Dual Time Stepping Algorithms With the High Order Harmonic Balance Method for Contact Interfaces With Fretting-Wear

TL;DR

This paper introduces a dual time stepping algorithm combined with a high order harmonic balance method to efficiently analyze contact interfaces with fretting-wear, improving computational speed and accuracy in vibrational analysis.

Contribution

It presents a novel dual time stepping approach integrated with high order harmonic balance for analyzing nonlinear contact problems with wear, enhancing efficiency over traditional Newton methods.

Findings

The first order dual time scheme yielded the best results.

The method successfully identified steady states in worn systems.

Faster convergence compared to Newton solvers.

Abstract

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-harmonic balance method (mHBM). The dynamic Lagrangian frequency-time method is used to calculate contact forces in the frequency domain. A new strategy for solving nonlinear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.