Research Papers: Design Automation

Tire-Rim Interaction, a Semi-Analytical Tire Model

[+] Author and Article Information
Federico Ballo

Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 1,
Milan 20156, Italy

Giorgio Previati, Massimiliano Gobbi, Gianpiero Mastinu

Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 1,
Milan 20156, Italy

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 28, 2017; final manuscript received December 15, 2017; published online January 30, 2018. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 140(4), 041401 (Jan 30, 2018) (12 pages) Paper No: MD-17-1586; doi: 10.1115/1.4038927 History: Received August 28, 2017; Revised December 15, 2017

This paper deals with the development and validation of a semi-analytical tire model able to compute the forces at the interface between tire and rim. The knowledge of the forces acting on the rim is of crucial importance for the lightweight design of wheels. The proposed model requires a limited set of data to be calibrated. The model is compared with complete finite element (FE) models of the tire and rim. Despite its simplicity, the semi-analytical model is able to predict the forces acting on the rim, in agreement with the forces computed by complete FE models. The stress state in the wheel rim, computed by the developed semi-analytical model matches fairly well the corresponding stress state coming from experimental tests.

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Fig. 1

Cross section of a pneumatic tire. Left: undeformed section. Right: deformed section when a force fv is applied.

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Fig. 2

Infinitesimal section of the sidewall of the tire as a curved beam

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Fig. 3

Expression of Kdc=Kdc(w) as function of the vertical displacement w (data in Table 2)

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Fig. 4

Simplified analytical tire model for radial deflection [24]. Left: tread belt modeled as a curved beam connected to the rim (fixed to the ground) by springs. Right: free body diagram of a portion ds of the curved beam representing the tread belt.

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Fig. 5

Portion ds of a general curved beam

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Fig. 10

Measured section of the considered tire

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Fig. 9

Test bench for tire stiffness measurement (left) and detail of the moving platform (right)

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Fig. 8

Estimation of the inclination of the plane of action of the pressure axial force on the rim. The inclination of the plane is defined as the inclination of the line connecting the extreme points of the pressure zone (dark gray zone in the lateral contact area). These points can be estimated as the end point of the fillet between bottom and lateral contact zone of the tire and the separation point between the upper part of the rim flange and the tire.

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Fig. 7

Forces acting on a section of a pneumatic tire when only the internal pressure is applied

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Fig. 12

Tire cross section, FEM model

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Fig. 6

Forces acting at tire-rim interface on an infinitesimal section of the tire

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Fig. 11

Tire radial force versus radial displacement—comparison between the semi-analytical model and experimental data

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Fig. 16

Reaction forces on the rim (Fig. 6) computed by the FE model and by the analytical model, respectively, for two inflating pressures (2.5 and 4.5 bar), radial load 8750 N

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Fig. 17

Resistive strain gauges located on the front (left) and back (right) side of the spoke

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Fig. 18

Resistive strain gauges located on the wheel rim

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Fig. 13

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

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Fig. 15

Comparison between FE model results and experimental data. Top: radial forces (inflation pressures: 2.1, 2.5, 3 and 4.5 bar). Bottom: lateral forces (inflation pressures: 2.1, 3 and 4.5 bar).

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Fig. 19

Cosine-distribution pressure for applying vertical load

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Fig. 20

Axial forces acting at the tire/rim interface

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Fig. 21

Node sets for applying radial and axial reactions

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Fig. 22

Complete FE model, deformed configuration




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