PM—Power and Machinery

Biosystems Engineering (2002) 82 (4), 393–406 doi:10.1006/bioe.2002.0090, available online at http://www.idealibrary.com on PM}Power and Machinery

A System with Potentiometric Transducers to Record Spray Boom Movements under Operating Conditions D. Pochi; D. Vannucci Agricultural Mechanisation Research Institute (ISMA), Ministry of the Agricultural Politics, Via della Pascolare, 16-00016 Monterotondo, Rome, Italy; e-mail of corresponding author: [email protected] (Received 24 February 2000; accepted in revised form 22 April 2002)

A test with the use of potentiometric transducers, was developed to investigate boom sprayers movements. The system was able to accurately record the movement of two points of a boom. The data processing procedure separated the movement into three vectorial components, calculated the velocity and acceleration of the inspected points and analysed these data to provide useful information, such as changes in position and velocity when evaluating boom sprayer stability. The system was combined with equipment for use on boom sprayers in operating conditions (test track or field), and to be easily dismantled, transported and reassembled in the place of the test. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved 1. Introduction Recently, research has been conducted in Europe (SPECS, 1998) to develop new methodologies to study boom sprayer movements under laboratory and field conditions. As a result of this research, one of these methodologies has been developed at the Agricultural Mechanisation Research Institute (ISMA), that took part in the project. This methodology is based on a system of potentiometric transducers described in detail by Pochi and Vannucci (2001) with the laboratory test to verify its accuracy and capability to record boom movements. The same system was tested on a boom under operating conditions and the results of the test on a track are reported in this paper. The movement data were processed to calculate some parameters, such as the over- and under-sprayed areas, that could be useful in the evaluation of boom sprayer stability.

2. Literature review The investigation of boom movements can be done, adopting various instruments, under controlled conditions. Different systems have been developed that are capable of shaking the tractor–boom system with controlled excitations (CEMAGREF-Montpellier, France; BBA-Braunschweig, Germany; KUL-Leuven, 1537-5110/02/$35.00

Belgium); mathematical models have been constructed, in order to predict the behaviour of the booms undergoing known excitations (Clijmans & Ramon, 1997; Clijmans et al., 1997; De Baerdemaker et al., 1983). These methods provided good results, but are, often, too sophisticated and expensive for large-scale inspection on boom movements. For such investigations, a moveable equipment should be more suitable and useful, allowing tests of boom sprayers under operating conditions (Sinfort et al., 1998; Lebeau & Destain, 1998; Fedrizzi et al., 1995; Vannucci et al., 1996).

3. Purpose This work would be a contribution to the investigation on the movements of boom sprayers in field conditions through the proposal of a system based on potentiometric transducers. The laboratory tests (Pochi & Vannucci, 2000) gave good results as regards its accuracy and reliability in recording the movement data, calculating the three vectorial components. The objective of this paper was to describe how such a system functions when applied to a boom in field conditions, reporting the results of the tests carried out on a test track and of the data processing. For this purpose, it has been necessary to develop and test equipment that supports the transducers and follows the boom during its movement, without being affected by 393

# 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved

394

D. POCHI; D. VANNUCCI

soil unevenness, so that the collected information would refer only to the boom movement with respect to the soil surface.

4. Materials and methods The system consisted of two groups of potentiometric transducers. Each group was connected to the boom and comprised of one wire transducer and two angular transducers. The combination of data resulting from the variation of the angles and the length of the wire was used to calculate the three spatial components of movement from each point. The system arrangement and the calculation of the three components of movement were the same as those adopted in the laboratory tests (Pochi & Vannucci, 2001). The main characteristics of the transducers are reported in Table 1. They are not sensibly affected by environmental conditions (except for rain) and do not need any calibration. The data were recorded at a frequency of 20 acquisitions per second and per channel (six analogu channels were utilized). In the data processing, the variations of the electric signals are converted into length or angle variations. The initial position is automatically assumed as 0 and the diagrams of the movements show their behaviour around 0. The system was tested on booms under operating conditions on rectilinear tracks in order to verify its reliability and capability to monitor their movements. The first problem was to make the sensors move at the same velocity as the tractor, to avoid them being affected because of the shocks through uneven soil. Only in this way can the sensors measure the movements of the boom with reference to the ground. For that purpose, a trolley has been developed running on rail tracks. It is schematically described in Fig. 1. The rectilinear rails are composed of 3 m long modular elements (in aluminium), connected with each other, allowing increases in length (now 27 m ). The rail track can be easily dismantled and reassembled to move it to the test place (test-track or field). It is a perfectly smooth surface on which the trolley (with splined wheels) runs, supporting the sensors. The trolley is connected to the lower part of the frame of the tractor to avoid the transmission of any impulses through bumps

