The addendum surface HIIcHc (for example) is a part of the conical surface on which the discrete lattice can be directly transformed from the point rotation on the common edge HI. The method of generating the discrete lattice of the root surface is the same as the top surface of the tooth. Hypoid gear large wheel structure 2.2 The rim of the left side of the rim of the two sides of the rim CDFE (for example) can be seen as an infinite number of conical lines arranged along the length of the tooth. The common edge FE is on the opposite side of the CD. Any point B is a point on the intersection of two conical surfaces. The two conical surfaces are AGBBcGcAc and CDDcCc.
A rectangular coordinate system is established on the rotating projection surface of the gear (as shown in Fig. 3), and the coordinate of the point A on the curve HI is (x0, y0, z0), and the coordinate of the B point on the boundary line of the B rim (x, y, z) is: x=[(y20 z20)1/2-tan(90b-<)]/[tanA-tan(90b-<)], y=(y0/z0){x0tanA/[1 (y0/z0 2] 1/2}, z = x0 tan A / [1 (y0 / z0) 2] 1/2, where: < is the taper angle of the gear section; A is the taper angle of the cone where the rim of the rim CDDcCc is located.
The discrete points on the left side can be obtained by rotating the corresponding points on the right side. The three curved surfaces of the front cone surface, the back cone surface and the bottom surface of the hub are respectively located on different three conical surfaces, and the discrete point calculation method is similar. The calculation process is illustrated by taking the back cone surface (the curved surface abcdef) as an example. The coordinates of the points on the boundary curves ab, bc, cd, de and af have been calculated. There is a directional curve between the two sides of the conical surface and there is only one shortest space-gauge hyperboloid gear. According to the law, if the coordinates of two points are known, the coordinates of any point on the curve can be obtained. Connect any two points m and n on the boundary, and set the coordinates to be: (x1, y1, z1) and (x2, y2, z2). When the curve segment mn is discretized into N segments, the coordinates of the i-th point are atan ( Y1/z1)]/N.
The six intermediate surfaces of the intermediate surface are located in the inner layer of the model, and their position and shape have little effect on the analysis results. Therefore, to facilitate the calculation and meshing, the surfaces 1 and 4 are taken at the middle symmetry of the model, 2 and 6 are taken at the root transition curve and the tooth surface, 3 and 5 are taken at half the thickness of the rim. These surfaces are fitted by a Kongsian surface. The specific equations are described in [3].
It can be seen from the above that once the parameters of the gear change, the coordinates of the discrete points on all the surfaces will change accordingly, and thus the discrete point coordinates of the parametric model are obtained.
After the finite element model is automatically generated to obtain the discrete points on all surfaces of the parametric model, the solid model of the gear is no longer created in the CAD software, but the sub-models are created in the finite element analysis software in a certain order. The layer entity, which ultimately produces a one-tooth solid model of the gear. Since the number of elements in the finite element model directly affects the accuracy, calculation time and storage space of the analysis results, the number of segments of the boundary curve of the model is controlled interactively by programming, so that the number of cells of the model can be modified arbitrarily. In order to align the cells neatly and avoid deformed meshes, the number of segments in the same direction is preferably the same. When dividing the grid, pay attention to the place where the stress is concentrated. The grid should be divided thinly, and the other places can be thicker and gradually transition from fine to coarse. The length of each line segment on the boundary curve is set to an equal ratio sequence, and the number of segments and the scale factor of the curve can be adjusted to control the number of cells and the grid thickness.
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