- Fabio Ragagnin – email@example.com Degree in Mechanical Engineering
- Marco Marin – firstname.lastname@example.org Degree in Mechanical Engineering
- Matteo Doni – email@example.com Degree in Mechanical Engineering
- Vittorio Zoppini – firstname.lastname@example.org Degree in Mechanical Engineering
The aim of the project is: “ Modellation and simulation of a front swingarm motorcycle with a dummy driver and a steering control”. We have used the software LMS Virtual Lab to model and make the simulations.
Modellation of the Motorbike and the Dummy
Initially we have found some CAD models from Web: the engine and the rims. We have imported them in the modeling software CATIA to be assembled in the LMS software. Then we have found some CAD of the rear and the front swingarm and we have modified them to improve our model.
The weight of the total model of the motorbike is about 155kg.
The engine group has been assembled with the “omega” chassis and is the main massive part of the motorcycle. In the upper part there is a saddle for the dummy and is sustained by a welded pipes frame.
The rear part is the classic solution with a swingarm, as for the totally of the bikes. The swingarm has the geometry with welded pipes and is connected to the frame using a revolute joint: is allowed the rotation around an axis. The swingarm is connected with another revolute joint to the rim with the tyre; this interfaces with the road using the “simple tyre” model present in the software LMS virtual motion: with this is possible to simulate the fundamental characteristics like the friction forces, the longitudinal sliding, the lateral drift, and the coupling between longitudinal and lateral forces. Complete this part a TSDA force (present also in the front), a simple spring-damper system: consist in a parallel of these two and connect the swingarm to a fixed point on the frame. It works both in compression and in traction. All these component are modeled separately from the rest of the bike and are imported like a subsystem.
Front swingarm and steering mechanism
The main characteristic of this motorcycle is the presence of a swingarm in the front part, respect the traditional forks, and the steering mechanism.
In the real mechanism along the swingarm there is a quadrilateral system. This is necessary to give to front wheel the trail, and the offset of the forecarrige. This quadrilateral (one for each motorcycle side) is composed by a rod and a plate, the other two sides are the swingarm itself and the omega chassis. Between two external plates there is a steering box. In this box, from a general point of view there are two orthogonal rotation axis: one for wheel rotation axis, and one for steering rotation axis.
To semplify the model, we have decided to drop the parallelogram and then the steering angle becomes variable with the position of the front suspension. However the amplitude of this variation is acceptable. In the LMS model this quadrilateral system has not been achieved, but has been defined a plan suitably inclined. In this way the hub of the steering rotates around an axis not orthogonal to the ground, but inclined of 24° respect to the vertical direction. So during the creation of the model, we have defined two Revolute Joints: one for the rotation of the steering axis around the inclined axis of 24°, and one for the rotation of the wheel around the rotation axis. With this steering axis’ inclination we can calculate a trail of about 137 mm, since that the wheel radius is 308 mm.
To complete the model , have been added a rim with its mass property, the two break discs, and a tire which has been modelled like Simple Tire in LMS software.The shock assorber is modeled as the rear.
The steering mechanism is composed by five pieces:
- A steering arm in the swingarm, called steering arm out in the picture, because is where the roll control acts through the mechanism. Around this steering arm the wheel can rotate around its rotation axis, and also the wheel can rotate around the steering axis, inclined of 24° respect to the vertical direction.
- A rod (rod 1), that develops from the steering arm insertion to the rocker pivot.
- The rocker, that connect the lower rod (rod 1) with the upper rod (rod 2). This rocker as well as to connect the rood, can rotate around an axis fixed on the omega chassis.
- Another rod (rod 2), that develops from the rocker to the upper steering arm.
- In the end another steering arm, called steering arm in, united the handlebar of the motorcycle, where acts the roll controll.
To realize this mechanism we used spherical joints between the rods, the steering arms and rocker. It is easy to see that in the real mechanism in the picture above the joints between the steering pieces are spherical.
Also during the building of the steering we have put particular attention to the transmission ratio. In fact the steering arms lengths are the same, to give an unitary transmission ratio. But an advantage of this steering mechanism is the possibility to change the transmission ratio changing the lenght of the steering arms (in and out).
The main disadvantage of this steering mechanism is reduced steering angle because the front wheel must be inside the swingarm, and also beyond a certain angle, that depends from the rocker length, there is the singular configuration of mechanism. This happens when the segments between the two revolute joints in parallel to rod 2.
Due to the complexity of the steering mechanism and to the problems for the coupling of the two rods, we adopt an equivalent system: the rods are removed and substituted with two distance constrains that have the same length of the rods.
The dummy driver is modeled with the Dempster Method (1955):
- 14 Links (head-neck, trunk, 2 arms, 2 forearms, 2hands, 2shanks, 2 thighs and 2 feet) The modelation is done by revolutes and extrusion, then Booleans operations.
