\n Gear tooth breakage due to bending fatigue is one of the most dangerous failure modes of gears. Therefore, the precise definition of tooth bending strength is of utmost importance in gear design. Single tooth bending fatigue (STBF) tests are usually used to study this failure mode since they allow to test gears, realized and finished with the actual industrial processes. Nevertheless, STBF tests do not reproduce exactly the loading conditions of meshing gears. The load is applied in a predetermined position, while in meshing gears, it moves along the active flank; all the teeth can be tested and have the same importance, while the actual strength of a meshing gear, practically, is strongly influenced by the strength of the weakest tooth of the gear. These differences have to be (and obviously are) taken into account when using the results of STBF tests to design gear sets. The aim of this article is to investigate in detail the first aspect, i.e. the role of the differences between two tooth root stress histories. In particular, this article presents a methodology based on high-cycle multi-axial fatigue criteria to translate STBF test data to the real working condition; residual stresses are also taken into account.

Gear Root Bending Strength: A Comparison Between Single Tooth Bending Fatigue Tests and Meshing Gears

Developing accurate design data to enable the effective use of new materials is undoubtedly an essential goal in the gear industry. To speed up this process, Single Tooth Bending Fatigue (STBF) tests can be conducted. However, STBF tests tend to overestimate the material properties with respect to tests conducted on Running Gears (RG). Therefore, it is common practice to use a constant correction factor fkorr, of value 0.9 to exploit STBF results to design actual gears, e.g., through ISO 6336. In this paper, the assumption that this coefficient can be considered independent from the gear material, geometry, and loading condition was questioned, and through the combination of numerical simulations with a multiaxial fatigue criterion, a method for the calculation of fkorr was proposed. The implementation of this method using different gear geometries and material properties shows that fkorr varies with the gears geometrical characteristics, the material fatigue strength, and the load ratio (R) set in STBF tests. In particular, by applying the Findley criterion, it was found that, for the same gear geometry, fkorr depends on the material as well. Specifically, fkorr increases with the ratio between the bending and torsional fatigue limits. Moreover, through this method it was shown that the characteristics related to the material and the geometry have a relevant effect in determining the critical point (at the tooth root) where the fracture nucleates.

Gear Root Bending Strength: A New Multiaxial Approach to Translate the Results of Single Tooth Bending Fatigue Tests to Meshing Gears

The effects of stress gradient and size effect on fatigue life are investigated based on the distribution of stress at the notch root of notched specimens of GH4169 alloy. The relationship between the life of notched specimens and smooth specimens is correlated by introducing the stress gradient impact coefficient, and a new life model of predicting notched specimens based on the Walker modification for the mean stress effect is established. In order to improve the prediction precision of life model with the equation parameters having a definite physical significance, the relationships among fatigue parameters, monotonic ultimate tensile strength, and reduction of area are established. Three-dimensional elastic finite element (FE) analysis of a vortex reducer is carried out to obtain the data of stress and strain for predicting its life. The results show that there is a high-stress gradient at the edge of the air holes of the vortex reducer, and it is thus a dangerous point for fatigue crack initiation. The prediction result of the vortex reducer is more reasonable if the mean stress, the stress gradient, and the size effect are considered comprehensively. The developed life model can reflect the effects of many factors well, especially the stress concentration. The life of notched specimens predicted by this model give a high estimation precision, and the prediction life data mainly fall into the scatter band of factor 2.

Fatigue Life Prediction of Vortex Reducer Based on Stress Gradient

The characterization of new materials for enabling gear design is definitely a fundamental objective in the gear industry and research. Single Tooth Bending Fatigue (STBF) tests can be performed to speed up this process. However, it is well known that STBF tests tend to overestimate material strength compared to tests performed directly on meshing gears (MG) which, in turn, require an excessively long test time. Therefore, it is common practice to use a constant correction factor fkorr of 0.9 to translate STBF results for designing actual MG (e.g., via ISO 6336). Recent works involving a combination of Finite Element Models (FEM) and multiaxial (non-proportional) fatigue criteria based on the critical plane concept have highlighted that the assumption of considering fkorr as a constant independent of the gear design parameters leads to inaccurate results. However, in previous studies, no correlation between fkorr and gear design parameters has emerged. In the present paper, the influence of the normal pressure angle (αn), the profile shift coefficient (x*), and the normal module (mn) on fkorr was investigated by analyzing FEM simulations with the Findley fatigue criterion. 27 gear geometries were studied by varying the above 3 parameters in 3 levels (full factorial DOE). These geometries were simulated in both MG and STBF configurations. The results of the 54 FEM simulations were analyzed by applying the Findley fatigue criterion and the corresponding fkorr were calculated. The correlation between fkorr and αn, x* and mn was investigated using the Analysis of Variance (ANOVA) technique. The results show that the only gear design parameter influencing fkorr is x* hence, a regression model for fkorr including x* has been developed. This latter has been then adopted for calculating and comparing fkorr values from other combination of the parameters found in literature, giving good correspondence.

