Multiple frictional impact dynamics of threshing process between flexible tooth and grain kernel

The flexible threshing tooth is of interest to researchers in agricultural mechanization, due to the fact that impact, knead force, and rate of damnification decreases obviously compared to the traditional rigid pole-tooth, and it is propitious to increase the synthesis benefit for grain production. The multiple frictional contact dynamics of the flexible threshing tooth against grain kernels is presented by using an addition-deletion constraints approach in this study. The flexible threshing tooth is based on flexible-rigid coupling theory. A correlation matrix and four contact points index metrics are introduced. The system formulations for separation, initial contact, stick, and slip are established respectively by using different Lagrange multipliers. The impulse-momentum method is adopted herein to calculate the jump discontinuities. And the concept of a tangential sliding friction potential is introduced to represent the sliding friction effects. The corresponding computational strategy and numerical simulation C++ software are implemented. Several numerical examples adopted to demonstrate the efficiency of the presented approach and algorithms. The peak collision forces on normal and tangential directions are not synchronized. The occurrence of numerous sub-collisions among one macro-collision arises from the coupling of rigid motion and high-frequency deformation vibration of the flexible tooth. The flexible tooth has a less impactful knead force than the rigid one for cracked grains or seed, so as to reduce rate of grain damnification, and is thus propitious for increasing the synthesis benefit for paddy production.