Determination of the contact map and load sharing of beveloid gears of parallel axes and straight teeth
DOI:
https://doi.org/10.5944/ribim.29.1.44280Keywords:
Beveloid gears, Contact map, Mesh stiffness, Load sharingAbstract
Involute bevel gears, also known as beveloid gears, are spur or helical gears whose outside radius varies linearly along the face width. Their transverse sections have the geometry of a spur gear, although the outside radius, root radius and shift coefficient are different in each one. Beveloid gears with parallel axes, with the same cone angle in pinion and wheel but with inverted cones, allow clearance control with small axial displacements, so they are used in precision positioners and robotic applications. Due to the different outside radii and shift coefficients in each transverse section, the start and end points of contact are different in each one, which means that each section starts and ends its meshing at a different moment –or different meshing position–. Consequently, despite being straight-toothed gears, they have an axial contact ratio that influences the contact conditions, which are determinant for the estimation of the load and strength conditions. On the other hand, although in this type of transmission the cone angle is small –usually, below 5º–, the variations in the shift coefficients caused by the beveloid gears geometry can be large enough to present problems of undercut or pointing in the teeth, even for small face widths, which must also be taken into consideration for the determination of the contact intervals in each meshing position. This work presents a study of the contact map and load distribution in straight-toothed beveloid gears with parallel axes, which considers the influence of the appearance of undercut or pointing in the teeth. Approximate equations are also presented for determining the pointing radius and the outside radius for a specific tooth thickness, which are necessary to introduce the appropriate corrections in the gear geometry.
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