– 13 Joints
The weight of the dummy is 75 kg and the height is 1750mm. For every single link the values are resumed in the following table:
- Fixed ankles, knees and hip.
- The trunk is linked at the vertebrae L5 with a Revolute Joint to let it flex.
- The shoulders are modeled with a Spherical Joint.
- The elbows are modeled with two Revolute Joint.
- The wrists are sferical joint.
- The hands are bracket to the handlebar.
To maintain a correct posture we have introduced some TSDA and RSDA:
– 2 TSDA from the arms to the forearms
– 1 RSDA in the L5 vertebrae.
The roll control has been implemented to give roll stability to the motorcycle and has been made up with the software for the control analyses included in LMS Virtual Lab.
The multibody software does not allow to directly take the roll anlge as the observed variable (input function); therefore we define a different approach: the control is based on the difference of the distance from the ground of two eccentric systems which are located one on the left and one on the right of the frame. This difference is continuously compared to a target function, imposed in these case to zero because we want to maintain the motorcycle as much as possible in the vertical position, ie with a zero roll angle.
The control used is the classic PID solution. The input is the error between the target function and the difference in height of the two eccentric systems. To calculate the three gains were made tests with different values to try to find the ones that can ensure the stability of the system.
Considering the effects:
- K i allows to reach the asymptote
- K d has a damping effect
- K p influences the speed of correction of the control
it was conducted an empirical optimization of the gains. The results are
- Ki = 3
- Kp = 60
- Kd = 10
With this control the motorcycle is stable and so is not necessary to use a steering dumper.
The image of the block diagram is the following picture:
We put also two zero fuctions input because the summer blocks present in the Virtual motion have three input nodes that have to be all filled.
The test for the simulation is the run of the motorcycle through a straight path. The mechanism is very complex and the degrees of freedom we must consider are lots.
In the following video there is the motorcycle in the initial instants of the simulation. It is possible to see that the motorcycle presents some low roll oscillations that are immediately corrected by the steering control system. After that, the motorcycle stabilizes itself.
The initial conditions of the simulation are:
- Null roll
- Speed = 17 m/s
- Height to the ground = 0 mm
The simulation is conducted with constant speed, straight path and plane surface.
The follower graph reported the roll angle of the motorcycle during the simulation of 1 min.
It is possible to see that the roll angle is very small: initially when the motorcycle starts the control acts immediately and correct the position. After that the oscillations are contained in a small range but the roll maintain a constant angle of 1.2 degree around the vertical position: this is due by the static unbalance of the frame mass and because for low angle the control can’t adjust the position. We can conclude that the motorcycle is stabilized by the controller.
The following graph reports the steering torque applied by the controller to the handlebar.
Another variables analyzed are the forces of the two shock absorber because the action of the controller loads and unloads the spring for the continuously roll angle variation.
-Red line – axial force of the rear shock absorber [N]
-Black line – axial force of the front shock absorber [N]
The difference of average values of the forces is due to the different linkages of the relative shock absorber. The loads distribution is about 50% in the rear and 50% in the front. The front shock absorber is the more loaded because has a lower lever arm to the rear, as present in the real motorcycle.
The last graph is the velocity of the motorcycle during the test.
The multibody software gives us all the natural frequencies of the system. We study the modal analysis to verify that there aren’t unstable frequency in the steering mechanism and in the motorcycle. From the table below is possible to see that the only unstable frequency are the one and the two, with the real part that has positive values but low frequency: they are almost a rigid motion.
From the modal analysis we recognize some vibration mode that are characteristic for the motorcycles. The presence of the dummy driver didn’t allow us to find the typical frequencies of the pure motorcycle.
We have studied the modal analysis in the range of velocity from 5 to 20 m/s with a step of 2,5 m/s to verify some main vibrational modes such as: front and rear hop, weave and the phenomena of the capsize. Below we report the rear and immaginary parts of the vibrational modes.
Real part over the speed of the weave and the capsize:
Frequency part over the speed of the weave and the capsize:
Immaginary part over the real part of the weave and the capsize:
Real part over the speed of the rear and front hop:
Frequency part over the speed of the rear and front hop:
Immaginary part over the real part of the rear and front hop:
- The system create is not perfectly stable as a real motorcycle.
- Respect to the usual fork suspension, this solution has the disadvantage to present two singularity configurations in the steering mechanism.
- The presence of a dummy influences the dynamic of the system so much that it has been necessary to modify the values of the gains of the control to adapt the system.
- The control works in the right way, reacting to the roll, but it is possible to create a different control more sensible to roll angle.
- The results of the modal analysis are comparable to the data in leterature, so the dynamic behaviour front swingarm motorcycle is similar to a typical fork suspension motorcycle.