A digital twin-based analysis method to assess geometric variations for parts in batch production

Abstract

Background: In mass production, engineers are more concerned with the statistical distribution accuracy of parts in mass production rather than just the qualification of individual parts. However, currently, the statistical analysis methods designed for product accuracy are relatively scattered, and most of them focus on nominal part models. Therefore, there is a need to design a statistical analysis method for parts in mass production based on the Digital Twin model. Methods: This paper presents a novel method to analyse the geometric variations of parts in batch production in the production line, which is based on digital twins to model and evaluate deviations contributed by the geometrical condition, assembly condition and material condition. Firstly, the statistical descriptions of the parts, particularly the features of a digital twin for parts in batch production related to the geometry and position, are classified into various hierarchies. Secondly, a covariance method is employed to analyse the law of their shape from the descriptions. Thirdly, the parts' shape feature similarity for different terms is derived, including the linear features of pose constraint, rotation deviation, and geometric deviation and the curve features like a geometric deviation. Finally, the probability distribution of discrete points on the manufacturing error caused by different reasons is calculated. Results: Two case studies of reducer and rail highlight the applicability of the proposed approach. The standard deviation of the points has similar trend with sample cases according to normal distribution. Conclusions:  This paper categorizes the deviations of batch parts into the linear features of pose constraint, rotation deviation, and geometric deviation. When batch parts exhibit any of these deviation types, the eigenvalues and eigenvectors of their covariance matrix show certain patterns, enabling the identification of the deviation type and calculation of the statistical deviation probability distribution for the corresponding features.