A Theoretical Rigid Body Model of Vibrating Screen for Spring Failure Diagnosis

mathematics Article A Theoretical Rigid Body Model of Vibrating Screen for Spring Failure Diagnosis Yue Liu 1, * , Shuangfu Suo 1, *, Guoying Meng 2, *, Deyong Shang 2 , Long Bai 3 and Jianwen Shi 1 1 2 3 * Department of Mechanical Engineering, State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China; School of Mechanical Electronic & Information Engineering, China University of Mining & Technology-Beijing, Beijing 10083, China; Mechanical & Electrical Engineering School, Beijing Information Science & Technology University, Beijing 100192, China; Correspondence: (Y.L.); (S.S.); (G.M.) Received: 7 January 2019; Accepted: 5 March 2019; Published: 9 March 2019



 Abstract: Springs are critical components in mining vibrating screen elastic supports. However, long-term alternating loads are likely to lead to spring failures, likely resulting in structural damages to the vibrating screen and resulting in a lower separation efficiency. Proper dynamic models provide a basis for spring failure diagnosis. In this paper, a six-degree-of-freedom theoretical rigid body model of a mining vibrating screen is proposed, and a dynamic equation is established in order to explore the dynamic characteristics. Numerical simulations, based on the Newmark-β algorithm, are carried out, and the results indicate that the model proposed is suitable for revealing the dynamic characteristics of the mining vibrating screen. Meanwhile, the mining vibrating screen amplitudes change with the spring failures. Therefore, six types of spring failure are selected for simulations, and the results indicate that the spring failures lead to an amplitude change for the four elastic support points in the x, y, and z directions, where the changes depend on certain spring failures. Hence, the key to spring failure diagnosis lies in obtaining the amplitude change rules, which can reveal particular spring failures. The conclusions provide a theoretical basis for further study and experiments in spring failure diagnosis for a mining vibrating screen. Keywords: mining vibrating screen; theoretical rigid body model; spring failures diagnosis; amplitudes change 1. Introduction Mining vibrating screens are important equipment for mine washing and processing, and are widely used for mine grading, dehydration, and desliming in China [1,2], working as a forced vibration system under alternating loads [3–5]. The SLK3661W double-deck linear mining vibrating screen is shown in Figure 1, and its main structures include a screen box and four elastic supports, designed using principles of symmetry. As shown in Figure 2, the screen box is assembled from an exciter, a lateral plate, an exciting beam, reinforcing beams, upper-bearing beams, under-bearing beams, an upper-screen deck, and an under-screen deck. Additionally, each elastic support is composed of several metal helical springs. These springs are critical components in a mining vibrating screen’s elastic supports, which directly affect the working performance of the mining vibrating screen [6,7]. However, long-term alternating loads are highly likely to lead to spring failure through spring stiffness decrease [8], causing a negative influence on the mining vibrating screen. On one hand, spring Mathematics 2019, 7, 246; doi:10.3390/math7030246 www.mdpi.com/journal/mathematics Mathematics 2019, 7, 246 Mathematics 2019, 7, x Mathematics 2019, 7, x 2 of 16 2 of 17 2 of 17 cracks [9–11]. [9–11]. On the other hand,damages, spring failures failures could produce loss of particle particle separation efficiency, failures could On lead toother structural such as beam fractureaa or lateral plate separation cracks [9–11]. On the cracks the hand, spring could produce loss of efficiency, thus hardly meeting practical process demands [12,13]. Therefore, it is necessary to diagnose the other hand, spring failures could produce a loss of particle separation efficiency, thus hardly meeting thus hardly meeting practical process demands [12,13]. Therefore, it is necessary to diagnose the spring failures of a mining vibrating screen for routing maintenance, which can help to ensure safety practical process Therefore, it is necessary to diagnose the spring failures of a mining spring failures ofdemands a mining[12,13]. vibrating screen for routing maintenance, which can help to ensure safety and reliability. vibrating screen for routing maintenance, which can help to ensure safety and reliability. and reliability. Figure 1. The SLK3661W double-deck linear mining vibrating screen, unloading side view. Figure Figure 1. 1. The The SLK3661W SLK3661W double-deck double-deck linear linear mining mining vibrating screen, unloading side view. Exciting beam Exciting beam Lateral plate Lateral plate Loading side Loading side Upper screen deck Upper screen deck Spring(×3) Spring(×3) Under screen deck Under screen deck Exciter Exciter Reinforcing beam（×2） Reinforcing beam（×2） Unloading side Unloading side Upper bearing Upper bearing beam (×6) beam (×6) Spring (×4) Spring (×4) Under bearing Under bearing beam(×6) beam(×6) Structures of the SLK3661W double-deck linear mining mining vibrating screen. screen. Figure 2. 2. Structures Figure of the SLK3661W double-deck linear mining vibrating vibrating screen. Proper In recent Proper dynamic dynamic models models provide provide aaa basis basis for for diagnosing diagnosing spring spring failures. failures. In In recent recent years, years, even even Proper dynamic models provide basis for diagnosing spring failures. years, even though many studies have reported vibrating screen dynamic models on optimization [14–16], though many studies have reported vibrating screen dynamic models on optimization [14–16], separation [17,18], and particle motion [19], there has been very little research research reported reported on on spring spring separation [17,18], and particle motion [19], there has been very little research reported on spring failure diagnosis. Aimed at spring failure diagnosis, Rodriguez et al. developed a two-dimensional, diagnosis. failure diagnosis. Aimed at spring failure diagnosis, Rodriguez et al. developed a two-dimensional, three-degree-of-freedom nonlinear model that considered one angular motion and damping, damping, which which three-degree-of-freedom nonlinear model that considered one angular motion and damping, which allowed for for the theprediction predictionofofthe the behavior of a vibrating screen when there was a reduction in behavior of of aa vibrating vibrating screen screen when when there there was was aa reduction reduction in in spring spring allowed for the prediction of the behavior spring stiffness, and they used thistomodel to determine limit on springbefore failures before separation stiffness, and they they used this model determine limit on onaspring spring failures separation efficiency stiffness, and used this model to determine aa limit failures before separ (...truncated)