Analysis of oscillatory conveyor separator.

Abrudan, Gheorghe ; Rus, Alexandru ; Vesselenyi, Tiberiu 等

1. INTRODUCTION

Pea harvesting can be quite difficult and time-consuming. Two key components the producer must consider are: knowing when to harvest, and taking steps to ensure that the peas are the best quality possible to obtain a high grade. The first component is beyond the purpose of this article. The second point, which consists of many steps itself, incorporates the goal of this paper: to provide a better understanding of the sorting process and provide technical solutions for the development of the optimal separation process to minimize the damage and percent of impurities in the final product.

A good understanding of the way the product is processed and transported through a combine harvester is not so easy. Every section of the machine has its own impact on the flow depending on geometrical dimensions and crop properties (Maertens et al., 2001). Some work has already been performed on these individual machine parts (Danila & Neculaiasa, 1987; Neculaiasa & Danila, 1995). This study will look at all the parameters that affect the sorting process, determine the pea bean movement on the conveyer belt and optimize the drums geometry, kinematic and dynamic parameters. The mathematical and simulation models developed in this paper could be easily modified to suite other type of products, not just peas. Finally, the analysis of the effect of the optimal sorting process, from a structural point of view, will be a topic of future study.

2. DEVELOPING THE MATHEMATICAL MODEL

2.1 Purpose of the functional forming operation of the peas sorting machine

In order to analyze the operation of the peas sorting machine, considering the vibrations generated by the belt conveyor, it would be useful to develop its mathematical model. The mathematical design is the basis for the generation of the program simulating the operation of the machine. This way, with the help of simulations, different operating states and vibrations generated for different values of the working parameters can be studied (Maertens et al., 2001). The operation of the belt conveyor implies a dynamic and not geometrical analysis (as the drums of the conveyor are not cylindrical), that is necessary for the process of peas sorting.

The complete elimination of vibrations and shocks is not possible, because of the fact that the sorting process itself is based on this kind of operation (Brindeu, 2001).

2.2 Rotation speed of conveyor idle drum.

The pea sorting machine's transporting belt is different from a conventional transporting belt because it carries out an oscillating movement and, at the same time, it moves forward in the direction given by the rotation of the drums (Abrudan, 2007).

The oscillating movement is due to the fact that the drums do not have a cylindrical shape, but consist of bars that make up the edges of prisms with polygonal bases. Currently, in the practical construction, three sided polygons are used as bases for the driving drum, and four sided ones for the idle drum. The difference between the numbers of sides for the two drums generates a specific oscillating movement that allows the sorting of pea beams from the pods and other impurities. The necessary elements for calculating the speed of the idle drum is given in Fig 1. The formula of the angular speed of the idle drum is:

[[omega].sub.b] = [r.sub.a] sin([alpha] + [gamma])/[r.sub.b] sin([beta] + [gamma]) [[omega].sub.a] (1)

The above formula (1) is the basis for simulating the movement of point B with respect to the movement of point A. The formulas are defined on time intervals with a continuous variation. Meanwhile, the simulation programs can be conceived only for a discrete variation of the parameters. This is the reason why the calculation formulas defined above have to be converted.

[FIGURE 1 OMITTED]

2.3 Determination of forces that influence the bearings of the idle drum

The forces, generated by the oscillating movement of the sorting belt, are transmitted to the frame of the machine through the bearings of the drums in Fig. 1, at points [O.sub.A] and [O.sub.B]. During the simulation program, the force acting on the bearing of the driving drum (point [O.sub.A]) is calculated; this has an oscillating character and can play the part of an excitation force exerted on the frame of the machine generating vibrations, Fig.2, (Abrudan, 2007).

[FIGURE 2 OMITTED]

The resistance force ([F.sub.r]) has two major components, the stretching force of the belt which is due to its weight ([F.sub.Gb]) and the stretching force that is due to the torque of friction in the idle bearing ([F.sub.fB]). After a few substitutions, the resistance force becomes:

[F.sub.r] = [M.sub.fb=B]/[r.sub.b]cos[gamma] + G sin ([theta] - [gamma]) (2)

The simulation results are compared with experimental data to validate the simulation program.

