Dynamic modeling and verification of paddy leveler based on rigid flexible coupling multibody systems

Abstract: Proper dynamic modeling is essential for the design and control of paddy field levelers which maintains a level plow while working regardless field unevenness. The simplified rigid multibody method of dynamic modeling, of which modeling and simulation can be handled by hand generally, does not work well in that they do not produce satisfactory results, and there is not easily available method for verifying the simulation results. This paper proposes a flexible multibody approach for the paddy field modeling and simulation, and a method for model verification based on high speed camera measurement. For the former method, it is simplified to decide which bodies to be classified to be rigid or flexible and the related constraint types by studying the structure and theory of the multibody system, while leaving the tedious tasks of building differential-algebra equations and equation solving to the computer-based simulation tools; and the latter method features a non-contact, stereo image way to find the 3D (three-dimensional) position of center of mass and attitude angles of a rigid body through positioning multiple surface points. 1) Modeling. By analyzing the structure and summing up the past experiences, considering that the 3 parallel rods hanging the installation block and plow showed significant flexibility in many directions, a flexible multibody system with 2 rigid bodies (plow and installation block) and 1 flexible body (representing the 3 rods with a flexible beam) and 3 revolute joints in between was built. It was assumed that the tractor body was stationary, which helped to simplify the subsequent simulation and verification by reducing the flexible beam to be a cantilever beam. 2) Simulation. The MapleSim was used to perform the simulation. By introducing the main multibody library models, i.e. flexible beam, rigid body and rigid body frame, and following general modeling procedures, the leveler model was expressed into MapleSim environment. The model parameters were determined by measurement (for dimensions) and computer software like CATIA (computer aided three-dimensional interactive application) and ADAMS (automatic dynamic analysis of mechanical systems) (for mass values and inertial momentums). Among simulation results, curves for the position of the leveler's center of mass and inclination angle were produced. 3) Verification. Formulae finding the position of mass center and attitude angles of the plow by multiple surface points' 3D positions (at least 3 points that do not fall on the same straight line) were proposed, and the surface points' 3D positions were determined by the stereo imaging system composed of 2 high-speed cameras and the professional image analysis software TEMA. Laboratory tests on specially designed fixtures were conducted, which produced the plow's 3D position of mass center and its inclination angle as measured results to be used against the simulated results for model verification. The verification showed that the 2 kinds of results generally coincided with each other well, indicating that the modeling, simulation and verification method proposed is feasible and practical, though a closer check showed the inclination curves agreed quite well, but the position curves of mass center revealed a maximum deviation of 10 cm at times. Some causes for the difference were proposed. The method proposed in this paper, which includes modeling by structure analysis, simulation using software, and verification by measuring 3D position of center of mass and attitude angles of a rigid body using high-speed cameras, is feasible and applicable to similar mechanical virtual prototyping applications featuring modeling, simulation and verification.