INTRODUCTION
In our work we modeled an innovative light snowmobile with the aim to get a safe, high performance vehicle with improved handling and stability.
Most of the accidents with snowmobiles are caused by the vehicle weight combined with the high specific power. The size of a gasoline engine has a strong influence on the design choices and limits the possibility of weight reduction. The key area was to reduce the vehicle weight and match it to the similar dynamics of a motocross bike. This opens the market up to more extreme possibilities and improves female use.
We took our inspiration from a snowmobile concept with motorbike styling designed by Chris Wyeth. He is a designer who presented this project for his Bachelor’s degree thesis in Automotive Design.
http://www.linkedin.com/pub/chriswyeth/2a/80b/193
We decide to adopt an electric propulsion to get a strong reduction of the motor size. So two electric wheel motors were inserted coaxially in the track front wheel and they are supplied by Lithiumpolymer batteries. The two swinging motors allow a lower center of gravity (CoG).
The vehicle concept is provided by double wishbone suspensions on the front and by a swing arm on the rear.
We have integrated the front suspension with an antiroll system similar to a device already available on the market. The device, whose commercial name is High Side Steering®, is made by Curve Industries:
The mechanism, actuated by the handlebar, acts in curve preloading the external ski and unloading the internal one. In our project we will call this mechanism Anti Roll Steering (ARS).
OBJECTIVE
The aim of this project is to study the different curve dynamic behaviors of an innovative light snowmobile provided by new layout of suspensions. All modeling and simulations were made by the multibody software LMS Virtual.Lab Motion® working on Dassault CatiaV5® environment.
SOLID & SURFACE MODELING
The software CatiaV5® within LMS.Virtual.Lab Motion® was used to design the entire vehicle. Due to the light weight of the vehicle the mass of the rider is extremely relevant so a dummy was used as a rigid body to perform more real simulations.
Some components modelled…the frame, the swinging arm, one front suspension arm, the ski…
MULTIBODY MODELING
Modeling of the steering mechanism
The mechanism should be the result of a kinematics optimization. The bodies dimensions and the links positions should be adjusted due to limit the characteristic steering angles into a precise range. Some simplifications are introduced because the optimization of the steering mechanism is not the target of this preliminary project. The steering arms are eliminated and the rotation of the skis is controlled by two tools named four body relative constraints. Giving a rotation to a body, this constraint forces the rotation of a second one selecting a suitable amplifier factor k. We put two of these constraint types, both with k equal to one, one between the steering shaft and the right ski and the other between the two skis. As a result, we designed a parallel steering. In addition to increased vehicle stability we put a ski convergence of one degree.
Modeling of the Anti Roll Steering mechanism (ARS)
The 13 rigid bodies, which compose the spatial mechanism, are linked by the joints indicated in the picture:
It is interesting to consider the spatial form of Gruebler’s formula: k = 6*(m1) – 5*C1 – 4*C2 – 3*C3 – 2*C4 – C5 k = number of DoF (Degrees of Freedom) m = number of rigid bodies, frame included
This is one of the cases in which this formula shows its weakness because it does not consider the geometry of the mechanism. The system has three DoF: two redundant rotations around the axis of the connecting rods with spherical joints and the only rotation around the steering axis. The mechanism is the result of a kinematics optimization in which we adjusted the bodies dimensions and the link positions. We got the right compromise between driving torque and roll angle statically imposed to the frame.
Modeling of the steering limit
A steering limit is modeled in order to prevent a singularity condition in the ARS and to be closer to the reality. The steering angle is limited at 25 degrees providing a suitable curvature radius to the vehicle. An added rocker arm is aligned with the left rocker arm of the ARS. An extreme of this body is joined with the frame by a revolute joint (RJ), the opposite one is joined with the ARS rocker arm through a planar joint. To avoid the singularity position we put a negligible value of spring constant in a Rotational Spring Damper Actuator Force Element (RSDA), placed in the RJ.
Steering Limit Explanation Video
Modeling of contacts between snowmobile and snow
To obtain a lower computational cost we chose to model the snow contacts using wheels rotating on a planar surface (road). The Simple tire model was chosen and two wheels are placed in correspondence to the front and rear ski boundaries. In particular, the wheels distance from the ski rotational axis are chosen with accuracy to generate the right amount of aligning reactive contact torque. We did the same thing modeling the two lower rear wheels with two simple tire models.
