Unification of the сycloidal gearbox calculation method and the cylindrical involute gear calculation method

The paper considers methods for calculating the cycloid gearboxes widely used in machine tool building, robotics and other industries. It was established that these methods, unlike methods in calculating the cylindrical involute gears (according to GOST 21354–87 and ISO 6336:2006), do not allow analyzing the influence of various factors (material parameters, pin diameter, eccentricity, transmission module, etc.) on the safety factor. It is shown that for a cycloid gear, the ZE coefficient, which takes into account the elastic moduli and the Poisson’s ratios for contacting bodies (pin and satellite), could be determined using the same formula as for the involute gear. The ZE coefficient values for various satellite materials are provided. Assuming that main condition for the cycloidal gearbox performance is contact endurance of the satellite-working surface, a formula was obtained to estimate contact stresses at the point of the satellite contact with the most loaded pin. This formula is similar to that for calculating the involute transmission. The ZH coefficient was proposed to take into account geometric parameters of the mating bodies (pin and satellite). To represent geometric parameters in the dimensionless form, calculation used the cycloid shortening coefficient that formed the satellite working profile; besides, the relative pin diameter was introduced equal to its diameter ratio to the transmission module. The proposed formula shows that the ZH coefficient could take the smallest value (3.3) when selecting optimal values of the cycloid shortening coefficient and the pin relative diameter. Graphical dependences of the ZH coefficient on the specified parameters are presented for gears with epi- and hypocycloidal satellites and with different pin numbers. The resulting graphs make it possible to quickly evaluate contact stresses in the cycloidal gearbox, which is convenient in the design calculations.

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