Shock and Vibration

Volume 2016 (2016), Article ID 4028583, 7 pages

http://dx.doi.org/10.1155/2016/4028583

## Nonlinear Model of Vibrating Screen to Determine Permissible Spring Deterioration for Proper Separation

Department of Mechanical Engineering, University of Concepcion, Edmundo Larenas 219, 4070409 Concepcion, Chile

Received 4 March 2016; Revised 2 August 2016; Accepted 8 August 2016

Academic Editor: Samuel da Silva

Copyright © 2016 Cristian G. Rodriguez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Springs of vibrating screens are prone to fatigue induced failure because they operate in a heavy duty environment, with abrasive dust and under heavy cyclic loads. If a spring breaks, the stiffness at supporting positions changes, and therefore the amplitude of motion and the static and dynamic angular inclination of deck motion also change. This change in the amplitude and in the inclination of motion produces a reduction in separation efficiency. Available models are useful to determine motion under nominal operating conditions when angular displacement is not significant. However in practice there is significant angular motion during startup, during shutdown, or under off-design operating conditions. In this article, a two-dimensional three-degree-of-freedom nonlinear model that considers significant angular motion and damping is developed. The proposed model allows the prediction of vibrating screen behavior when there is a reduction in spring stiffness. Making use of this model for an actual vibrating screen in operation in industry has permitted determining a limit for spring’s failure before separation efficiency is affected. This information is of practical value for operation and maintenance staff helping to determine whether or not it is necessary to change springs, and hence optimizing stoppage time.

#### 1. Introduction

Vibrating screens are important machines used to separate granulated ore materials based on particle size. In copper industry, the most used vibrating screens are of linear motion and with horizontal, sloped, or multisloped (banana) screen. Most of vibrating screens in copper industry are supported at four positions of the vibrating screen deck, and at each of these supporting positions there are two or more steel coil springs (depending on vibrating screen size there may be more supporting positions and springs). The springs of vibrating screens are prone to fail due to fatigue because they operate continuously in a heavy duty environment, with abrasive dust and under heavy cyclic loads.

If a spring in one supporting position breaks, then the stiffness of the supporting position decreases. If the stiffness decreases, then the amplitude of motion and the static and dynamic angular inclination of deck motion are expected to change in comparison to those expected at design operating conditions. A change in amplitude motion of 15% could produce a loss of separation efficiency of 5% [1]. A change in the angular inclination of deck motion produces a change in separation efficiency; for example, there are cases where the efficiency is 86% at design operating conditions and for a change of 2° in angle the separation efficiency drops to 55% [2, 3]. Xiao and Tong [4] show a drop of separation efficiency from 55% to 35% with a change of only 1°. The exact loss of efficiency due to amplitude or inclination deviation depends on the specific vibrating screen and the ore material characteristics. In order to ensure separation efficiency, the vibrating screen vendor provides a range of admissible amplitude and angle deviation for deck motion to operate. The proper amplitude and angle are checked during commissioning making measurements with accelerometers located at particular positions of vibrating screen deck.

In order to assure operation under design conditions (at a high separation efficiency), the evaluation of amplitude and angle of inclination due to spring condition would allow limiting spring deterioration. To be able to determine amplitude and angle of inclination due to spring condition from vibration measurements, it is necessary to have a model able to predict how the deck will move when all springs are working at design conditions and how it will move when there is a loss of stiffness due to deteriorated springs.

Models of vibrating screens in literature are focused on separation [4–10], particles motion [11, 12], and failures in deck structure [13, 14]. Regarding vibrating screen motion, He and Liu [15] developed a three-degree-of-freedom linear model of a vibrating screen supported at two positions with equal stiffness for a circular motion vibrating screen. This model assumes stationary motion and a phase relationship between force and vibration of 0° in horizontal and vertical motion. With this assumption, a phase relationship of 90° between horizontal and vertical displacement is imposed, and the movement of vibrating screen center of mass results in an ellipse or a circle with a vertical or horizontal principal axis with no inclination. Liu et al. [16] developed a linear model of a vibrating screen supported in four different positions with different stiffness under a vertical force. This model did not consider the possibility of lateral motion of vibrating screen deck. They simulate supporting positions with loose of stiffness but because of model formulation they obtain a change in amplitude of the vertical displacement of the center of mass but movement could not change its inclination. Liu et al. [17] considered a linear model similar to He and Liu [15] but with a quadruple exciter mechanism. He and Liu [15], Liu et al. [16], and Liu et al. [17] consider no damping in their models. L. I. Slepyan and V. I. Slepyan [18] considered a linear model with damping and a tensile force for a linear motion vibrating screen with equal stiffness in all supporting positions. These linear models assume that angular motion of vibrating screen deck is low ( and ) and are useful for determining motion under nominal operating conditions because angular displacement is not significant but are not able to predict deck motion during the startup, during shutdown, or under off-design operating conditions such as the loss of stiffness in supporting positions. In practice, there is significant angular motion that occurs in vibrating screens during startup, during shutdown, and under off-design operating conditions.

In this article, a two-dimensional three-degree-of-freedom nonlinear model that considers significant angular motion and damping is developed in order to predict and evaluate the vibrating screen motion during startup, during shutdown, and under stationary operation conditions with deteriorated springs. The model simulates different deterioration levels of springs in order to determine its effect on amplitude and inclination of deck motion. The simulation is performed considering empty screen and full load. Empty screen is simulated because, after commissioning, the vibrating screen is tested empty in order to verify adequate amplitude and angle of inclination of motion. Full load is simulated because it is the normal operating condition and it is also the condition where springs operate under higher dynamic forces. With this simulation, it is possible to predict a range for acceptable spring deterioration in order to maintain proper motion to achieve an adequate separation efficiency. Finally, the model is compared with field measurements taken from a vibrating screen in use at a copper mine.

#### 2. The Model

In linear motion vibrating screens, motion is obtained by the action of a linear dynamic force produced by one or more exciter mechanisms. The linear force in the exciter mechanism is obtained by pairs of unbalanced masses mounted in pairs of different shafts that rotate at the same velocity but in different directions. Figure 1 shows a schematic of a vibrating screen with the exciter mechanism at the top of the deck.