The effect of different profile modifications on the static and dynamic transmission error of spur gears

Profile modifications are a common practice to mitigate torsional dynamics and enhance mechanical efficiency in geared systems. Therefore, it is necessary to develop analytical tools that accurately predict the effect of such modifications on mesh stiffness and dynamic behavior of gear trains under both design and off-design conditions. This paper presents a novel analytical mesh stiffness model for spur gears that embodies conventional compliance phenomena with the effects of profile modifications and the enlargement of the line of action under load. The model accuracy is verified by comparing the results with FEM simulations. Subsequently, a dynamic model for spur gears incorporating time-varying backlash introduced by the modification is presented and validated using experimental data available in literature. Moreover, both the static and dynamic models are applied to conduct a sensitivity analysis of various profile modifications, aiming to capture the effects of intentional and unintentional deviations from the ideal involute profile. Notably, this type of analysis highlights the effects that modifications have on the harmonics associated with gear mesh stiffness and on the dynamic behavior of the system under varying loads. This exploration establishes the foundation for microgeometric optimizations of these types of system.