Citation: Concli, F. Numerical Study
of the Impact of Shot Peening on the
Tooth Root Fatigue Performances of
Gears Using Critical Plane Fatigue
Criteria. Appl. Sci. 2022, 12, 8245.
https://doi.org/10.3390/
app12168245
Academic Editors: Alberto
Campagnolo and Alberto Sapora
Received: 19 July 2022
Accepted: 10 August 2022
Published: 18 August 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the author.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Numerical Study of the Impact of Shot Peening on the Tooth
Root Fatigue Performances of Gears Using Critical Plane
Fatigue Criteria
Franco Concli
Faculty of Science and Technology, Free University of Bolzano/Bozen 1, 39100 Bolzano, Italy;
franco.concli@unibz.it; Tel.: +39-0471-017748
Abstract:
Gears are one of the the most widespread mechanical components and their design is
supported by standard calculation methods. Among all the possible failure modes of gears, tooth
root bending is the most critical and could lead to catastrophic failures. In this regard, different
surface treatments could be exploited to improve the gear strength. Among them, shot peening
is the most common. The aim of this study is to evaluate the effectiveness of shot peening on
improving the tooth root bending resistance. This is achieved by exploiting the Finite Element
Method (FEM) in combination with advanced multiaxial fatigue criterion based on the critical plane
concept. A standard Single Tooth Bending Fatigue test was reproduced numerically via FEM. Beside
the wrought gears, shot peened ones were also simulated. The state of stress induced by the shot
peening was obtained numerically by simulating the surface treatment itself with non-linear dynamic
analyses. The results have shown quantitatively how the residual stresses promote an improvement
in the resistance and how the local hardening could lead to different early paths of nucleation and
propagation of cracks on the tooth fillet.
Keywords: gears; shot peening; FEM; fatigue
1. Introduction
Gears are mechanical components aimed at transmitting mechanical power [
1
]. The
torque is transferred via the mesh of two teeth. These could typically fail due to different
failure modes [
2
–
4
]. In the presence of high contact pressures and poor lubrication, the
sliding–rolling contact between the flanks usually lead to wear [
5
], scuffing [
6
], pitting [
7
,
8
]
or micropitting [9].
In addition, the meshing of the flanks induces pulsating stresses at the tooth root
fillet [
10
,
11
]. Failures due to tooth root bending could lead to catastrophic consequences:
while other failure modes foresee a progressive deterioration of gear performance with
increasing noise, vibration and loss of positioning accuracy (increasing transmission error),
the failure due to tooth root bending occurs instantaneously without notice. The high
periodic stresses promote the nucleation of surface cracks. Once nucleated, the cracks
propagate below the surface. Once the resistant area is no longer capable of withstanding
the load, an instantaneous detachment of the tooth occurs. This failure mode is usually
referred as Tooth (Root) Bending Fatigue (TBF) [12].
In the gear industry, the Tooth Bending Strength (TBS) is the main design crite-
rion
[13,14].
TBS is usually evaluated using standards. Specifically, the most used ones
are the ISO 6336-3 [
13
] and the AGMA 2001 [
15
]. Both prescribe simplified methods to
evaluate the actual stress in the tooth root region
σ
F
and provide tabulated data for the
maximum permissible stress
σ
FP
the most common materials can withstand. However,
according to ISO 6336-5 [
13
], for unusual materials and special treatments,
σ
FP
has to be
estimated experimentally. The permissible stress
σ
FP
directly depends on the fatigue limit
of the material
σ
Flim
. Its determination can relay on different typologies of tests. The most
Appl. Sci. 2022, 12, 8245. https://doi.org/10.3390/app12168245 https://www.mdpi.com/journal/applsci
