A Study of Suspension Geometry for Personal Mobility Vehicles (PMVs) with Inward Tilt Mechanism

: Personal Mobility Vehicles (PMVs) have a long history as compact and highly efficient vehicles, but in recent years, a completely new PMV concept, which tilts inward during turning, has attracted attention. The authors have been studying the social suitability of the two front wheels one rear wheel PMV with an active inward tilting mechanism. Although, PMV that tilts inward during turning, may has a tendency for pitching during turning like automobiles depending on the roll axis arrangement, the suspension spring constants are not allowed to be set high like motorcycles, therefore it is difficult to suppress the pitching. For this reason, it is strongly required to suppress the pitching tendency with the suspension geometry itself. However, since the PMV that tilts inward during

Although, PMV that tilts inward during turning, may has a tendency for pitching during turning like automobiles depending on the roll axis arrangement, the suspension spring constants are not allowed to be set high like motorcycles, therefore it is difficult to suppress the pitching.For this reason, it is strongly required to suppress the pitching tendency with the suspension geometry itself.However, since the PMV that tilts inward during turning is a new concept, there are not such theoretical studies, previously.
If the aim is equalization the amount of sinking in the front and rear during turning, the requirements for the suspension geometry can be analyzed using the force balance model in the back view as shown in Figure 1, in which the vehicle mass is divided by the front and rear distribution.
Table 1.Vehicle specifications.In a PMV with two front wheels and one rear wheel, there are various types of suspensions for the front, such as a double wishbone type and a telescopic type, but for the rear, there is essentially only a full trailing arm (swing arm) type similar to a motorcycle.Therefore, the pitching will be suppressed by a method of matching the front amount of sinking during turning with the rear amount of sinking of the full trailing arm type.
First, Figure 2 shows the state of force balance during turning of the full trailing arm rear suspension.Since the reaction force that supports the tire lateral force generated during turning occurs only in the axial direction of the virtual suspension arm, the force in the direction that causes the vehicle body to sink remains.Using the spring constants of the rear suspension in Table 1, the relationship between the turning lateral acceleration (a) and the amount of vehicle body sinking in the vertical direction is obtained as shown in Figure 3.It can be seen that this sinking amount (ΔGCHr2) is strongly nonlinear comparing with the decrease in the center of gravity height (GCH) of the vehicle due to the inward tilt during turning (ΔGCHr1).And then, the front amount of sinking will be adjusted to the rear amount of sinking by the front force balance during turning.

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Next, Figure 4 shows the force balance when a double wishbone type is used for front suspension as in automobiles.The force (FLift) in the direction that lifts the vehicle body due to force balance is given by Equation (1).The relationship between lateral acceleration (a) and the amount of sinking of the vehicle is shown in Figure 5. (1) Figure 6 shows the relationship between α, Rα and lifting and sinking of the vehicle body.With respect to the diagonal or horizontal lines in the diagram showing the relationship between α and Rα when ΔGCHf 2 = 0, the vehicle body sinks in the upper left area and lifts in the lower right area.When using a double wishbone type suspension, a compromise must be accepted between body pitching and road disturbance, because the sinking geometry on double wishbone is not easy.
And then, Figure 7 shows the force balance during turning using a telescopic type suspension commonly used in motorcycles.The mechanism of the vehicle body lifting and sinking (Equation ( 2)) is equivalently same as Figure 2. In a PMV that tilts inward during turning, there is no need for load transfer between the left and right wheels during a steady turn.Therefore, both the pitching suppression of the vehicle body and the requirement of free from the road disturbance are compatible.Generally, in PID control for active inward tilt tracking, the actual tilt angle delays significantly with respect to the lateral acceleration (a) of the vehicle.If the inward tilt angle has not yet occurred at all, significant load transfer between the left and right wheels occurs as same as of automobiles.However, the front and rear body do not sink, and pitching does not occur, because α of front suspension is zero in case the telescopic type.When an inward tilt angle that is just in balance with the turning lateral acceleration (a) is generated, no load transfer occurs between the left and right wheels.Therefore, the front body sink as much as of the rear body, and pitching does not occur either.In other words, unlike the double wishbone type, the telescopic type almost satisfies the requirements of suppressing pitching of the vehicle body and the free from road disturbance.
The only cause of pitching in the telescopic type suspension that should be considered might be the time delay in load transfer due to the roll inertia (Ix) of the vehicle body given by Equation (3).

Figure 1 .
Figure 1.Balance model divided into front and rear.
Dynamics and Control of Single Track Vehicles 18 -20 October 2023, Delft University of Technology, The Netherlands