Dynamic symulation and experiment on a sprayer boom structure.

Lupea, Iulian ; Tudose, Lucian ; Stanescu, Cristina Mihaela 等

1. INTRODUCTION

The dynamic behavior of agriculture sprayer mechanisms trailed by tractors has been constantly observed and analyzed (Ramon & De Baerdemaeker, 1997); (Kennes et al., 1999). The sprayer boom is a large and relatively slender component, used to support the spray nozzles. It is important to control and minimize the vibration of the structure on the vertical and horizontal planes, in order to insure the uniformity of pulverization over the field (Lupea et al., 2008). The horizontal and vertical movements, as well as the geometrical features of the sprayer boom, influence the pulverization quality. It has been made (Lebeau et al., 2004) a spray controller aiming to compensate the effect of the horizontal boom movements on the spray deposits homogeneity. In this paper the dynamic study of a sprayer boom structure of about 12m length on each side is presented. Initially, the real boom has been optimized in terms of minimizing the vertical vibration, considering the dynamic model of the whole sprayer mechanism excited from the ground when is following a standard bumpy path. In that approach the dynamic model of the whole sprayer mechanism and a rigid sprayer boom were considered. A similar downscaled (1/10) boom structure has been manufactured and tested. An important parameter of the dynamic behavior is the boom tip vibration amplitude. This parameter is observed in the finite element analysis of the optimized structure considered at a natural scale and in the experimental approach of the downscaled structure, resulting a good correlation (considering the scale factor). During the tests of the manufactured structure, scale factors such as the time factor and the force factor for transient dynamic load, have been considered. Other similar parameters, such as the resonant frequencies, have been observed in both models. This work was supported by the grant of the Romanian Government PNII Idei id 1077 (2007).

[FIGURE 1 OMITTED]

Further research is aiming a better understanding of the similarities of the real boom structure, the associated finite element model and the down-scaled real structure used for tests in the laboratory.

2. FINITE ELEMENT ANALYSIS

Starting from the CAD model of the sprayer boom structure, a standard mesh procedure as a preprocessing step of a finite element analysis has been followed. Mainly shells, a reduced number of solid elements, rigid connections and a few spring elements were used. Some small components were replaced by lumped masses and finally, the same mass in both, the model and the real structure has been reached.

The model was prepared with HyperMesh preprocessor (2007, HyperWorks) for normal modal analysis with Optistruct solver which is using Nastran similar cards in the deck file. The frequency band of interest was between 0.1 and 60Hz. Some modes of vibration are preponderant moving on the vertical plane, others are on the horizontal plane and some are moving on both planes. The lowest mode is a lateral bending of the structure. The most important modes of vibration are in general the lowest ones, which generate large amplitude at the free end of the sprayer boom. Other important modes of vibration are those which can be excited by active loads. Hence, a typical time dependent load coming from the ground has been used to excite the sprayer boom arm structure. This load was derived from the dynamic simulation of the whole agriculture sprayer machine (including the suspension) trailed by a tractor when is following a standardized bumpy path.

In order to find out the sprayer tip (node #202497, Fig.1.) vibration amplitude as a response to the dynamic load, a modal transient response procedure by using finite element analysis, has been applied. The time variable load coming from the dynamic modeling of the sprayer mechanism excited from the ground has been applied at the level of the symmetry line of the structure. The free end motion and the amplitude of the boom have been registered in three perpendicular directions (Fig. 2). The vertical (Oy) response amplitude is the most important (0.068m), followed by the lateral one (Oz) and finally the response along the length (Ox) of the arm. The modal method, instead of the direct integration method, has been chosen. The modal damping, experimentally measured on a similar downscaled (1/10) real structure which was manufactured for testing, has been plugged into the finite element model.

[FIGURE 2 OMITTED]

3. EXPERIMENTS

3.1 Measurement Set-up

A similar down-scaled (1/10) boom arm structure has been manufactured in order to perform tests in the laboratory, in parallel to the field tests.

