A number of analysis methods for the process with chatter vibration have been proposed so far. These methods can be used to improve processes stability resulting in better production efficiency. However, the poor estimation accuracy of the phenomenon severely limits the performance of process optimization using the simulation-assisted approach. One of the causes of accuracy deterioration is the modeling error of the phenomenon accompanied by chatter vibration with finite amplitude. In this study, we developed a model that can consider the non-linear uncut chip thickness fluctuation caused by the influence of finite amplitude and the process damping due to the contact of the tool flank face against the finished workpiece surface. Furthermore, we developed a time domain simulator that implements the proposed model, and estimated the finished surface profile of the workpiece based on the results of the time domain simulation. To verify the proposed method, corner machining experiments with an end mill were conducted. Corner machining is frequently used in industrial, but it is known that chatter vibration is likely to occur. In corner machining, machine tools generate motions that accompany acceleration and deceleration. The motion of this feed drive system strongly depends on the dynamic characteristics of the machine tool and the trajectory generation algorithm, which greatly affects the emersion angle of the cutter. Therefore, we simulated the dynamic corner machining process considering the measured data of the motion trajectory of the feed drive system. The estimation result of chatter vibration in corner machining is in good agreement with the measurement result of the machining process. In addition, high-precision estimation of the machined surface profile with chatter mark has been realized.