CAD/Tolerancing integration: Mechanical assembly with form defects

Abstract Geometric deviations affect the assemblability and functional compliance of products, since small part variations accumulate through large-scale assemblies and lead to malfunctions. The Digital Muck Up (DMU) upgrade requires a tolerance consideration in CAD models. The improvement of tolerancing leads to industrial success. Therefore, improving the CAD model to be closer to the realistic model is a necessity to verify and validate the mechanical system assemblability. In previous work, an approach to consider the dimensional, positional and orientation tolerances in CAD models was developed. In this paper, the above approach is improved to take into account form defects in CAD models. To model the component with form defects, the toleranced face is modeled by gird vertices. According to form tolerance values, a White Gaussian Noise (WGN) of gird vertices is computed. The realistic face is obtained by an interpolation based on the tessellation using Thin Plate Surface (TPS) modeling. The realistic assembly configurations were performed by updating the mating constraints. In fact, in realistic modeling, a new method to redefine constraints, while respecting the Objective Function of the Assembly (OFA), is established. In the case of a planar joint, a sub-algorithm based on Oriented Bounding Box (OBB) and the matrix transformation is developed. Relative part displacements are simulated with or without guaranteeing contact. Tolerance impacts on the realistic assembly motion are quantified. The realistic cylindrical joint is performed using an optimization method: the minimum cylinder inside a realistic hole and the maximum cylinder outside a realistic pin. Finally, in the case of a revolute joint, a sub-algorithm to redefine the mating constraints between two realistic parts is performed. This paper proposes a new approach to incorporate tolerances on CAD models in the case of planar and cylindrical faces by determining configurations with positional, orientation and form defects. This approach provides an assembly result closer to the real assembly of the mechanical system. Integrating tolerances in CAD allows the simulation and visualization of the mechanical assemblies’ behavior in their real configurations.

[1]  Sandro Wartzack,et al.  A Quantitative Comparison of Tolerance Analysis Approaches for Rigid Mechanical Assemblies , 2016 .

[2]  K. Rohr,et al.  Thin-plate spline approximation for image registration , 1996, Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[3]  Vijay Srinivasan,et al.  An Integrated View of Geometrical Product Specification and Verification , 2003 .

[4]  Pierre-Antoine Adragna,et al.  How Form Errors Impact on 2D Precision Assembly with Clearance? , 2010, IPAS.

[5]  Serge Samper,et al.  On the role of form defects in assemblies subject to local deformations and mechanical loads , 2012, The International Journal of Advanced Manufacturing Technology.

[6]  Lazhar Homri,et al.  Comparison of Optimization Techniques in a Tolerance Analysis Approach Considering Form Defects , 2016 .

[7]  Zhihua Zou,et al.  A gap-based approach to capture fitting conditions for mechanical assembly , 2004, Comput. Aided Des..

[8]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  G. Marsaglia.  Choosing a Point from the Surface of a Sphere , 1972 .

[10]  Sven Skyum,et al.  A Simple Algorithm for Computing the Smallest Enclosing Circle , 1990, Inf. Process. Lett..

[11]  Hoai-Nam Le,et al.  Experimental and Theoretical Investigations of Mechanical Joints With Form Defects , 2014, J. Comput. Inf. Sci. Eng..

[12]  Zhengshu Shen.  Tolerance Analysis with EDS/VisVSA , 2003, J. Comput. Inf. Sci. Eng..

[13]  Mervin E. Muller,et al.  A note on a method for generating points uniformly on n-dimensional spheres , 1959, CACM.

[14]  Sandro Wartzack,et al.  Skin Model Shapes: A new paradigm shift for geometric variations modelling in mechanical engineering , 2014, Comput. Aided Des..

[15]  Joseph K. Davidson,et al.  A Comparative Study Of Tolerance Analysis Methods , 2005, J. Comput. Inf. Sci. Eng..

[16]  Pierre-Antoine Adragna,et al.  Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces , 2009, J. Comput. Inf. Sci. Eng..

[17]  Jie Sun,et al.  Solution Methodologies for the Smallest Enclosing Circle Problem , 2003, Comput. Optim. Appl..

[18]  Abdelmajid Benamara,et al.  An algorithm for CAD tolerancing integration: Generation of assembly configurations according to dimensional and geometrical tolerances , 2015, Comput. Aided Des..

[19]  Wentao Sui,et al.  Four Methods for Roundness Evaluation , 2012 .

[20]  Nicolas Gayton,et al.  Statistical tolerance analysis of a mechanism with gaps based on system reliability methods , 2013 .