Numerical Modelling of the Crack Propagation Path at Gear Tooth Root

2003 ◽  
Author(s):  
Damir T. Jelaska ◽  
Srecko Glodez ◽  
Srdjan Podrug
Keyword(s):  
Fatigue Crack ◽  
Service Life ◽  
Crack Propagation ◽  
Experimental Testing ◽  
Gear Tooth ◽  
Fatigue Crack Initiation ◽  
Propagation Path ◽  
Tooth Root ◽  
Stress Cycles

A numerical model for determination of service life of gears in regard to bending fatigue in a gear tooth root is presented. The Coffin-Manson relationship is used to determine the number of stress cycles Ni required for the fatigue crack initiation, where it is assumed that the initial crack is located at the point of the largest stresses in a gear tooth root. The simply Paris equation is then used for the further simulation of the fatigue crack growth, where required material parameters have been determined previously by the appropriate test specimens. The functional relationship between the stress intensity factor and crack length K = f(a), which is needed for determination of the required number of loading cycles Np for a crack propagation from the initial to the critical length, is obtained numerically. The total number of stress cycles N for the final failure to occur is then a sum N = Ni + Np. Although some influences were not taken into account in the computational simulations, the presented model seems to be very suitable for determination of service life of gears because numerical procedures used here are much faster and cheaper if compared with the experimental testing.

Comparison of Numerical Models for Gear Tooth Root Fatigue Assessments

2005 ◽  
Author(s):  
Damir T. Jelaska ◽  
Srdjan Podrug ◽  
Srecko Glodez
Keyword(s):  
Fatigue Crack ◽  
Service Life ◽  
Numerical Models ◽  
Experimental Testing ◽  
Gear Tooth ◽  
Moving Load ◽  
Fatigue Crack Initiation ◽  
Homogeneous Material ◽  
Force Model ◽  
Tooth Root

A several kinds of numerical models, including moving force model, for determination the service life of gears in regard to bending fatigue in a gear tooth root, is presented. The critical plane damage model, Socie and Bannantine [1], 1988, has been used to determine the number of stress cycles required for the fatigue crack initiation. This method determines also the initiated crack direction, what is good base for a further analyses of the crack propagation and the assessment of the total fatigue life. Finite element method and linear elastic fracture mechanics theories are then used for the further simulation of the fatigue crack growth under a moving load. Moving load produces a non-proportional load history in a gear’s tooth root. An approach that accounts for fatigue crack closure effects is developed to propagate crack under non-proportional load. Although some influences (non-homogeneous material, traveling of dislocations, etc.) were not taken into account in the computational simulations, the presented model seems to be very suitable for determination of service life of gears because numerical procedures used here are much faster and cheaper if compared with the experimental testing. The computational results are compared with other researchers’ numerical results and with service lives of real gears. The fatigue lives and crack paths determined in this paper exhibits a substantial agreement with experimental results and significant improvement compared with the existing numerical models.

Dynamic characteristics of cracked gear and three-dimensional crack propagation analysis

2012 ◽  
Vol 227 (6) ◽  
pp. 1341-1361 ◽  
Author(s):  
Renping Shao ◽  
Purong Jia ◽  
Feifei Dong
Keyword(s):  
Crack Propagation ◽  
Dynamic Characteristics ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Beam Theory ◽  
Circular Crack ◽  
Propagation Path ◽  
Tooth Root ◽  
3D Crack Propagation ◽  
Three Dimensional Finite Element

The dynamic model and three-dimensional finite element analytical model of cracked gear structure are established respectively according to the cracked beam theory, and the dynamic characteristics (natural frequency, vibration shape) of cracked gear body are investigated. Further the influences of crack position and crack length on the dynamic characteristics of gear structure are simulated and discussed. On this basis, the fracture and damage of gear structure are investigated according to the theory of fracture mechanics. Using FRANC3D software, the three-dimensional (3D) propagation of crack at tooth root for involute gear is simulated, and stress intensity factor (SIF)s of semi-circular crack at tooth root including three types are analyzed, their variation laws are gained, then the expressions of SIFs are obtained by numerical fitting FEM results. Based on this, the 3D crack propagation path at tooth root is simulated and discussed, then, it is verified by comparing to experimental results, according to the mutation of the maximum SIF at crack tip, the fracture and damage of gear tooth are judged, and its work life also is predicted. These have very important value for damage monitoring and diagnosis of gear.

