updated on February, 2017
In the world of motorcycles racing, and generally in any motorsport competition, it has always been a matter of weight.In the logic of “the lightest, the better” there has always been a constant research and development of new technologies and ideas to fulfill this need. Every component must be as light as possible and, keeping that in mind, even replacing the mechanical spring (0.7kg ca) of a rear shock absorber with an air spring (weight of the standard shock absorber is 4kg ca), can make the difference. That’s exactly what has been done, and the project here presented aims to test and verify the behavior of an air shock absorber, comparing it to a traditional one.
The goal is to firstly verify the velocity ratio between the rear shock and the wheel, making sure that the mechanism and the link used are designed in the right way. The behavior of the two different shocks, one with a mechanical spring and the other with an air spring, is simulated next. Specifically, it has been investigated how the two solutions work during a stoppie maneuver, where the rear wheel is lifted from ground, a situation in which they are put in stressful conditions. The air spring has been modeled (see paragraph 3.3) in such a way that the two solutions are expected to behave in the same way when subjected to a similar deformation during the maneuver.
3. The modelling problem
The air shock absorber behavior study and its comparison with a traditional one are conducted supposing to mount them on the motorbike of the Motostudent “Quarto di Litro” Motorcycle Racing Team of the University of Padua (www.quartodilitro.it). In the following table there’s a list of the major bike’s specifications.
|Engine||HONDA CBR 250cc|
|Chassis||Tubolar 25CrMo4 Steel trellis with optimization of lateral and torsional stiffness|
|Swingarm||Two-sided, 25CrMo4 Steel|
|Dry Weight||100 kg|
|Max Power||28 Cv|
|Max Speed||173 km/h|
|Final Drive||415’ Chain; Front sprocket 15, rear sprocket 38|
|Tank capacity||9 liters|
|Intake System||Kehin 38mm, airbox with two frontal air intakes|
|Front Suspension||USD Bitubo|
|Rear Suspension||Bitubo with Pro Link System|
|Front Brakes||Single 290mm TK disc, 2 JJuan piston calipers (34 & 30 mm)|
|Rear Brakes||Single 220mm TK disc, 1 JJuan piston caliper (25 mm)|
The figure below shows the entire rear train of the bike as it has originally been designed in CATIA.
The swingarm has been manufactured using steel pipes (25CrMo4) with a φ30mm or φ15mm diameter and 1.5mm thickness. This is due to the fact that one of the team’s sponsor was specialized in laser cut technology. The rear suspension design is based on the Honda Pro Link (four bar linkage). The parameters that have to be considered in the design of the rear suspension are:
- Velocity ratio between spring velocity and vertical velocity of rear wheel pivot:
For super sport motorcycle it’s recommended to use a value of near 0.5  (Cossalter, 2014)
- Rear wheel pivot vertical travel between full extended configuration and full compressed, ≤ 100, this value is recommended in super sport motorcycle  (Cossalter, 2014).
The connecting rods are directly attached to the rear low engine attachments.
In order to recreate the rear train in Adams, all the unnecessary components (e.g. disk brake, spacers, brake caliper, rear rim, etc. ) have been removed to simplify the model and make the importing operation easier. As a matter of fact, when the assembly got complicated, with many bodies and components, some difficulties have been detected and in the worst case the model couldn’t be imported.
The picture below shows the simplified Adams model used to valuate the speed ratio. It includes four bodies (Swingarm,rear tyre, triangular link, two connecting rods) and a translational spring-dumper element that simulate the air/traditional rear shock, depending on which parameters are set.
Again, for the comparison of the two shocks, other bodies have been added in order to truly simulate the motorbike and the shock behavior in particular. These are: frame (along with the steering plates and the sub-frame, they all have been imported as a single body due to the importing limitations of the ADAMS student version), front tyre hub, front tyre and two translational spring-damper element that simulate the front forks, a 1.7(newton-sec/mm) daming coefficient has been assigned to this two elemets, according to what reported in the “Motorcycle Dynamics” book . A picture of the entire model is shown below.
