Abstract
A tire model can be used to predict vehicle dynamics behaviour, such as braking or turning. This paper proposes a method for testing/modelling a tire with a roller brake tester. It requires two speed sensors installed on the roller and idler. That additional sensors are used to estimate roller brake tester inertia and measure tire slip during testing. After involving inertia in the calculation, the brake tester measurement becomes accurate in all points from zero until maximum slip. These results are better than the existing roller brake tester which is only accurate when the steady state condition of the roller is achieved. The modified brake tester and tire testing were modelled and simulated using MATLAB® Simulink. Furthermore, the influence of the brake tester arrangement on measurement characteristics has been identified.
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Abbreviations
- \({{\ddot \theta }_{id}}\) :
-
Idler angular acceleration
- \({{\dot \theta }_{id}}\) :
-
Idler angular velocity
- \({{\ddot \theta }_m}\) :
-
Electric motor shaft angular acceleration
- \({{\dot \theta }_m}\) :
-
Electric motor shaft angular velocity
- \({{\ddot \theta }_r}\) :
-
Roller angular acceleration
- \({{\dot \theta }_r}\) :
-
Roller angular velocity
- \({{\ddot \theta }_w}\) :
-
Wheel angular acceleration
- \({{\dot \theta }_w}\) :
-
Wheel angular velocity
- μ FX :
-
True friction coefficient/braking efficiency
- μ I :
-
Friction coefficient/braking efficiency estimated by the existing brake tester
- μ IC :
-
Friction coefficient/braking efficiency estimated by the modified roller brake tester
- μ P :
-
Peak friction coefficient between roller surface and tire
- μ s :
-
Sliding friction coefficient between roller surface and tire
- μ m :
-
Electric motor viscous damping
- F act :
-
Action force acting on the vehicle wheel consists of braking torque, rolling resistance torque, and inertia of the wheel and idler
- F bl :
-
Braking force/friction force estimated by the existing roller brake tester
- F I :
-
Force measured by load cell
- F IC :
-
Friction force/braking force estimated by the modified roller brake tester
- F rear :
-
Friction force on non-tested wheel
- F x :
-
Total friction force on roller 1 and 2
- F x1 :
-
Friction force acting on roller 1
- F x2 :
-
Friction force acting on roller 2
- F x2max :
-
Maximum friction force on roller 2
- F xm :
-
Maximum friction force on roller surface
- F xs :
-
Sliding friction force on roller surface
- J C :
-
Correction inertia consists of ring gear and rollers inertia
- J id :
-
Idler moment of inertia
- Jm :
-
Electric motor moment of inertia
- J r :
-
Roller moment of inertia
- J ring :
-
Ring gear moment of inertia
- J tot :
-
Total inertia consists of electric motor, ring gear, and roller inertia
- J W :
-
Wheel moment of inertia
- N 1 :
-
Normal force acting on roller 1
- N 1y :
-
Vertical component of normal force on roller 1
- N 2 :
-
Normal force acting on roller 2
- T b :
-
Braking torque
- T d :
-
Electric motor load torque
- T m :
-
Electric motor torque
- T rr :
-
Rolling resistance torque
- T W1 :
-
Roller 1 torque
- T W2 :
-
Roller 2 torque
- r id :
-
Idler radius
- r pin :
-
Pinion gear effective radius
- r r :
-
Roller radius
- r ring :
-
Ring gear effective radius
- r W :
-
Wheel effective radius
- L :
-
Length of gearbox lever
- N :
-
Total normal force of roller 1 and 2
- W :
-
Heel/tire normal load
- i :
-
Slip between vehicle wheel and roller
- β :
-
Angle formed by two normal forces acting on roller 1 and 2
- F XC :
-
Critical friction force
- K t :
-
Initial slope of friction force vs slip curve
- k t :
-
Tangential stiffness of tire
- l t :
-
Length of contact patch
- λ :
-
Length in front of contact patch deformed
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Acknowledgments
This work was supported by The Indonesian Endowment Funds for Educational/Lembaga Pengelola Dana Pendidikan/LPDP (No. 201701210110284). The authors also thank Politeknik Keselamatan Transportasi Jalan (PKTJ) of Ministry of Transportation for providing data of a roller brake tester.
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Ery Muthoriq received B.Eng. in mechanical engineering from Sebelas Maret University, Indonesia, in 2007 and M.Eng. from Institut Teknologi Bandung, Indonesia, in 2013. He is currently a doctoral degree candidate in mechanical engineering at Institut Teknologi Bandung, Indonesia. His research interest mainly focus on brake testing, vehicle dynamics, and system modelling.
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Muthoriq, E., Abidin, Z., Hariyanto, A. et al. Enhancement of a roller brake tester for modelling the tire. J Mech Sci Technol 37, 3379–3391 (2023). https://doi.org/10.1007/s12206-023-0605-4
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DOI: https://doi.org/10.1007/s12206-023-0605-4