Rolling bearings serve as the most widely utilized general components in drive systems for rotating machinery, and they are susceptible to regular malfunctions. To address the performance degradation encountered by current convolutional neural network-based rolling-bearing-fault diagnosis methods due to significant noise interference and variable working conditions in industrial settings, we propose a rolling-bearing-fault diagnosis method based on dual multi-scale mechanism applicable to noisy-variable operating conditions. The suggested approach begins with the implementation of Variational Mode Decomposition (VMD) on the initial vibration signal. This is succeeded by a denoising process that utilizes the goodness-of-fit test based on the Anderson–Darling (AD) distance for enhanced accuracy. This approach targets the intrinsic mode functions (IMFs), which capture information across multiple scales, to obtain the most precise denoised signal possible. Subsequently, we introduce the Dynamic Weighted Multi-Scale Feature Convolutional Neural Network (DWMFCNN) model, which integrates two structures: multi-scale feature extraction and dynamic weighting of these features. Ultimately, the signal that has been denoised is utilized as input for the DWMFCNN model to recognize different kinds of rolling-bearing faults. Results from the experiments show that the suggested approach shows an improved denoising performance and a greater adaptability to changing working conditions.

This paper addresses the issue of noise interference and variable working conditions in the production and machining environment, which lead to weak tool life features and reduced prediction accuracy. A tool lifetime prediction method based on AVMD-DAMResNet is proposed. The method first adapts the parameters of the variational modal noise reduction algorithm using an improved sparrow optimization algorithm, and then reconstructs the original vibration signal with noise reduction. Second, the residual module of the deep residual network is enhanced using a two-dimensional attention mechanism. A parallel residual network tool prediction model (DAMResNet) was constructed to optimize the model’s weight allocation to different features, achieving multi-channel and multi-dimensional feature fusion. Finally, the noise-reduced signal was input into the DAMResNet model to accurately predict tool lifetime. The experimental results show that, compared with the original ResNet model, the proposed AVMD-DAMResNet model improves the coefficient of determination (R²) by 5.8%, reduces the root mean square error (RMSE) by 31.2%, and decreases the mean absolute percentage error (MAPE) by 31.4%. These results demonstrate that the AVMD-DAMResNet-based tool lifetime prediction method effectively reduces noise and achieves high prediction accuracy.

Aunified analytical framework is developed for an XYZAC five-axis CNC machine tool to establish a physically consistent connection between practical machining-task variables, rigid-body screw motion, and inverse dynamics. The tool-tip/tool-axis task is represented in ${\mathbb{R}}^3\times S^2$, while the product-of-exponentials formulation is used to establish the forward- and inverse-position kinematics. A topology-constrained two-stage mapping converts the machining-task rate first into the actual six-dimensional rigid-body twist and subsequently into the five generalized axis velocities. A supplementary constrained motion screw and reciprocal screw/wrench duality are employed to construct the corresponding analytical inverse. At the acceleration level, task-space geometric effects and mechanism-configuration effects are explicitly separated, after which the generalized states are coupled with the physical rigid-body chains through Newton–Euler equations and virtual work. A singularity analysis gives ${\sigma }_{\min }=\left|\sin q_A\right|$ and ${\kappa }_2=1/\left|\sin q_A\right|$, quantitatively revealing the degeneration of the orientation mapping as $q_A\to 0$. Closed-loop kinematic validation yields maximum RMSEs of $3.811000\times {10}^{-14}$ mm and $2.657723\times {10}^{-15}$ deg and maximum absolute errors below $1.110223\times {10}^{-13}$ mm and $1.272222\times {10}^{-14}$ deg, while force/torque benchmarking gives maximum RMSEs of 0.0821185 N and 1.39897 N·mm and maximum absolute errors of 0.531176 N and 8.76912 N·mm relative to simulation. The results demonstrate consistent task-to-motion-to-load propagation within the investigated rigid-body regime and provide a unified interface for subsequent elastodynamic and machining-load coupling analyses.