Figure 3.4 Full motorbike as modelled in ADMAS
It has been assigned a correct value of its mass to each body of the model by phisically wheigting each component and manually setting each value in Adams in the “Mesure” section of all the components. It must be said that has been assigned to the frame a value of mass that also includes the wheigt of the engine and the weight of the pilot, in order to have a more realistic model of what actually is going on. In detalils, these are:
- Front tire and rim: 5,40 kg
- Rear tire and rim: 6,95 kg
- Swingarm: 3,2 kg
- Triangular link: 300 g
- Connecting rods: 298 g each
- Front tire axel: 1 kg
- Frame: 120 kg (frame + engine + pilot)
In order to connect the different bodies various kinds of conncectors have been used:
- 4 Revolute Joints (2 on the wheels’ axels; 1 on the swingarm axle, between the frame and the swingarm, 1 between the link’s left rod and the frame)
- 4 Spherical Joints (1 between the link’s right rod and the frame, 2 between the two rods and the link’s triangle and one between the link’s triangle and the swingarm)
- 1 Translational Joint (between the fork and the frame)
- 1 Fixed Joint (between the road, modeled as a single body, and the ground)
- 1 Planar Joint (between the frame cm and the ground, in order to study a two-dimensional problem focusing on the suspensions and ignoring the motion out of the symmetry plane of the bike)
3.1 Mechanical Spring Rear Shock Absorber
The behaviour of the traditional rear shock absorber can be simulated in Adams by setting a finite value to the stifness k of the translational spring- dumper element. This value is 85 N/mm, the same used during the Motostudent competition.
Instead of using a finite stiffness value though, it has been used a force curve obtained by combining two mechanical springs, one for the compression and one for the rebound.
In details, down here are shown their characteristics:
Km = 85000 [N/m] main spring stiffnes
Lpm = 0.009 [m] preload lenght
Kr = 150000 [N/m]rebound spring stiffness
Lr = 0.008 [m] operating length
Fr = Kr*(Lr-c) [N] force generated by the rebound spring
Fr((Fr<0)) = 0 zero is assigned to negative force values
The resulting force is calculated using the following formula:
c is the travel of the shock.
The plot of the resulting force is shown in the figure below:
This curve has been later imported in ADAMAS in the same way as the air one has been imported, as specified in the next paragraph.
3.2 Air Spring Rear Shock Absorber
The air shock absorber has been studied and designed separately as the writer’s thesis project. It has two chambers filled with air at a certain pressure which can act like springs as the air pressure is building to resist the force on it. One works as the main spring, the other as the rebound one. The damping is operated by oil contained in the middle chamber. A drawing of the shock is shown below.
The design and developing of the prototype can be summarized with the simple concept of fitting the force curve of the air spring to the one of the mechanical spring: given the shape, geometry and general dimension of the shock and the single chambers, same values of stiffness and force are imposed at two given travel values for the two types of springs.
On a side note, many checks have been made regarding different aspects, such as: the influence of the operating temperature on the shock behavior, the effect of the oil expansion due to the increasing temperature, and the occurrence of air condensation due to the decreasing volume and the consequent increasing pressure, besides all the structural checks.
So, using the force curve of the mechanical spring shown in figure 3.6 to do the fitting with, the resulting air spring force curve can be seen in the picture below.
The behaviour of the air shock absorber can be simulated in Adams by determining the stiffness k as a function of the force and deformation. Specifically, instead of a finte value of stiffness, it is defined a spline (F = f(defo)) as a set of points (50 in this case) that recreates the red curve in the graph above.
It must be said that all the values have been imported in ADAMS with their sign changed in order to have the compression of the two shocks with concordant signs , this is because in the previous MATLAB analysis positive deformation values were given to the compression, instead in Adams the compression is associated by default to positive values.
The Motostudent organization supplied the team with a set of dry-condition slicks , composed by:
- Front tire: Dunlop model KR149 M size: 95/70R17; wheel mass considering also the rim’s weight: 5.40 kg
- Rear tire: Dunlop model KR133 C size: 115/70R17; wheel mass considering also the rim’s weight: 6.95 kg
Originally they have been drawn in CATIA and imported in ADAMS, but then they have been modeled using the torus feature with a resulting radius of 300 mm for the front one and 298 mm for the rear one. This is because the problems occurred while setting the contact forces between the tires and the ground it was thought were due to the not water sealed shapes of the imported tires.
The Adams tire model, an advanced feature not available in the student edition, was not used.