(it has been observed that when the rear wheel of the tractor crosses a 5 cm high bump with a slope angle of 458, the trolley is pushed forward only by 10 mm). There is a horizontal bar under the boom which is exactly parallel and is fixed to the centre of the trolley. It supports the sensors on both sides. The dimensions of the different components of the system are reported in Table 2. Since there were two groups of sensors, they were used in two ways: (1) The groups of sensors were installed on each side of the boom (symmetrically), on both ends of the lower bar to record the behaviour of the two sides under the same conditions. (2) Both groups of sensors were installed on the same side of the boom (near a joint and on the end of the boom), so it was possible to observe the behaviour all along the arm. They were placed at the end of the bar. To reach the end of the boom, one of them has been inclined and connected to a light, thin wire (of high tensile strength) to lengthen the wire of the transducer. A data acquisition system and a notebook for the data processing were placed on the trolley. When using the equipment described above, it is very important to set the tractor in the correct position before the beginning of the test: its longitudinal axis must correspond to the longitudinal axis of the rail track; the bar with the sensors must be exactly parallel under the boom (the wires of the transducers must be vertical); in this way, it is possible to calculate the horizontal (X-axis), transversal (Y-axis) and vertical (Zaxis) components of boom movements with reference to the relative position of the bar considered as zero. During the test, the tractor should be steered as straight as possible. The equipment can only be used on rectilinear trajectories. Some preliminary tests were done to check the stability of the bar during the displacement of the tractor–boom system. To this purpose a second rail track was built similar and parallel to the first one. The trolley on this second rail track was pulled by the other trolley on the first rail track as they were connected rigidly. One group of the transducers was placed on the

Table 1 Main characteristics of the potentiometric transducers and of the data acquisition system Transducer type Wire Angular

Max. wire length mm

Max. angular velocity deg s
1

Linearity, %

Electrical signal range mV

Max. wire speed m s
1

Re-winding spring N

Temp. range 8C

1320 }

} 3000

001 005

0–5000 0–5000

76 }

392 }


40/+90
55/+90

A SYSTEM WITH POTENTIOMETRIC TRANSDUCERS

395

Fig. 1. Scheme representing the equipment and its use: (a) side view with the dotted drawing representing the tractor–boom–trolley system at ground level, while the continuous drawing shows it crossing a 5 cm bump; (b) rear view showing how the trolley–rail track equipment must be used; (c) particulars of the connection of the transducers with the boom and an example of the measurement of the boom movement: A, angular and position transducers; B, boom; Ba , boom articulation; Bt, boom tip; B0, boom starting position; B1, boom during movement; C, bar supporting the transducers; D, trolley moving on a horizontal rail track and trailed by the tractor by mean of E, the trolley supporting the data acquisition system and a notebook; F, horizontal rail that can be used both in concrete and in field; G, 5 cm bump; H, articulated connection between trolley and tractor avoiding the transmission to the trolley of the tractor impulses caused by soil unevenness; I, data acquisition system and personal computer on the trolley; T, tank; ‘a,0 and ‘a,1: lengths of the wire of the position transducer connected at Ba, respectively, in position 0 (boom initial position) and 1 (boom during movement); ‘t,0 and ‘t,1: lengths of the wire of the position transducer connected at Bt, respectively, in position 0 (boom initial position) and 1 (boom during movement); a and a1 , angles recorded by the angular transducers on the vertical plane perpendicular to the advancing direction; b and b1 , angles recorded by the angular transducers on the vertical plane parallel to the advancing direction (the angles and lengths are used to calculate the vertical and horizontal components of the movements in the point of application of A); Dx and Dx1 , horizontal components of the movement, respectively, near the articulation and at boom tip; Dy and Dy1 , transversal components of the movement, respectively, near the articulation and at boom tip; Dz and Dz1 , vertical components of the movement, respectively, near the articulation and at boom tip

second trolley and connected with the edge of the bar in order to monitor its movements during the displacement of the tractor, particularly when crossing the 5 cm bump. The tests were done under two conditions (Fig. 2). (1) The first set of conditions comprised a horizontal gravelly track [Fig. 2(a)], with rectilinear trajectory, at a velocity of 36 km h
1, using a 12 m, suspended, mounted boom. The boom had a central section (length of 2 m) and two sections on each side, whose lengths, proceeding towards the boom tip were 2

