Development of Direct Linearization Method in Tolerance Analysis of Mechanical Assemblies by Using NURBS Curves

With the advancement of the manufacturing processes and the continuing need for increasingly precise assemblies, consideration of dimensional and geometric tolerances has been of great importance in tolerance analysis of mechanical assemblies. Therefore, in recent decades, several methods have been developed and implemented for calculating the influences of geometric errors of components on the final performance of the assembly. One of the proposed methods for tolerance analysis is the Direct Linearization Method (DLM). However, DLM has significant advantages in dimensional tolerance analysis, due to simplifications used in this technique, it does not have the ability to solve assemblies including free form profiles. In this research, a new method has been proposed to consider the complex profiles in the process of DLM. In the proposed combination method, rational Bezier curves have been used to define component profiles such as elliptical profiles, cams, edge joints, and non-circular profiles that have a complex error variation. Then, by using principles of DLM and rational Bezier equations, the developed algorithm is successfully accomplished. In this way, we can not only use significant advantages of DLM in dimensional tolerance analysis but also it is possible to solve assemblies including a component with complex profiles without any simplification. The developed hybrid approach has been presented in detail by solving an example of assembly tolerance analysis. Finally, validation has been performed and the accuracy of the proposed approach was confirmed using Monte Carlo simulation.