Nicholas Cognolato – firstname.lastname@example.org Degree in Mechanical Engineering
Sidecar is a vehicle with three wheels obtained from the coupling of a motorcycle with a “coach”. The first sidecar goes back to the early 20th century as a viable economic alternative to cars and chassis cab was sometimes used for carrying. All automotive houses produced several models of sidecars for both civil and military use. Today, the sidecar is a vehicle not at all common and known and new models are produced only on order.
The targets of the working are the modeling of a sidecar and the analisy of the dynamic behaviour of the system using the software LMS Virtual Lab. Several simulations are performed with the aim to observe the behavior of the vehicle during acceleration and braking. It is also performed a path control of the vehicle.
The first phase of the project has been to define the general dimensions of the vehicle. The various components of the vehicle have been modeled individually (chassis, suspension, tires and rims) and only later have been assembled. The motorcycle chassis has been based on a Yamaha R6, while for the sidecar the dimensions have been taken from a website image found on the internet. The motorcycle’s chassis weighs about 193 Kg, while the weight of the sidecar is 63 Kg.
The front suspension of the bike was built by a telescopic fork catalog. The rear suspension has been modified compared to the base version, adopting the Full Floater typology, as shown in the picture. In this way, this system compresses the shock absorber at the same time both from above and from below. The triangular element is used for the suspension of the sidecar.
To model the effect of the groups spring-damper has been used a TSDA model (Translation Spring Damper Actuator). The following table shows the characteristic values adopted.
|TSDA||Front Suspension Motorcycle||Rear Suspension Motorcycle||Suspension Sidecar|
|Free Lenght Spring [mm]||690||302||302|
|Spring Costant [N/m]||10000×2||40000||25000|
|Damping Coefficient [Kg/s]||1000×2||3000||4000|
To simulate the contact forces between the road and the tires we use the model SIMPLE TIRE, inserting the characteristic values given in the table. Tires and rims are joined by a bracket joint.
|SIMPLE TIRE||Front Tire Motorcycle||Rear Tire Motorcycle||Tire Sidecar|
|Damping Costant [Kg/s]||200||200||200|
|Cornering Stiffness [N/rad]||12000||17000||8000|
|Vertical Stiffness [N/m]||100000||120000||110000|
Are finally assembled suitably all the various components with constraints of various type (bracket joint, revolute joint, translational joint) to obtain the assembly shown in the following pictures.
From a dynamic analysis of the modeled system have been found some vibrations of the entire vehicle. In particular in correspondence of the wheel of the sidecar there was an outstanding oscillation of the lateral force, both in straight and in curve during the test of path control, as shown in the next picture.
For this reason we have changed the main geometrical parameters of the vehicle (the front wheel trail, the slope of motorcycle compared to the vertical direction and the sidecar compared to the feed direction, relative positioning between the motorcycle’s chassis and sidecar’s chassis, inclination of the wheel of the sidecar). Have been also modified the suspensions of the vehicle to improve the dynamic behaviour.
The final configuration includes an inclination of the sidecar’s wheel of 3 degrees from the vertical, an inclination of the motorcycle’s chassis of 1 degree from the vertical and a front wheel trail of 119 mm. In this way we have minimized the magnitude of the sidecar’s vibrations.
In this simulation the sidecar must run at a constant speed following a generic path (54 km/h), by implementing a control system of the trajectory (path follower control input) that acts on the steer of the motorcycle. The path is composed initially of a straight stretch, followed by a lane change, a curve to the left and one to the right having the same radius of curvature, as shown in the picture to the left. The gains used in the path control are shown in the picture to the right.
The graph below shows how the actual trajectory of the vehicle follows the nominal one.
From the graphs we can observe the behaviour of the vehicle’s tires. During the entire path the forces acting on the rear tire of the motorcycle have the same trend as those acting on the front tire. On the rear tire of the motorcycle the normal force presents a higher variation than the one on the front tire because the rear of the motorcycle is more loaded than the rest of the vehicle.