Dimensions
Overall Length  2450 mm 
Overall Height  1150 mm 
Overall Width  1190 mm 
Ski Center Distance  500 mm 
Track Width  280 mm 
Track Print Length  870 mm 
Ski Length  1100 mm 
Maximum Ski Width  200 mm 
Weights
Overall Weight (without dummy)  130 kg 
Frame Weight  20 kg 
Batteries Weight  30 kg 
Overstructures Weight  20 kg 
Dummy  70 kg 
Overall Weight  200 kg 
Finally, a mass distribution of 50% on the front and 50% on the rear is obtained. Due to the absence of the overstructures their weight (20 kg) is put in the frame increasing the density of the material (20 > 40 kg). In order to reproduce correctly the real weights distribution, it should be cosidered that the rider makes significant moviment of his body to avoid the overturning. The rider moves his body as much as possible inside the curve to reach a sharp turning into the corners. The total CoG (snowmobile+pilot) moves towards the turning center and lowers its position from the ground. Consequently the overturning limit is higher. However these movements are not considered in the modeling, so the dummy is fixed to the frame with a braket joint. This picture shows the obtained CoG position:
Suspensions Settings
The vehicle is provided by six shock absorbers: two inside the track, two to control the swinging rear arm and two in the front double wishbone suspensions. There is also a steering damper. A simplification is made about the track in which the rear shock absorber is locked and only the front one is kept active. An optimal tuning of the suspensions would have been too long and too complex to do. Thus we chose the values of stiffness and damping in order to satisfy stability and limit the weight transfer during cornering, acceleration or braking within our tests. We reached the following setting:
Stiffness coefficient (N/m)  Damping coefficient (N·s/m)  
Double Wishbone shock absorbers  50 000  8 000 
Swinging rear arm shock absorbers  60 000  6 000 
Track shock absorber  60 000  6 000 
Steering damper    200 (kg·m²/s/rad) 
SIMULATIONS
Free vibration analysis
In order to calculate the free vibrational modes the snowmobile was run in a straight path at constant speed (32 km/h) leaving the steering free to rotate. A striking point is that the steering remains perfectly straight. We verified the right positions of the wheels in the ski provide a correct aligning reactive contact torque. All that is shown by the video below.
The free vibration modes are calculated linearizing the equations of motion every second from 1 to 15 s. Once the entire vehicle was assembled, we got 17 DoF. Consequently 34 state variables and 34 eigenmodes are obtained. All the eigenmodes are stable because the real parts of the eigenvectors are negative (damped modes):
The first three modes are rigid motions of the entire snowmobile because they have both real and imaginary part equal to zero. The 9^{th}, 10^{th}, 12^{th} and 13^{th} eigenvectors (in ascending frequency order) have positive real parts but they are not real vibrations because they are rotations of the ski wheels.
Progressive suspensions
We designed the geometry of the short long arms suspension in order to obtain an increase of stiffness with the increase of compression that is a progressive suspension. This choice was made to keep the natural pulsation of the suspension slight constant with different rider weights. To show the diagram force vs movement the frame is fixed to the ground and a vertical movement of the double wishbone suspension is imposed. An arbitrary speed is settled in a One body velocity driver applied to the ski connecting rod. An arbitrary value of spring constant is imposed. Finally we obtained the following diagram:
The green curve shows the relation between force and movement and the brown one is its derivate that is the stiffness. The suspension is progressive because the stiffness increases with the increase of the suspension travel.
Measure of the speed limit of lateral overturn
The aim of this test is to evaluate the configuration with ARS. The ARS device permits the snowmobile to reach and higher speed of lateral overturning. Different tests are conducted by fixing different value of steering angles and imposing a ramp of speed with constant acceleration. For every steering angle the snowmobile is laterally overturned and the relative rate is recorded. We compared the two different speeds with and without Anti Roll System. Two series of tests are made setting the simple tires with two different friction coefficients (1 and 10). The higher value is set to avoid the effect of the drift in the circular path. With negligible drift the curvature radius is lower, the centrifugal force is higher and consequently the general overturning speed is lower.
The following tables show the final results.
Series with friction coefficient equal to 1
Steering Angle (°) 
Speed with ARS (km/h) 
Speed without ARS (km/h) 
5 
30,6 
29,9 
10 
23,5 
23,0 
15 
20,5 
19,3 
20 
18,5 
17,1 
25 
17,9 
15,5 
Series with friction coefficient equal to 10
Steering Angle (°) 
Speed with ARS (km/h) 
Speed without ARS (km/h) 
5 
30,3 
29,5 
10 
22,5 
22,2 
15 
20,0 
18,0 
20 
18,3 
15,8 
25 
15,8 
14,2 
To verify these results found out in motion we also conducted two trials of static overturning. We reproduced the effect of the centrifugal force by applying in the CoG a vectorial force (action reaction with the ground) with same versus and direction of the centrifugal one. We made it proportionally rising with the simulation time and we recorded its value at the overturning time. That value was compared with the centrifugal force calculated by the lateral acceleration in the tests in motion. The final result shows a marginal difference between the forces highlighting the absence of computational mistakes.
