Toothing Kinematics of a Combination Hyperboloid Gear

This article examines the potential of gear tooth cutting for a single-sheet hyperboloid of revolution workpiece. The known methods of gear cutting based on a single-sheet hyperboloid of revolution workpiece involve the line-by-line material removal from the stock with a shank tool, that increases the labor intensity of manufacturing significantly. For this reason, such gears have not gained widespread acceptance due to their potential replacement by other transmission types with intersecting axes. This article examines toothing kinematics for gears using a single-sheet hyperboloid of revolution workpiece by means of gear turning. Analytical relationships for tooth shapes for gears produced on a single-sheet hyperboloid of revolution workpieces by means of gear turning are derived. It is shown that for gears with a single-sheet hyperboloid of revolution initial surface shape, the tool-to-gear shaping process is possible only for a given gear ratio, even with the same modulus. For this reason, the tool will have the same number of cutting edges (“plates”) as the machined gear to be engaged with. To reduce labor intensity, parametric models of the pitch hyperboloids of the gear being machined and the tool are proposed. Due to the specific tooth geometry of such gears, tooth flank machining is proposed to be performed in two setups. During toothing, the correct position of the cutting edges relative to the gear flank is adjusted using setup bases. It is necessary to develop a rational design for the cutting tool and plate geometry for further study the toothing kinematics, and study the feasibility of tooth shaping on multi-axis CNC machines using simulation and real-life models.