Table 2 Dimensions of the trolley-rail track equipment Total length of the rail, m Number of modular elements Length of the single elements, m Height of the rail, cm Width of the rail, cm Length of the bar supporting the sensors, m Height of the bump, cm

27 9 3 7 40 6 5

and 3 m, respectively. During transport, the last section can be folded vertically on the second section by means of an articulation [joint A in Fig. 2(a)]; then a horizontal articulation [joint B in Fig. 2(a)] allows them both to be folded again behind the tank. The total length of the rail track was 27 m, but, as the system needed some time and space (about 1 s and 1 m) to reach a constant velocity at the outset, the first 2 m section of each repetition was not considered and the data refer to 25 m. Along the track, on the left of the rail tracks, there was a 5 cm high bump (14 m from the starting point). The sensors were placed as described above: one group on each side, near the joint A, at a distance of 3 m from the centre; both the groups on the same side, reaching the joint A and the boom tip. As the characteristics of the joint A can heavily affect the vertical movements of the last section of the boom with reference to the second section, in both cases, it has been considered as a point to be detected. The observed horizontal movement allows, at any rate, to evaluate the influence of joint B on it.

396

D. POCHI; D. VANNUCCI

Fig. 2. Test locations of the tests and trolley–rail track equipment: (a) boom–tractor combination moving on a gravelly track (both the groups of sensors are placed on the left side of the boom) and (b) trailed boom tested on a very irregular surface with a group of sensors on each side (this track has a slight transversal slope whose behaviour is followed by the rail track and the bar); joint A, vertical articulation; joint B, horizontal articulation

(2) The second set of conditions comprised a field, as shown in Fig. 2(b), using a 6 m, unsuspended, trailed boom, at a velocity of 5 km h
1. The boom consisted of a central 2 m section integral with the frame and a 2 m section on each side, connected by means of horizontal articulation joints [joint B in Fig. 2(b)] allowing the side sections to be folded behind the tank for the transport. In this case, the distance considered appropriate for the tests was 21 m. As the bar supporting the transducers had almost the same length as the boom, the two groups of sensors were placed one on each side, near the last nozzle. In Fig. 2(b), a slight transversal slope can be seen at the test location, but the rail track and the bar with the

sensors were capable of following the soil profile without difficulty. A special software has been developed for the data processing in order to collect more detailed information about the behaviour of the boom. The flow chart in Fig. 3 shows how the electrical signals were treated. The first data obtained are the three spatial components of the movements of the inspected points. Their interpretation facilitate the calculation of the three components of velocity and acceleration. Further analysis gives the frequency distribution of the values of the three components of movement and velocity. These elements have been used to define some relevant parameters for the evaluation of boom performance and are fully described in the discussion of the results.

397

A SYSTEM WITH POTENTIOMETRIC TRANSDUCERS

Y axis movement, mm

The tests were conducted to investigate the behaviour of the bar with the transducers and the boom movements during displacement, under two different soil conditions. Each test took about 5 m, including the positioning of the tractor, the test itself and the transfer of the data into the computer. The software needed another 5 m to transmit (a) the diagrams of the boom movements in three dimensions; (b) the velocity and acceleration (referring to the two monitored points of the boom); and (c) other information, such as the frequency distribution of the data for the movement and velocity of the boom. The following diagrams are examples of the test results. The diagrams of Fig. 4 refer to the preliminary tests conducted to check the stability of the bar with the transducers. Each diagram shows four lines resulting from four repetitions which display a common trend. Table 3 shows the values of the coefficient of variation (CV) for the three components of the movements of the bar on the rail track. The bar seemed to be stable, as minimal oscillation (few millimetres) was observed on the longitudinal axis (X-axis). Referring to the vertical movements (Z-axis), a 30 mm oscillation appeared because of the varying ground level under each rail (the surface was not perfectly horizontal); the 20 mm movement recorded on the transversal line (Y-axis) seemed to be due to the

Z axis movement, mm

5. Results and discussion

X axis movement, mm

Fig. 3. Flow chart of the analysis of signals transmitted by the sensors

50 25 0 _25 _50

0

5

10 15 Distance, m

20

25

0

5

10 15 Distance, m

20

25

0

5

10 15 Distance, m

20

25

50 25 0 _25 _50

50 25 0 _25 _50

Fig. 4. Movements of the transducer bar during the displacement of the tractor-boom combination along the 25 m rail track; the four lines drawn from four repetitions display a common trend

398

D. POCHI; D. VANNUCCI

Coefficient of variation

1 2 3 4

X-axis

Y-axis

Z-axis

3319 3719 3342 3727

4975 5096 5141 4893

4576 4406 4288 4640

small variation in the distance between the two rails. The stability of the bar did not seem to be affected by the bump.

