A ball mill is a type of complex grinding device. Having knowledge of its charge-load behavior is key to determining the operating conditions that provide the optimum mill throughput. An elaborate description of the charge movement inside the ball mill is essential. This study focuses on a laboratory-scale ball mill and utilizes a discrete element simulation model to investigate the impact of mill speed and ball filling on charge-load behavior. Initially, the EDEM 2.7 (Engineering Discrete Element Method) software contact parameters were calibrated through heap-angle experiments. Subsequently, four charge-motion characteristic parameters were defined and analyzed based on Powell’s theory to understand the variations in charge-load behavior. This research proposes a theoretical calculation model for predicting power in a ball mill, highlighting the significance of the CoC (Center of Circulation) and CoM (Center of Mass) in reflecting changes in charge-load behavior. The theoretical model for mill-power prediction is effective and aligns well with the EDEM simulation and experimental results, providing valuable insights for optimizing large-scale ball mill structures and controlling charge motion during production.

Optical mirrors have high requirements for surface precision, requiring ultra-precision processing. The revolving movement of a computer-controlled optical surfacing (CCOS) grinding system will induce vibrations in a five-degrees-of-freedom hybrid processing robot (5-DOF-HPR) and a flexible support system (FSS) in a large optical mirror processing system (LOMPS). As a result, the mirror surface will vibrate, which will ultimately affect the surface accuracy of the final optical mirror. Therefore, the differential equation representing the vibration of the 5-DOF-HPR is established based on the spatial beam unit, which transforms the generalized coordinates into modal coordinates, thereby removing the coupling terms of the vibration differential under generalized coordinates. At the same time, a dynamic analysis of the CCOS grinding system is performed, and the magnitude and direction of the centrifugal force and reaction force are calculated. Then, the natural frequencies of the 5-DOF-HPR and the FSS are measured experimentally and compared with the simulation results; thus, the accuracy and effectiveness of the model are verified. Finally, the vibration characteristics of the processed optical mirrors under different influencing factors are obtained. A theoretical and experimental basis for parameter optimization and path planning of the LOMPS is provided to improve the surface accuracy of the processed optical mirror.

In large optical mirror processing (LOMP), the robot is required to carry a computer-controlled optical surfacing (CCOS) polishing tool capable of both fully covering the required material removal profile and maintaining sufficient redundancy for process adaptability. The designed LOMP robot is a five-degree-of-freedom (5-DOF) hybrid robot, where the workspace of its parallel mechanism is constrained by dimensional parameters, including the moving platform radius, the fixed/moving platform radius ratio, and link lengths. This paper presents an optimization study of dimensional parameters for robotic systems, aimed at meeting the workspace requirements of 1250 mm-diameter large optical mirrors. First, analytical models of the robot’s effective workspace and driving torque under different dimensional parameters are derived. Subsequently, workspace requirements and driving torque are established as optimization constraints, and a differential evolution algorithm is implemented to determine the optimal dimensional parameters for the LOMP system. To improve computational efficiency, the conventional differential evolution algorithm is enhanced through the integration of adaptive mutation and crossover operators, resulting in a modified adaptive differential evolution algorithm (ADEA) that demonstrates accelerated convergence characteristics while maintaining solution accuracy. Finally, MATLAB simulations demonstrate that the proposed ADEA successfully obtains optimal dimensional parameter combinations while satisfying all specified constraints. Based on the optimal dimensional parameters, an engineering prototype was manufactured. Experimental results verified the accuracy of the optimized design, providing a valuable reference for optimization of dimensional and structural parameters in similar engineering equipment.

The dynamic performance of parallel robots directly determines the machining accuracy in large optical mirror processing (LOMP). However, limitations in traditional dynamic modeling methods hinder their application in real-time control, constraining further improvements in robotic precision. This paper aims to establish a high-precision and practical dynamic model that considers joint friction for parallel robots used in LOMP, and to design an efficient real-time friction compensation control strategy to effectively enhance trajectory tracking and repetitive positioning accuracy. The novelty of this work lies in proposing a dynamic modeling approach that integrates the static mechanics-based “Disassembly Method” with a “Coulomb + Viscous” friction model. First, static analysis of the mechanism is conducted using the “Disassembly Method” to accurately compute the joint constraint reactions in any pose, providing critical input for friction calculation. Subsequently, a complete dynamic model incorporating friction in joints such as Hooke joints, composite spherical hinges, and ball screws is developed based on the Newton–Euler formulation. This method overcomes the shortcomings of traditional approaches in solving joint reactions and managing model complexity. Numerical simulations demonstrate that, compared to conventional friction-neglected models, the proposed model reveals a maximum increase of approximately 350 N in driving chain joint reaction forces and significant peaks in driving forces at motion reversal instants (e.g., 0.28 s, 0.45 s), quantitatively proving that neglecting friction severely underestimates the actual system loads. Experimental validation shows that the feedforward PD friction compensator designed based on this model reduces the rotational tracking errors of the moving platform around the X- and Y-axis from 0.295° and 0.286° to 0.134° and 0.128°, respectively, achieving an error reduction of about 55% and effectively improving motion control accuracy. This study provides a reliable dynamic modeling foundation and an effective real-time control compensation solution to address force output errors and trajectory deviations caused by joint friction in high-precision LOMP.