# Variation analysis for aircraft assemblies

## This post is about our project with Airbus dedicated to variation simulation for the assembly process. Our research team in the SPbPU has been developing this area since 2006.

When we design a mathematical model for the assembly process it is important to remember that in reality, the assembled parts do not fully coincide with their theoretical shapes. All parts coming to the assembly line have some random deviations from their nominal shapes due to different inaccuracies and errors of mass production. These imperfections in the parts can affect the quality of assembled construction. Thus, the variations of parts should be considered during the optimization of the assembly process since we usually want to speed up the assembly but keep the high-quality level for the finished product. This is especially important for the aircraft industry as quality requirements in this area are usually very tight.

The variation analysis of the assembly process helps to predict the impact of part deviations on the contact quality. The most general approach for variation analysis is based on the Monte Carlo simulations. The idea behind this approach is to try to simulate all possible situations that can be obtained in practice due to the presence of random deviations. In our work with Airbus, we create a modification of this standard approach. We minutely consider the specific features of aircraft assembly, thus it helps us to obtain a more accurate prediction of deviations for aircraft structures.

Our approach is based on modelling the assembly process by solving a reduced contact problem. When solving the contact problem initial positions of parts can be set by the initial gap. The solution gives us the displacement of the parts during the assembly process and, thus, the residual gap between the parts.

The initial gap represents the distance between parts before joining. As it appears due to random deviations of the part shapes, it has stochastic nature. The residual gap describes the distance between the parts after assembly. For aircraft assembly, the distribution of the residual gap values evaluates the quality of the contact between parts.

Therefore, the random deviations can be considered through the initial gaps and the quality of the assembly can be estimated through the obtained residual gap values.

The corresponding variation simulation procedure has three stages:

• Stage 1. Generation of initial gaps. A large batch of initial gaps is generated. The generation can be done either based on the modeling of the initial gap or based on the interpolation of measured data.
• Stage 2. Modeling the assembly process. For each initial gap, the contact interaction of the parts is simulated: by solving the contact problem, the displacements of the parts are calculated and the values ​​of the residual gap between the parts are evaluated.
• Stage 3. A statistical estimation of contact quality. Based on the obtained batch of residual gaps, the probabilistic characteristics of this gap are estimated.

This approach allows us to precisely predict the contact quality for any assembly technology before its implementation on the assembly line. It was successfully used in several tasks from Airbus for optimization of real assembly processes. For example, for A350 S19 splice joint assembly process this variation simulation method helps to find a new optimal fastener pattern for robotic drilling: the number of fasteners is smaller but the quality of contact remains the same.

References

Lupuleac S., Shinder J., Churilova M., Zaitseva N. et al. Optimization of Automated Airframe Assembly Process on Example of A350 S19 Splice Joint. SAE Technical Paper, 2019.