5.1. Tests on a track

600 400 200 0 _ 200 _ 400 _ 600 0

10 15 Distance, m

20

25

600 400 200 0 _200 _ 400 _600 0

5

10 15 Distance, m

20

25

600 400 200 0 _200 _400 _600 0

(a)

5

600 400 200 0 _200 _ 400 _600

600 400 200 0 _ 200 _ 400 _ 600

Z axis movement, mm

Z axis movement, mm

Y axis movement, mm

X axis movement, mm

Fig. 5 shows examples of the boom movements recorded during the rail track tests, applying, firstly, a group of sensors on each side of the boom [Fig. 5(a)] and, then, both groups on the same side [Fig. 5(b)].

X axis movement, mm

Replicate

In both cases, the diagrams show a wider oscillation for the lines of X and Z axes (respectively, horizontal and vertical components of the movements) than for the line of the Y-axis (transversal component). In addition, the Y-axis data are important because they contribute to increasing the accuracy in the calculations of the X and Z data. In Fig. 5(b), the different behaviour of the two points can be observed, with a wider oscillation at the end of the boom than at the joint. In the diagram of the transversal component (Y-axis), only one line is reported (referring to the joint), on the assumption that the rotation of the boom around the suspension centre would lead to a constant transversal displacement all along the boom. In the prosecution of the work, only the data referring to the conditions of Fig. 5(b) have been considered. They were first used to calculate the three components of the velocity and acceleration: their behaviour is shown in the diagrams of Fig. 6. Then, the data of movement, velocity, and acceleration were processed giving the frequency distribution of their values (Fig. 7). Each value refers to the movement of the boom during the acquisition time (005 s). The

Y axis movement, mm

Table 3 Coefficients of variation for the three components of the movement of the bar

5

10 15 Distance, m

20

0

5

10 15 Distance, m

20

25

0

5

10 15 Distance, m

20

25

5

10 15 Distance, m

20

25

600 400 200 0 _200 _ 400 _ 600 0

25 (b)

Fig. 5. Diagrams showing the results of the different usage of the system: (a) test on a track with a bump of 5 cm placed 14 m from the starting point, using a 12 m long suspended boom with a group of sensors on each side (3 m from the centre) in order to record the movements during the test of the left side (grey line) and the right side (black line) and (b) test on the same track, positioning both the sensors on the same side, showing the boom tip movements (grey line) and articulation point (3 m from the centre of the boom) movements (black line)

399

5

10 15 Distance, m

20

25

0.0 _ 2.5 _ 5.0 5

10 15 Distance, m

200 100 0 _100 _200

0

5

10

15

20

25

Distance, m

5.0 2.5

0

X axis acceleration, m/s2

0

20

25

Y axis acceleration, m/s 2

30 20 10 0 _10 _ 20 _ 30

20 10 0 _10 _20

0

5

10 15 Distance, m

20

25

0

5

10 15 Distance, m

20

25

30 20 10 0 _10 _20 _30 0

(a)

5

10 15 Distance, m

20

25

Z axis acceleration, m/s

Z axis velocity, m/s

2

Y axis velocity, m/s

X axis velocity, m/s

A SYSTEM WITH POTENTIOMETRIC TRANSDUCERS

(b)

200 100 0 _100 _200

Fig. 6. Diagrams of the three components of (a) velocity and (b) acceleration calculated on the basis of the movements shown in Fig. 5b:}}, boom tip and }}, articulation joint

difference between the distributions of the values referring to the boom tip and the joint is evident. Based on the data of Fig. 7, Table 4 shows an attempt to give some relevant parameters, for the evaluation of the behaviour of boom sprayers, as based on the ratios rx and rz , indicative, respectively, of the transmission of the horizontal and vertical impulses through the joint and r1 and r2 indicative of the total horizontal oscillation of the two detected points. They are defined as follows: X X x1 = x2 ð1Þ rx ¼ P P where x1 and x2 are summations of the horizontal movements of the boom tip and articulation (joint); X X z1 = z2 ð2Þ rz ¼ P P where X 1 and X 2 are summations of the vertical movements of the boom tip and articulation (joint); ! X r1 ¼ S 0 þ ð3Þ =S0 X1

