In this paper, the relationship between the frequency split and the mode-coupling in the disc doublet mode, which is expressed according to the pattern of the surface of the disc, is utilized by using of 3 types(Chaos, Vent-hole, Normal). As the frequency split between the doublet mode disc that is expressed in the model through the interpretation is larger, and analogy through interpretation mode-coupling instability also lower. Vent-hole, which has a relatively large frequency split of disc doublet mode in 3 types(Chaos, Vent-hole, Normal) model, showed a large value of critical coefficient of friction in which mode-coupling instability is expressed. In addition, it was confirmed by analysis that the Vent-hole had a relatively large frequency split than the other models by analyzing the change in contact stiffness. It can be concluded that the larger the frequency split of the disc doublet mode, the lower the instability due to the mode-coupling.