The kinematic and dynamic characteristics of the grinding media during the wet grinding process are investigated using a coupled Discrete Element Method (DEM)–Computational Fluid Dynamics (CFD) approach. Firstly, a coupled DEM-CFD model of the vertical spiral agitator mill is established and validated with experimental torque measurements. Subsequently, a velocity analysis model is established using the vector decomposition method. The cylinder is then divided into multiple regions along its radial and axial directions. The effects of spiral agitator rotational speed, diameter, pitch, and media filling level are investigated with respect to the circumferential velocity, axial velocity, collision frequency, effective energy between media, and energy loss of the grinding media. The average effective energy between media is an innovative metric for evaluating the grinding effect. The results indicate that the peripheral region of the spiral agitator demonstrates superior kinematic and dynamic performance. The rotational speed of the spiral agitator exerts a highly significant influence on the kinematic and dynamic characteristics of the media. With a maximum rise of 0.2 m/s in circumferential velocity and a 16.7 J gain in total energy. The media filling level demonstrates a negligible influence on media kinematics, while it profoundly affects dynamic properties, evidenced by a substantial increase of 83.09 J in the total media–media energy. As the diameter increases, the peak media circumferential velocity shifts outward, and the total media–media energy rises by 5.4 J. The spiral agitator pitch has a minimal impact on both the kinematic and dynamic characteristics of the media.

The ball mill is a critical size reduction equipment in industries such as mining and metallurgy. However, the sustainable reliability modeling of the entire system is challenging due to its complex service conditions. This paper presents a systematic framework for the reliability analysis of ball mills based on Stress–Strength Interference Theory (SSIT). Based on a reliability block diagram (RBD), this study establishes a system-level reliability model for the ball mill. Within this framework, the cylinder model is developed using the energy conservation principle between impact energy and strain energy; the gear model comprehensively considers both contact and bending fatigue failure modes; and the bolt model is constructed through mechanical analysis in conjunction with Hooke’s law. In the case study, a laboratory-scale mill (Φ5.5 × 2.6 m shell, effective grinding chamber: 5.3 m inner diameter × 2.376 m length) operating at 14 RPM under dry grinding conditions is analyzed. The reliability of individual components and the entire system is computed using Monte Carlo simulation. The results indicate that the overall system reliability increases when one of the following three conditions is met: the surface hardness of the gear is higher and the tangential force is lower; the impact velocity on the cylinder is lower and the impacted area is larger; or the tensile force on the bolt is reduced.

Leg stretching devices are one of the main instruments used to improve human function. To solve the limitations of existing leg stretching products, such as single function and low degree of coincidence, a leg stretching device satisfying ergonomics was studied in this paper. Firstly, the Box–Behnken Design (BBD) response surface methodology was applied to establish a regression model for leg force. Secondly, a motion analysis was conducted on the leg lifting mechanism using analytical methods, and the model data were coupled by Creo Parametric and Automatic Dynamic Analysis of Mechanical System (ADAMS) 2019 software to develop the kinematic model. Then, the motion characteristics during the whole process were studied, and the motion parameter curves were obtained. Next, ABAQUS 2022 software was employed to create the finite element simulation model of the leg lifting device, and key component strength was also analyzed. Finally, a prototype of the device was made and experimentally validated with leg lifting. The results show that in the case of different heights and weights, the lifting angle of the human leg has a significant effect on the force state during the leg lifting process. When the leg is lifted 0–30°, the force on the leg is small. As the leg lifting angle increases, the force on the leg also increases. In the process of leg lifting, the angular velocity and angular acceleration of the leg lifting mechanism change more gently, and there is no obvious mutation. The maximum stress of the driving rod is 102.5 MPa, the maximum stress of the lifting rod is 88.12 MPa, and the maximum stress of the leg placing plate is 40.5 MPa, all of which meet the strength requirements and provide a reference for the research of the human leg stretching device.

The upper limb stretching device plays a key role in enhancing physical function. Current commercial upper limb stretching devices often suffer from limited functionality and are poorly aligned with the biomechanics of the human arm. To address these limitations, this paper presents the design of an ergonomic device for upper limb stretching. Firstly, the development of a regression model for the upper limb force test was carried out through the Box–Behnken Design (BBD) response surface methodology. Secondly, the Denavit-Hartenberg (D-H) method was adopted for the kinematic analysis of the human upper limb stretching mechanism. Subsequently, a kinematic model was established by coupling the data from Creo Parametric and ADAMS models. The kinematic characteristics were then investigated throughout the entire range of motion, yielding the corresponding kinematic parameter curves. Next, the finite element method was employed within ABAQUS to model the upper limb stretching mechanism, to allow for a detailed strength analysis of its key components. Finally, a prototype was manufactured and tested through upper limb stretching experiments to validate its performance. The results demonstrate that the designed stretching mechanism achieved the desired range of motion, with its angular velocity and angular acceleration exhibiting smooth variations. The maximum stress observed is 195.2 MPa, which meets the design requirements. This study provides a valuable reference for the development of future human stretching devices.