Toothed gear design and manufacturing method

Abstract

A method of gear design perfects design of gear teeth geometry (,) instead of limiting gear-tooth design to present cutter geometry and manufacturing methods. A pair of varied-diameter cutters (,), such as hypoid cutters, have a geometric form that generates variable diameter toothed elements. Structures of hypoid or other varied-diameter cutters are achieved with a cutting tool (,) having a design cross-sectional shape of an idealized space between gear teeth on both of a pair of cutters. The cutter tool is rotated and reciprocated in shaping or machining relationship to other cutter blanks (,) or workpiece (,) in design rotation on cutter axes of a cutting-machine spindle (,). The cutter axes have variable heights above the cutter tool. Simultaneously with shaping or machine cutting either cutter blank, the angle of reciprocation and linear positioning of the cutter tool and height of center of the cutter axes are varied designedly. Appropriate cutting edges (,) are then formed on or attached to the varied-diameter cutter so formed. Pairs of gear blanks are then cut to perfected gear form by the pair of varied-diameter cutter tools. The same method and machine used for making varied-diameter cutters can be employed for cutting gears (,) directly. The machine can also be used to manufacture dies or molds to produce toothed bodies. The method is based on general new mathematical formulations for conjugate surfaces in space for any motion or load transmission between generally oriented axes.