محاسبه‌ي سفتي درگيري دندانه چرخ‌دنده‌ي مارپيچ به‌كمك تابع تنش

Helical gears are widely used in power transmission systems due to the gradual engagement of teeth an‎d a favorable load distribution. One of the key parameters in the dynamic analysis of these gears is the time-varying mesh stiffness, which plays an important role in transmission error an‎d the vibrational response of the system. In this research, an analytical method is presented for eva‎luating the mesh stiffness of a helical gear tooth based on a three-dimensional stress function an‎d the total strain energy method. To this end, the three-dimensional stress distribution induced by the different components of the meshing force is analyzed, an‎d a stress function consistent with the bending, shear, an‎d torsional stress fields within the tooth is formulated. Using this stress function, the strain energy associated with the various deformation modes of the tooth is computed, an‎d the single-tooth-pair mesh stiffness an‎d, subsequently, the overall time-varying mesh stiffness are determined. For validation, the analytical results are compared with those obtained from finite element simulations, an‎d a good agreement between the two sets of results is observed.

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