David Dooner graduated from the University of Florida in 1991. Afterwards, he was a visiting scientist with the Russian Academy of Sciences in Moscow and joined the University of Puerto Rico-Mayaguez (UPRM) in 1994. Since joining UPRM, he has been involved with teaching, services, and research. His research focus involves a mathematical approach for the design and manufacture of general hypoid gear pairs. He currently teaches mechanism design, machine design, and senior capstone design. He is currently a member ASME, ASEE, and AGMA.
This paper presents the geometric design of hypoid gears with involute gear teeth. An
overview of face cutting techniques prevalent in hypoid gear fabrication is presented. Next,
the specification of a planar involute rack is reviewed. This rack is used to define a variable
diameter cutter based upon a system of cylindroidal coordinates; thus, a cursory presentation
of cylindroidal coordinates is included. A mapping transforms the planar involute rack into a variable diameter cutter using the cylindroidal coordinates. Hypoid gears are based on the envelope of this cutter. A hypoid gear set is presented based on an automotive rear axle.
A very important parameter when designing a gear pair is the maximum surface contact stress that exists between two gear teeth in mesh, as it affects surface fatigue (namely, pitting and wear) along with gear mesh losses. A lot of attention has been targeted to the determination of the maximum contact stress between gear teeth in mesh, resulting in many "different" formulas. Moreover, each of those formulas is applicable to a particular class of gears (e.g., hypoid, worm, spiroid, spiral bevel, or cylindrical - spur and helical). More recently, FEM (the finite element method) has been introduced to evaluate the contact stress between gear teeth. Presented below is a single methodology for evaluating the maximum contact stress that exists between gear teeth in mesh. The approach is independent of the gear tooth geometry (involute or cycloid) and valid for any gear type (i.e., hypoid, worm, spiroid, bevel and cylindrical).