Empirical relations to predict the probable percentage of reduction in root fillet stress in spur gear with circular stress relief feature

摘要

This work presents the possibilities of percentage of reduction in the root fillet stress of spur gear by introducing circular stress relieving feature of various sizes at different locations. Two categories of systematic analyses are carried out using finite element model of spur gear. In the first category of analyses emphasize is given to determine the maximum root fillet stress which is required as reference to determine the stress reduction factor. In addition to this, the effect of number of teeth, pressure angle, and basic parameters of rack cutter on root fillet stress is investigated. In second category which is the prime focus of this work; the effect of introducing geometric stress relief feature is carried out. Circular stress relief feature of different size at strategic locations on a spur gear tooth are introduced. This reduces the root fillet stress. The magnitude of the load shared by a gear tooth depends on the position of the point of contact of teeth engagement along the line of action. It also depends on contact ratio. High contact ratio gear teeth pairs are subjected low load in comparison low contact ratio gear for transmitting same amount of torque. A tooth is released from the load as soon as it disengages with the mating gear tooth and it is taken by the next conjugate tooth. Therefore the gear teeth are subjected varying (fatigue) load. If a gear fails by bending fatigue, the failure is catastrophic and occurs with little or no warnings. The maximum root fillet tensile stress is one of the key factors which determine the fatigue life of the gear. Therefore the magnitude of the maximum value of the root fillet tensile stress can be treated as the index of fatigue life of gear. Even slight reduction in root fillet stress leads to a large increase in fatigue life of the gears designed for the stress level above endurance limit. This type of design consideration is very common, where safety and light weight are the principal design criteria. Therefore for all the reasons cited above, this work is of more practical importance. The program is coded in ANSYS Parametric Design Language (APDL). It automates the task of creation of model, meshing, applying boundary conditions, choosing the appropriate density of the mesh depending on the stress gradient. It also provides a means for defining the diameter and location of the circular stress relief features.