Prediction of thin-rimmed gear crack propagation from a factorial design approach

Abstract

A B S T R A C T Gear failure involving bending fatigue can have catastrophic consequences depending on the propagation path direction. Therefore, anticipating and preventing eventual critical fracture are crucial at the design stage. However, none of the methods available can give rapid and quantitative evaluation of gear fatigue crack evolution. Aiming to provide fast predictions of crack propagation paths, this paper proposes a factorial design approach for gear bending fatigue simulation. Six parameters related to gear geometry and initial crack configuration are considered in this study. Factorial design experiments are numerically conducted with an efficient 2D boundary element model assuming linear elasticity. Then, bending fatigue damage is modelled using polynomial functions. The resulting prediction model can instantly establish the crack trajectory in thin-rimmed gear for any cycle numbers. Application of the approach is illustrated by several case studies, while its precision and reliability are demonstrated through an exhaustive validation procedure. a = crack length a 0 = initial crack length da = crack propagation step h r = rim thickness K I , K II = mode I and II stress intensity factors m = gear module me = median N = crack propagation cycle number n p = pinion tooth number R = load ratio R v = gear speed ratio W = transmitted load α 0 = initiation point fillet relative position β = kurtosis γ = skewness δ = finite crack face separation θ 0 = initial crack orientation μ = mean of a distribution σ = standard deviation ϕ = pressure angle Correspondence:

Modeling and monitoring of tooth fillet crack growth in dynamic simulation of spur gear set

“…Moreover, since the factorial design method has been shown to offer accurate evaluations of K I and K II [23], the present work exploited this approach to develop a K I prediction formula. The equation covers the application domain described for the tooth rigidity evaluation.…”

“…Ref. [23] describes the BE modeling procedure. In general, the calculated values show that K I increases with the crack length and with a displacement of the load towards the tip radius.…”

“…However, since a flexible gear body causes stiffness reduction, the present paper proposes an improved version accounting for the complete gear body. Moreover, two of the present authors have demonstrated that the factorial design approach could also offer very accurate evaluations of K I and K II , and therefore, ensure precise predictions of crack trajectories, even for thin-rimmed gears [23]. In addition to its accuracy, by avoiding any mesh solving, the factorial design strategy provides instantaneous evaluations.…”

Influence of high speed on crack propagation path in thin rim gears

“…Lalonde et al investigated the effect of six parameters (teeth number, speed, rim thickness, initial crack length, initial crack orientation and relative fillet position) influencing the crack path propagation by boundary element simulations.…”

Effect of rim and web interaction on crack propagation paths in gears by means of XFEM technique

“…Some other papers deal with fatigue cracks in gears. As an example, Lalonde et al . investigated by boundary element simulations the effect of six parameters (teeth number, speed, rim thickness, initial crack length, initial crack orientation and relative fillet position) influencing the crack path propagation, and they predicted the crack paths by means of the factorial design approach.…”