Based on Laplace transform and Hurwitz stability criterion, the system characteristic equation and algebraic stability criterion of the two degree-of-freedom angular free vibration of dry gas seal are derived. The effects of rotational inertia, stiffness and damping parameters on the angular free vibration stability of dry gas seal are analyzed by using the root locus method and the concept of the closed-loop dominant pole. The results show that the constraint condition of rotational inertia is the most demanding of all stability conditions. Both the angular main damping and main stiffness are not simply the larger the better, but there are preferred values in the interval greater than the stability threshold. The approach of the absolute value of the cross coefficient to zero is beneficial to the suppression of angular free vibration. There is a threshold of rotational inertia, which makes the cross stiffness change from having only the lower limit value to both the upper and lower critical values at the same time.

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