Davide Turcato – turcato.davide@libero.it – Degree in Mechanical Engineering
updated on July, 2016

## Introduction

In this work is proposed the study of a light truck prototype, off-road category with rear-wheel drive. The system is characterized by a four-bar linkage front suspension and a rear rigid axle. It is powered by a Honda engine, 600cc – 4 cylinders with 98 hp maximum power at 12500 rpm and 61 Nm torque at 10200 rpm. Three analyses were conducted:
The Kinematics of the angles and the characteristic parameters of the steering.
The Dynamic analysis on the straights.
The Dynamic cornering analysis.

## Objectives

In the kinematic analysis of the steering, the fundamental parameters variations are measured in function of the vertical excursion of the tyre. The carried measurements involve the toe-in angle, the camber angle, the trail, the front and rear reduced stiffness by the speed ratios. In the straight line dynamic analysis it was evaluated the stability of the vehicle, the pitch angle during acceleration and braking, and the load transfer from the rear to the front as a function of the braking. In the cornering dynamic analysis it is determined the oversteering behavior of the vehicle, measuring the yaw rate as a function of the driving speed, for different values of the radius of curvature.
To get some feedback parameters, a Pajero 2800cc SWB vehicle is considered for the comparison. On this car some experimental measurements are carried on to determine the main vibration modes.

### Measurements and parameters calculated on the Pajero vehicle

To compute the gravity center position the following parameter are measured: the total mass, the mass on each axis, the pitch and the load transfer from the front to the rear axle as a result of a front rise. The center of gravity is calculated by: Rr=Rf=375 mm To estimate the reduced stiffness of the suspension a known force is applied on the forecarriage, and then to the rear axle. Measuring the resulted excursion, it was possible to determine the equivalent stiffness of the car. The system is assumed linear around the static equilibrium position; infact the reference car presents a suspension system characterized by a four-bar linkage with torsion bar only at the forecarriage (there aren’t spring) and, to the rear, by a rigid axle connected to the frame with vertical springs. Therefore this system has null progression behaviour. Reduced stiffness-front = 34.85 N/mm
Reduced stiffness-rear = 26.17 N/mm

#### comparison between measured and calculated front stiffness:

measured stiffness = 17.4 N/mm The vibration modes of the Pajero vehicle are calculated assuming bounce and pitch modes decoupled:

## Static stiffness of the Pajero car tyre was then measured, both radial and lateral: the same tyre  will be adopted for the prototype.

tyre: MARIX 235/70 R16 recostructed.  M=26.8 Kg    P=2.2 bar
( l is the deflection, F is the applied force. Lo and Fo are the initial conditions ) ## ### Prototype’s measurements

Finally, the stiffnesses of the springs and the viscosity coefficient of the damper adopted for the prototype were estimated. A single compression measurement is carried on for the damper, with only one known speed. Is therefore assumed that the response is linear both in traction and in compression, and that the damping coefficient in extension has a double value that in compression. As a preliminary comparison , the center of gravity of the prototype is determined, estimating its mass and approximating the mass of the engine equal to 25 % of the mass of the motorcycle (140Kg). with a 70 kg pilot, bounce became 0.58 Hz and pitch 0.65 Hz.

( Reduced stiffness are the result of the simulator measurements, and will then be reported ).

## The modelling problem

The prototype was first modeled with a CAD ( SolidWorks ) then imported in MSC ADAMS, reassembled with the appropriate constraints. For the kinematics study, the front suspension system is considered. In function of the vertical excursion of the wheel, were measured: toe angle, camber angle, trail, reduced stiffness at the front. In the rear, only the reduced stiffness was measured. A movement of the damper housed in the spring was imposed, equal to the maximum excursion allowed by the limit costrain of real damper. The resulting vertical wheel excursionl and the above parameters were measured. The reduced stiffness was found by measuring the speed ratio between the deformation of the spring and the vertical displacement of the wheel. For the dynamic study, the wheel geometry and its model with the calculated parameters was inserted, estimating a slip stiffness of 15 rad^-1. A variable torque from 60Nm to 100Nm was applied to the rear wheels. When starting from standstill at maximum power an instability is detected, probably caused by rear sideslip and the wheels’ excursion and the variation of the characteristic angles, so the vehicle tends to bend. A PD control was then added, proportional to the deviation from the rectilinear trajectory, and to the deviation speed from that trajectory. The pitch angle and the load transfer, function of the braking torque applied to all 4 wheels, were then measured. In the cornering motion, known values, gradually increasing, of the excursion of the steering box were set and than the corresponding theoretical bending radii were calculated. For the different radii of curvature, yaw rate was measured as a function of vehicle speed. For the first cornering motion simulation, it was also measured the load transfer between the outer wheels, from the rear to the front, in order to verify that it is larger on the front.

## Simulations and analysis of results

Carried out the three described simulations, the results were analysed.

#### Kinematics:

Characteristic angles and reduced stiffness of suspension system. #### Dynamic in straightline:

Load transfer in a constant acceleration and deceleration. Adimensional load transfer in braking increase. #### Dynamic cornering:

In dynamic cornering, after 6 s there is adherence loss, with 0.7 g centrifugal acceleration. Other vibration modes have frequencies over 10 Hz.  Kinematics: https://youtu.be/Nm7yc2Rd7wc
Dynamics straightline: https://youtu.be/h7AqybkPAtE
Dynamics cornering: https://youtu.be/qjoE9V97JoY

#### Results:

The conduced analyses suggest to change the rear spring with another one with a 1,25 N/mm stiffness in order to make the vibration frequencies similar to those of the comparative vehicle. Several times the coefficients of the PD control were adjusted to allow a stable straight trajectory. The weight transfer under braking conditions is small: this is caused by the low gravity center of the prototype. Another result is the system’s oversteering behavior, with the increasingly divergent yaw velocity.

## Conclusion

From the results obtained it can be said that it is necessary to review the geometry of the front suspension, so as to reduce the toe-in angle variation during the wheel excursion; the aim is to give a greater straight-line stability without the intervention of “human control”. In order to adopt the available springs (K=15.8 N/mm) it is also necessary to modify the rear springs positioning: this allows to maintain the same reduced stiffness.

## References

Vittore Cossalter, “MOTORCYCLE DYNAMICS”, 2014.
Alberto Doria, Vittore Cossalter, “Appunti di DINAMICA DEL VEICOLO”, 2013-2014