<p>Dry hobbing provides a promising solution for industrial gear production with high productivity and superior environmental benefits. However, the presence of chatter vibrations poses a significant challenge to productivity and attainable geometric accuracy, which is commonly predicted with a stability lobe diagram (SLD). The complex spatial engagement relationship and the coupling dynamics of the hob and workpiece pose a challenge in constructing a reliable SLD for dry hobbing. To this end, this study develops a hob-workpiece coupling dynamic model to predict the stability boundary of dry hobbing. First, the engagement relationship between the hob and workpiece is modeled, and the effects of multi-axis vibrations on regenerative chip thickness are deduced based on homogeneous coordinate transformation. Then, the parametrical representations of dynamic cutting forces induced by regenerative chip thickness are derived. After that, the cutting dynamic model of the hob-workpiece coupling system (HWCS) is established, and the SLD expressed in terms of hob rotation speed and feed rate combination is predicted by solving the dynamic model using the semi-discretization method (SDM). Meanwhile, numerical simulations are performed to analyze the effect of hob posture variation on the predicted SLD. Lastly, experimental tests were performed to validate the accuracy of the developed model, and experiment results were in good consistency with analytical predictions. It is demonstrated that the coupling dynamics and hob posture have noticeable impacts on the hobbing stability boundary, which should be considered for a stable hobbing process. This study can provide a basis for process parameters optimization with chatter-free and high-efficiency dry hobbing.</p>