Multi stage gear shaft model of shearer cutting part

(a) Axis node settings (b) Timoshenko beam element

Gear shaft is a solid or hollow cylindrical member with variable cross-section, and its finite element model can be established by beam element. A series of shaft nodes are set along the axis to divide the gear shaft into several shaft segments. These nodes are mainly selected at the abrupt change of the shaft section, the center points of each gear, the center points of each bearing, the power input and output points, etc., as shown in Figure 1 (a). The two nodes and the axial segment between them are represented by a beam element. Euler Bernoulli beam is a classical spatial beam element, but it ignores the effect of shear deformation, so it is generally used for slender beams with aspect ratio (axial length / section diameter) greater than 15. Timoshenko beam considers the effect of axial shear deformation, and is suitable for both slender beam and short thick beam. Fig. 1 (b) is the schematic diagram of Timoshenko beam element. There are two nodes, each with 6 degrees of freedom.

(a) Schematic diagram of gear shaft (b) Gear shaft matrix

It is not difficult to write the mass matrix and stiffness matrix of Timoshenko beam element, and it is not the focus of this paper. Here, the method of constructing gear axis matrix from beam element matrix is simply introduced, as shown in Figure 2. Taking a 5-node gear shaft model as an example, the shaft contains four Timoshenko beam elements, and the mass matrix or stiffness matrix of the shaft is composed of four element matrices in the way shown in Fig. 2 (b).