The theoretical simulation and the experimental control of the calibration process of the potato tubercles.

Pirna, Ion ; Candea, Ioan ; Popescu, Aurelian 等

1. INTRODUCTION THEORETICAL RESEARCHES

The functional schedule of a calibration machine with sieve band is presented in figure 1, falling into band 1, elliptical rollers 2, drive cylinder 3, rotary brush 4, fixed wheel 5 and the band tension elevation wheel 6.

[FIGURE 1 OMITTED]

The bodies system from figure 1 is a vibration generator named vibrating mass and which assimilate with a mechanic system, which realize in line forced vibrations with amortization. The vibration generating disturbing force has an inertia nature and its expression is:

[F.sub.p] = m[rho][[omega].sup.2] sin [theta] (1)

Theoretically, the calibration machine with sieve band reduces the vibration of a machine with rotating unbalanced masses, which dynamically adapted schedule on present in figure 2.

On consider the band between machine and foundation like an elastic element of constant C, on note the machine mass with M, the eccentric mass with m and the block mass results as being the difference M-m.

[FIGURE 2 OMITTED]

The movement differential equation is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Using the complex variable method, to this differential equation correspond for the oscillatory movement amplitude, the amplitude:

a = m[rho][[omega].sup.2]/[square root of (K - M[[omega].sup.2] + C[[omega].sup.2])] (3)

If K=0 and C=0 result the oscillatory movement amplitude:

[a.sub.0] = m[rho]/M (4)

For practical applications is useful to compare the ratio a/[a.sub.0], which results behind following notations: K/M = [p.sup.2], where p is the vibratory system pulsation, C/M = 2[alpha] and a/p = c/[c.sub.0] is the critical amortization coefficient and [xi] is amortization agent, thus result:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

By analysis of the relation (5) on detect that for [omega]/p=0 ([omega]=0) we do not have vibrations generator and result the system movement amplitude a=0. In this case, the calibration band does not execute oscillatory movement; its movement being an in line transport movement and the potatoes calibration effect is minimum. Also, on realise the potato tubercles calibration only for the potatoes with sizes smaller than the calibration sieve band holes.

For the calibration, precision increase is necessary the ratio a/[a.sub.0] increase which grows in the same time with the ratio [omega]/p increase. As the ratio a/[a.sub.0] is in terms of the ratio [omega]/p and p is given, result that must be determinate the angular speed [omega] of elliptical wheels for which on obtain the calibration imposed of the agro technical requirements for the seed potato tubercles.

If on note the elliptical wheels semi-axis with r and R, then the vibration limits of the angular speed are: [[omega].sub.max] - [v.sub.t]/r and [[omega].sub.min] = [v.sub.t]/R, where [v.sub.t] represent the linear speed of the calibration sieve band.

Another theoretical aspect is when the ratio [omega]/p has small values and in the relation (5) the terms [([omega]/p).sup.2], [([omega]/p).sup.4] may be unlooked towards the unit, in this case result the relation:

a [congruent to] 1/[p.sup.2] [a.sub.0][[omega].sup.2] (6)

In the relation the coefficient 1/[p.sup.2] represent the calibration machine constant, thus, the amplitude depends on the acceleration applied to band, that is the elliptical wheels angular speed [omega].

The kinematics analysis of elliptical wheels, which drive the calibration, determinates the operational chart, which is present in fig. 3. In this way, the calibration band falls into two operational areas: area I between the elliptical wheels, which get the material (the potatoes mixture), and area II between the second elliptical wheel and the drive cylinder. From the kinematical analysis result that a potato tubercle situated on the calibration band has an initial speed oblique towards the band what leads on at the capacity and calibration precision increase.

The action areas on the potatoes, which must be gauged, depend on the montage position of the intermediary elliptical wheel.

[FIGURE 3 OMITTED]

Following the theoretical study results, the ratio between the elliptical wheels semi-axis and the montage position of the intermediary elliptical wheels can be determined. For the experimental researches, we denoted:

V is the transport band speed;

R is the elliptical wheel size;

P is the elliptical wheel montage position.

2. THE EXPERIMENTAL RESEARCHES RESULTS

The experimental researches for two potatoes tubercles varieties, the oval DESIREE variety and the round PROCURA variety are presented. The results obtained are presented in table 1 for the sieve band with holes of 60 mm.

