A Study On Elastic Meshing Effect Of The Internal Gearing With Small Tooth Number Difference

The internal gearing with small tooth number difference finds its application in many fields due to the advantages such as large transmission ratio, high load capability, compact volume and simple structure, etc.The tiny clearances between working profiles of each non-contact tooth pair near the action line may diminish under heavy load, which makes the actual contact teeth number exceed the theoretic contact teeth number calculated by contact ratio. In other word, the load supposed to be applied on one teeth pair is now shared by multiple teeth pairs. Thus, the load capacity of the gearing is increased greatly. This phenomenon is called Elastic Meshing Effect (EME). It is of great significance to explore EME to increase the load capacity, to minimize the volume and to reduce the manufacturing cost.By considering the teeth deformation, normal contacting stiffness, and base pitch errors, a mathematic model is developed in this thesis to explore the state of multi-teeth contact and load distribution. The correctness of this model is validated by the simulated results of a finite element analysis (FEA). The base pitch error is treated as normal distributed error and calculated into the clearances between the working profiles. A mass of teeth pairs as well as gearings with different errors are analyzed to reveal the effect of the errors with Monte Carlo Random Simulation method. The analysis indicates that the base pitch errors counteract the active effect of the EME. The FEA simulation also confirms the negative effect of base pitch errors.To compensate the negative effect of pitch errors, a method called Strengthening with Over Loading (SOV) is proposed. To be detail, the gearing is running at a load twice or triple of normal load for several hours before its actual use. Plastic deformation will take place in the roof of every gear and residual stresses are produce to counteract the normal working stress. The traditional formulas for gear roof stress are modified on the basis of mass of FEM calculations for internal gearing with small tooth number difference. And the factor of EME is introduced into these formulas.The research provides a theoretical guideline for the study on EME, with which we can increase the load capacity of internal gearing with small tooth number difference.