Optimization of preloading sequence of anchor bolts based on constraint analysis and PSO-GA algorithm

Reasonable assembly is crucial for reducing dynamic motion errors and enhancing the structural stability of large computer numerical control (CNC) machine tools. During the assembly of the machine bed, anchor bolts must be tightened with uniform preloads to improve the contact performance between the machine tool and its foundation. However, the uniformity of the preload on the anchor bolts greatly depends on the preloading sequence. An improper preloading sequence can lead to a reduction in the contact performance between the machine bed and the foundation. This paper proposes an optimization method for the preloading sequence of anchor bolts based on constraint analysis and a hybrid particle swarm optimization-genetic algorithm (PSO-GA). By analyzing the impact of local deformation of the machine bed on the contact state between the machine bed and the foundation, a constraint model for the preloading sequence of anchor bolts is developed to avoid inappropriate preload sequences, ensuring a fully contact state between the machine bed and foundation. A measurement strategy for the elastic interaction coefficients is introduced to predict the residual preload distribution of anchor bolts in any generated preloading sequence. Furthermore, to optimize the preloading sequence, a combination of particle swarm optimization (PSO) and genetic algorithm (GA) is employed. Updates to the position of swarm particles, including strategies for adjusting the position and velocity of exchanged dimensions, are also proposed. Finally, a preloading experiment is designed and conducted, involving three preloading sequences: the optimized sequence obtained by the proposed method and two sequences previously used by machine tool manufacturers. After measuring the residual preload, the results show that the proposed method reduces the standard deviation of the residual preload to 5.4 kN, which is approximately one-third and one-fifth of the values achieved by the two conventional sequences, respectively. This quantitative improvement demonstrates that the method effectively optimizes the preloading sequence for enhanced preload uniformity.