A new composite vibrating mode is presented in this paper. Modeling and dynamic analysis are studied according to twodegreeoffreedom systems theory. The effects of vibration parameters, including swing angle, swing frequency, vibrating direction angle, and translation frequency, on the screening efficiency were researched by means of experiment research over a new laboratoryscale composite vibrating screen which is designed based on the new composite vibrating mode. The results are analysed in terms of curves and fitting equations. Compared to the translation mode and swing mode, the screening performance of the new composite vibrating mode, both in screening efficiency and in processing capacity, is significantly improved.
The vibrating screens are widely used in industrial activities ranging from mining and construction to pharmaceuticals and food production. Improving the processing capacity and screening efficiency of vibrating screening has always been the areas of research focus and the driving force for growth in the vibrating screen industry. The classical measures—enlarging the screen scale and vibration intensity, which are limited by manufacturing costs and working life—however, cannot meet the growing production demand. Besides the classical measures, many studies regarding innovative types of vibrating screens are published. These latter screens are related to difficult materials and high efficiency. Linear vibrating screens and banana screens are to be mentioned in this category.
Owing to the fact that linear vibrating screens have constant transport velocity and throw index, which are very likely to bring about poor separation, changing throw index for a high screening performance was discussed [
Banana screen, as an innovation, has a series of continuous slopes of the screen surface, so that it can maintain a constant bed thickness when screening [
There are also a few studies regarding the new vibrating mode. Inspired by manual sieving, Xiao and Tong [
In this work, a new composite vibrating mode is first presented. The mode is a composite of both translation and swing, which combines the merits of the two modes. The new mode has been applied to a new laboratoryscale vibrating screen, which is designed to be adjustable for the need of single factor experiments. The effects of vibrating parameters on the screening efficiency are quantitatively researched through a serial of controlled numerical experiments in this new vibrating screen. The detailed comparison of screening performance of the composite mode and the other modes is also made in this work. The results show a better screening performance in the composite vibrating mode, which is helpful to design the industrial composite vibrating screen.
The model of translationswing composite vibrating screen is a typical twodegreeoffreedom vibration system. This kind of vibration system can be regarded as coupling of two single degreeoffreedom vibration systems, and therefore, there have been no essential differences between the two systems in problem description, solving method, and vibration characteristic.
The structural model of the composite vibrating screen is shown in Figure
Structure schematic of the composite vibrating screen. (1) Screen box, (2) isolation devices, (3) inertial vibration exciter, and (4) screen surface.
Inertial vibration exciter, which consists of two vibration motors, is mounted in the middle position of the screen box. When the motors rotate in a synchroreverse way, it can generate the sinusoidal force which leads to a translation motion of the screen.
The two swing excitation forces
When the screen vibrates with the action of the two kinds of exciters simultaneously, motions of the screen will get coupled, that is, a composite vibrating mode.
In principle, twodegreeoffreedom systems require two generalized coordinates to describe the motion. In order to further understand the composite vibrating mode, which consists of the translation mode coupled to the swing mode, the dynamic analyses of translation and swing will be, respectively, given below.
As shown in Figure
Translation dynamic model.
Obviously, screen’s simple harmonic motion along the vibration direction leads to
Realizing
As shown in Figure
Translation dynamic model.
Thus, the translationswing composite vibration can be obtained when the two vibration modes get coupled using the above method.
There are three kinds of motion of the particle on the screen surface: static, sliding, and throwing, each of which greatly affects screening processes. So much of these motions depend on force of the screen surface acting on particles. Consider the force of the screen surface acting on a single particle shown in Figure
Force analysis diagram of a single particle on the screen surface.
Applying Newton’s second law to the particle,
Recalling that
Substituting Equations (
Thus, the force analysis of the particle under the composite vibration mode is determined by deriving Equation (
Applying the above analysis of the composite vibration mode, a translationswing composite vibrating screen was constructed that allowed precise control of the vibration parameters, combined with the ability to accurately measure the amount and size distribution of particles through the screen. A photo of the composite vibrating screen and a schematic diagram of the CAD geometry are shown in Figure
Photo of the composite vibrating screen (a) and schematic showing the CAD model (b). (1) Vibration motor, (2) screen surface, (3) screen box, (4) translation isolation springs, (5) composite isolation springs, (6) electromagnetic vibration exciters, (7) support frame, (8) base frame, (9) collection bin, (10) vibration motors mounting frame, and (11) vibration motors [
Particles with a density of 2678 kg/m^{3} were used in the experiment. Images of the rock particles are shown in Figure
A sample of rock particles used in the experiment.
The size of distributions of feed particles for each experiment.
Size (mm) 

