In the assembly process of an aero-turboshaft engine， the coaxiality errors of the curvic couplings are an important techni? cal index， significantly affecting the performance and service life of the whole system. This study takes the turbine blade-casing of an aero-turboshaft engine as an example. The coaxiality errors （including both positional and orientation errors） of the curvic cou? plings are introduced into the clearance function of the blade tip-casing， the nonlinear dynamic model of a rotating taper-blade cas? ing system is then proposed based on the Hamilton variational principle and the Galerkin method. The effectiveness of the proposed model is verified using ANSYS software. Two different acceleration functions are proposed： Function 1 assumes a constant accel? eration value， while Function 2 adopts a cosine wave form for acceleration. The effects of different coaxiality errors of the curvic couplings on the transient response during both acceleration functions are further investigated using Newmark-β numerical method. Simulation results show that an increase in the coaxiality error of the curvic coupling leads to a reduction in the minimum clearance between the blade tip and casing， resulting in a more serious amplitude amplification induced by blade-tip casing rubbing. Com? pared with Function 1， Function 2 enables the system to pass through the critical speed more quickly， which advances the start time of rubbing. In addition， the maximum rubbing force and penetration depth can be effectively reduced due to the effects of the deceleration， weakening the rising and jumping phenomena in the system.