Geometric Tolerancing using the Jacobean torsor

In the industrial field, there is always an unavoidable risk when assembling an assembly composed of several parts, the complexity of this risk comes from the performance of the latter is only discovered at the assembly time. Designers always looking to predetermine the performance of an assembly before the assembly phase. Our work will help them to predict the behavior of the components of an assembly by using the known tolerances of the components as parameters in the Jacobian torsor model. In order to analyze the tolerances in a statistical way we will integrate in this work the jacobian torsor model and the simulation of the monte carlo. The assembly in this model is subdivided into surfaces, we will base on The parameters of the small displacement rotor (SDT) in order to express the relative position between two surfaces of the assembly. From a surface graph and the Jacobian Torsor model, we can create a 3D dimensional chain. In the last step, we will analyze the tolerances statistically with the Monte Carlo method. To analyze three-dimensional tolerances a numerical example will be used.