Determination of Initial Stages of Fatigue on the Basis of Fatigue Tensile and Fatigue Bend Testing

2016 ◽  
Vol 713 ◽  
pp. 123-126
Author(s):  
Nenad Gubeljak ◽  
M. Cvetić
Keyword(s):  
Fatigue Crack ◽  
Stress Concentration ◽  
Crack Propagation ◽  
Fatigue Crack Propagation ◽  
Fatigue Crack Initiation ◽  
Fatigue Threshold ◽  
Linear Elastic ◽  
Initial Stage ◽  
Propagation Parameters

Fatigue crack initiation usually starts from defects or inclusion (s) in the material in the zone of stress concentration. The stress concentration zone can be at the surface of the specimen or inside the material. The fatigue crack starts to propagate, depending on stress amplitude, if the range of the stress intensity factor is higher than the fatigue threshold. The aim of this paper is to present the procedure for determining the fatigue crack initial stage by using the Wöhler S-N curve and the fatigue crack propagation parameters obtained by experiment for the loading range R=-1. Determination of the fatigue initial stage has been determined by the analysis of tensile smooth specimens and notched bending specimens. Results show that linear elastic fracture mechanics is applicable in order to establish a model for fatigue crack propagation.

Dynamic Simulation of Planetary Gearbox With Tooth Root Crack Based on a Rigid-Flexible Coupled Model

2019 ◽  
Author(s):  
Jianchuan Dai ◽  
Hang Niu ◽  
Chenggang Hou ◽  
Xiaodong Zhang
Keyword(s):  
Crack Propagation ◽  
Dynamic Models ◽  
Gear Tooth ◽  
Coupled Model ◽  
Vibration Signal ◽  
Propagation Path ◽  
Tooth Root ◽  
Crack Propagation Path ◽  
Planetary Gearbox ◽  
Root Crack

Abstract Tooth root crack is one of the most common failures in the gearbox which can lead to the failure of the whole transmission system. However, it is difficult to simulate the gear fault impact in practical work. To solve this problem and to study the relationship between tooth crack propagation and vibration features, various dynamic models have been built. However, the crack propagation path and the bearings are simplified in most of the models, which leads to obvious deviation in the dynamic response. In this paper, a rigid-flexible coupled model of a single-stage planetary gearbox in normal and fault conditions are built by ADAMS software. The crack propagation path is considered a parabolic curve and the thickness of the crack decreases along the path. As a reference, a rigid-body model has also been built to prove that the rigid-flexible coupled model can be more accurate and suitable for analyzing the response of the planetary gearbox with fault. Afterward, the effects of gear tooth root crack size on the gear dynamics are simulated and the corresponding changes in statistical indicators are investigated. By studying the torsional vibration signal of the planetary gearbox with varying severity of the damage, the fault characteristics and damage evolution mechanics can be analyzed and by comparing the fault sensitivity of these indicators, the critical and sensitive fault indicators are screened out.

Analysis on Fatigue Crack Initiation and Fatigue Crack Propagation in a Gear

2018 ◽  
Vol 4 (7) ◽  
pp. 13
Author(s):  
Anand Mohan Singh ◽  
Mrs. Madhulata Sharma
Keyword(s):  
Fatigue Crack ◽  
Crack Initiation ◽  
Crack Propagation ◽  
Failure Modes ◽  
Gear Tooth ◽  
Crack Depth ◽  
Dynamical Behavior ◽  
Fatigue Crack Initiation ◽  
Design Guidelines ◽  
Operating Conditions

An effective gear design balances strength, durability, reliability, size, weight and cost. Because of the advantage of gear, gearbox was used widely. But its fault also brought many losses of the production and society. It was necessary to research and analysis on the dynamical behavior of the gear system. The engineering structures may fail due to crack, which depends on the design and also on operating conditions in which it operates. It can be avoided by analyzing and understanding the manner in which it originates. It is necessary to develop design guidelines to prevent failure modes considering gear tooth fracture, by studying the crack propagation path in a gear. In variety of gear tooth geometry the crack propagation paths are predicted at various crack initiation location. The objective of this study was to follow the crack propagation in the tooth foot of a gear by the Finite Element Method (FEM). The study concludes with the analysis of available for standard gears, to highlight the different behavior in crack propagation. The influence of crack position and crack depth etc. on dynamic characteristics of gear has also been studied.

