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Research Papers: Design Automation

Motorcycle Tire Modeling for the Study of Tire–Rim Interaction

[+] Author and Article Information
Federico Ballo

Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 1,
Milan 20158, Italy
e-mail: federicomaria.ballo@polimi.it

Massimiliano Gobbi

Mem. ASME
Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 1,
Milan 20158, Italy
e-mail: massimiliano.gobbi@polimi.it

Gianpiero Mastinu

Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 1,
Milan 20158, Italy
e-mail: gianpiero.mastinu@polimi.it

Giorgio Previati

Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 1,
Milan 20158, Italy
e-mail: giorgio.previati@polimi.it

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 8, 2015; final manuscript received December 31, 2015; published online March 31, 2016. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 138(5), 051404 (Mar 31, 2016) (13 pages) Paper No: MD-15-1472; doi: 10.1115/1.4032470 History: Received July 08, 2015; Revised December 31, 2015

For the lightweight design of the wheel rim of motorcycles, the knowledge of the way in which contact forces are transmitted by the tire is of crucial importance. In this paper, an analytical model of the tire is developed and explicit formulae giving the distribution of the radial and axial forces acting on the wheel rim for a given vertical load are derived. The analytical model is validated by means of a finite element method (FEM) model and experimental tests. The proposed analytical model is able to predict the radial deflection of both a front and a rear tire for a racing motorbike with very good accuracy over a wide range of inflating pressures and vertical loads. The force distributions are in very good agreement with the results of the FEM model. Experimental tests show that the force distribution at the interface between the tire and rim can be used to predict the stress distribution in the rim with a good accuracy.

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Figures

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Fig. 1

Simplified analytical tire model for radial deflection [14]

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Fig. 2

Portion ds of a general curved beam

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Fig. 3

Free-body diagram of a portion ds of the curved beam

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Fig. 4

Tire analytical model with a distributed load

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Fig. 5

Tire reaction forces in lateral direction: undeformed tire (left) and deformed tire (right)

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Fig. 6

Tire radial forces when only an inflation pressure is applied

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Fig. 7

Tire residual stiffness k as a function of the inflation pressure: front tire (left) and rear tire (right). Dots: experimental data. Continuous line: expression of k from Table 1.

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Fig. 8

Front tire radial displacement: vertical load 2500 N and inflation pressure 2.1 bar

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Fig. 9

Rear tire radial displacement: vertical load 2500 N and inflation pressure 1.8 bar

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Fig. 10

Tire cross section: FEM model

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Fig. 11

Tire cross section subjected to inflation pressure: 2D axisymmetric model

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Fig. 12

Three-dimensional tire model for stiffness test simulation

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Fig. 13

Tire radial (left) and lateral (right) stiffness test simulation

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Fig. 14

Test bench for tire radial and lateral stiffness measurement

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Fig. 15

A 120/75 R420 front tire radial stiffness for two different inflation pressures: 1.8 bar (left) and 2.5 bar (right)

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Fig. 16

A 200/60 R17 rear tire radial stiffness for different inflation pressures: analytical model (dashed lines) and experimental measurements (dotted lines)

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Fig. 17

A 200/60 R17 rear tire radial stiffness for different inflation pressures: FEM model (continuous lines) and experimental measurements (dotted lines)

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Fig. 18

A 200/60 R17 rear tire lateral stiffness for p = 1.8 bar: FEM model and experimental measurements

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Fig. 19

Measured and FEM-simulated footprint: vertical load 2500 N and p = 1.8 bar. The two pictures have the same scale.

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Fig. 20

Distributed forces acting on the rim in radial (left) and axial (right) directions: 200/70 R17 rear tire, inflation pressure 1.8 bar, and vertical load 2950 N

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Fig. 21

Distributed forces acting on the rim in radial (left) and axial (right) directions: 200/70 R17 rear tire, inflation pressure 2.5 bar, and vertical load 3180 N

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Fig. 22

Curved beam model with a general distributed load

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Fig. 23

Vertical stiffness of a 200/60 R17 tire at 1.8 bar: experimental (black) and nonlinear model (gray)

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Fig. 24

Comparison of the radial forces acting on the wheel rim: 200/70 R17 rear tire, inflation pressure 1.8 bar, and vertical load 2950 N

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Fig. 25

Location of the SG applied on the wheel rim

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Fig. 26

Node sets for applying radial and axial reactions

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Fig. 27

Scheme of axial forces acting on the wheel rim—adapted from Ref. [5]

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Fig. 28

Complete FE model of the tire and wheel rim subjected to a vertical load

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