where S0 isPthe total length of the basic test (expressed in mm) and sX 1 is the sum of the absolute values of P the horizontal movements of the point near the joint, sX 1 and r1 being as close as possible to 0 and 1, respectively;

and  X  sX2 =S0 r2 ¼ S0 þ

ð4Þ

P where of the X 2 is the sum of the absolute values P horizontal movements of the boom tip, and r2 X2 being as close as possible to 0 and 1, respectively. The data, reported in Table 5, were further analysed to estimate the total surface in m2 ha
1 in which distribution has not been uniform. Considering the nominal tractor speed v of 1 m s
1, it was assumed that the distribution should be acceptable if the horizontal component of the velocity of the boom remains, for example, in the interval between 075 and 125 m s
1. This means that the velocity of the inspected points, with respect to the tractor, must be included in the interval between
025 and+025 m s
1, corresponding to an average movement of 125 mm during the acquisition time. The same interval as the reference interval for the transversal and vertical components of the velocity has been considered for greater convenience. The analysis also gives the number of velocity values of the inspected points outside of the interval 025 m s
1. As the velocity values refer to the time

X axis frequency

400

80

200

200

150

60

150

150

100

40

100

100

20

50

50

0 22 44 66 88 110 132

54

105

0

_ 9 _7 _ 6 _ 4 _ 2 _1 1 3 4 6 7

0 _100 _65 _30

200

200

100

60

150

150

80

40

100

100

20

50

50

0 22

44

66

88 110 132

80 Z axis frequency

3

80

0

60

0 _ 150 _ 99 _ 48

3

54

105

0 _ 2.0 _1.3 _ 0.6 0.1

5

40

75

60 40 20 0.8

1.5

0 _10 _7 _5 _2

150

300

150

100

200

100

50

100

50

0

3

6

8

40 20 0 0

(a)

0 _150 _ 99 _ 48

20 40 60 80 100 120 140 Movement classes, mm

0 _ 150 _ 99 _ 48 3 54 105 Movement classes, mm (b)

0

_10 _ 6.5 _3.0 0.5 4.0 7.5 (c) Velocity classes, m/s

0 _ 100 _ 66 _32 2 36 70 (d) Acceleration classes, m/s 2

Fig. 7. The data of Figs. 5(b) and 6 have been processed to obtain: (a) frequency distribution of the absolute values of the components of boom movements [referring to Fig. 5(b) with class amplitude of 1 mm]; (b) frequency distribution of the components of the movements values [referring to Fig. 5(b) with class amplitude of 3 mm]; (c) frequency distribution of the components of the velocity (referring to Fig. 6(a) with class amplitude: of 0.05 m s for the X-axis, 005 m/s for the Y-axis and 025 m s
1 for the Z-axis]; frequency distribution of the components of the accelerations [referring to Fig. 6(b), with class amplitude of 1 m s
2 for the X-axis, 01 m s
2 for the Y-axis and, 1 m s
2 for the Z-axis]: &, articulation joint and ), boom tip

D. POCHI; D. VANNUCCI

Y axis frequency

0

50

401

A SYSTEM WITH POTENTIOMETRIC TRANSDUCERS

Table 4 Relevant stability parameters based on the data Fig. 5(b) to evaluate behaviour of boom sprayers* Articulation Parameter S0 P Psxi szi

x1 Mm Mm Mm

Boom tip

z1

x2

z2

25 000 2267

18 953

20 324 P P rx ¼ sx1 = sx2 836 P P rz ¼ sz1 = sz2 934 P 109 176 r1 ¼ ð sx1 þ S0 Þ=S0 P r2 ¼ ð sz2 þ S0 Þ=S0 P P *S0, distance; sxi , sum of the absolute values of the horizontal movements of the inspected points; sxi , sum of the absolute values of of the vertical movements of the inspected points (05i5n; n, number of acquisitions); rx, rz, r1 and r2, ratios defined in Eqns (1)–(4); x1, horizontal movement near the articulation; x2, horizontal movement at the boom tip; z1, vertical movement near the articulation; z2, vertical movement at the boom tip.

between two acquisitions (t ¼ 005 s), the multiplication of this by the number of values outside the interval gives the total time (in seconds and in percentage of the time needed to travel the 25 m distance) during which the boom movements, for the inspected points, were not compatible with the conditions assumed to guarantee a good distribution. The velocity values along the boom decrease, proceeding towards the centre and the results in Table 5 show that the boom tip had a poorer behaviour than the articulation joint, with higher velocity frequencies out of the selected interval, for both horizontal and vertical directions. A frequency decrease means a time decrease.

