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Research Papers

In-Plane Flexible Beam on Elastic Foundation With Combined Sidewall Stiffness Tire Model for Heavy-Loaded Off-Road Tire

[+] Author and Article Information
Zhihao Liu

Department of Mechanic,
Xi'an Research Institution of High Technology,
Xi'an 710025, China
e-mail: liuzh_1989@126.com

Qinhe Gao

Department of Mechanic,
Xi'an Research Institution of High Technology,
Xi'an 710025, China
e-mail: qhgao201@126.com

Hailong Niu

Department of Mechanic,
Xi'an Research Institution of High Technology,
Xi'an 710025, China
e-mail: 17602910959@126.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 19, 2017; final manuscript received November 30, 2018; published online February 21, 2019. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 141(6), 061006 (Feb 21, 2019) (15 pages) Paper No: DS-17-1623; doi: 10.1115/1.4042546 History: Received December 19, 2017; Revised November 30, 2018

Combining the flexible carcass beam and the radial sidewall element, flexible beam on elastic foundation with combined sidewall stiffness tire model is proposed for heavy-loaded off-road tire with a large section ratio. The circumferential vibration of flexible carcass is modeled as Euler beam and the influence of inflation pressure on the circumferential vibration of flexible carcass is investigated with the modal experiment and theoretical modeling. The structural stiffness caused by the sidewall curvature and pretension stiffness caused by the inflation pressure is combined for the radial sidewall element. The influence of the sidewall structural parameters on the combined stiffness of sidewall and modal resonant frequency is researched and discussed. The nonlinear combined stiffness of sidewall is investigated with respect to the radial sidewall deformation. Experimental and theoretical results show that: (1) the combined stiffness of sidewall can character the pretension stiffness caused by inflation pressure and the structural stiffness led by the sidewall curvature and material properties and (2) the combined stiffness of sidewall is nonlinear with respect to the radial sidewall deformation, which is prominent with high inflation pressure. Taking the flexibility characteristic of tire carcass and the nonlinear stiffness of sidewall into consideration, flexible beam on elastic foundation with combined sidewall stiffness tire model is suitable for the heavy-loaded off-road tire with a large section ratio or tires under impulsive loading and large deformation.

Copyright © 2019 by ASME
Topics: Stiffness , Tires , Pressure , Roads
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Figures

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Fig. 1

Section ratio of heavy-loaded off-road tire

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Fig. 2

Flexible beam on elastic foundation with combined sidewall stiffness tire model

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Fig. 3

Flexible beam on elastic foundation tire model: (a) simplification form of heavy-loaded off-road tire, (b) scheme of flexible beam on elastic foundation tire model, and (c) force/moment analysis of microsection of carcass beam

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Fig. 4

External force of carcass microsegment

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Fig. 5

Planar experimental modal test: (a) planar experimental modal test implementation and (b) scheme of planar experimental modal test

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Fig. 6

Calculated transfer functions of exciting point and responding point: (a) amplitude of experimental transfer function and (b) phase of experimental transfer function

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Fig. 7

Calculated transfer functions under different inflation pressure conditions: (a) amplitude of experimental transfer function and (b) phase of experimental transfer function

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Fig. 8

Identified modal parameters of heavy-loaded off-road tire under different inflation pressure condition (0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 MPa): (a) modal resonant frequency and (b) modal damping

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Fig. 9

Radial stiffness kr of sidewall with different inflation pressure

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Fig. 10

Compared figure between the experimental and analytical modal resonant frequency of heavy-loaded off-road tire under different inflation pressure (0.3, 0.4, 0.5, 0.6, 0.7 and 0.8 MPa). (a) Inflation pressure: 0.8 MPa, (b) inflation pressure: 0.7 MPa, (c) inflation pressure: 0.6 MPa, (d) inflation pressure: 0.5 MPa, (e) inflation pressure: 0.4 MPa, and (f) inflation pressure: 0.3 MPa.

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Fig. 11

Scheme of sidewall geometry

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Fig. 12

Pretension stiffness of sidewall resulting from inflation pressure

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Fig. 13

Additional structural feature of sidewall

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Fig. 14

Compared result between the analytically and experimentally combined stiffness of sidewall

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Fig. 15

Influence of sidewall elasticity modulus on the sidewall combined stiffness

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Fig. 16

Influence of sidewall arc angle on the sidewall stiffness: (a) influence of sidewall arc angle on the pretension stiffness and (b) influence of sidewall arc angle on the structural stiffness

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Fig. 17

Combined stiffness of sidewall under different inflation pressure (0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 MPa): (a) inflation pressure: 0.8 MPa, (b) inflation pressure: 0.7 MPa, (c) inflation pressure: 0.6 MPa, (d) inflation pressure: 0.5 MPa, (e) inflation pressure: 0.4 MPa, and (f) inflation pressure: 0.3 MPa

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Fig. 18

Nonlinear stiffness relationship of sidewall with respect to the radial deformation of sidewall: (a) compared figure between the linear and nonlinear stiffness relationships of sidewall under normal inflation pressure, (b) nonlinear stiffness relationships of sidewall under different inflation pressure, and (c) rate of sidewall radial stiffness change under different inflation pressure

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Fig. 19

Influence of sidewall structural parameters on tire modal resonant frequency: (a) elasticity modulus of the radial sidewall segment, (b) length of sidewall arc, (c) sidewall arc angle, and (d) inflation pressure

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