Crack growth based tooth root life prediction model—an influence quantity analysis

Abstract

One of the key challenges of epicyclic gearboxes in turbo gearbox applications is the high number of load cycles reached by the gearbox components. Standards such as ISO 6336 deliver design guidelines for bending strength up to a limiting number of NG = 3∙106 and AGMA up to 107 load cycles which is far less than the expected lifetime of turbo gearbox applications.To design gears for geared turbofans safely and weight-optimized, the tooth root load capacity in the very high cycle fatigue (VHCF) range must be known as precisely as possible. Most VHCF SN-curve concepts show a continuously decreasing fatigue strength, so that a consideration of a constant fatigue strength level does not meet the material behavior. A life prediction model can be used to determine the specific load that can be carried for each number of load cycles.In this paper, the nasgro crack growth equation is applied to gears to determine the tooth root life in the VHCF range. A lifetime for surface and sub-surface induced fractures is calculated, resulting in a stepped SN-curve. Most of the cycles until fracture occur during crack initiation and micro crack growth, while the macro crack is a small part of the total number of load cycles until tooth root fracture. The nasgro equation is able to represent micro and macro crack growth and is extended by further approaches to the threshold of crack initiation Kth, which also consider the characteristics of short and long crack growth. In addition, the tooth root stress depth curve (via FEM), the hardness depth curve, the residual stress depth curve and the defect distribution will be included in the life-time prediction as important influencing variables of the VHCF tooth root load capacity. The influence of the inputs is determined in an influence quantity analysis. In the future the lifetime prediction model is validated with rig tests up to the VHCF range.