Method for optimizing the tolerancing of a set of flexible parts subjected to forces
A method for optimizing the tolerancing of a set of flexible parts subjected to forces. At the design phase, an optimum tolerancing for flexible parts is defined according to the assembly process plan and the desired functional requirements. The structural digital models are considered as parts to be assembled and composed of a plurality of assembly points, a plurality of structural points, and mathematical relations or mechanical stiffness, such as a non-null relative displacement of a structural/assembly point in relation to the other structural/assembly points in a single digital model, modify tensor in each structural/assembly point. From a mechanical point of view, these mathematical relations express the existence of an elastic recovery property between the points that make up the digital model. The issue of optimization is simplified by: the definition of influence factors; the simulation of parts deviating from the nominal by a distortion vector.
1. A method for determining an optimal production tolerance for producing a first part to be assembled with a second part according to interface surfaces and in compliance with an assembly functional requirement, the first and second parts being represented by their structural digital mockups, the method comprising the steps of:
acquiring a nominal theoretical position of a plurality of assembly points on the interface surfaces of the digital mockups of the first and second parts;
acquiring a nominal theoretical position of a plurality of structure points distributed over the interface surfaces of the digital mockups of the first and second parts;
acquiring, for the plurality of assembly points and the plurality of structure points of the digital mockups of the first and second parts, a mechanical restoring stiffness for returning the first and second parts to their initial position in the form of a rigidity matrix;
acquiring a variable of interest, comprising a scalar variable representative of the assembly functional requirement and a cost function defining a value of the variable of interest as a function of the discrepancy of the scalar variable with respect to a nominal of the assembly functional requirement;
acquiring a set of distortion vectors of the digital mockups of the first and second parts, said distortion vectors being normal to the interfaces surfaces of the digital mockups;
computing influence coefficients linearly relating each distortion vector to the value of the variable of interest when the digital mockup of the first part, distorted by said each distortion vector, is assembled with the digital mockup of the second part;
simulating the assembly of the first and second parts by placing the assembly points of the two digital mockups in coincidence to provide an optimal production tolerance for the first and second parts in compliance with the assembly functional requirement;
selecting positioning devices and assembly tools to assemble the first and second parts manufactured in accordance with the optimal production tolerance for the first and second parts; and
assembling the first and second parts, manufactured in accordance with the optimal production tolerance for the first and second parts, using the selected positioning devices and the selected assembly tools.
2. The method as claimed in claim 1 , further comprising the step of reproducing natural modes of transverse vibrations of the first part by combining distortion vectors.
3. The method as claimed in claim 1 , wherein the assembly points of the two digital mockups exhibit discrepancies tangential to assembly surfaces, and further comprising the step of updating the rigidity matrix of the digital mockups deformed during a simulation of the assembly of the first and second parts.
4. The method as claimed in claim 1 , further comprising the steps of:
acquiring an assembly range for the digital mockups;
generating a plurality of first and second digital mockups distorted by combinations of distortion vectors;
performing assemblies of said plurality of first and second digital mockups according to the assembly range;
determining an influence variable for each performed assembly; and
performing the step of computing the influence coefficients by a Monte Carlo method based on the influence variable.
5. The method as claimed in claim 1 , further comprising the steps of:
acquiring an initial positioning system and an initial stressing system for the digital mockups; and
computing a displacement of the assembly and structure points of the digital mockups subjected to the initial stressing system from their initial positions in the initial positioning system.
6. The method as claimed in claim 5 , further comprising the steps of modifying the initial positioning system or the initial stressing system; and repeating the step of computing the influence coefficients with new initial conditions.
7. The method as claimed in claim 4 , further comprising the step of modifying the assembly range and repeating the step of performing assemblies of said plurality of first and second digital mockups.
8. The method as claimed in claim 1 , wherein the structure points and the assembly points of the first part are nodes of a mesh; and further comprising the step of computing the mechanical restoring stiffness by a finite element model using the mesh.
9. The method as claimed in claim 5 , wherein the initial stressing system is gravity.