0.7–0.8  0.8–0.9 


Mass (g)  150  70  50  30 
Total mass (g)  300 
The experiment initial conditions are listed in Table
Summary of experiment initial conditions [
Aperture size (mm)  0.9 
Wire diameter (mm)  0.4 
Translation amplitude (mm)  2 
Swing frequency (Hz)  8 
Inclination angle (°)  30 
Translation frequency (Hz)  11 
Angle of the vibrating direction (°)  45 
Swing angle (°)  0.68 
When an experiment began, the feed particles continuously fell under gravity to hit the screen surface. Then, the particles were either captured in a collection bin placed under the screen surface or in the overflow bin at the end of the screen. The size distributions of the particles collected in the overflow bin were also determined in the way that was used to determine the feed size distribution. Then, the data from the size distributions can be used to calculate screening efficiency.
The screening efficiency here is defined by
The screening efficiency of particles of separation size 0.8 mm at swing angles ranging from 0.5° to 1.1° is calculated according to a series of experiments, which yield the curve shown in Figure
Screening efficiency at different swing angles.
Meanwhile, the experiment data are fitted with the following equation:
The coefficients and error of Equation (
Separation size 




Adj. 

0.8 mm  0.11979  0.29507  3.57059  59.21374  0.98187 
Effect of the swing frequency is also studied. Figure
Screening efficiency at different swing frequencies.
The experiment data of swing frequency are fitted with the following equation:
The coefficients and error of Equation (
Separation size 




Adj. 

0.8 mm  10.07477  1.10777  15.61996  58.62234  0.96559 
Effect of the vibration direction angle is shown in Figure
Screening efficiency at different vibration direction angles.
The experiment data of the vibration direction angle are fitted with the following equation:
The coefficients and error of Equation (
Separation size 




Adj. 

0.8 mm  52.21302  13.22476  370.50157  44.73626  0.92792 
Effect of translation frequency is studied as part of the present work, as shown in Figure
Screening efficiency at different translation frequencies.
The experiment data of the translation swing are fitted with the equation:
The coefficients and error of Equation (
Separation size 




Adj. 

0.8 mm  587.391  −143.242  12.460  −0.348  0.96706 
This part redefined the comprehensive screening performance. The ratio of screening efficiency to screening time is defined as screening efficiency per unit time. Screening time indicates screening capacity. The shorter the screening time of the same batch of materials, the better the screening capacity. For the translation mode and swing mode, the effects of vibration parameters on screening efficiency are also studied through a series of experiment research under the same initial conditions as the composite vibrating mode. The optimal vibration parameters for each vibration mode are obtained, as shown in Table
The optimal vibration parameters for three vibration modes.
Vibration mode  Swing angle (°)  Swing frequency (Hz)  Translation amplitude (mm)  Translation frequency (Hz)  Vibration direction angle (°) 

Translation mode  —  —  2  16.5  45 
Swing mode  1.1  9  —  —  — 
Composite vibration mode  0.84  8  2  12  45 
Comparison of the screening performance under the translation mode, swing mode, and composite vibrating mode.
Vibrating mode  Screening time (s)  Screening efficiency (%)  Screening efficiency per unit time (%/s) 

Translation mode  11.32  69.55  5.949 
Swing mode  12.57  85.17  6.775 
Composite vibrating mode  11.60  89.81  7.742 
It can be seen that the screening efficiency of the composite vibrating mode is the best among them, considering its screening time is the second least just slightly after that of the translation mode, and hence, the composite vibrating mode has the best overall screening performance, as shown in screening efficiency per unit time. It should be noted that accumulation of particles occurs around the center of the screen surface for the swing mode; this is because the amplitude of vibration decreases to almost zero from the end of the screen to the center of the screen, which is reasonably in accordance with the theoretical analysis. This result clearly shows that the translationswing composite vibrating mode will be a creative exploration in the research field of vibrating and screening.
A new translationswing composite screen has been proposed. The effects of vibration parameters of the new composite vibrating screen on screening efficiency have been studied by means of single factor experiment research. The following conclusions can be drawn from this work:
Design and dynamic analysis of the new composite vibrating screen based on twodegreeoffreedom system theory are proved viable. The constructed laboratoryscale composite vibrating screen performs well in meeting requirements.
The fitting functions built depending on the experiment data based on the new composite vibrating screen show that each of optimal vibration parameters, including swing angle, swing frequency, vibration direction angle, and translation frequency, can be obtained. These optimal parameters can guide the industrial production.
Compared to the translation mode and swing mode, the translationswing composite vibrating mode yields better screening performance, both in screening efficiency and in capacity.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest to this work.
The authors gratefully acknowledge the support from the Program for Scientific and Technological Innovation Flats of Fujian Province (2014H2002), Key Projects of Fujian Provincial Youth Natural Fund (JZ160460), Fujian Natural Science Foundation (2017J01675), and 51st Scientific Research Fund Program of Fujian University of Technology (GYZ160139).