## 3 Comparison of the Models
However, due to the lateral displacement having already reached \(-32\) mm, according to Figure 7, two-point contact between the rail and the left wheel will happen. Then, the dynamic process fundamentally changes and leads to another IRW's dynamic characters, which is out of remit in this paper. Figure 11: Lateral dynamics simulation results (V5-S1-C1). (**a**) Lateral displacement; (**b**) yaw angle; (**c**) differential wheel rotational speed; (**d**) \(y-\psi\) phase diagram. Figure 10: Lateral dynamics simulation results (V1-S10-C10). (**a**) Lateral displacement; (**b**) yaw angle; (**c**) differential wheel rotational speed; (**d**) \(y-\psi\) phase diagram. When yaw suspensions are added, as shown in Figure 12, the IRW enters the steady convergent process after some vibrations. The \(y-\psi\) phase curve is a convergent spiral line with the yaw angle's damping at the beginning. When the vibration disappears, the \(y-\psi\) phase curve turns into a straight line along axis \(\psi=0\) and toward the origin point \((y=0,\psi=0)\). Figure 13 shows almost the same curve pattern as the condition V1-S10-C10. But at a faster longitudinal speed, the speed of the lateral convergence toward 0 is also faster than that at \(v=1\) m/s, which is in accordance with the analysis of Equation (46) in Section 2.5. Figure 14 shows an interesting phenomenon on the IRW. When the longitudinal speed is fast enough, the IRW regains self-guidance ability on the straight track without yaw suspension. As analyzed in Section 2.3, owing to gyroscopic effects, if the angular  
Figure 12: Lateral dynamics simulation results (V5-S6-C6). (**a**) Lateral displacement; (**b**) yaw angle; (**c**) differential wheel rotational speed; (**d**) \(y-\psi\) phase diagram. Figure 13: Lateral dynamics simulation results (V5-S10-C10). (**a**) Lateral displacement; (**b**) yaw angle; (**c**) differential wheel rotational speed; (**d**) \(y-\psi\) phase diagram. momentum of the wheels is large enough, the direction of the angular momentum regains self-stabilizing ability. For an IRW at high longitudinal speed, the derailment tendency caused by the gravitational restoring moment can be conquered by the gyroscopic moment. Then, the IRW regains self-guidance ability. This phenomenon is named the slight self-guidance ability of the IRW in this paper. Although the IRW regains self-guidance ability at high longitudinal speeds, the gyroscopic effects can be suppressed by yaw suspension. As shown in Figure 15, the IRW enters the steady convergent process in 4 s with an initial step input of 5 mm lateral deviation. Under this condition, the yaw stiffness is 50 kNm/rad, and the yaw damping is 500 kNms/rad, which is just about 1% of the coefficients on a conventional bogie with SWs. In view of these results, for the IRW at high speeds, firstly, the self-guidance ability is regained owning to the gyroscopic effects. Secondly, the oscillation motion can be stabilized by yaw suspension with much smaller suspension coefficients, which makes the IRW much more accessible to pass curves with small radii than the SWs. As demonstrated in Figure 16, the oscillation is almost completely suppressed with larger yaw suspension coefficients. In addition, at longitudinal speed \(v=45\) m/s, the speed of the lateral convergence toward 0 is much faster than that at \(v=1\) m/s. If the simulation duration is expanded to 100 s, the whole steady convergent process can be demonstrated in Figure 17. The curves show the negative-exponential convergent process, as Equation (46) describes. Because the convergence duration is more than 60 s with initial step-input \(y=5\) mm and even at speed \(v=45\) m/s, an extra self-guidance control is necessary to be developed to speed up this convergent process. Especially if the longitudinal speed is too slow, such as during the standing start process, the convergence duration for the IRW may become too long to be practically acceptable. Thus, self-guidance control is crucially essential for the IRW at low speeds.