2176

For example, in the boom section between joints A and B, the measurement system gives the frequency of the horizontal velocity values in the joint A during the interval and the relative total time; in the joint B, frequency and time are 0 because they are integral with the boom frame and the velocity is the same as that of the tractor. This way, the whole section works irregularly for a time equal to the average of the time values in the two joints. In Table 5, the distribution under Section 2 of the boom (between joint A and boom tip) was irregular, because of the variation in the horizontal component of velocity, for an average time of 3204% of the total time.

Table 5 Results of the calculation to estimate the over- and under-sprayed surface on the basis of the data of the track tests described in Fig. 5(b) Parameter

X-axis

Z-axis

Transducer Artic. Boom tip Total frequencies Total frequencies with v 5
025 and v> 025 m s
1 Total time, in s with v 5
0.25 and v >025 m s
1 Time per cent with v 5
025 and v >025 m s
1

501 31 155 619

500 290 1450 5788

Transducer Artic. Boom tip 501 0 000 000

X-axis

Z-axis

Boom section* 1 2 Average time percenty with v 5
025 and >025 m s
1 in each section Surface irregularly sprayed by each section, m2 ha
1

309 10313

501 94 470 1876

3204 160180

Boom section* 1 2 000 000

938 46906

*Boom section: (1) section between the joints A and B; (2) section between the boom tip and the joint A. In this case it has been supposed a symmetrical distribution and the data are calculated considering both the sides of the boom. yPer cent of the working time during which the distribution has been irregular under each section, considering both the sides of the boom.

9

12

15

18

0 Y axis speed, m/s

100 0 _ 100 _ 200 3

6

9

12

15

18

_1.0

21

6

9

12

15

18

21

0.5 0 _ 0.5 _1.0 0

200

3

1.0

21

3

6

9

12

15

18

0 _ 100 _ 200 0

3

6

9 12 Distance, m

15

18

21

Z axis acceleration,

100

0.5 0 _ 0.5 _1.0 0

(b)

3

6

9

12

Distance, m

15

18

25 15 5 _5 _15 _25

21 (c)

0

3

6

9

12

15

18

21

0

3

6

9

12

15

18

21

0

3

6

9

12

15

18

21

25 15 5 _5 _15 _25

21

1.0 Z axis speed, m/s

Z axis movements, mm

6

200

0

(a)

3

X axis acceleration, m/s2

0

m/s 2

_ 200

0 _ 0.5

Y axis acceleration,

0 _ 100

0.5

25 15 m/s 2

X axis speed, m/s

100

1.0

5 _5 _15 _25 Distance, m

Fig. 8. The three components of movement (a), velocity (b), and acceleration (c) resulting from the field test: }}, left side and }}, right side

D. POCHI; D. VANNUCCI

Y movements, mm

X axis movements, mm

402

200

30 20 10

Y axis frequency

0 5 9 14 18 23 27 32 36 41 45 50 50

40

40

30

30

20

20

10

10 0

Z axis frequency

0 5 9 14 18 23 27 32 36 41 45 50

0 _200 _140 _80 _20 40 100 160

20

60 50 40 30 20 10 0 _1.5 _1.1 _0.7 _0.3 0.1 0.5 0.9 1.3

20

20

20

40

15

15

30

10

10

20

5

5

10

0

0 _200 _140 _80 _20 40 100 160

0 5 9 14 18 23 27 32 36 41 45 50 (a)

0 _ 200 _140 _80 _20 40 100 160

60 50 40 30 20 10 0 _1.5 _1.1 _0.7 _0.3 0.1 0.5 0.9 1.3

Movement classes, mm

(b)

Movement classes, mm

0 _1.5 _1.1 _0.7 _0.3 0.1 0.5 0.9 1.3 (c)

Velocity classes, m/s

15 10 5 0

_20 _16 _11 _6 _2 3

7 12 16

_20 _16 _11 _6 _2 3

7 12 16

10 8 6 4 2 0 _20 _16 _11 _6 _2 3

7 12 16

15 10 5 0

(d)

