Theory of the Process of Vibratory Digging of Carrot Root from the Soil

Mechanical interaction during carrot harvesting can impair root quality, motivating analysis of the lifting stage before damage assessment. Therefore, an important task is the design and research of working bodies that reduce this negative impact on root crops. The aim of this study is to develop a reduced-order analytical model of the bilateral contact between a carrot root and the two digging shares and to establish the corresponding centre of mass velocity and displacement relations. The closed form solution is an approximation to the retained positive-force branch under the assumed bilateral-contact regime. It identifies the formal influence of the effective harmonic contact force amplitude, oscillation frequency, and forward motion terms on root kinematics. For an illustrative, uncalibrated case at 10 Hz, increasing the effective force amplitude per share from 1 to 3 N increases local lift from 2.93 to 39.43 mm. At 2 N, lift is 20.45 mm, peak vertical velocity is 0.821 m·s–1, and the frozen-angle approximation overestimates endpoint lift by 4.05%. Direct calculations quantify amplitude, frequency and forward speed effects within the retained model. The model is intended for preliminary kinematic analysis and does not predict carrot deformation or damage.