Aiming at the gyroscopic effect of the wheelset, the hunting motion mechanism is researched with the energy integration method, and the energy flow of the wheelset hunting motion is obtained. The Hopf bifurcation is analyzed using the shooting method, and a comparison between the gyroscopic system and the non-gyroscopic system is presented, along with the effect of the wheel spin phenomenon on critical speed. Moreover, the definition of the stability coefficient and gyroscopic forces contribution rate are proposed, and the impact of gyroscopic forces on stability is quantitatively analyzed. The results show that the gyroscopic force does not work in the wheelset system, but the system becomes more stable. The gyroscopic contributory ratio for stabilization significantly increases with increasing velocity when the operation speed is high enough. Thus, the effect of gyroscopic forces cannot be ignored and should be a key factor in the actual analysis.