3.3.1 Contact force
The contact forces between the tires and the ground must be carefully chosen in order to truly recreate the real contact conditions that occur when the bike is moving.
The parameters that has been used are shown in the pictures below.
Regarding the front tire, in order to get the rear tire lifted in the air, it has been used a static coefficient of 1.2 and dynamic coefficient of 1. In the “stiffness” dialog box the Carcass radial stiffness, calculated with the tyremeter of the DMRG, of the two tires have been inserted.
3.3.2 Tires slip
In order to make sure that the tires aren’t slipping while the bike is moving, and to get a better understanding of the vehicle’s behavior, the slip of the two tires has been calculated.
Generally, if the tires are slipping their translational velocity is minor than the theoretical one, calculated with the following: vt = ωr.
The slip has been calculated using the following formula: In the following pictures the slip value for the two tires while the bike is moving , obtained with the contact force parameters seen before while the bike is moving unruffled, is shown.
As seen in the figure above, the slip is zero meaning that the tires are fully rolling with no slipping involved. Therefore contact force parameters can be considered correct.
4. Simulations and analysis of results
4.1 Velocity ratio
Regarding the first phase of the project, it has only been taken in exam the rear train, it has been imposed a constant displacement on the rear tire and the velocity ratio has been calculated.
As seen in the picture below, the mechanism and the linkage are well designed as the velocity ratio is 0.5, for a wheel travel range from 0 to 100 mm.
4.1 Comparative Test
Regarding the second objective of the project, in order to make a comparison of the two shocks, a “stoppie” maneuver has been simulated.
The stoppie is a motorcycle and bicycle trick in which the back wheel is lifted and the bike is ridden on the front wheel by carefully applying brake pressure .
In order to simulate this maneuver the bike has been launched on the road with an initial velocity of 50km/h and after a few seconds, a breaking torque in this case of approximately 450 Nm has been applied between the front tire and the front tire rod, opposite to its rotation, so the bike slows down while the rear tire is lifted up in the air. In this way, when the rear tire hits the ground, the shock is quickly compressed and accuses a violent load. So, repeating this maneuver for both the shocks, it is possible to compare the behavior of the two for most of their travel.
In order to avoid an opposite spinning of the front tire, while this is braking, the braking torque has been expressed with this following formula:
Torque= -450000*SIGN( 1 , .RearSuspension.Front_tire_angularv )
It has been used a scripted simulation to simulate this maneuver. The script is shown below:
DEACTIVATE/SFORCE, ID=4 (deactivate the torque before the simulation starts)
SIMULATE/DYNAMIC, DURATION=1.5, DTOUT=0.05
ACTIVATE/SFORCE, ID=4 (activate the torque after 1.5 s of simulation)
DEACTIVATE/MOTION, ID=2 (deactivate the initial translational velocity of the bike)
SIMULATE/DYNAMIC, DURATION=0.3, DTOUT=0.05
DEACTIVATE/SFORCE, ID=4 (deactivate the torque after 0.3 s of simulation)
SIMULATE/DYNAMIC, END=1.0, DTOUT=0.05
Once the simulations are over, the deformation curves of the two shocks can be plotted and easily compered, as it is shown in the figure below.
Looking at the picture above, there’s a compression of the shock at the starting of the simulation, which is not taken in consideration. This is because the simulation starts and the bike “lands” on the road to find its initial conditions.
After 1.5 seconds the torque is activated, the bike brakes and the rear wheel loses contact with the ground and is lifted up in the air. As a consequence, the shock extends as it is visible in the picture.
Again, at 1.8 seconds there is a small compression due to the fact that the torque stops and the shock finds its new condition of equilibrium.
At approximately 2.2 seconds the rear wheel touches the ground again and the shock is compressed, as it’s shown in the figure. After that, the shock settles at its initial compression.
Looking at figure 4.3, it is clear that the two shocks roughly behave in the same way as they are subjected to a similar deformation during the maneuver. This agrees on what it was expected, as a matter of fact, in the way the air shock was designed, with its force-deformation curve fitted on the one of the mechanical spring, it provides the same value of stiffness for the entire travel of the suspension. Other simulations can be easily run changing the variables involved: it can be used a different value of braking torque acting for a different period of time. This is possible by changing the script and torque’s value.
 Vittore Cossalter, “Motorcycle dynamics”