https://www.mdpi.com/2076-3417/12/8/3950/pdf?version=1650032807

Effect of Gear Design Parameters on Stress Histories Induced by Different Tooth Bending Fatigue Tests: A Numerical-Statistical Investigation

Les engrenages roues et vis sans fin sont une solution avantageuse pour transmettre le couple entre des axes perpendiculaires non concourants. Ces engrenages offrent une solution simple et efficace en terme de cout dans les applications de transmission de puissance, ou un grand rapport de reduction est necessaire, en comparaison avec les engrenages classiques a axes paralleles qui necessitent normalement deux ou trois etapes pour obtenir les memes reductions avec une augmentation consequente de complexite et du nombre de pieces. L’usure de surface est un des modes de defaillance observes dans la vie des engrenages roues et vis sans fin qui influe sur la portee de contact, les caracteristiques de transmission et le bruit resultant. La premiere etape de ces travaux est la mise au point d’un modele numerique pour etudier le comportement quasi statique des engrenages roues et vis sans fin avec une roue en bronze et une vis en acier. Le modele est base sur la resolution des equations de compatibilite des deplacements ainsi que sur la methode des coefficients d’influence. Les effets globaux de flexion et les effets locaux de contact ont ete separes. Les effets de contact ont ete obtenus par la theorie de Boussinesq. Les coefficients de flexion sont estimes par la combinaison d’un calcul Elements Finis et des fonctions d’interpolation, permettant d’une part de prendre en compte l’environnement de l'engrenage (la geometrie des arbres, des jantes et des voiles, l’emplacement des roulements,...) et d’autre part de reduire significativement les temps de calculs. Dans une seconde etape, une methodologie est proposee pour modeliser l’usure de la surface de dent de la roue. Le modele de contact quasi-statique de la repartition des charges est combine avec un modele d’usure d’Archard. Ce modele suppose que la profondeur d’usure est directement proportionnelle a la pression de contact et a la distance de glissement et inversement proportionnelle a la durete du materiau. Cette loi d’usure est modifiee pour prendre en compte l’influence des conditions de lubrification en utilisant un coefficient d’usure local, dependant de l’epaisseur du film lubrifiant, rapportee a l’amplitude des rugosites des surfaces. L’enlevement de matiere par l’usure du flanc de la roue influe sur la repartition des pressions et donc les modifications de la geometrie des dents doivent etre incluses dans la prediction de l’usure. Le calcul des pressions de contact est ainsi mis a jour pour tenir compte des changements de geometrie. Enfin, pour valider le modele developpe des comparaisons du modele avec des resultats experimentaux issus de la bibliographie ont ete effectuees.

Prise en compte de l’usure dans la modélisation du comportement sous charge des engrenages roues et vis tangentes

In this study, a crack initiation life prediction methodology for the tooth bending fatigue of hypoid gears is proposed. This methodology employs a previously developed finite-element based hypoid gear root stress model (Hotait et al. 2011, “An Investigation of Root Stresses of Hypoid Gears with Misalignments,” ASME J. Mech. Des., 133, p. 071006) of face-milled and face-hobbed hypoid gears to establish the multiaxial stress time histories within the root fillet regions. These stress time histories are combined with a multiaxial crack initiation fatigue criterion to predict life distributions along roots of the pinion and the gear. The predictions of the multiaxial fatigue model are compared to those from a conventional uniaxial fatigue model to establish the necessity for a multiaxial approach. The model is exercised with an example face-milled hypoid gear set from an automotive application to demonstrate the impact of various misalignments well as the key cutting tool parameters on the resultant tooth bending lives.

M. A. Hotait

Papers

Estimation of Bending Fatigue Life of Hypoid Gears Using a Multiaxial Fatigue Criterion