Based on the method of lumped parameter modeling, the torsional vibration coupling model of the tractor power output transmission system is established, as shown in the figure. The model consists of engine sub model, tractor gear transmission sub model and load sub model. The engine sub model is composed of an engine and a pair of clutches. The moment of inertia of the engine is mainly considered in the modeling. The tractor gear transmission sub model consists of two pairs of gear, internal gear, driving shaft, driven shaft and support bearing. In modeling, the mass of each bearing and transmission shaft is distributed and concentrated on the adjacent tractor gear. The load submodel includes flexible coupling and rotary tiller. Spring element and damping element are used to simulate the elastic stiffness and damping of the coupling in the process of power transmission.
The model consists of 7 rigid bodies with 17 degrees of freedom. Each tractor gear has 3 degrees of freedom, including vertical (Y), lateral (X) and rotation（ θ） Exercise. The engine and load only consider the movement in the direction of rotation. The rotation angle of engine, gear and load is θ e、 θ i（i=1，2，3，4，5）、 θ 50. The lateral and vertical displacement of the tractor gear is xi, yi (i=1, 2, 3, 4, 5).
The complexity of the model depends on the required calculation accuracy, the purpose of dynamic analysis, the contribution of each component in the dynamic response and other factors. In essence, the current model is very close to the actual system structure. In the process of simplifying the actual power output transmission system to the existing physical model, the main assumptions are as follows: the interaction between the transmission shaft system and the connecting structure is not considered, so the resonance of the gearbox box is ignored; The mass of the transmission shaft and bearing is concentrated on the tractor gear; In the process of tractor gear transmission, the transmission error of gear teeth is ignored; The resistance of the internal tractor gear pair is very small.