Bending Fatigue Analysis of PM Gears

2017 ◽  
Vol 754 ◽  
pp. 299-302 ◽  
Author(s):  
Srečko Glodež ◽  
Marko Šori
Keyword(s):  
Service Life ◽  
Computational Model ◽  
Gear Tooth ◽  
Tooth Root ◽  
Experimental Procedure ◽  
Bending Fatigue ◽  
Custom Made ◽  
Root Strength ◽  
Service Life Estimation

The paper discusses the computational and experimental approach for determination of the PM gears service life concerning bending fatigue in a gear tooth root. A proposed computational model is based on the stress-life approach where the stress field in a gear tooth root is determined numerically using FEM. The experimental procedure was done on a custom made back-to-back gear testing rig. The comparison between computational and experimental results has shown that the proposed computational approach is appropriate calculation method for service life estimation of sintered gears regarding tooth root strength. Namely, it was shown that in the case of proper heat treatment of tested gears, the tooth breakage occurred inside the interval with 95 % probability of failure, which has been determined using proposed computational model.

scholarly journals Fatigue Crack Growth Analysis with Extended Finite Element for 3D Linear Elastic Material

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 397
Author(s):  
Yahya Ali Fageehi
Keyword(s):  
Finite Element ◽  
Fatigue Crack ◽  
Fatigue Life ◽  
Crack Propagation ◽  
Crack Growth ◽  
Mixed Mode ◽  
Propagation Path ◽  
Loading Conditions ◽  
Extended Finite Element ◽  
Linear Elastic

This paper presents computational modeling of a crack growth path under mixed-mode loadings in linear elastic materials and investigates the influence of a hole on both fatigue crack propagation and fatigue life when subjected to constant amplitude loading conditions. Though the crack propagation is inevitable, the simulation specified the crack propagation path such that the critical structure domain was not exceeded. ANSYS Mechanical APDL 19.2 was introduced with the aid of a new feature in ANSYS: Smart Crack growth technology. It predicts the propagation direction and subsequent fatigue life for structural components using the extended finite element method (XFEM). The Paris law model was used to evaluate the mixed-mode fatigue life for both a modified four-point bending beam and a cracked plate with three holes under the linear elastic fracture mechanics (LEFM) assumption. Precise estimates of the stress intensity factors (SIFs), the trajectory of crack growth, and the fatigue life by an incremental crack propagation analysis were recorded. The findings of this analysis are confirmed in published works in terms of crack propagation trajectories under mixed-mode loading conditions.

scholarly journals Crack Propagation in the Tibia Bone within Total Knee Replacement Using the eXtended Finite Element Method

2021 ◽  
Vol 11 (10) ◽  
pp. 4435
Author(s):  
Ho-Quang NGUYEN ◽  
Trieu-Nhat-Thanh NGUYEN ◽  
Thinh-Quy-Duc PHAM ◽  
Van-Dung NGUYEN ◽  
Xuan Van TRAN ◽  
...  
Keyword(s):  
Fatigue Crack ◽  
Crack Initiation ◽  
Crack Propagation ◽  
Fatigue Crack Initiation ◽  
Fracture Prevention ◽  
Patient Specific ◽  
Extended Finite Element ◽  
Tibia Bone ◽  
Age Related ◽  
Final Failure

Understanding of fracture mechanics of the human knee structures within total knee replacement (TKR) allows a better decision support for bone fracture prevention. Numerous studies addressed these complex injuries involving the femur bones but the full macro-crack propagation from crack initiation to final failure and age-related effects on the tibia bone were not extensively studied. The present study aimed to develop a patient-specific model of the human tibia bone and the associated TKR implant, to study fatigue and fracture behaviors under physiological and pathological (i.e., age-related effect) conditions. Computed tomography (CT) data were used to develop a patient-specific computational model of the human tibia bone (cortical and cancellous) and associated implants. First, segmentation and 3D-reconstruction of the geometrical models of the tibia and implant were performed. Then, meshes were generated. The locations of crack initiation were identified using the clinical observation and the fatigue crack initiation model. Then, the propagation of the crack in the bone until final failure was investigated using the eXtended finite element method (X-FEM). Finally, the obtained outcomes were analyzed and evaluated to investigate the age-effects on the crack propagation behaviors of the bone. For fatigue crack initiation analysis, the stress amplitude–life S–N curve witnessed a decrease with increasing age. The maximal stress concentration caused by cyclic loading resulted in the weakening of the tibia bone under TKR. For fatigue crack propagation analysis, regarding simulation with the implant, the stress intensity factorand the energy release rate tended to decrease, as compared to the tibia model without the implant, from 0.152.5 to 0.111.9 (MPa) and from 10240 to 5133 (J), respectively. This led to the drop in crack propagation speed. This study provided, for the first time, a detailed view on the full crack path from crack initiation to final failure of the tibia bone within the TKR implant. The obtained outcomes also suggested that age (i.e., bone strength) also plays an important role in tibia crack and bone fracture. In perspective, patient-specific bone properties and dynamic loadings (e.g., during walking or running) are incorporated to provide objective and quantitative indicators for crack and fracture prevention, during daily activities.

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