The longitudinal forces of all wheels remain constant during the route because the vehicle proceeds at a constant speed. The lateral force on the sidecar’s tire has small oscillations and it has about zero value. During the curve the normal force on the tire of the sidecar has about the same trend but the opposite direction compared to the normal forces on the tires of the motorcycle.
The simulation starts at 15 s, with the vehicle at constant speed. Up to 17 s the vehicle travels a first straight stretch and the lateral forces on the tires of the motorcycle appear to be negligible. During the lane change, from 17 to about 32 s, is noted as the lateral forces of the tires of the motorcycle change the direction to allow the vehicle to follow the trajectory. Subsequently there is an additional straight stretch in which the lateral forces return to values approximately equal to zero. When the vehicle enters in the curve to the left (36 s) there are peaks of the normal and lateral forces on the tires of the motorcycle, which then remain constant during the curve. In the end of the curve there is a momentary reversal of lateral forces, which remain constant during a next straight stretch, present between 50 and 55 s. Subsequently, the vehicle enters in the curve to the right and the lateral forces behave similarly to the previous curve, but with opposite sign.
Regards to the forces on the suspension, are observed trends similar to those of the normal forces of the tires. When the forces of the motorcycle’s suspension increase, a decrease of the force on the suspension of the sidecar occur and vice versa. From the graphs it is observed that the rear suspension is the most loaded, according with the behaviour observed previously on the graphs of the normal forces on the tires. The force on the suspension of the sidecar has an average value approximately as equal as the force on the fork of the motorcycle but appears to have higher load variations during the path. In the left curve the sidecar’s suspension is discharged almost completely, while those of the motorcycle, and in particular the rear, are loaded. In right curve the load moves to the suspension of the sidecar and the forces on the motorcycle’s suspension decrease.
ACCELERATION AND BRAKING
In this test we consider the vehicle initially at low speed and provides an acceleration of 1.2 m/s². After another stretch at a constant speed (54 km/h) is simulated braking of 1.7 m/s². These speeds and accelerations have been obtained by setting an appropriate trend of the rotation speed of the rear wheel of the motorcycle (velocity driver), as shown in the picture.
The tire and suspensions forces are analyzed.
The acceleration of the vehicle is developed from 4 to 10 s. In this interval it is observed that the normal force on the front tire of the motorcycle is less than what happens in the next stretch at a constant speed. An opposite behaviour occurs on the sidecar’s tire and on the rear motorcycle’s tire. On the rear tire of the motorcycle there is a constant longitudinal force of 400 N because in this wheel is set the torque. On the remaining tires the longitudinal force appears to be negligible during the entire test.
From 10 to 25 s the vehicle moves at constant speed. In this stretch the normal force on the front tire of the motorcycle increases, while those on the rear and on the sidecar decrease. The longitudinal force on the rear of the motorcycle is back to low values.
The braking is developed between the 25 and 33 s. In this stretch the forces on the tires have an opposite behaviour compared to what happens in the acceleration phase. In fact, the normal force on the front increases while the ones on the rear and on the sidecar decrease. The longitudinal force on the rear of the motorcycle presents negative values to allow the deceleration of the vehicle.
In the acceleration stretch the suspensions of the motorcycle are discharged while that of the sidecar charging. This causes a lowering of the sidecar and a small global elevation of the motorcycle. The variation of force on the rear appears to be of magnitude higher than the front. In the stretch at a constant speed the vehicle is stabilized and the forces on the suspension present constant values. During the braking instead of the motorcycle is lowered, charging the relatives suspensions. The sidecar is raised slightly, as evidenced by the reduction of force on the suspension.
The project has been developed starting from modeling of a prototype of sidecar until the development of a path control system and through simulations that show the dynamic behaviour of the vehicle. We started from an initial configuration of the sidecar in which were observed evident vibrations of the vehicle, which were then reduced to the minimum thanks to an appropriate setting of the sidecar. We obtained an acceptable behaviour of the vehicle in path control, in acceleration and braking.