The frequency response function--inertance of the downscaled manufactured structure has been measured.

A measuring set-up available in the Vibration & Noise Measuring Laboratory (www.viaclab.utcluj.ro) has been used. It is based on an acquisition system, a shaker, a force transducer, a light accelerometer and a Labview application.

A simplified measurement set-up is shown in Fig. 3. The device under test (DUT) is excited from the output channel 0, while the force transducer and the mini-accelerometer are monitored by using the input channel 0 and channel 1, respectively.

[FIGURE 3 OMITTED]

3.2 Measurement of the FRF-Inertance

The force transducer measures the force transfered from the shaker to the DUT. The accelerometer, glued on the structure's free end is monitoring the vertical acceleration. From the FRF peaks (Fig.4), the resonant frequencies of the structure in vertical plane and the modal damping values have been derived. A mean damping ratio value of 0.02, derived by using the bandwidth method for resonant peaks, has been plugged into the finite element simulation. The structure has been considered as lightly damped.

For the FRF-inertance (magnitude--phase) derivation, a Labview application based on sine sweept procedure in the frequency band of interest has been used (2008, Labview).

[FIGURE 4 OMITTED]

3.3 Down-scaled Structure Free End Response

A Labview application has been developed. The application derives the manufactured structure compliance by double integrating the measured FRF-inertance, finds the main harmonics of the down-scaled time varying load acting on the similar down-scaled structure and calculates the structure responses for each harmonic (magnitude and phase) excitation. Finally, the application superposes the responses of the downscaled structure to the main harmonic excitations (Lupea, 2005). The time varying load imposed on the real structure is similar (down-scaled: 1/100) to that used for excitation on the modal transient response finite element simulation.

After the superposition of the harmonical responses, the structure's tip vibration is depicted in Fig. 5.

[FIGURE 5 OMITTED]

4. CONCLUSION

A transient response simulation of a real-sized and an experimental approach on the down-scaled sprayer boom structure have been performed. The free end boom structure vibration amplitude derived from FEA is in good correlation with the one obtained from the experiment based on the measured FRF-inertance. Resonant frequencies resulted from the simulation of the boom structure, the measurements on the real structure and on the down-scaled structure, correlate as well. By improving the finite element model, better results are expected. Other standard excitations will be imposed on the structures, observing the responses.

5. REFERENCES

Kennes, P.; Ramon, H. & De Baerdemaeker, J. (1999). Modeling the effect of the passive suspensions on the dynamic behavior of sprayer booms. Journal of Agricultural Engineering Research, Vol. 72, Issue 3, 1999, pp 217-229

Lebeau, F.; El Bahir, L.; Destain, M.; Kinnaert, M. & Hanus, R. (2004). Improvement of spray deposit homogeneity using a PWM spray controller to compensate horizontal boom speed variations, Computers and Electronics in Agriculture, Vol. 43, Issue 2, 2004, pp 149-161

Lupea, I. (2005). Vibration and noise measurement by using Labview programming, Casa Cartii de Stiinta Publisher, Cluj-Napoca, ISBN 973-686-840-0

Lupea, I.; Stanescu, C. & Drocas, I. (2008). Measurements on the Sprayer Boom Vibration, The Fifth International Symposium about forming and design in mechanical engineering, COD 2008 Proceedings pp. 331-334, ISBN 978-86-7892-104-9, ADEKO Association for Design, Elements and Constructions, Belgrade, 15-16. April 2008, Novi Sad

Ramon, H. & De Baerdemaeker, J. (1997). Spray boom motions and spray distribution - part 2: experimental validation of the mathematical relation and simulation, Journal of Agricultural Engineering Research, Vol. 66, Issue 1, 1997, pp 31-39

*** (2008) Labview--Sound and vibration toolset, National Instruments, Austin, Texas

*** (2007) HyperWorks (HyperMesh and Optistruct), Altair Engineering Inc., Troy - Michigan