There are limited analytical solutions on fretting fatigue in the public domain due to its complexity. Finite element methods have become attractive to provide detailed information about contact stress, crack initiation, crack propagation and fatigue life estimation. This paper demonstrates that fretting fatigue damage at blade attachment caused by resonant vibration can be studied in the time-domain using an efficient finite element-based approach utilizing the Velocity Perturbation Method (VPM). The method consists of a one-time injection to the steady state solution of a velocity profile matching the resonant modal shape. The mechanical behavior at the contact interface is then assessed in the time domain by processing the main parameters affecting fretting fatigue such as deformation, cyclic contact stress and sliding distance.

In this paper, numerical simulation, showing design fretting fatigue characteristics based on fundamental Ruiz and Smith-Watson-Tupper criteria, is demonstrated on two models, simplified and representative. The simplified model was used for detail analysis set-up and basic post-processing while the representative model illustrated the difference in non-linear contact response of an industrial compressor under bending and torsional modes captured in the time domain. In both models, the transient analysis is carried in 3 main steps.

Step1: Steady-state analysis. The first transient step is to reach a steady-state condition for the structure. For the disk/blade system, this usually means applying rotation speed, gas loads and temperature profile. The contacts have their regular (non-bonded) formulation. The result of this step is essentially the same as the pre-stress condition of the modal analysis, except that this is now conducted as a transient analysis in the time domain. Step 2: Modal Velocity perturbation. The steady-state loads are maintained. The perturbation is introduced to instantly change the velocity of the structure to the profile it would have if oscillating around the steady-state condition. Step 3: The velocity perturbation is removed. The steady-state loads are maintained. The transient analysis continues after the removal of the velocity perturbation. The blade is now in a free oscillation state around its steady-state position. Due to the velocity profile, the blade will naturally oscillate at a frequency and shape equal to the mode shape.

Transient analysis with velocity perturbation method shows the evolution of stress in the entire structure. The results can be processed to capture a variety of phenomena, from High Cycle Fatigue to more elusive fretting fatigue behavior. Basic data processing is illustrated for a group of parameters related to Ruiz criteria in crack nucleation and  a group of parameters related to the dovetail attachment fatigue life, used in the Smith-Watson-Tupper criteria in crack propagation.

 

This Finite Element velocity perturbation approach can be used to study the main factors affecting fretting of any two bodies in contact: load, coefficient of friction, contact geometry and impact of different frequencies or modal shapes in the time domain.


Finite Element Velocity Perturbation Application in Investigating Compressor Dovetail Fretting in Time Domain

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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