updated on January, 2017

## Introduction

The purpose of the project was to model and simulate the *TyreMeter* machine [1,2] developed and installed at the University of Padova – Department of Industrial Engineering. The system has been modelled in CATIA 3D, then imported in ADAMS. Three operating conditions have been simulated: pure slip test, pure roll tests and rolling resistance tests.

## Objectives

The objectives of the study were to analyze the accuracy of the formulas used to convert the load cells signals of the *TyreMeter* into tyre forces and moment. In order to do that, a multibody model of the machine has been created including the ADAMS tyre element (PAC2002 model) [3]. In particular the tyre lateral force, yawing moment and rolling resistance have been analyzed.

## The modelling problem

The *TyreMeter* machine has been modelled in CATIA 3D, than it has been imported in SOLIDWORKS in order to convert it in **.x_t* extension. Afterwards the parasolid model has been imported in ADAMS. Load cells are simulated using very high stiffness springs (1e6 N/mm) without damping. Formulas are used to estimate the tyre forces and moments using load cells measurements. Such formulas arise from equilibria around the leftmost vertical axis in Fig.3, the axis through B in Fig.3 and the vertical axis through the black point in Fig.4.

## Simulations and analysis of results

A supersport 600cc motorcycle rear tyre has been considered in the simulations:

- Unloaded radius = 300mm
- Width = 180mm
- Toroid radius = 90mm = Width/2

The tyre profile has been modelled as a toroid, computed by an excel sheet; Fig. 5.

All the simulations has been run with GSTIFF I3 integrator and error = 10^{-3}. GSTIFF SI2 has been tried, but large oscillations were obtained. Before running any simulation is necessary to set the *zero* of the load cells and initial conditions. The following ‘design variables’ have been used to better control the simulations: velocity of the angular motor related to the rotating disk, position of the angular motor related to the slip angle, position of the angular motor related to the roll angle. Each simulation elapses 4s and uses 400 steps. The inputs (either slip angle or roll angle – controlled through motors) are implemented using the following *step function*:

- 1s with zero slip and zero roll (the tyre reaches steady state rolling according to the disk rotation);
- 2s step motion in slip or roll motors;
- 1s of costant slip or roll angle.

Three simulations are analyzed below: pure slip, pure roll and zero slip and zero roll (for rolling resistance estimation). It should be noted that even when both the slip and camber are zero the tyre experience some turn slip because it is rolling on a rotating disk.

### Pure Slip

**(***Disk_speed *= 30°/s; *Slip_angle* = 2°)

*Disk_speed*= 30°/s;

*Slip_angle*= 2°)

The response to a 2deg step in the slip angle is shown in this section. The disk is rotating at a constant speed of 30deg/s. The steady state lateral force (COMP_Lat_force in Fig.6) and steady state aligning moment (MOD_Aligning_torque in Fig.7) estimated with the load cells formulas compare very well with the forces measured on the tyre element (tire contact forces in Fig.6 and Fig.7), with a errors around 1%. Note that the tyre lateral force at the beginning is zero, then after a 1s is around 700N: this is a turn-slip related force due to the curvature of the rotating disk.

### Pure Roll

**(***Disk_speed* = 30°/s; Roll_angle = 30°; Setting initial conditions with *Roll_angle* = 0°**)**

*Disk_speed*= 30°/s; Roll_angle = 30°; Setting initial conditions with

*Roll_angle*= 0°

The response to a 30deg step in the roll angle is shown in this section. The disk is rotating at a constant speed of 30deg/s. The steady state lateral force (COMP_Lat_force in Fig.8) and steady state aligning moment (MOD_Aligning_torque in Fig.9) estimated with the load cells formulas compare well with the forces measured on the tyre element (tyre contact forces in Fig.8 and Fig.9), with a below 1% for tyre forces and around 15% for yawing moment.

### Zero Slip & Zero Roll

**(***Disk_speed* = 30°/s)

*Disk_speed*= 30°/s)

In this section the motors for slip and roll are kept to zero, while the disk is rotating a constant speed of 30deg/s. Longitudinal force are estimated with an error around 10% and the rolling resistance with an error around 8%.

## Conclusion

A tyre testing machine has been modeled and simulated including the ADAMS tyre element that compute tyre forces and moments as a function of slip, camber and load according the Magic Formula. The model has been used to analyze compare the estimation of tyre forces and moments from load cells signals against those computed by the ADAMS tyre model. A good agreement has been found.

## References

[1] Cossalter, V. , Doria, A. , Lot, R. , Ruffo, N. and Salvador, M. (2003) ‘Dynamic Properties of Motorcycle and Scooter Tires: Measurement and Comparison’, Vehicle System Dynamics, 39: 5, 329 — 352.

[2] V. Cossalter, A. Doria, E. Giolo, L. Taraborrelli & M. Massaro (2014) Identification of the characteristics of motorcycle and scooter tyres in the presence of large variations in inflation pressure, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, 52:10, 1333-1354

[3]** **Pacejka, H.B. “Tyre and Vehicle Dynamics”, 1st edition, 2002