A Practical Approach for Modeling a Bevel Gear
|Publication Date:||1 October 2014|
The modern bevel gear design engineer is often faced with knowing the basic appearance of the bevel gear tooth that he is designing. The geometry of the bevel gear is quite complicated to describe mathematically, and much of the overall surface topology of the tooth flank is dependent on machine settings and the cutting method employed. AGMA 929-A06, Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius, lays out a practical approach for predicting the approximate top land thicknesses at certain points of interest regardless of the exact machine settings that will generate the tooth form. The points of interest that AGMA 929-A06 is concerned with consists of toe, mean, heel, and the point of involute lengthwise curvature. The following method expands upon the concepts described in AGMA 929-A06 to allow the user to calculate not only the top land thickness, but the more general case, the normal tooth thickness anywhere along the face and profile of the bevel gear tooth. This method does not rely on any additional machine settings; only basic geometry of the cutter, blank, and teeth are required to calculate fairly accurate tooth thicknesses. The tooth thicknesses are then transformed into a point cloud describing both the convex and concave flanks in a global Cartesian coordinate system. These points can be utilized in any modern computer aided design software package to assist in the generation of a 3D solid model. All pertinent macro tooth geometry can be closely simulated using this technique. Furthermore, a case study will be presented evaluating the accuracy of the point cloud data to a physical part.