Preliminary issues in the reverse engineering of an spur gear with non-standard geometric parameters

Abstract

The paper presents issues related to an attempt to recreate the geometry of an involute spur gear with non-standard geometric parameters such as: module m = 4.98 mm, radial clearance factor c* = 0.383, addendum modification y = 0.795, profile shift x = 0.0695, profile angle α = 26.325° and with straight teeth, made in the 6 degree IT, using conventional techniques and measuring instruments. In the process of recreating the geometry of the tested gear, a completely different set of parameters was obtained: m = 5 mm, c* = 0.418, y = 0.81, x = 0.0143, α = 26.806°. The correctness of the reconstructed geometry was assessed by comparing the position of the contour of the involute of the nominal gear with the contour of the involute of the reconstructed gear, establishing that the error value ∆e along the radius leading tangent to the base circle of the restored gear was 0.0054 mm. However, the most important stage of this work is to demonstrate that two involute gears with straight teeth can be identical despite using different geometric parameters in most of them (including, in particular, different modules m and different nominal profile angles α). A formula was derived to calculate the exact value of the profile shift for a new, alternative set of geometric parameters with a different module. A matrix was developed that allows making calculations to derive two identical gears with alternative sets of geometric parameters. Therefore, a proper and valid alternative set of geometric parameters was adopted for the reproduced gear for which the modulus was m = 5 mm, together with c* = 0.380, y = 0.793, x = 0.0325, α = 26.784°. The paper also outlines further research plans.

Reverse engineering of geometric design parameters using shape information of non‐standard spur gear

“…The center distance (c 1 ) of the profile shifted gear is calculated by applying the center distance modification coefficient (y) to the center distance (c 0 ) of the standard gear and is the same as Formula (7). Here, ym is the difference between c 1 and c 0 , and if 0.8 is substituted into the modulus, y is calculated as 0.6.…”

“…Gear reverse engineering, like design, is a complex process involving numerous design parameters and elements. This complexity makes finding gear design parameters a very difficult requirement [7][8][9]. Previous research on gear reverse engineering utilized 3D scanning, scanning and rapid prototyping, and machine learning to extract the gear geometry of powertrains such as automatic transmission systems, damaged motor cam gears, and gear wheels, and compared them with the original products [10][11][12][13].…”