As the critical performance index of ball screws, the contact characteristics have a significant influence on the lubricant properties, tribological properties, and wear properties of ball screws, which further directly affect the service life of ball screws. The non-uniform load distribution induced by geometric errors results in imbalances among balls along the nut, negatively impacting the service life of ball screws. This study focuses on the load distribution of single-nut ball screws under low-speed working conditions. This paper proposes a self-adjustable model of load distribution that considers the flexibility of the screw and nut with respect to the determination of the non-bearing ball. A refined model for axial stiffness is proposed to systematically analyze the influence of geometric errors on stiffness variations under various loading conditions. The results confirm the ability of the proposed model to reveal the static load distribution in view of geometric errors. The greatest discrepancy observed between the theoretical predictions and the experimental data was 9.22%. The numerical simulations demonstrate variation trends in the normal contact load, the loaded-ball number, and the axial deformation of a nut with geometric errors. Furthermore, the relationship between the axial stiffness of a single-nut ball screw and the geometric error is obtained. The self-adjustable model of load distribution is helpful for studying the carrying capacity of a single-nut ball screw. The findings of the study provide a definite reference for optimization of structural design and wear life prediction.

As a critical precision transmission element in numerical control (NC) machines, the linear rolling guide (LRG) suffers from surface wear degradation, which significantly impairs machining accuracy and operational reliability. Despite its importance, effective identification methods for LRG degradation remain limited. In this study, a hybrid approach combining multi-scale fuzzy entropy (MFE) with a gray wolf-optimized random forest (GWO-RF) algorithm was proposed to identify the surface wear state of the LRG. Preload degradation and vibration signals were collected at three surface wear stages throughout the LGR’s service life. The vibration signals were decomposed and reconstructed using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), followed by multi-scale fuzzy entropy analysis of the reconstructed signals. After dimensionality reduction via kernel principal component analysis (KPCA), the processed features were fed into the GWO-RF model for classification. Experimental results demonstrated a recognition accuracy of 97.9%.

Ball screws have been receiving increasing attention in the aerospace and military industry for their high reliability and high positioning accuracy. Under such extreme working conditions, ball screws are required to bear heavy loads in a short time, where they are mainly subject to fatigue elastic failure mode. Traditional reliability modeling methods based on the fatigue pitting failure mode are not suitable any more. However, reliability based on fatigue elastic failure in ball screws has not been investigated yet. To this end, we first established a degradation mechanism model for the fatigue elastic of ball screws. Subsequently, we proposed the degradation reliability model for ball screws, along with a novel Expectation Maximization method for parameter estimation. Additionally, we proposed a novel test method for the fatigue elastic life for ball screws utilizing a designed test bench. The mean curve for the degradation model almost exhibited a relative error less than 5%, confirming the validity of the proposed model. Lastly, we conducted a sensitivity analysis of structural parameters on fatigue elasticity, finding that the helix angle significantly influences the rated elastic life, while the ball diameter has a minimal effect. These findings contribute valuable insights for reliability evaluation and reliability design for ball screws under extreme working conditions.

Ball screw feed systems are critical components of CNC machine tools, and their health condition directly affects positioning accuracy and operational reliability. However, variations in rotational speed under changing operating conditions can cause substantial shifts in fault characteristics, limiting the generalization capability of conventional fault identification methods developed under a single operating condition. To address this issue, a feature-enhanced multi-kernel domain adaptation framework is proposed for cross-domain fault identification of ball screw feed systems. First, an attention-based feature enhancement module is developed to adaptively reweight vibration features, thereby emphasizing informative feature components and suppressing redundant and noise-related information. Subsequently, a residual feature extraction and fusion module is employed to learn hierarchical fault representations and improve feature discriminability. Finally, a multi-kernel maximum mean discrepancy (MK-MMD) strategy is integrated with adversarial domain adaptation to reduce feature distribution discrepancies between source and target domains under different rotational speeds and ball screw specimens. Local spalling fault experiments were conducted on the developed test bench, where vibration signals were collected using an accelerometer under various operating conditions and subsequently used to validate the proposed framework. Experimental results demonstrate that the proposed method achieves an average identification accuracy of 92.9% across the 12 investigated cross-domain tasks, compared with 69.7% for the optimized source-only CNN, with the performance gap becoming particularly pronounced under cross-specimen transfer conditions. The results indicate that the proposed framework improves the learning of fault-discriminative and domain-invariant representations, thereby improving the robustness of ball screw fault identification under variable operating conditions.

The automatic sketching of kinematic chain topological graphs can provide an effective method for the computerized graphical representation of mechanism models in quantity. It is also helpful to establish a visual atlas database for mechanism optimization and selection. Due to the defects of line crossings and point-line overlaps for the existing methods of topological graph sketching, this paper proposes a new method for automatic layered sketching of topological graphs based on the optimized branch chain matrix. First, a tree-structured diagram is employed to illustrate the internal connected relations of the kinematic chain, and the concepts of the main chain, branch chains, and branch chain matrix are introduced. Then, the branch chain matrix is established by searching connection relationships between links. Based on the proposed definition of the proximity between branch chains, as well as the decision rules and calculation method of intersections, the optimized branch chain matrix corresponding to the diagram is further acquired, with no intersections or the least number of intersections. Moreover, the method for obtaining the outermost-loop links is formulated. Finally, based on the point distribution of the regular polygon for the outermost loop and combined with a layer-by-layer sketching approach, the bicolor topological graph is obtained with no or minimal intersections of kinematic chains, which avoids the point-line overlaps. According to the case analysis, it is demonstrated that the topological graph sketching method proposed in this paper has several advantageous features, including no or minimal intersections, high symmetry, avoidance of point-line overlaps, and improved visibility.