Dynamics of a cross beam with a straight crack in a mining linear vibrating screen

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.