Bolted joints are widely used in aeroengine rotor systems to connect multiple components into an integrated structure and provide sufficient stiffness. The mechanical properties of a bolted joint have a significant effect on rotor dynamics. For modern aeroengine designs, the blade-tip clearance is gradually reduced to improve efficiency, which may lead to rubbing damage and affect safe operation. The mechanical properties of a bolted joint change significantly during the blade−casing rubbing process and influence the dynamic properties of the rotor system. Based on the finite element (FE) modeling method, a 15-node bolted joint rotor system model is established in this paper, in which the bolted joint is represented by a 2-node joint element, and the blade−casing rubbing force is considered. The Newmark method is used to solve the motion equations. The dynamic model is validated by comparing the frequency response characteristics for different numbers of blades with the results provided in other published studies. Based on the established model, the effects of the rotational speed, number of blades, and rubbing stiffness on the dynamic responses, normal rubbing forces, and bending stiffness of the bolted joint are evaluated by numerical simulation. The results show that the response amplitude and bending stiffness of the bolted joint change significantly under blade−casing rubbing faults, and the mean value of the vibration response deviates significantly from 0 as the number of blades increases. Meanwhile, the amplitude of the frequency component fVC and the maximum value of the normal rubbing force also increase as the number of blades increases. The main contribution of this paper is the establishment of a new model for a bolted joint rotor system, considering the time-varying bending stiffness of the bolted joint and the blade−casing rub fault, comparing the simulation results to obtain some general results bridging the current research gap. Meanwhile, the numerical results in this paper can provide a cognitive basis for the blade−casing rubbing fault mechanism of a bolted joint rotor system under the influence of speed, number of blades, and rubbing stiffness. The nonlinear dynamic characteristics observed in the present paper can be applied to the blade−casing rubbing fault diagnosis of turbomachines.