This paper proposes an enhanced multi-strategy sparrow search algorithm to optimize the trajectory of a six-axis industrial robot, addressing issues of low efficiency and high vibration impact on joints during operation. Initially, the improved D-H parametric method is employed to establish both forward and inverse kinematic models of the robot. Subsequently, a 3-5-3 mixed polynomial interpolation trajectory planning approach is applied to the robot. Building upon the conventional sparrow algorithm, a two-dimensional Logistic chaotic system initializes the population. Additionally, a Levy flight strategy and nonlinear adaptive weighting are introduced to refine the discoverer position update operator, while an inverse learning strategy enhances the vigilante position update operator. These modifications boost both the local and global search capabilities of the algorithm. The improved sparrow algorithm, based on 3-5-3 hybrid polynomial trajectory planning, is then used for the time-optimal trajectory planning of the robot. This is compared with traditional sparrow search algorithm and particle swarm algorithm optimization results. The findings indicate that the proposed enhanced sparrow search algorithm outperforms both the standard sparrow algorithm and the particle swarm algorithm in terms of convergence speed and accuracy for robot trajectory optimization. This can lead to the increased work efficiency and performance of the robot.

Trajectory planning for flexible manipulators is a critical area of research in robotics. A trajectory tracking controller can enhance the accuracy of the manipulator's path and reduce vibrations. However, current flexible manipulators remain largely in the research phase, with many studies revealing issues such as poor accuracy in dynamic modeling, weak tracking performance in controller design, and insufficient vibration suppression capabilities. To address these challenges and improve the trajectory tracking performance of the manipulator, this paper focused on vibration suppression and trajectory planning for a two-link flexible manipulator and proposed a novel control method that integrates a modified adaptive particle swarm optimization algorithm (MAPSO) with fuzzy proportional–derivative (PD) control to achieve effective trajectory tracking. Firstly, the dynamic equations of the two-link flexible manipulator system were derived using the assumed modal method in conjunction with Lagrangian dynamics. Next, a 3-5-3 hybrid polynomial algorithm based on MAPSO was proposed to optimize the trajectory of the manipulator. Simulation results demonstrated that the optimization algorithm significantly enhances efficiency. Specifically, the number of iterations required for the two joints was reduced by 33 % and 54 %, respectively, when compared to the original algorithm. Additionally, this optimization led to a total reduction in running time of 0.03 s. Subsequently, the MAPSO algorithm was utilized to enhance the fuzzy PD controller based on the previously obtained optimal trajectory, leading to the development of a trajectory tracking controller known as MAPSO-FuzzyPD. Simulation results indicated that the proposed algorithm significantly reduced the maximum starting torque for both joints. Specifically, the maximum starting torque of joint 1 was decreased by 61.3 % and 40.3 % when compared to PD control and fuzzy PD control, respectively. Additionally, the maximum starting torque of joint 2 was reduced by 57.9 % and 42.1 % in comparison to the same control methods. Finally, an experimental platform for the flexible manipulator was established, and the experimental results further validated the effectiveness and feasibility of the algorithm proposed in this paper concerning joint trajectory tracking.

Labyrinth seals, extensively used in aerospace and turbomachinery as non-contact sealing devices, undergo accelerated wear and enhanced leakage due to repeated rub-impact between rotating shafts and sealing rings. To address the problem of increased leakage under rub-impact conditions, this research integrates experimental and numerical methods to investigate the deformation mechanisms and leakage characteristics of thermoplastic labyrinth seals. A custom designed rub-impact test rig was constructed to measure dynamic forces and validate finite element analysis (FEA) models with an error of 5.1% in predicting tooth height under mild interference (0.25 mm). Computational fluid dynamics (CFD) simulations further demonstrated that thermoplastic materials, such as PAI and PEEK, displayed superior resilience (with rebound ratios of 57% and 70.3%, respectively). Their post-impact clearances were 4.8–18.3% smaller than those of PTFE and F500. Leakage rates were predominantly correlated with interference, causing a substantial increase compared to the original state; at 0.25 mm interference (reverse flow), increases ranged from 151% (PAI) to 217% (PTFE), highlighting material-dependent performance degradation. Meanwhile, tooth orientation modulated leakage by 0.5–3% through the vena contracta effect. Based on these insights, two optimized inclined-tooth geometries were designed, reducing leakage by 28.2% (Opt1) and 28.1% (Opt2) under rub-impact. These findings contribute to the development of high-performance labyrinth seals suitable for extreme operational environments.

Against the backdrop of the rapid development of the manufacturing industry, online monitoring of tool wear status is of great significance for enhancing the reliability and intelligence of CNC machine tools. This paper presents an intelligent tool wear condition monitoring model (CPSO-CNN-BiLSTM-AM) that integrates the improved Chaotic Particle Swarm Optimization (CPSO) algorithm with the CNN-BiLSTM network incorporating an attention mechanism. The aim is to extract the global features of long-sequence monitoring data and the local features of multi-spatial data. Chaos theory and the mutation mechanism are introduced into the CPSO algorithm, which enhances the algorithm’s global search ability and its capacity to escape local optimal solutions, enabling more efficient optimization of the hyperparameters of the CNN-BiLSTM network. The CNN-BiLSTM network with the introduced attention mechanism can more accurately extract the spatial features of wear signals and the dependencies of time-series signals, and focus on the key features in wear signals. The study utilized the IEEE PHM2010 Challenge dataset, extracted wear features through time-domain, frequency-domain, and time-frequency domain methods, and divided the training set and validation set using cross-validation. The results show that in the public PHM2010 dataset, the average MAE of the model for tools C1, C4, and C6 is 0.83 μm, 1.01 μm, and 1.34 μm, respectively; the RMSE is 0.99 μm, 1.79 μm, and 0.88 μm, respectively; and the MAPE is 0.95%, 1.41%, and 1.01%, respectively. In the self-built dataset, the average MAE for tools A1, A2, and A3 is 1.35 μm, 1.19 μm, and 1.83 μm, respectively; the RMSE is 1.41 μm, 1.98 μm, and 1.90 μm, respectively; and the MAPE is 1.67%, 1.55%, and 1.81%, respectively. All indicators are superior to those of comparative models such as LSTM and PSO-CNN. The proposed model can effectively capture changes in different stages of tool wear, providing a more accurate solution for tool wear condition monitoring.