectorial tolerance representation and analysis for the surfaces of different components. However, only five standard surfaces are typically considered (plane, cylinder, sphere, cone, and torus) [8; 9; 10; 11]. Consisting of a hypothetical volume ofpoints, a T-Map contains all the possible locations for geometrical features, and is used to illustrate the accumulation of product variations [12; 13; 14]. The SDT model uses screws and constraints to establish the extreme limits of part tolerance zones [15; 16; 17]. To overcome the lack of analytical models between the target feature and each feature on the dimensional chain, HTM was combined with T-Map to obtain an expression of the decoupling pose of tolerance features [18]. Since the Jacobian matrices are quite suitable for deviation propagation [19], the unified Jacobian-Torsor model was developed for product precision performance estimation [20; 21; 22]. Furthermore, some innovative modeling methods, such as neural network [23], volumetric envelope [24], modal analysis [25; 26] and graph theory [27; 28] have also been applied to model the mating tolerance of both parts and assemblies. Some of the aforementioned models have contributed to the mainstream commercial computer-aided tolerancing software, such as 3 DCS Variation Analyst, eM-TolMate, VisVSA, and CETOL 6 Sigma [29]. However, most of these tolerancing models excel at estimating the precision of a mechanical product at one state, while they cannot adapt to simulate a sequence of degradation trajectories. Moreover, the simplification of form deviation into a series of tiny dimensional, rotational, and translational deviations of geometric features in some of these models brings about inaccurate virtual representation in the modeling stage and unneglectable simulation errors in the synthesizing and optimizing stages. As a response, the Skin Model Shape theory was introduced as a new paradigm for the modeling of product geometry considering shape variability. The theory of Skin Model Shapes is an integration of international geometric standards and the concept of the Skin Model [30; 31; 32; 33]. Within the theoretical framework of GeoSpelling [34], the Skin Model Shape is commonly formed by discrete geometry schemes such as point clouds and surface meshes.