Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface
Abstract
:1. Introduction
2. Materials and Methods
2.1. Computer Simulation
2.2. Mathematical Contact Model
- m1, m2—particle mass (kg);
- S1, S2—contact force (N);
- t—time (s);
- v1, v2—velocity (m s−1).
- c1, c2—damping parameter (kg s−1);
- k1, k2—contact stiffness (N m−1);
- x1, x2—overlap (m).
- tk—contact time (s).
- − Poisson parameter—0.2 (-);
- − Kirchhoff’s module—9.0 (MPa);
- − Particle friction parameter—0.25 (-);
- − Damping parameter—1.0 (Ns·m−1);
- − Grain diameter—5.0 (mm);
- − Grain velocity—2.0 (m·s−1);
- − Grain density—765 (kg·m−3).
- − Sensor diameter—10.0 (mm);
- − Disc thickness—2.0 (mm).
- − Constant contact stiffness—k1 = 1 × 104 (N·m−1), k2 = 1 × 105 (N·m−1),
- − Force sensor resonance frequency—f = 20, 40, and 200 kHz.
3. Results
4. Conclusions
- The key influence on the precision of impact force course modelling was the frequency of the free vibrations (resonance frequency) of the force sensor and the grain size.
- If the duration of the contact force pulse was longer than half of the sensor’s own vibration period, the measurement signal coincided significantly with the contact force course. This occurred for large and soft grains with a higher moisture content.
- If the duration of the contact force pulse was shorter than half of the sensor’s own vibration period, the results of the contact force measurement were not reliable because the first cycle of the measurement signal lasted longer than the actual contact time. Moreover, with hard fine grain, the signal itself was always close to half a sinusoid of a period corresponding to the resonance vibration period of the force sensor, regardless of the shape of the contact force pulse resulting from the shape of the grain mechanical properties.
- For large grains (e.g., maize, pea, and Pisum arvense) with a diameter greater than 5.0 mm, the modelling of the impact force by the sensor response signal with free vibrations of approximately 40 kHz could be considered adequate.
- For fine grains (e.g., rape) with a diameter of less than 2.0 mm, the exact modelling could only be obtained by a sensor with a free vibration frequency exceeding 200 kHz. Piezoelectric force sensors available for sale have a free vibration frequency of 70 kHz, which does not allow the credible impact force value to be measured for fine grain e.g., rape and mustard.
- To reliably measure the course of the impact force, impact force sensors of a special design with high resonance frequency should be used. The technological capabilities of manufacturers of such sensors allow resonance frequencies of up to 200 kHz.
- The most crucial factors influencing the measurement accuracy of the grain impact force course were the grain dimensions (diameter) and the force sensor resonance frequency.
- In DEM calculations, where the contact force course is of key importance, the empirical research results of the force courses for fine grain should be approached carefully, by only relying on theoretical models (rheological) of the force courses.
Author Contributions
Funding
Conflicts of Interest
References
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Kęska, W.; Marcinkiewicz, J.; Gierz, Ł.; Staszak, Ż.; Selech, J.; Koszela, K. Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface. Appl. Sci. 2021, 11, 466. https://doi.org/10.3390/app11020466
Kęska W, Marcinkiewicz J, Gierz Ł, Staszak Ż, Selech J, Koszela K. Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface. Applied Sciences. 2021; 11(2):466. https://doi.org/10.3390/app11020466
Chicago/Turabian StyleKęska, Włodzimierz, Jacek Marcinkiewicz, Łukasz Gierz, Żaneta Staszak, Jarosław Selech, and Krzysztof Koszela. 2021. "Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface" Applied Sciences 11, no. 2: 466. https://doi.org/10.3390/app11020466
APA StyleKęska, W., Marcinkiewicz, J., Gierz, Ł., Staszak, Ż., Selech, J., & Koszela, K. (2021). Simulation Verification of the Contact Parameter Influence on the Forces’ Course of Cereal Grain Impact against a Stiff Surface. Applied Sciences, 11(2), 466. https://doi.org/10.3390/app11020466