Contact stress reliability analysis based on first order second moment for variable hyperbolic circular arc gear

Zhang, Qi; Wen, Guilin; Chen, Zhuo; Zhou, Qin; Gao, Xiang; Yang, Guangchun; Zhang, Xuegang

doi:10.1177/16878132221111210

Cited by 6 publications

(2 citation statements)

References 17 publications

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“…Ahmed Bahloul [5] conducted a fatigue crack growth life prediction study for 7075-T6 aerospace aluminum alloy and confirmed the significance of the stress intensity factor as a contributing factor to component failure; Zhiying Chen [6] employed the extended finite element method (XFEM) to numerically predict crack propagation paths and fatigue life under cyclic loading. The study validated the accuracy of the calculated stress intensity factor and crack expansion； Zhang Qi [7] proposed a reliability analysis of hyperbolic circular gear contact strength using a combination of the kriging model and the first second-order method. The results demonstrated the feasibility of analyzing reliability using the first second-order moment method;M.P.F.…”

Section: Introductionmentioning

confidence: 64%

Reliability analysis of structures containing cracks based on kriging model

Liao,

Zhang,

Zhang

2023

Preprint

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The fatigue reliability of structural elements with penetration cracks under stress loading is analysed using the Kriging model. The model is established using the “FEM + M integral” stress intensity factor modelling method, and the reliability of the numerical modelling is determined by comparing the theoretical and simulated values of the stress intensity factor. A kriging probability model is established, and the reliability of the cracked structure is obtained based on the mean point method and the Monte Carlo method. The influence law of the statistical characteristics of the random parameters on the reliability of crack containment specimens is investigated. It is concluded that the stress P is the most sensitive to the influence of the reliability of the cracked structure, followed by the crack length a, and the plate width W is the least sensitive to the influence of the reliability.

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Section: Introductionmentioning

confidence: 64%

Reliability analysis of structures containing cracks based on kriging model

Liao,

Zhang,

Zhang

2023

Preprint

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“…Another study established the reliability analysis model for cylindrical gear with a variable hyperbolic circular arc tooth line. This work delved into the reliability sensitivity and robust optimization of contact strength [19,20].…”

Section: Introductionmentioning

confidence: 99%

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Zhang,

Chen,

et al. 2024

CMES

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Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace (referred to as CATT gear), a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis. In this study, a mathematical relationship between design parameters and contact stress is formulated using the Kriging Metamodel. To enhance the model's accuracy, we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm, leveraging the strengths of each. Additionally, the "parental inheritance + self-learning" optimization model is used to fine-tune the Kriging Metamodel's parameters. Following this, a mathematical model for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace (VH-CATT) gears using the optimized Kriging model was developed. We then examined how different gear parameters affect the VH-CATT gears' contact stress. Our simulation results show: (1) Improvements in R 2 , RMSE, and RMAE. R 2 rose from 0.9852 to 0.9974 (a 1.22% increase), nearing 1, suggesting the optimized Kriging Metamodel's global error is minimized. Meanwhile, RMSE dropped from 3.9210 to 1.6492, a decline of 57.94%. The global error of the GA-IQPSO-Kriging algorithm was also reduced, with RMAE decreasing by 58.69% from 0.1823 to 0.0753, showing the algorithm's enhanced precision. In a comparison of ten experimental groups selected randomly, the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress. Results revealed a maximum error of 12.11667 MPA, which represents 2.85% of the real value. (2) Several factors, including the pressure angle, tooth width, modulus, and tooth line radius, are inversely related to contact stress. The descending order of their impact on the contact stress is: tooth line radius > modulus > pressure angle > tooth width. (3) Complex interactions are noted among various parameters. Specifically, when the tooth line radius interacts with parameters such as pressure angle, tooth width, and modulus, the resulting stress contour is nonlinear, showcasing a multifaceted contour plane. However, when tooth width, modulus, and pressure angle interact, the stress contour is nearly linear, and the contour plane is simpler, indicating a weaker coupling among these factors.

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Evaluation of the Spatial Variability of the Mechanical Properties of Rocks Using Non‐Iterative Green's Function Approach and the FOSM Method

Mesquita,

Sotelino,

Peres

2024

Num Anal Meth Geomechanics

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The present work proposes a new version of the Green‐FOSM (first‐order second moment) method, which eliminates the iterative calculation process of the original version and, simultaneously, solves the convergence problems related to the mechanical properties of rocks that form the geological formation. In this calculation scheme, the iterative process is eliminated by using a matrix that correlates the nodal displacement vector with the strain vector. Considering the same computational resources, this non‐iterative version of the Green‐FOSM method is up to 200 times faster than the original iterative process. In addition, it allows analyzing problems with more than 10,000 random variables, value that in the original method is less than 3000. To demonstrate its validity, the proposed method is applied to two hypothetical models subjected to different fluid extraction processes. For all the different levels of correlation and spatial variability, the statistical results obtained by the proposed method agree well with the results obtained via Monte Carlo Simulation (MCS). The relationship between CPU times demonstrates that the proposed method is at least 50 times faster than MCS. In the end, the non‐iterative Green‐FOSM method is used to obtain the displacement, strain, and stress fields of a geological section constructed from a seismic image of Brazilian pre‐salt oil region. The results found show that, depending on the levels of spatial variability, the analyzed fields can assume values up to 30.6% higher or lower than the values obtained deterministically.

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Contact stress reliability analysis based on first order second moment for variable hyperbolic circular arc gear

Cited by 6 publications

References 17 publications

Reliability analysis of structures containing cracks based on kriging model

Reliability analysis of structures containing cracks based on kriging model

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Evaluation of the Spatial Variability of the Mechanical Properties of Rocks Using Non‐Iterative Green's Function Approach and the FOSM Method

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