Profile Tolerances Modeling And Analysis For Aircraft Surfaces Based On Degrees Of Freedom

Computer Aided Tolerancing(CAT) is the crucial link in the product life cycle, which not only facilitates the sharing and exchange of product data, but also supports systematic methods to the control and management of precision, quality and cost of the product. From 1970 s when it is proposed, CAT has obtained lots of theoretical and practical achievements; however, it is always lagging behind other computer aided technologies such as CAD and CAM to a great extent which has become one of the bottlenecks to the integration of these technologies. Hence, it urgently needs to enhance CAT to assist the full implementation of the integrated development and management in the product life cycle.In CAT research, it not only needs to consider the tolerance of the feature with regular shape, but also needs to consider the tolerance of the feature with irregular shape for the completeness and compatibility to the standard. As a class of irregular features, curves and surfaces exist extensively within the mechanical parts and assemblies, even though the simple product or structure could be found this class features. However, there is little research about curves and surfaces for their tolerance design which imminently needs a further study and investigation.The models based on the pattern of degrees of freedom(DOF) are widely used and studied in tolerancing because of its immense advantages:(1)supports a lot of geometrical features and tolerance types;(2)supports numerous rules and conventions about tolerance semantics in the standards;(3)supports tolerance zone oriented three dimensional tolerance analysis and verification;(4)supports automated and intelligent reasoning about tolerance information;(5)avails data sharing and integration between CAT sub-domains. Furthermore, it is applicable to the digital assembly coordination for the aircraft.On the basis of DOF pattern, this paper carries out the study of the modeling and analysis of profile tolerances for aircraft curves and surfaces features, which could facilitate the integration of CAD and CAM and integrated development in the product life cycle. The methods proposed in the paper provide a unified framework for the curves and surfaces features in the CAT research for aircraft. The key research works covered in the dissertation are as follows:Firstly, the feasibility of the DOF pattern is analyzed for representing profile tolerances of curves and surfaces features. Due to the complex shape of the curves and surfaces features, there are two classes of problems when using DOF model to represent their tolerances. In order to solve these two classes of problems, approximation method is applied to translate them into the two types of errors(noted as type 1 and type 2 error) and the solution is quantified to the calculation and assessment of these two types of errors.Secondly, a ASDOF(Assessment, Split, and Degrees of Freedom) method is proposed to fully implement the process of tolerance modeling and analysis of the curves and surfaces features. The tolerance modeling is composed of three parts: assessment of the two types of errors, split of the curves and surfaces features and extraction of the DOF parameters, where the first and second parts are used to eliminate the two types errors and the third part is used to construct the variation intervals of the DOF parameters and their mutual constraint expressions. The tolerance analysis is used to construct the assembly stack-up equations and complete the simulation of the functional tolerances for the curves and surfaces features.Thirdly, refer to the assessment of the two types of errors; two classes of algorithms are proposed to give the detailed steps and directions for the assessment process. These algorithms translate the problem into the calculation of the maximum values of the two type errors, which avoids the countless assessments of the overall points. The main techniques utilized by these assessment algorithms are rotational transformation, parameter substitution, region principle, differential method and genetic algorithm.Fourthly, refer to the split of the curves and surfaces features; the split algorithm is proposed to give the detailed steps and directions for the split process. For those features whose two type errors cannot be ignored, the split algorithm is used to split them into sub features which makes the two type errors of the sub features can be ignored. The split algorithm translates the problem into the calculation of the maximum curvature and uses the recursive method to ensure the normal termination of the process. This algorithm has the advantages of high efficiency and self-adaption.Fifthly, detailed steps and directions for the extraction of DOF parameters and construction of assembly stack-up equations are proposed to complete the whole process of the unified framework. The variation intervals of the DOF parameters and their mutually constraints are constructed based on the geometrical dimension, tolerance value and confinement of the tolerance zone boundary. The assembly stack-up equations are constructed by the homogenous transformation matrix and Monte-Carlo simulation is used to conduct the remaining of tolerance analysis.Finally, the implementation with the lug assembly of an aircraft indicates that the unified framework is capable of representing profile tolerances with enhanced accuracy thus supports the feasibility of the proposed approach in this paper. This framework for the aircraft curves and surfaces features in tolerance design has provided basic and abundant resource for the CAT research, which is of important theoretical guiding significance and practical values.