Study of an Optimized Mechanical Oscillator for the Forced Vibration of the Soil Cutting Blade
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Mechanical Oscillator and the Vibrating Blade
2.2. The Differential Equation of the Forced Vibration with Coulomb Friction
2.3. Den Hartog Solution Applied to the Vibrating Blade
2.4. The Vibrating Blade While Cutting the Soil
2.5. Soil Cutting Time and Energy Required
2.6. Experimental Evaluation of Cutting Torque and Maximum Displacement
3. Results and Discussion
4. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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Quantity | Symbol | Oscillator Old | Oscillator New |
---|---|---|---|
Linear spring rate | kl (N m−1) | 572,000 | 1,140,000 |
Number of springs | z | 4 | 4 |
Lever arm of the springs | bS (m) | 0.087 | 0.108 |
Torsional springs rate | k (N m rad−1) | 17,318 | 53,227 |
Number of masses | n | 4 | 4 |
Mass | m (kg) | 1.27 | 2.41 |
Eccentricity | yG (m) | 0.0212 | 0.028 |
Mass lever arm | bG (m) | 0.163 | 0.200 |
Moment of inertia | JO (kg m2) | 0.38 | 1.30 |
Quantity | Symbol | Values | ||
---|---|---|---|---|
Blade Diameter | D (m) | 0.6 | 0.9 | 1.2 |
Moment of inertia (blade) | JB (kg m2) | 0.32 | 1.02 | 3.40 |
Moment of inertia (oscillator) | JO (kg m2) | 1.30 | 1.30 | 1.30 |
Moment of inertia (system b+o) | J (kg m2) | 1.62 | 2.32 | 4.70 |
Natural frequency | ωn (rad s−1) | 181.2 | 151.4 | 106.4 |
Quantity | Symbol | Values | ||
---|---|---|---|---|
Blade Diameter | D (m) | 0.6 | 0.9 | 1.2 |
Cutting torque | Tcut (N m) | 1268 | 3190 | 6324 |
Standard deviation | S.D. (N m) | 89 | 182 | 286 |
Friction torque | TF (N m) | 176 | 892 | 2819 |
Quantity | Symbol | Values | |||
---|---|---|---|---|---|
Blade Diameter | D (m) | 0.6 | 0.9 | 1.2 | |
Calculated | Max. angular displacement | α0 (rad) | 0.0407 | 0.0264 | 0.0108 |
Max. linear displacement | A0 (mm) | 12.2 | 11.9 | 6.5 | |
Measured | Max. angular displacement | α0 (rad) | 0.0396 | 0.0253 | 0.0101 |
Max. linear displacement | A0 (mm) | 11.9 | 11.4 | 6.1 |
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Friso, D. Study of an Optimized Mechanical Oscillator for the Forced Vibration of the Soil Cutting Blade. Vibration 2023, 6, 239-254. https://doi.org/10.3390/vibration6010015
Friso D. Study of an Optimized Mechanical Oscillator for the Forced Vibration of the Soil Cutting Blade. Vibration. 2023; 6(1):239-254. https://doi.org/10.3390/vibration6010015
Chicago/Turabian StyleFriso, Dario. 2023. "Study of an Optimized Mechanical Oscillator for the Forced Vibration of the Soil Cutting Blade" Vibration 6, no. 1: 239-254. https://doi.org/10.3390/vibration6010015
APA StyleFriso, D. (2023). Study of an Optimized Mechanical Oscillator for the Forced Vibration of the Soil Cutting Blade. Vibration, 6(1), 239-254. https://doi.org/10.3390/vibration6010015