Bevel gear transmission is characterized by strong load capacity, stable transmission, and compact structure. It is a key component in power transmission systems for vehicles, ships, machine tools, oil drilling equipment, aerospace, and other industries. Amid the rapid development of electrification, gears remain indispensable in mechanical systems. Bevel gears are typically machined using gear shaping or dual-cutter disk milling methods, which are efficient but require specialized machines, resulting in high procurement costs. These methods are also unsuitable for machining large gears or small-batch production. Inspired by the linear mechanism of the internal pendulum, this paper proposes a CNC machining method for straight bevel gears based on hypocycloid mechanisms. By leveraging the straight-line properties of hypocycloid motion, straight bevel gears are machined via milling or grinding on a five-axis machining center using the end-face hobbing method. This method transforms the traditional non-continuous machining into continuous indexing machining and enables CNC machining on a general five-axis machining center. This approach reduces the cost of specialized equipment and improves the efficiency of straight bevel gear manufacturing.

Freeform machining of impellers involves extended cycle times, leading to high energy consumption and costs necessitating efficient process optimization. This study develops a CAD/CAM-integrated hybrid Taguchi-Artificial Neural Network (ANN) model to optimize machining parameters for a freeform impeller. Four controllable factors, namely cutting feed ($C_f$), feed Z ($F_z$), retract feed ($R_f$), and cutter diameter ($C_D$), were investigated at five levels using an L25 orthogonal array, with machining time as the response. Taguchi analysis identified cutting feed as the most dominant factor, while retract feed was insignificant, and a first-order regression model yielded an R² of 95.88%. A two-layer feedforward neural network with six hidden neurons achieved an R² of 0.9999 and a mean absolute error of 0.0976 min. To rigorously validate generalization, leave-one-out cross-validation was employed, identifying three hidden neurons as optimal with a cross-validated R² of 0.9823, RMSE of 0.5350 min, and MAE of 0.3429 min. The final model trained on all samples achieved an R² of 0.9996. Comparison with a quadratic regression model on the same test set confirmed the superior predictive capability of the ANN ($R^2=0.9992$ vs. $0.9983$). Optimal parameters ($C_f=\mathrm{12,000} \mathrm{m}\mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$, $F_z=600 \mathrm{m}\mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$, $R_f=4000 \mathrm{m}\mathrm{m}/\mathrm{m}\mathrm{i}\mathrm{n}$, $C_D=6 \mathrm{m}\mathrm{m}$) were validated through simulation, yielding a machining time of 11.05 min, representing a 52.6% reduction from 23.32 min. The hybrid Taguchi–ANN framework effectively optimizes freeform impeller machining, significantly enhancing productivity while maintaining process reliability.

To address the limitations of traditional analytical modeling in capturing complex surface topographies, this paper presents comprehensive research on the error sensitivity mechanism, loaded tooth contact analysis (LTCA), and load-bearing contact characteristics of curved face gears based on high-precision point cloud modeling. The primary objectives are threefold: (1) to establish a high-fidelity topological reconstruction framework using Non-Uniform Rational B-Splines (NURBS) to bridge the gap between discrete data and finite element analysis (FEA); (2) to reveal the inherent mechanical response and sensitivity mechanism to spatial installation misalignments; and (3) to evaluate the contact performance and transmission error fluctuations under operational loads. Specifically, an analytical discretization method is proposed for point cloud generation, followed by a dual-path validation system integrating “rigid tooth contact analysis (TCA)” and “loaded FEA”. The results demonstrate that the proposed reconstruction achieves a superior accuracy with a Root Mean Square Error (RMSE) of 2.2 × 10⁻³ mm. Furthermore, shaft angle error is identified as the dominant sensitivity factor affecting transmission smoothness and edge contact, exerting a more significant influence than offset and axial errors. Compared with existing research on arc-tooth and helical face gears, this work provides a more robust closed-loop verification for curved profiles, revealing that material elastic deformation increases transmission error amplitude by 10.1% to 17.2%. These insights offer a theoretical reference for the high-precision assembly and tolerance allocation of helicopter transmission systems.

High-speed machining of complex freeform geometries faces fundamental challenges in balancing computational efficiency, kinematic constraints, and precision, particularly in high-curvature regions where traditional interpolation methods suffer from geometric errors and jerk-induced vibrations. This study presents a Galerkin-NURBS interpolation framework that integrates Galerkin projection to optimize NURBS parameterization, minimizing geometric approximation error, and couples it with a jerk-limited S-curve trajectory planning algorithm that enforces $C^3$ continuity while respecting feedrate, acceleration, and jerk constraints. Numerical simulations and machining experiments were conducted on butterfly-shaped and horse-shaped curves using a five-axis CNC machine equipped with rotary/linear encoders and validated via profilometer-based surface roughness measurements. The proposed method achieved a 32.9% reduction in processing time (3.091 s) compared to the CQSF method (4.61 s) and a 35.1% reduction in interpolation steps relative to FSRC. Surface roughness ($R_a$) values ranged from 0.1271 μm to 0.2009 μm, with most measurements compliant with ISO 21920-1:2021; the maximum value (0.2009 μm) represents the upper bound of the standard’s high-precision threshold for aluminum alloy 6061. These findings demonstrate that the proposed framework significantly improves machining efficiency and surface quality while maintaining geometric fidelity, making it suitable for precision manufacturing applications where sensor-guided process optimization is critical.

Spiral bevel gear drives are widely used in mechanical transmission devices due to their compact structure, smooth transmission, and cost-effectiveness. With the continuous improvement in mechanical product quality, higher and higher requirements are set for the precision, smoothness, and power density of gear transmission devices. Chatter can lead to poor workpiece surface finish on spiral bevel gears, excessive tool wear, and even damage to machine tools. Therefore, the effective prediction of milling chatter during the processing of spiral bevel gears is essential. Regenerative chatter is one of the most fundamental types of vibration in machining processes. This paper presents an improved fully discrete algorithm for predicting the stability of time-delayed cutting in the milling process of spiral bevel gears. The method is validated using single- and double-degree-of-freedom models, demonstrating its accuracy and computational efficiency. The results show that the proposed method improves computational efficiency while ensuring accuracy.