Miante Alberto – firstname.lastname@example.org – Degree in Mechanical Engineering
The Vespa is a two-wheeled vehicle designed towards the end of the 40s; the model in the picture is a Vespa of the 70s. It has some features which differentiate it from classic scooters. The most relevant features are: the engine located laterally and which causes a displacement of the centre of gravity, and the front suspension that is a single sided trailing-link fork. The project is focused on this last peculiarity.
In the past, punctures of the tires happened with frequency, so the single sided suspension was used especially to make the substitution of the wheel faster. It is characterized by a single rigid fork, connected to the middle of an arm, by a rotational joint. The arm is also connected to the front wheel hub. The spring and the damper are connected to this arm and to the fork, as shown in the figure.
The limitation of this kind of suspension is that the fork stroke is short, anyway it is suitable for the road use, especially with the use of tires with a tall sidewall.
The next paragraphs explain how to model the vehicle and how the simulations have been performed. Both the geometric modeling and the simulations have been executed using the LMS Virtual Lab software, which is supported by the CATIA software for the part of modeling.
The aim of the present work is to analyze the behavior of the vehicle when it has to get over the irregularities of the road. The first part of the project consists in the analysis of the behavior of the front suspension when it has to cross speed bumps and road pits.
The second part of the project tries to give an answer to a question that derives from a real situation: the question is if the vehicle is able to make a jump, preserving the structural integrity of the front suspension. It will be better explained in the following paragraphs.
The vehicle model has been realized in a 1:1, starting from the chassis. All the components, necessary to the vehicle to move on, are located in the rear part of this body, so it includes the engine, the tank, the saddle and other elements. The rear part of the chassis is connected to the front part by a footboard, which includes the rear brake pedal. The front part of the chassis is characterized by a shield which is where the fork is connected. All these elements have been simplified to make the simulations faster and to focus the attention to the front suspension.
The following step consists in the modeling of the front axle, which includes the single sided fork but also the handlebars and the headlight; the single sided fork has been realized as good as possible, to have acceptable results from the simulations.
The wheel is composed by tire and rim. Moreover the front wheel has an inner rim that can rotate with respect to the rest of the wheel, so it is possible for the arm to move and rotate forward, causing the displacement of the suspension.
The front fender and other elements, considered unimportant for the aim of the simulation, has not been represented. Total mass of the body is 95 Kg. The wheelbase is 1200 mm. The driver has not been represented, but the mass of the vehicle has been increased by 75 kg, which is the body weight of a generic person.
Damping coefficient = 2000 kg/s
Spring constant = 35000 N/m
Free length spring = 180 mm
Subsequently the road has been represented, modeling the irregularities as shown in the following figures; the first figure represents a road pit, the second is a speed bump.
SIMULATIONS AND ANALYSIS OF RESULTS
In the following paragraphs the simulations and the consequent results are explained. Graphs which are represented, concern the displacements and forces acting along the direction of the suspension; in addition graphs of the forces acting on the cylindrical joint between the fork and the arm are reported.
In the first simulation executed, the vehicle has constant speed and it moves in straight lines;
speed = 40 km/h
Dimensions of the speed bump:
height = 18 cm
horizontal length = 260 cm
oblique lengths = 100 cm
The results in the graphs below show the displacements of the spring and the damper. Then they are represented in the same graph so it is possible to make a comparison.
The graphs show that, after the first adjustment of the vehicle on the road, the suspension doesn’t change the configuration. When the vehicle crosses the irregularity of the road the spring and the damper stretch and shorten together. Once the off road has been crossed the suspension return to the initial configuration, thanks to the damping coefficient.
In the following graphs it is possible to observe how the elastic and the damping forces, along the displacement directions, vary when the vehicle crosses the speed bump. It is also added, in the second graph, the variation of the forces acting along the vertical direction on the cylindrical joint, during the test. The progress of the two kinds of force are similar, in effect, at the crossing time, they swing arriving at forces values not too high. In particolar the meaning of the values in the second graph is that the forces don’t represent a problem for the structural integrity of the suspension.
When the vehicle gets over the speed bump, at the moment of the downhill, a “sinking” of the front suspension happens. This displacement provoke a decrease of the vehicle stability, caused by the reduction of a parameter called trail. Trail is defined as the horizontal distance from where the steering axis intersects the ground to where the front wheel touches the ground. Trail is considered positive if the front wheel ground contact point is behind (towards the rear of the vehicle) the steering axis intersection with the ground. So when trail has negative values, there is a generation of a moment around the steering axis which causes a decrease of vehicle stability. The more trail value is high, the more the vehicle is stable. The “sinking” effect causes a reduction of trail, so the vehicle loses a bit of its stability. This problem is accentuated if the road is slippery and in this case the driver risks to fall off the bike.
