Numerical Approach for Detecting the Resonance Effects of Drilling during Assembly of Aircraft Structures

This paper is devoted to the development of a numerical approach that allows quick detection of the conditions favorable for the beginning of noticeable vibrations during drilling. The main novelty of the proposed approach lies in taking into account the deviations of the assembled compliant parts during non-stationary contact analysis by means of variation simulation. The approaches to stationary analysis of assembly quality are expanded and generalized for modeling such non-stationary effects as vibration and resonance. The numerical procedure is based on modeling the stress–strain state of the assembled structures by solving the corresponding transient contact problem. The use of Guyan reduction, the node-to-node contact model and the application of the generalized α method allow the reformulation of the contact problem in terms of a series of quadratic programming problems. The algorithm is thoroughly tested and validated with commercial software. The efficiency of the developed numerical procedure is illustrated by analysis of the test joints of two aircraft panels. The unsteady process of drilling the panels with periodic drilling force was simulated. The influence of deviations in the shape of the parts on the non-stationary interlayer gap was modeled by setting different initial gaps between parts. It is shown that the oscillation amplitudes of the interlayer gap depend on the initial gaps and do not correlate with the mean value of the stationary residual gap. Thus, non-stationary analysis provides new information about the quality of the assembly process, and it should be applied if the assembly process includes periodic impact on the assembled parts.