Study of an Optimized Mechanical Oscillator for the Forced Vibration of the Soil Cutting Blade

Abstract

In the nursery sector, the transport and planting of trees must occur with the roots wrapped in a ball of the original earth. The cutting of the original soil can be carried out with a semicircular vibrating blade moved by an oscillator mounted on a self-propelled machine. The oscillator produces an excitation torque supplied to the blade together with the soil cutting torque. The advantage of the vibrating blade is a reduction in the cutting torque of up to 70%. However, to correctly design the oscillator, we need to investigate the link between the maximum displacement of the blade, the maximum oscillation velocity, the cutting velocity, the dry friction, the excitation torque, the elastic torque, the cutting torque, the required power, the required energy, and the excitation frequency. The maximum displacement and velocity ratio need to have the right values to minimize the cutting torque and to avoid the springs reaching the end of stroke; otherwise, vibrations are transmitted to the machine and to the operator. Therefore, starting from the forced oscillation differential equation and using an approximate solution method developed by Den Hartog, along with some experimental data, a mathematical model was constructed to optimize the oscillator design. After construction, it was coupled to blades of various diameters (0.6, 0.9, and 1.2 m) to undergo experimental tests. The soil cutting tests highlighted the achievement of the above objectives and, at the same time, confirmed the validity of the Den Hartog equations used to calculate the phase lag and the maximum displacement, resulting in an average error of 4.4% and a maximum error of 6.4%.