文档介绍：Helicoids’ Project
The helicoid calculation is very simple and can be easily guessed using simple trigonometry,
however, manufacturing does not follow the same trend.
The unfold calculation of the helicoid made using the classic and trigonometric method is shown in
the figure below using the following data as an example:
All the mathematics of the solution is based on the following geometric conditions:
1- There are two lengths which are the hypotenuses of the triangles formed by the pitch and the
perimeters of the helix (both the internal and external helix). In the example, these two
lengths are and .
2- These two lengths must be traced on the plate in a concentric way and kept apart from each
other by the distance of the height of the helix, in the example, 243mm. To make this
possible, an external radius of the unfolded part is calculated to meet this condition. In the
example, . The external radius will then be the sum of the internal radius and the
height of the helix: 939 + 243 =
3- With the external radius = and the perimeter = , using the classic
trigonometric formula: Angle=perimeter/radius, that is, = radial or
degrees.
What normally happens when manufacturing the auger (mainly using thicker plates) are the
following problems:
a) Difficulty in conforming which usually results in a great distortion in the original geometry and
frequently it is necessary to use a flame (heating with fire) to help in the deformation. This very
promises the fidelity of the unfold calculation with the final result.
b) Difficulty in reaching the perfect positioning of the internal hélice of the auger with the
hypothetical hélice external to the tube forcing thus, the axial growth of the auger (apparent
increase of the pitch)