A new approach for the calculation of worm shaft deflection in worm and crossed helical gear drives

Worm gear drives are characterized by a simple design, which allows the realization of a high gear ratio within one stage. Furthermore, they are characterized by low vibration and noise behavior. For these reasons, they are used both as power transmissions and servo drives in various drive solutions. The allowable load and the lifetime of the gearbox is usually limited by wear on the softer worm wheel. The stiffness and the associated worm shaft deflection is considered as an influence factor on the wear as well as the Noise, Vibration, Harshness (NVH) behavior of worm gear drives. According to the current state of the art, the worm shaft deflection can be calculated according to AGMA 6022, DIN 3996 and ISO/TR 14521. In this paper, the current calculation status for worm shaft deflection is discussed. The underlying experimental results for the calculation of the worm shaft deflection according to DIN 3996 and ISO/TR 14521 are analyzed. A new approach for the worm shaft deflection calculation is developed. Therefore an analytical model for the bending stiffness of a worm shaft is developed. The model was validated through various FEM simulations. As a result, a new calculation method for the equivalent bending diameter of a worm as well as the formulae for the calculation of the worm shaft deflection are presented. The developed calculation method details the current state of the art, thus providing a basis for more optimized worm gear design. Furthermore, with this calculation it is now possible to calculate the bending stiffness of overhung worm shafts as well as worms of reduced tooth thickness which are usually used in crossed helical gear boxes. The new calculation method is presented within this paper and compared to the current state of the art for calculating the worm shaft deflection according to AGMA 6022, DIN 3996 and ISO/TR 14521.