In this second simulation the vehicle hits a road pit at the speed of 50 km/h, as if the pit were unexpected.
speed = 50 km/h
Deep of the pit = 15 cm
In the graph above it is possible to observe that, after the first adjustment caused by the initial acceleration, the displacement of the suspension reaches maximal values near to 40 mm. Concerning the real sensations that the driver feels during the motion, these values mean that the drive is not at all comfortable, when the vehicle crosses this kind of road irregularities. These considerations are confirmed by the graph below, in which the values of the forces, along the directions respectively of the spring and the damper, are represented. The maximum value, in modulus, registered is around 1500 N, at the crossing time of the pit. Similarly to the previous case, the force acting along the vertical direction on the cylindrical joint has the same progress of the forces along the suspension direction, but the values are higher.
It could be explain saying that the pit is characterized by a sort of jump, while the speed bump has a gradational slope. It is possible to observe that the pit is more dangerous for the structural integrity of the suspension, than the speed bump. It has to be said that the road pit analyzed has relatively high dimensions but it has been decided to exceed with the values because it is possible to hit road pits when the speed is higher than 50 km/h, so in this way it has been considered condition of safety advantage.
Analysis of a jump
In this second part, the aim of the simulation is to understand if the vehicle is able to make a jump of a staircase which has a length of 3-4 meters and a height of 2 meters. The initial speed of the vehicle is 0 km/h and it has a track which has a length of 80 meters. It is important to evaluate if the vehicle is able to make the whole jump or if it fall on the staircase, and to know if the front suspension preserves its structural integrity.
If the simulation gives positive results, it will be possible to try to make the jump. The staircase is photographed in the picture on the right.
The staircase has been modeled in a simplified way. It must be said that in the figure below a little climb is represented, but it has to be considered as a graphic imperfection.
Length = 3,7 m
Height = 2,1 m
Acceleration = 1.5 m/s^2
Speed after 80 m = 55 km/h
The vehicle starts moving with a speed equal to zero and, at the moment of the jump, so after 80 m, the speed is 55 km/h. From the simulation it is possible to see that the vehicle has made the jump right but it seems that the suspension doesn’t preserve its structural integrity.
In the graph above the forces acting along the direction of the suspension are represented. The values found are higher than the results of the previous simulations, as it were possible to expect. The forces, at the time of the jump, are about 3000 N and they provoke significant stresses on the whole system which characterizes the suspension.
As further explanation, the following graphs show the values of the forces acting on the cylindrical joint which connects the fork to the arm, along the directions of the axis system chosen for the simulation. Along the lateral direction the component (first graph) of the force acting on the cylindrical joint is near to zero, but in the other directions, vertical (second graph) and longitudinal (third graph), the components of the force increase in an exceeding way. This condition lets to understand that the cylindrical joint is subject to an elevate stress which could bring to a breaking of the suspension.
In the graph below the displacements of the spring and the damper are represented. After the initial adjustment of the suspension, the vehicle starts moving on the track, then it lands loading all the mass on the front suspension, damaging it.
The values found this time outclass the results of the previous simulations. It is possible to notice that the maximum displacement has a value around 70 mm and the maximum amplitude of the swing motion is around 90 mm. These results indicate excessive stresses and deformations of the suspension, which bring to its structural failure. Click on the link below to see the video of the simulation at the time of the jump.
The results are compatible with reality. The front suspension absorbs in a good way the effects of the road irregularities but they are less comfortable than other models of suspension. This is explainable with the fact that this kind of suspension has a low stroke. However the values found in the first simulations are not so high to compromise the structural integrity of the suspension.
Concerning the second part of the project, the results have shown that it is possible to state that the jump can be made, so the vehicle, with the condition considered, passes the staircase, not falling on it. However it is probable to happen a breaking both of the spring and the damper because of the high values of acting forces and displacements of that components. From the simulation it has been concluded that it is not recommended to try this kind of trial with a vehicle like the chosen one, because of the risk of compromising the structural integrity of the suspension. Otherwise it is suggested to equip the vehicle with another kind of suspension.