Tolerance analysis of a compliant assembly using random Non-Uniform Rational B-Spline curves and isogeometric method

Abstract

Abstract Non-Uniform Rational B-Spline (NURBS) is one of the most versatile tools of computer-aided design. The concept of random NURBS curves is introduced for modeling the geometrical errors in mechanical parts and assemblies. The proposed idea is utilized to solve an example problem involving deformable components. For this purpose, profile tolerances of the parts are transformed into covariance matrices of NURBS control polygon parameters. Then, the control polygons are used as vector chains to calculate geometrical error propagation. Afterwards, isogeometric analysis (IGA) is invoked to express deformations of the parts during the assembly process as changes in the shape of the underlying control polygons. Finally, the result of the calculations is translated back into the tolerance zone of the assembly. Numerical examples are employed to examine the effect of NURBS structure (degree, knot vector, and control points) on convergence and stability of results. Outcomes of the theory are compared with direct measurements of actual assemblies and results of a Monte Carlo finite element simulation to illustrate the validity of the results. Furthermore, the developed model is used to obtain practical guidelines regarding the reduction of geometrical errors by the optimum design of the assembly.