It is well known that in various arrangements and shapes on the plane, the hexagonal honeycomb (see Figure 1) is the densest and most uniform. The most fundamental and important feature of this arrangement is that any point is The distance between all the adjacent 6 points is equal. The "point" here can also be called "node". In industrial applications, the shape of the hexagon is usually applied to any shape that requires dense mesh. In the shape of a honeycomb, for example, the mesh shape of the screen is almost a replica of the honeycomb, and the hollow portion is a regular hexagon (or a variant close to a regular hexagon), and the remaining portion is the side length of the regular hexagon; The arrangement of vents, louvers, and the like of some mechanical, electrical, or electronic devices mostly conforms to such a regular hexagonal honeycomb shape.
Here is how to drill a hexagonal honeycomb distribution hole group on a cylindrical surface.
The four-axis CNC milling machine is used here. Because it is only drilling, the machine does not necessarily need to be a four-axis four-axis "true four-axis", even those that are additionally installed on the basis of the three-axis linkage machine. The so-called "pseudo four-axis" that can be four-axis and three-link is also applicable, so it has high practical value in actual production.
Fig.1 Schematic diagram of a regular hexagonal honeycomb cell group on a cylindrical surface
For the cylindrical structure with small wall thickness, if it is a batch production, combined with the processing technology and economy, it will generally be realized in the form of a sheet metal part, that is, the flat six-plate is punched out by the cold-punching die. The shape of the honeycomb honeycomb hole; if the amount is too small (like the prototype), you can also consider using a CNC punch or CNC drilling machine to machine the holes, then make the cylinder by the coiling method, and then weld the interface, this is not in this paper. Within the scope of the discussion.
For the cylinder shown in Fig. 1, the wall thickness is large, which is difficult to realize in the form of sheet metal parts; or because of the special use, it is necessary to use a seamless pipe structure; or the dimensional accuracy is high, and then it is necessary to use Rotate the workbench to assist machining. There are two ways here: one is to install a common indexing head on a general three-axis linkage machine, and clamp the cylinder on the indexing head, determine the corner of each time by calculation, and manually divide the indexing head. Let it stay at each preset angle in turn, and then complete the drilling work with a simple procedure. Obviously this is not within the scope of this article; the other is the application of the four-axis machining method described in this article.
Fig. 2 Schematic diagram of the development of a regular hexagonal honeycomb hole group on a cylindrical surface
It is assumed here that the fourth axis (rotation axis) is the A axis, and the A axis is parallel to the X axis. As shown in Fig. 2, the expanded view of the cylindrical surface, the hole groups in the figure can be divided into two groups according to the characteristics, and the two groups are staggered. In the calculation, it is necessary to consider the mutual positional relationship between the two groups of holes. In each group, the holes are evenly distributed equidistantly in both the X-axis and the A-axis. Since the expansion map is expressed here, the calculation of the hole spacing is performed. And the determination is not as simple as drilling holes in a plane.
As shown in Figure 2, the "equal distance" of the hole in the length of the X-axis is completely a linear "equal" on the X-axis. The control and calculation of the length is divergent, and the precise calculation mode will not How much inconvenience and error is brought.
The "equal distance" of the hole in the circumferential direction of the A-axis is completely "equal" from the angle of the central angle of the X-axis axis, specifically "equal angle". The calculation of the angle of the central angle is convergent, because the arc closes one axis is 360°, while the calculation on the circumference of the circle is still divergent, the radius of the cylinder is different, the corresponding arc length is also different, and then directly Affecting the hole spacing on the circumference of the circumference, how to coordinate the relationship between the two becomes a key to the mathematical expression in this case.
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