Xiao Linjing, Yan Fangping, Lu Hao
Department of Electrical and Information, Shandong University of Science and Technology, Jinan, 250031, Shandong Province, China.
College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao, 266590, China.
Heliyon. 2024 Jul 23;10(15):e35017. doi: 10.1016/j.heliyon.2024.e35017. eCollection 2024 Aug 15.
Cross beam fracture is one of the common failures of vibrating screens, and crack is the early manifestation of fracture, which is hard to detect. In order to meet the screening requirement of the vibrating screen and improve the service life of the cracked beam, the cracked Euler-Bernoulli beam model is established to investigate the dynamics of the cross beam with a straight crack under different weights of eccentric block, processing capacities, and Rayleigh damping coefficients based on the finite element method in this paper. The local flexibility coefficients are derived from the principles of fracture mechanics and strain release energy and solved by the adaptive five-point Gaussian Legende algorithm. The stiffness matrix of the cracked beam element is calculated through the inverse method of total flexibility. The four order Runge-Kutta algorithm and MATLAB tools are used to solve the dynamic equation of the cracked cross beam. The relationship between the vibration amplitude of the cracked cross beam and the weight of the eccentric block is studied by fitting formulas using the least squares method. The influence of different weights of eccentric block, processing capacities, and Rayleigh damping coefficients on the vibration amplitude and service life of the cracked beam are discussed. The results show that the greater the weight of the eccentric block, the shorter service life of the beam. When the damping is greater, the service life of the cracked beam is longer.
横梁断裂是振动筛常见故障之一，裂纹是断裂的早期表现，难以检测。为满足振动筛的筛分要求并提高裂纹梁的使用寿命，本文基于有限元法建立裂纹欧拉 - 伯努利梁模型，研究不同偏心块重量、处理能力和瑞利阻尼系数下含直裂纹横梁的动力学特性。局部柔度系数由断裂力学原理和应变释放能导出，并采用自适应五点高斯勒让德算法求解。通过总柔度的逆方法计算裂纹梁单元的刚度矩阵。利用四阶龙格 - 库塔算法和MATLAB工具求解裂纹横梁的动力学方程。采用最小二乘法拟合公式研究裂纹横梁振动幅度与偏心块重量之间的关系。讨论了不同偏心块重量、处理能力和瑞利阻尼系数对裂纹梁振动幅度和使用寿命的影响。结果表明，偏心块重量越大，梁的使用寿命越短。阻尼越大，裂纹梁的使用寿命越长。
