Research status of stress intensity factors for low speed and heavy duty gears

Under the action of long-term repeated load, gear is easy to produce fatigue microcracks, which leads to the decrease of strength and service life. In order to predict the fatigue life of gears, some researchers use stress intensity factors to predict the fatigue life of gears. Stress intensity factor (SIF) is an important parameter to characterize the fracture behavior of materials, which reflects the strength of the stress field at the crack tip on the basis of on-line elastic theory. By calculating SIF, the fracture condition of gear crack can be judged, and the damage condition of gear can be analyzed, so as to provide a theoretical basis for predicting the fatigue life of gear. In recent years, the research on the stress intensity factor and fracture failure characteristics of gears at home and abroad has achieved certain results, and most researchers use numerical calculation method to study the fracture characteristics of gears.

In 2008, madia m and others analyzed the fracture problem of gear shaft in railway system, solved three types of stress intensity factors according to semi elliptical crack, and then studied the influence of rotary bending and press fit on stress intensity factor. Press fit has great influence on stress intensity factor and fatigue crack propagation, but rotary bending has little influence on it.

In 2009, fajdiga g et al. Calculated the pitting crack life of gear under contact fatigue, and divided the fatigue life into crack initiation period and crack propagation period. The process of crack initiation and pitting was simulated by virtual crack propagation method, and the effect of crack length on stress intensity factor was analyzed.

In 2010, based on linear elastic fracture mechanics, Zouari. S and others used ANSYS to simulate the crack growth of two-dimensional spur gear, solved the stress intensity factor, analyzed the influence of crack depth and crack angle on the stress intensity factor, and finally predicted the crack growth path considering bending fatigue.

In 2011, M. Liu et al. Obtained the stress intensity factor (SIF), crack length and friction between crack surfaces in the process of sliding mode crack growth by using the traditional fatigue testing machine. Through the AC potential method, a new idea for solving the SIF of mode II crack was provided.

In 2011, Ling y et al. Solved the stress intensity factor using Gaussian process surrogate model under the condition of complex geometry and multiaxial variable amplitude load, which provided a method for quantifying uncertainty in fatigue crack analysis and theoretical support for the research of crack model.

In 2012, Ananda Kumar eriki et al. Calculated the crack propagation direction angle using the stress intensity factor at the crack tip, predicted the crack propagation path of spur gear using the mixed mode criterion and the crack propagation criterion, and analyzed the gear meshing stress.

In 2012, based on linear elastic fatigue mechanics and boundary element method, Dong Feifei and others simulated the variation of three types of stress intensity factors with crack length, load, number of teeth, modulus, crack angle and modification coefficient by using FRANC3D. Their research results laid a foundation for fracture characteristics and life prediction of gears.

In 2014, Wu Jinliang and others used FRANC3D to analyze the variation of the stress intensity factor (SIF) of the pinion crack with the crack location of the 5th gear of a transmission, and predicted the fatigue life of the gear according to the SIF, which provides a new method for the life prediction of helical gears.

In 2017, heirani. H and others used ABAQUS to simulate the crack propagation path of two-dimensional spur gear. Based on linear elastic fracture mechanics, according to different initial crack locations, the components were loaded, and the crack initiation and propagation were simulated according to the mode II stress intensity factor at the crack tip.

In 2017, Hiung Fung Zen and others used the extended finite element method to study the influence of different torques on the stress intensity factor of cracks, which overcomes the limitations of traditional finite element method and saves the time of re meshing.

In 2018, Li youtang and others used ABAQUS to study the effect of crack inclination on the growth characteristics of helical gears. With the increase of crack inclination, the crack growth path, stress intensity factor and crack tip displacement will change correspondingly, which lays a good foundation for predicting the fatigue life of helical gears with cracks.

In 2018, Yunxia Chen et al. Proposed a method to estimate the life of Cracked Gear by degradation model. Firstly, the two-dimensional finite element model of Cracked Gear was established by using FRANC2D software, and the propagation path under different initial crack angles was studied; Then, the vibration responses of gears with different initial crack angles are obtained by using the improved meshing stiffness model and lumped mass dynamic model; Finally, the quantitative relationship between the crack growth process and the deterioration level is established, which can be used to predict the life of gears.

In 2018, Xinxiao Bian et al. Carried out fatigue fracture experiments on gears with cracks, and obtained the propagation path and stress intensity factor. Compared with the results of linear elastic fracture mechanics theory and FRANC3D simulation, the results show that in the early stage of crack propagation prediction, the results of FRANC3D simulation are close to the results of linear elastic fracture mechanics theory, With the increase of the crack length, the difference between the two is larger and larger; However, comparing the experimental results with the simulation results of FRANC3D, the difference between the two results is very small, the error is 2.4% – 13.3%, so the simulation is closer to the experimental results.

Although many scholars use three-dimensional solid model to calculate the stress intensity factor to simulate crack growth, there are many factors that affect the stress intensity factor, which need to be analyzed from different angles. In this paper, a three-dimensional semi elliptical cylinder is used to simulate the initial crack of the tooth root of the low-speed and heavy-duty gear, and a finite element model of the fatigue propagation of the low-speed and heavy-duty gear is established. Then, the stress intensity factor of the gear is calculated. Finally, on the basis of the model with semi elliptical crack, the effects of crack size, crack shape and load on SIF are discussed.

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