2.4 Determination of the magnitude and direction of the pea's speed after the impact with the sorting belt

The simulation program accomplishes the calculation of the trajectory of the pea after the impact with the transporting belt. It is considered that the pea starts from a point above the belt, with the coordinates [X.sub.ma0] and [Y.sub.ma0] and has a uniformly accelerated movement until the moment of its first impact with the transporting belt. The position of the pea ([X.sub.ma0], [Y.sub.ma0]) and its speed have to be calculated for each cycle of the simulation program (Abrudan, 2007). Also, the distance between the pea and the points A and B (Fig.1), is being tested in every cycle. If the sum of the distances to the points A and B is close to the distance between the points A and B that means that the pea is near the contact point. Next, the proximity of the pea to the sorting belt is tested, so that the following impact can be detected, using the same formulas as for the first impact. Previous to every impact, the components of the pea's velocity are updated and the iteration is continued.

2.5. Determination of the relationship between the movements of the sorting belt and the pea

In order to achieve the results of the real time working of the sorting belt, a correlation has to be established between the step size used in the simulation program and the real time. The size through which this correlation takes place is given by the number of simulation cycles that correspond to a second of real time working of the belt.

N = 2[pi] n/60 / [DELTA][alpha] (3)

Where n is the revolution of the driving drum in rotations/minute, and [DELTA][alpha] is the angle that this drum turns for one of the simulating program's cycle. The real time is calculated ([DELTA]t), in seconds, which corresponds to a cycle in the simulating program, is inverse proportional to N. Using this correlation, the speeds and accelerations that characterize the movement of the belt and the pea can be calculated.

3. THE SIMULATION RESULTS

After running the simulation program, different diagrams were obtained that were used to analyze the mechanics of the sorting belt and detect the critical operating states.

[FIGURE 3 OMITTED]

Analyzing the pea trajectory for different parameters of the simulation (the revolution of the idle drum, the drums' number of bars, different coefficients of return), the mathematical values of these parameters, for which the sorting reaches its optimal level, can be found. A result of the pea's trajectory simulation is presented, in the case of a 3-bar driving drum and 4-bar idle drum, Fig 3. Simulations have been carried out for revolutions of the driving drum from 16 to 38 rotations/minute and for return coefficients of 0.05; 0.15, respectively 0.25.

4. CONCLUSIONS

As a result of this study, with the evolution of the kinetic and dynamic parameters of the separating belt on the pea's trajectory in mind, it has been concluded that: generally, once the number of revolutions increases, the number of collisions between the pea and the belt decrease slightly; concerning the influence of the restoration coefficient on the trajectory, it has been established that for higher values of the restoration coefficients, the number of collisions between the pea and the belt decreases. The pods, impurities, vegetal remainders, which have a low restoration coefficient and implicitly a high number of collisions, will be forwarded by the belt in its upper side; the number of bars of the drum is directly proportional to the acceleration of the separating belt and implicit to the belt's oscillations' amplitudes. Even though this study offers several important findings, there are some limitations to it. First, the transporting belt has not been realistically modelled. Also, a greater number of sensors used, at more locations, would have provided a more accurate description of the process when matched with the simulation program. Finally, the analysis of the effect of the optimal sorting process, from a structural point of view, will all be a topic of future study.

5. REFERENCES

Abrudan, G., (2007). The Dynamics of the Oscillating Belt Conveyer, Issue "Polytechnic", Timisoara, pages 60-65.

Brindeu L(2001). Vibrations and Vibro-percussions. Basic Mechanical Vibrations and Vibro-Percussions, Issue Polytechnic, Timisoara

Danila, I.; Neculaiasa, V. (1987). Agricultural Harvesting Machinery, vol. III, Timisoara Polytechnic Institute.

Maertens, K.; De Baerdemaeker J.; Ramon H.; De Keyser R. (2001): An Analytical Grain Flow Model for a Combine Harvester, Part II: Analysis and Application of the Model Journal of Agricultural Engineering Research, Volume 79, Issue 2, June 2001, Page. 187-193.

Neculaiasa, V.; Danila, I. (1995). The Working Process and Agricultural Harvesting Machinery, Issue A92, Iasi.