This work details research on the formation mechanism of wheel polygonalization in high-speed trains and its effect factors by numerical modeling in order to prevent the increasingly prevalent problem of wheel polygonal wear. The lateral self-excited vibration model of a wheel was developed using the LuGre friction model and self-excited vibration theory. The properties of wheel self-excited vibration and the crucial condition of Hopf bifurcation were investigated; the process of wheel polygonal wear was simulated and the results were validated using field tracking data. The results demonstrated that periodic self-excited vibration generated by Hopf bifurcation is a required condition for polygonal wheel attrition at a given speed. The wheel’s polygonal wear has the following characteristics: “Constant speed—Self-excited—Fixed frequency—Divisible.” The order of the polygon is determined by the ratio of the wheel lateral self-excited vibration frequency to its rotational frequency. Wheel polygonal wear was caused by the vertical dynamic force of the wheel rail. The findings of the study can serve as a theoretical foundation for the prediction and reduction of wheel polygonal wear.