Justification of roller geometry for stable rotation of potato tubers in optical sorting machines

This paper proposes a geometric model of the working surface of potato tuber rollers used for transporting and rotating tubers, based on approximating the tuber shape with an ellipsoid of revolution. It is shown that when using cylindrical rollers, contact is limited to a single point, leading to unstable and chaotic rotation, complicating optical surface assessment. To improve stability and increase the contact area, a single-sheet hyperboloid of revolution roller shape is proposed. Analytical relationships are developed describing the intersection of the ellipsoid and hyperboloid, and an equation for the contact curve is derived, taking into account the geometric parameters of the tuber. The resulting model ensures an increased contact zone, stable rotation without slippage, and is suitable for practical implementation in roller designs.

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