ARS 
noARS 

Overbending Lateral Acceleration (m/s^2) 
4,3 
3,7 
Centrifugal Force (in motion) (N) 
861 
741 
Overturning Force (static) (N) 
852 
737 
Lane change test
A Path Follower Control Input is used to ride the snowmobile through a lane change with the geometry outlined below. The control output torque is applied to the steering axis.
Straight  15 m  
Lane change  Offset 10 m  Length 15 m 
Straight  15 m 
The following control torque is relative to a test made with a constant speed of 26 km/h. Control torque without/ with ARS and relative videos
The charts highlight that there is about a 40% increase in driving torque for the snowmobile with ARS.
RESULTS ANALISYS
The general trend of these tests clearly shows that the lateral overturn speed of the snowmobile is always higher with ARS. The mechanism introduced matches our goal: to improve the curve dynamic behavior. The reasons behind this result must be investigated into the changing of the kinematics and inertial properties introduced by the ARS. The case study set up with 25° of steering angle and friction coefficient equal to 1 explains the results.
 First, the roll angles of the two configurations are compared.
Roll angle vs time: configuration without/with ARS
As shown the values before the lower overturning time are significantly different with more than 5° in favour of the ARS configuration (roll towards the curvature center). At the overturning time of the snowmobile without ARS the roll angle is 8°, unlike the snowmobile provided with ARS still has a positive roll of 2,5°.
 Secondly, the values of the normal forces on the ski tires are plotted versus the time to define the point of overturning. The instant of overturning is considered when the normal forces go down to zero in both the internal wheels.
Normal Forces vs time: configuration without/with ARS
It is interesting to highlight the different load transfer of the two solutions: the one with ARS starts with a higher level of load on the internal ski and as a result it overturns at a higher speed. All the tests prove that the value of centrifugal force that causes the overturning of the snowmobile with ARS is higher than the one without it. In fact, at the crash time for the vehicle without ARS, the speed and the curvature radius are almost the same for both. The ARS snowmobile does not fall and its overturning happens at a higher speed with almost the same curvature radius. The explanation of this dynamic behavior can be given by measuring the position of both the tires contact points and the CoG to a reference system fixed on the frame. The origin of the reference system is in the rear wheel contact point, the x axis longitudinal and parallel to the road, the y axis trasversal and parallel to the road and the z axis vertical and perpendicular to the road. This kinematics study shows that with a steering angle different from zero the CoG is lowered and moved towards the curvature center. So this new configuration works against the overturning, increasing the load on the internal ski.
The contact points and the CoG displayed
The contact points & CoG coordinates projected on the road with a steering angle of 25°
ASR 
noARS 

Points 
X (mm) 
Y (mm) 
X (mm) 
Y (mm) 
1 
0 
0 
0 
0 
2 
864 
0 
864 
0 
3 
1556 
483 
1560 
460 
4 
1862 
621 
1867 
598 
5 
1569 
562 
1563 
577 
6 
1871 
415 
1866 
431 
CoG 
1016 
60 
1013 
1 
Z CoG (mm) 
602  608 
The ARS mechanism introduces a lowering of the CoG by 6 mm with a steering angle of 25°.
CONCLUSIONS
Overall, this preliminar project shows a model of an innovative snowmobile that is safer, higher performing and potentially a zero emissions vehicle. The adoption of light alloys and electric motors has significantly decreased the overall weight. Also the size of the vehicle was decreased to get a very compact snowmobile. We obtained a satisfactory dynamic stability as shown by the eigenmodes study. The stability was improved by the introduced Anti Roll Steering (ARS). On the other hand the driving torque is 40% higher with the ARS but this one can be reduced by an optimization of the lever arms of the mechanism. Finally is evident that the positive effects on the curve dynamic behavior must be related to the Center of Gravity motion towards the curvature center and into a lower position. In this prototype the load transfer, which preloads the internal ski and unloads the external one, gives a real advantage because the lateral acceleration achievable is almost 14% higher. In conclusion, this snowmobile is light as a feather, can make faster curves and preserves the clean air of the mountains.
We came upon this in a google search. Nice work and great project idea!
Thank you so much for your positive comments, from all the team.