This paper is to study errors of a milling machine used for the machining of Circular-Arc-Tooth-Trace (CATT) cylindrical gears. A topological structure model of the milling machine is established using the lower numbered body array...

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.

The kinematics of a robotic manipulator is critical to the real-time performance and robustness of the robot control system. This paper proposes a surrogate model of inverse kinematics for the serial six-degree of freedom (6-DOF) robotic manipulator, based on its kinematics symmetry. Herein, the inverse kinematics model is derived via the training of the Vector-Quantified Temporal Associative Memory (VQTAM) network, which originates from Self-Organized Mapping (SOM). During the processes of training, testing, and estimating of this neural network, a priority K-means tree search algorithm is utilized, thus improving the training efficacy. Furthermore, Local Linear Regression (LLR), Local Weighted Linear Regression (LWR), and Local Linear Embedding (LLE) algorithms are, respectively, combined with VQTAM to obtain three improvement algorithms, all of which aim to further optimize the prediction accuracy of the networks for subsequent comparison and selection. To speed up the solving of the least squared equation, which is common among the three algorithms, Singular Value Decomposition (SVD) is introduced. Finally, data from forward kinematics, in the form of the exponential product of a motion screw, are obtained, and are used for the construction and validation of the VQTAM neural network. Our results show that the prediction effect of the LLE algorithm is better than others, and that the LLE algorithm is a potential surrogate model to estimate the output of inverse kinematics.