基于LM优化算法的无试重动平衡方法

Method for Dynamic Balancing without Trial Weight Based on LM Optimization Algorithm

摘要: 针对传统转子动平衡方法依赖试重实验、需频繁启停机且效率较低的问题，提出一种基于仿真影响系数与Levenberg-Marquardt优化算法相结合的无试重动平衡方法。首先，以砂轮机转子为研究对象，建立双圆盘–双支承转子有限元模型，并通过施加单位不平衡量获取影响系数矩阵，实现仿真替代试重实验。其次，在最小二乘影响系数法基础上引入LM算法，并结合惩罚函数构建带约束优化模型，以提高求解稳定性并满足振动限值要求。最后，通过不同不平衡质量工况下的仿真与实验验证方法有效性。结果表明，该方法可显著降低转子振动响应，在3 g不平衡工况下平衡效率达到87%以上，验证了其良好的稳定性与有效性。

Abstract: Addressing the issues of traditional rotor dynamic balancing methods, which rely on trial weight experiments, require frequent start-ups and shutdowns, and have low efficiency, a no-trial-weight dynamic balancing method based on the combination of simulation influence coefficients and Levenberg-Marquardt optimization algorithm is proposed. Firstly, taking the grinder rotor as the research object, a finite element model of a dual-disc, dual-support rotor is established, and the influence coefficient matrix is obtained by applying a unit unbalance, achieving simulation as a substitute for trial weight experiments. Secondly, based on the least squares influence coefficient method, the LM algorithm is introduced, and a constrained optimization model is constructed in combination with a penalty function to improve the stability of the solution and meet vibration limit requirements. Finally, the effectiveness of the method is verified through simulations and experiments under different unbalanced mass conditions. The results show that this method can significantly reduce the rotor vibration response, achieving a balancing efficiency of over 87% under a 3 g unbalanced condition, verifying its good stability and effectiveness.