Optimization of modal characteristics of a feed system based on joint stiffness modeling

Abstract

The feed system, as a core component of machine tools, has modal characteristics that directly affect machining accuracy and operational stability. However, existing research on modal optimization of feed systems generally suffers from two limitations: the optimization variables rarely involve joint stiffness, and the optimization methods are predominantly based on orthogonal experiments, which are inefficient in handling the complex nonlinear relationship between joint stiffness and natural frequencies. To address these issues, this study approaches the problem from the perspective of joint stiffness and proposes a novel optimization method to improve the modal characteristics of the feed system, thereby reducing the resonance risk caused by an insufficient low-order natural frequency. First, a finite element model of a typical feed system is established and validated through modal experiments, yielding the first five natural frequencies and corresponding mode shapes. Subsequent operating-condition analysis reveals that the maximum screw rotational speed corresponds to an excitation frequency of 88 Hz, while the first-order natural frequency of the current design is only 100.49 Hz. Considering factors such as load fluctuations and environmental disturbances, this narrow safety margin is clearly inadequate and indicates a potential resonance risk. To address this, an improved particle swarm optimization algorithm (IPSO) is proposed. Building upon the standard particle swarm optimization (PSO) framework, IPSO incorporates a Tent map and random solution selection mechanism, nonlinear variation strategies for the inertia weight and learning factors, as well as an orthogonal opposition-based learning mechanism based on lagging individuals and random leaders. The algorithm is compared with classical algorithms (PSO, Genetic algorithm) and recent single-objective optimization algorithms (real-coded genetic algorithm and particle swarm optimization, sine-cosine intelligence algorithm) on seven benchmark functions, and the results demonstrate that IPSO achieves the best convergence performance. On this basis, a neural network model is constructed to capture the complex nonlinear mapping between the key joint stiffness parameters—namely the screw-nut joint, guide rail-slider joint, and bearing joint—and the first-order natural frequency. The IPSO algorithm is then coupled with this neural network surrogate model to perform system parameter optimization. The optimization results show that the first-order natural frequency increases from 100.49 Hz to 114.24 Hz, successfully exceeding the safety threshold and effectively enhancing the resonance resistance of the feed system.