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This paper focuses on the application of principal component analysis (PCA) to thoroughly analyse and interpret multidimensional data from a cold rolling process. The analysis includes the effects of variables on the final properties of strips in a cold rolling mill. Unscrambler software was used to analyse and identify hidden variables. Variable correlations were also used to derive correlations between the control parameters. The results of this research will be used to improve the selection of material in order to reduce the occurrence of defects in the cold rolling process and to improve the adjustment of the set points that are performed in every pass or section of the cold rolling process. The hot rolled strips that enter the cold rolling mill are made of different materials and are produced by different strip manufacturers. Some strips break during the thickness reduction process in the cold rolling mill. This paper focuses on two possible causes of breakage: non-uniform strip material properties and failures in the rolling mill process. Two types of rolled strips (those that break and those that do not break) were compared to identify causes of breakage. The results indicate that breakages are caused by material or process failures. PCA was applied to the dataset in order to identify and analyse the relationships between the variables in the process. This information was used to interpret and diagnose the process behaviour. Swarm analysis and relating observations to process behaviour were able to distinguish between different start-up conditions, and between desirable and undesirable process conditions. [ABSTRACT FROM AUTHOR]

The first step of a geometrical and dimensional tolerance analysis is to determine kinematic loops that affect the functional requirements and the tolerances that influence the relative positioning between two topological elements of a part. This process is called the interpretation of geometric and dimensional tolerances. The second step is a solution procedure to verify if the functional requirements will be met with the current tolerances. This paper presents the implementation of a C++ library for the interpretation of geometric and dimensional tolerances in order to accomplish the first step of the tolerance analysis process. First, the data structures that allow storing the tolerances, the toleranced part data model, and the assembly graph model are introduced. This is followed by the description of the algorithms for retrieving the relevant kinematic loops from the assembly graph and the tolerances that affect the relative positioning between any two topological elements. Finally, an example demonstrates how to use the interpretation data obtained from the library to calculate and verify the functional requirements. [ABSTRACT FROM AUTHOR]