Shock and Vibration

Volume 2015, Article ID 247193, 7 pages

http://dx.doi.org/10.1155/2015/247193

## Similarity Analysis between Scale Model and Prototype of Large Vibrating Screen

College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061, China

Received 6 February 2015; Revised 31 May 2015; Accepted 1 June 2015

Academic Editor: Tai Thai

Copyright © 2015 Zerong Zhang 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

In order to predict the physical characteristics of the large vibrating screen from its scale-down model, the similarity ratios of the frequency response functions, mode shapes, and dynamic stresses between the prototype and the scale model screen are built according to the similarity theory. The natural frequencies and modal shapes are extracted from the frequency response function by means of modal tests, in which the relative error of the natural frequencies is less than 9% and the modal shapes are consistent between the prototype and the model. The operating condition parameters including dynamic stress, displacement, velocity, and acceleration were also measured and conform to the similarity criteria. The results show that the inherent and operating condition parameters of the large vibrating screen can be obtained from the scale-down model conveniently, which provides an effective method for structural optimization and substructure coupling analysis of the large vibrating screen.

#### 1. Introduction

Large vibrating screens are widely used for sieving and dewatering in mining, metallurgy, and chemical industry. The screen acceleration, frequency, and amplitude affect the separation efficiency and the fatigue life of the vibrating screen; thus, an optimization design should be done for the vibrating screen [1]. For novel large vibrating screen, making prototype will increase the research costs and the test cannot be performed easily and effectively because of the severe operating conditions [2]. Therefore, according to the principle of similarity using scale-down model is an essential method for structural dynamic analysis and optimal design [3]. Rezaeepazhand and Simitses [4] have established a scale model for predicting the free vibration and buckling of laminated shell. Wu et al. [5] have presented the scaling laws for the prediction of the vibration characteristics of a full size crane structure from those of a scale model by means of the similitude theory. Lin et al. [6] have analyzed the influence of pile modulus similarity ratio and geometry similarity ratio on the piles similarity of deflection behavior between model and prototype piles. De Rosa et al. [7] proposed a similitude for the analysis of the dynamic response of acoustoelastic assemblies. The objective of this paper is to predict the physical characteristics of a full size large linear vibrating screen by means of a scale-down model screen.

#### 2. The Similarity Analysis of Modal Parameters between Scale Model and the Prototype

##### 2.1. The Similarity Derivation of Modal Parameters of the Large Vibrating Screen

According to the similarity theory [8, 9], the prototype and scale model need to meet the following similarity criteria: geometry similarity, stress-strain similarity, mass and the gravity similarity, and the initial conditions and boundary conditions similarity. When only studying the inherent characteristics of the vibrating screen structure, the inertial force and the elastic restoring force need to obey the similitude rules. The gravity has less effect on the natural vibration characteristics; thus, its similar requirements could be ignored [10–12].

The free vibration equation of the prototype of the large vibrating screen is

The subscripts and represent the prototype and the scale model, respectively, and if we define , , , , , and as similarity ratio of mass, density, length, displacement, time, and modulus of elasticity between the vibrating screen prototype and model, respectively, then (1) can be rewritten as

Then, the similarity ratio of the natural frequency can be derived:

The similarity ratio of the frequency response function can be deduced as follows:

The similarity ratio of the mode shape is

The scale factor of the mode shape is a constant ratio when the material and size of the vibrating screen have been confirmed. Since the mode shape is the amplitude ratio of each point, if each of the mode shapes of the prototype and model is standardized at the same location, then

According to the expression of the frequency response function,

When ,Then, we obtained

Thus, the similarity ratio of the modal mass can be derived:The similarity ratio of the modal stiffness can be deduced as follows:According to the viscous damping theory,With the similarity theory, (12) can be rewritten as

Then, the similarity ratio of the modal damping can be derived:

According to the similarity ratios of the modal parameters derived from the above, the similar relations of the modal parameters of the large vibrating screen were calculated and listed in Table 1 when the 1 : 5 similar test model and the prototype both are manufactured using the same material of mild carbon steel.