Dynamic stall significantly limits the flight performance of helicopters. To reveal the mechanism behind the variations in aerodynamic moments and damping characteristics under unsteady freestream， a numerical simulation method for the unsteady flow field around rotor airfoils is developed using the finite volume method， moving-embedded grid， Roe-MUSCL scheme， and S-A turbulence model. Based on this approach， numerical simulations are conducted on the unsteady aerodynamic characteristics of the SC1095 airfoil and its modified airfoils under steady/unsteady freestream and angle-of-attack conditions. Comparative analysis of the results shows that the formation and convection of the dynamic stall vortex （DSV） are the primary causes of moment stall. The trailing edge vortex （TEV） causing the DSV to lift off from the airfoil surface is the main factor contributing to the peak of the negative pitching moment coefficient. Within the scope of this paper， under steady freestream conditions， the airfoil exhibits leading-edge stall characteristics， while under unsteady freestream conditions， the stall pattern of the airfoil is influenced by its aerodynamic shape， leading to both leading-edge and trailing-edge stall behavior. The convective velocity and strength of DSV are significantly lower under unsteady freestream conditions compared to steady freestream conditions， although the differences in DSV convective velocity between airfoils of varying shapes are relatively small under both freestream conditions. Changes in airfoil camber， thickness， and leading-edge radius lead to regular increases or decreases in the phase angle of moment divergence， the range of negative damping phase angles， the peak value of nose-down moment coefficient， and its phase angle. The influence of changes in airfoil camber， thickness， and leading-edge radius on the formation and evolution of DSVs differs under steady and unsteady freestream conditions.