The analysis of data from table 1 for DESIREE variety shows that for the same position of elliptical wheel at speed [V.sub.1-4] there are no relevant differences in the calibration precision. The band speed Vs decrease gets to the very important deterioration of calibration precision.

In the same band speed exposure, the calibration precision does not have an important modification for various montage positions of the elliptical wheel; in the speed [V.sub.5] case, the optimum montage position is the position A.

In the PROCURA variety case on detect that the calibration precision at the same elliptical wheel position has an unimportant change for the speed [V.sub.1-3] and decrease for the speeds [V.sub.4-5].

Regarding for the elliptical wheel montage position for constant speed, on detect very important differences favourable only when on work with [V.sub.4] for the montage position B.

3. CONCLUSION

The potatoes tubercles calibration precision is determined by the calibration of the sieve band kinematics' regime. In addition, the elliptical wheel positions affect the calibration precision at low speeds Vs for the lengthened potatoes tubercles.

4. REFERENCES

Candea, I., s.a. (2003). Mechanics-Dynamics, The Transylvania University Publishing House, Brasov

Mangeron, D. & Irimiciuc, N. (1978, 1980, 1981). The Rigid Mechanics with Applications in Engineering, vol. I, vol. II, vol. III, Technical Publishing House, Bucharest

Popescu, A. (1986). Theoretical and Applicative Researches Regarding the Type and Reliability Index at the Potatoes Calibration Machines, Ph. Thesis, ASAS

Radoi, M. & Deciu, E. (1918). Mechanics, The Didactic and Educational Publishing House, Bucharest

Voinea, R., Voiculescu, D. & Ceausu, V. (1983). Mechanics, The Didactic and Educational Publishing House, Bucharest

Tab. 1. Title of table, left justified, subsequent text indented

 DESIREE

The The The
elliptical sieve elliptical
wheel band wheel The V
size speed position variation
(R) (V) (A) The at R and P
 (B) calibration constant
 (C) precision
 DL5% =0.535
 DL1% =0.728
 DL0.1% =0.979

 DIF S

The 1 B 99.71 0.30 --
elliptical A 99.50 0.04 --
wheel C 99.54 0.00 --

 2 B 99.83 0.42 --
 A 99.45 0.01 --
 C 99.58 0.04 --

 3 B 99.41 [M.sub.1]/B --
 A 99.46 [M.sub.1]/A --
 C 99.54 [M.sub.1]/C --

 4 B 99.29 -0.12 --
 A 99.70 0.24 --
 C 99.66 0.12 --

 5 B 98.20 -1.21 000
 A 99.29 -0.17 --
 C 96.87 -2.67 000

 DESIREE PROCURA

The The
elliptical sieve
wheel band The P
size speed variation
(R) (V) at R and P
 constant

 DL5% =0.446 The
 DL1% =0.596 calibration
 L0.1% =0.784 precision

 DIF S

The 1 0.21 -- 99.79
elliptical [M.sub.1] -- 99.62
wheel 0.04 -- 99.54

 2 0.38 -- 99.83
 [M.sub.1] -- 99.7
 0.13 -- 99.62

 3 0.05 -- 99.37
 [M.sub.1] -- 99.33
 0.08 -- 99.20

 4 -0.41 -- 99.20
 [M.sub.1] -- 98.41
 -0.03 -- 98.75

 5 -1.09 000 98.45
 [M.sub.1] -- 98.75
 -2.42 000 97.37

 PROCURA

The The
elliptical sieve
wheel band The V The P
size speed variation variation
(R) (V) at R and P at R and V
 constant constant

 DL5% =0.454 DL5% =0.443
 DL1% =0.613 DL1% =0.593
 DL0.1% =0.819 DL0.1% =0.779

 DIF S DIF S

The 1 0.42 -- 0.17 --
elliptical 0.29 -- [M.sub.1] --
wheel 0.34 -- -0.08 --

 2 0.46 -- 0.13 --
 0.37 -- [M.sub.1] --
 0.42 -- -0.08 --

 3 [M.sub.1]/B -- 0.04 --
 [M.sub.1]/A -- [M.sub.1] --
 [M.sub.1]/C -- -0.13 --

 4 -0.17 -- 0.79 +++
 -0.92 000 [M.sub.1] --
 -0.45 0 0.34 --

 5 -0.92 000 -0.30 --
 -0.58 0 [M.sub.1] --
 -1.83 000 -0.38 --