# Assembly Tolerance Design Based on Skin Model Shapes Considering Processing Feature Degradation
## 1 Introduction
It provides an approach for the employment of computational techniques on the Skin Model. Research studies have shown that the Skin Model Shape has great efficiency for the representation of product geometry considering geometrical deviations and form errors [29; 35; 36]. Besides, since deviations in the Skin Model Shape are generated mainly by duplicating a sample pattern from the non-ideal manufacturing process, real part measurement, shape defect simulation, and statistical shape analysis are employed on Skin Model Shapes for convenience. For example, finite element analysis is introduced to help reduce local modeling drawbacks and improve model quality [37]. In addition, the discrete form of the Skin Model Shape has been proven to have great potential in further assembly simulation, performance evaluation, and tolerance analysis [38; 39; 40]. Significant efforts have been made to improve the accuracy of product models when processing features are taken into consideration. Processing features, including systematic geometric deviations and microscopic form patterns, are essentially affected by and have been employed as an estimation for the performance of machine tools. The pattern of machining defects is detected in order to provide a comparison between the ideal model and the actual machining result, which is usually obtained by a coordinate measuring machine [41]. Most of the previous research has identified the machining state as a Boolean attribute: precision reliable or precision failure. If the measured degradation reaches a threshold, precision failure occurs, and the product fault time is defined. However--mainly due to the wear of the driving system, transmission gear, and cutting tool--a stochastic process, rather than binary classification, is more suitable for simulating and predicting the deterioration of machining precision and degradation of processing features. [PERSON] et al. [42] emphasized that tool wear is a dynamic process extending from sharp to worn and possibly to breakage, and that multi-state classification could provide a more timely and accurate estimation. [PERSON] et al. [43] pointed out that the degradation paths would be different between one product and another. They conducted a comparison of Gaussian and logarithmic distribution in order to establish the degradation model. [PERSON] and [PERSON] [44] verified the effect of tool wear on machining surface roughness and established a statistical model for prediction under various cutting conditions. [PERSON] et al. [45] made the assumption that the next state of machine tool wear only depends on its current wear state. So, a non-homogeneous continuous-time Markov process model was used for modeling the total experience over the target life. After that, a linear mixed-effects model and maximum likelihood estimation was implemented to assess the wear evolution and lifetime of the tool [46]. Distribution of the residual life up to the wear threshold and estimation of the wear level have also been researched. [PERSON] and [PERSON] [47] modeled the gradual degradation of a mechanical device as a continuous-time degradation process with multiple discrete states. A condition-monitored device based on an unsupervised parameter estimation method was developed with only incomplete information observable. A homogeneous continuous-time, finite-state semi-Markov model was established based on the past history of components by [PERSON] et al. [48]. It was verified to be of great help in improving the diagnostic performance of an empirical classification system involving the degradation of mechanical systems. These applications of stochastic processes in manufacturing modeling have shown great potential in simulating the tolerance of a large branch of mechanical products in mass production based on measuring data. The intention of this paper is to propose a solution to assembly tolerance design problems considering processing feature degradation.