A SYSTEM WITH POTENTIOMETRIC TRANSDUCERS

X axis frequency

40

30 25 20 15 10 5 0

Acceleration classes, m/s2

Fig. 9. The data of Fig. 8 have been processed to obtain: (a) frequency distribution of the absolute values of the components of boom movements [referring to Fig. 8(a) with class amplitude of 1 mm); (b) frequency distribution of the components of the movements values [referring to Fig. 8(b) with class amplitude of 3 mm]; (c) frequency distribution of the components of the velocity (referring to Fig. 8(c) with class amplitude of 005 m s
1); (d) frequency distribution of the components of the accelerations [referring to Fig. 8(d), with class amplitude of 03 m s
2]: &, left side and , right side

403

404

D. POCHI; D. VANNUCCI

Considering both the sides of the boom, the width of the area covered by this section is 50% of the total boom length; if the distribution has a symmetrical behaviour, the corresponding surface S irregularly sprayed is S ¼ 10 000 03204 050 2

ð5Þ


1

giving 16018 m ha . Similar considerations, better described in Fig. 10, were made for the vertical component of boom velocity and for Section 2 (between joints A and B). The results, shown in Table 5, indicate that the horizontal component of the velocity determined a total surface irregularly sprayed of 170493 m2 ha
1 and, for the vertical component, it was 469 m2 ha
1.

5.2. Field tests

50

50

40

40 Time,%

Time, %

A similar assessment as that described above has been made for the field test with the 6 m trailed boom, but the results assume now a different meaning: they describe the symmetry of working and the possible variations in stability of the two sides of the boom. The diagrams in Fig. 8 show worse movement with regard to velocity, and acceleration of the right side (particularly the horizontal component), shown by their respective frequency distribution (Fig. 9) and by the interpretation of the results in Figs 10(c) and 10(d ) and in Tables 6 and 7. In Table 6, rx and rz are determined as the ratios between the data of the right and the left side and are

greater than 1. Considering ratios r1 and r2 , the former is nearer to 1 than the latter. Based on the considerations in Fig. 10, Table 7 shows that on the right side the horizontal and vertical components of boom movements under the 2 m section between the boom tip and the joint, determined an irregular distribution, of 1451% and 2334% of the working time, respectively. The surface sprayed by the boom section is 3333% of the total sprayed by the 6 m boom. The surfaces S irregularly sprayed were 4837 and 77813 m2 ha
1 for the horizontal and vertical components, respectively. The left side had a better behaviour, with 379 and 2050% irregularly sprayed, respectively, for the horizontal and vertical components and the resulting surfaces were 1262 and 6835 m2 ha
1. The horizontal component of boom movement determined a total surface irregularly sprayed of 6099 m2 ha
1, as for the vertical component it was 14616 m2 ha
1. These were only examples of a proposed method and, obviously, the advancing velocity should be increased. Further experiences will be helpful in the choice of the most appropriate intervals of tolerance, that could be different for the horizontal and vertical components of the velocity. Nevertheless, they represent an attempt to give some parameters for the evaluation of boom sprayer stability. They could also be useful for the formation of a simulation program providing detailed data about the distribution all along the boom in working conditions simply by collecting the data of the movements.

30 20

20 10

10 0

30

_7

_5

_3

0

_1

1

3

5

7

_4

_2

50

50

40

40

30 20 10 0 _7

(a)

Time, %

Time, %

c

0 d

2

4

30 20 10

_5

_3

_1

1 3 5 Distance from the boom centre, m

0 _4

7 (b)

_2

0 2 Distance from the boom centre, m

4

Fig. 10. Irregular distribution as a percentage of boom working time: (a) due to horizontal movement during a track test of a 12 m suspended boom with a fixed central section (
1 to +1 m); (b) due to horizontal movement during a field test of a 6 m boom with a fixed central section (
1 to +1 m); (c) due to the vertical movement relative to the suspension centre of the 12 m boom during the track test; and (d) due to the vertical movement relative to the boom centre of the 6 m boom during a field test: }}, boom section behaviour and }}, average for each section

405

A SYSTEM WITH POTENTIOMETRIC TRANSDUCERS

Table 6 Relevant stability parameters based on the data of Fig. 8 to evaluate behaviour of boom sprayers Leftside Parameter S P0 Psxi szi

x1 mm mm mm

Rightside

z1

x2

z2

21 000 1351

2489

4338 P P rx ¼ sx1 = sx2 184 P P rz ¼ sz1 = sz2 121 P r1 ¼ ð sxi1 þ S0 Þ=S0 P r2 ¼ ð szi2 þ S0 Þ=S0 106 112 P P *S0, distance; sxi , sum of the absolute values of the horizontal movements of the inspected points; sxi , sum of the absolute values of of the vertical movements of the inspected points (0 5i5n; n, number of acquisitions); rx, rz, r1 and r2, ratios; x1, horizontal movement of the left side; x2, horizontal movement of the right side; z1, vertical movement of the left side; z2,vertical movement of the left side.

