Coupled moment analysis of stacked counter-rotating eccentric-mass tree shaker energy-wheel system

•Stacked eccentric-mass energy-wheel tree shakers have coupled moments.•We developed a Coupled Moment and Planar Force (CMPF) equation model.•Accelerator data confirmed the new CMPF model and the existence of coupled moments.•Coupled moments cause lifting and compressing forces to the tree trunk.•Coupled moments apply an alternating positive and negative rotation.

This paper expands the historical “Planar model” equation for inertial tree shakers using stacked counter-rotating eccentric-mass energy-wheels and accounts for coupled moments using a “Planar Force and Moment Model”. The energy-wheel configuration utilised by many tree shakers creates planar forces and coupled moment maxima and minima. When the centrifugal acceleration force vectors of each energy-wheel are aligned, this creates a force maximum, acting radially about the tree. The stacked energy-wheels assembly produces a coupled moment due to the centrifugal acceleration force vectors acting on a lever arm. The lever arm vectors extend from a coordinate system coincident with the shaft centre line, and between the upper and lower energy-wheels centre of gravity. A coupled moment maximum occurs when the energy-wheel force vectors are opposing, the planar force is a minimum. The shaker head will roll, pitch, and yaw about the tree trunk due to the instantaneous coupled moment. The rotational and non-normal planar forces are more likely to cause tree trunk bark injury. Subsystems, such as lubricated pads and slings, are required to mitigate transmission of damaging forces. The Planar Force and Coupled Moment Model identifies the force causing vertical tree displacement. Though the Planar model shows that the timing of the energy-wheels produces the observed bi-directional pattern of force maxima, addition of the Coupled Moment shows that timing cannot eliminate non-normal forces. The new model provides a more complete representation of forces applied to the tree and could be used to optimise design for reduced tree damage.