Tooth Influence on Flexural and Torsional Flexibility, and Model Tooth Number Prediction for Optimum Dynamic Simulation of Wide-Faced Spur Gears

Refined dynamic analyses of gear pairs, including precise tooth contact description, often lead to unreasonable simulation requirements. Therefore, numerous models employ simplifications, such as two-dimensional deflection of the engaged gear set, which is inappropriate for wide-faced wheels. Other models propose three-dimensional (3D) representation of one tooth on a complete hub. This approach introduces the torsional and flexural deflection of the gear body, but underestimates the corresponding stiffness. Since forthcoming improvements of gear analysis should offer efficient 3D dynamic simulation of wide-faced gear sets, this paper primarily quantifies the flexibility error levels implied with 3D one tooth full hub spur gear models. Subsequently, a procedure is developed to determine the number of teeth required for a 3D model so that it will include the torsional and flexural flexibility of the spur gear body, within acceptable error levels. This procedure offers an efficient approach to optimize the (precision)/(simulation time) ratio. The method deals with gears of any diametral pitch, and covers the common face width and tooth number ranges.