6. Conclusions The equipment based on the trolley–rail track system proved to be easy to use and adaptable to the ground conditions of the tests, representing a suitable technique for monitoring boom movements in working conditions. Using different sensors, a trolley–rail track system could be used as a support for any other measurement system. An increased length of rail track would give the possibility of conducting tests at higher velocities, nearer to those adopted during work. The instrumentation based on potentiometric transducers and the equipment to use it represents a satisfactory system for a boom-movement investigation.

3587

According to the results of the laboratory tests, the measurement of boom movements was accurate, as the trolley–rail track system avoids errors from soil unevenness on the accuracy when the tractor-sprayer combination is moving. The system works quickly and its use does not require any particular training apart from a knowledge of the most common software programs. The number of the test points on the boom can be increased for a better investigation of the boom during work. The characteristics of such an equipment would make it possible to start an investigation of boom sprayers on a larger scale, by testing them under conditions similar to real work (for example, directly in field or defining the

Table 7 Results of the calculation to estimate the surface irregularly sprayed on the basis of the data of the field tests described in Fig. 8 Parameter

X-axis

Z-axis

Side of sprayer Left Right Total frequencies Total frequencies with v 5
025 and v > 025 m s
1 Total time, in s with v 5
025 and v >025 m s
1 Time per cent with v 5
025 and v >025 m s
1

317 24 120 757

317 92 460 2902

Side of sprayer Left Right 317 130 650 4101

X-axis

Z-axis

Boom section* 1 2 Average time per centy with v 5
025 and >025 m/s
1 in each section Surface irregularly sprayed by each section, m2 ha
1

379 12618

317 148 740 4669

1451 48370

Boom section* 1 2 2050 68349

2334 77813

*Boom section: (1) section between the boom tip and the joint A in the left side of the boom; (2) section between the boom tip and the joint A in the right side of the boom. yPer cent of the working time during which the distribution has been irregular under each section.

406

D. POCHI; D. VANNUCCI

characteristics for the realization of standard test tracks reproducing soil unevenness) and estimating the boom movements and their effects on the spray distribution.

References Clijmans L; Ramon H (1997). The experimental modal analysis technique to study the dynamic behaviour of sprayers. Aspects of Applied Biology, Optimising Pesticide Applications, 48, 9–16 Clijmans L; Ramon H; De Bardemaeker J (1997). Sensitivity analysis of the dynamic behaviour of agricultural Machines. Landtechnik International, 52(2), 90–91 Clijmans L; Standaert B; De Bardemaeker J; Ramon H (1998). Model based approach to study sprayer boom dynamic. EurAgEng Paper No. 98-A-002. International AgEng’98 Meeting, Oslo, September 1998 De Baerdemaker J; Jacques M; Verdonck E (1983). Modelling the dynamic behaviour of sprayer booms. Paper No. 83– 1507. ASAE Meeting, Chicago, December 1983 Fedrizzi M; Menesatti P; Pari L; Vannucci D (1995). Sistema Laser per il Rilievo del movimento di una Barra Irroratrice

Orizzontale: Strumentazione, Metodologia e Primi Risultati Sperimentali. [Laser system for the movement track of a horizontal spray boom: equipment, methodology and first experimental results.] Rivista di Ingegneria Agraria, n.3, Settembre Lebeau F; Destain M F (1998). Measurements of the sprayer boom displacements with a laser sensor. EurAgEng Paper No. 98-A-004. International AgEng’98 Meeting, Oslo Pochi D; Vannucci D (2001). Laboratory evaluation of linear and angular potentiometers for measuring spray-boom movements. Journal of Agricultural Engineering Research, 80(2), 153–161, doi:10.1006/jaer.2001.0731 Sinfort C; Schmidt K; Rabatel G; Lardoux Y; Bonicelli B (1998). Test method for field sprayer inspection at the farm level. EurAgeng Paper No. 98-A-024. International AgEng’98 Meeting, Oslo SPECS (1998). European system for field sprayer inspection at the farm level. AIR3. CT94-1170 (1998). Final Report: 1 November 1994–30 April 1998 Vannucci D; Pochi D; Limongelli R (1996). The effect of forward speed and tractor mass on spray boom oscillation. EurAgEng Paper No. 96-A-144. International AgEng ‘96, Madrid