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

元建模 克里金 粒子群优化 接触力学 压力(语言学) 弧(几何) 跟踪(心理语言学) 可靠性(半导体) 遗传算法 算法 数学 结构工程 计算机科学 数学优化 工程类 有限元法 统计 几何学 物理 语言学 哲学 功率(物理) 量子力学 程序设计语言
作者
Qi Zhang,Zhuo Chen,Yang Wu,Guoqi Xiang,Guang Wen,Xuegang Zhang,Yongchun Xie,Guangchun Yang
出处
期刊:Cmes-computer Modeling in Engineering & Sciences [Tech Science Press]
卷期号:140 (1): 593-619 被引量:1
标识
DOI:10.32604/cmes.2023.046319
摘要

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 R2, RMSE, and RMAE. R2 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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