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Topology Optimization of Inserts Structure of Run-Flat Tire under Zero-Pressure Driving Condition

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Abstract

In order to improve the zero-pressure driving performance of the inserts supporting run-flat tire and solve the problems of heavy weight and large moment of inertia, the topology optimization theory based on variable density method was used to optimize the inserts structure of run-flat tire. The mechanical model of zero-pressure driving and the contact finite element model between insert, tire and ground was established. Further, stiffness, strength and modal characteristics of the inserts structure under zero-pressure driving condition before and after optimization were compared and simulated. The results show that under the maximum load of the tire, the optimized inserts structure can reduce the weight by 19.4 % with the requirements of the stiffness and strength, and the load bearing performance of the inserts structure is optimized, and the accuracy of the design is improved. On the premise of satisfying the design requirements of the tire dynamic characteristics, the natural frequency of each order for the optimized inserts structure is reduced. The static load characteristics of the tires under zero-pressure conditions before and after optimization were verified based on the tire load characteristics test bench. The research results provide a reference for the design and optimization of the inserts supporting run-flat tire.

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Abbreviations

θ :

wrap angle of the insert on the tread, °

δ :

wrap angle of the tire footprints length, °

α :

contact length of the insert on the tread, m

β :

length of the tire footprint, m

r :

radius of the insert, m

R :

radius of the tire, m

G :

weight of the insert, kg

ω :

tire rolling angular velocity, rad/s

v :

tire speed, m/s

R :

free radius of the tire, m

r :

outer diameter of the tire insert, m

r I :

rolling radius of zero-pressure driving, m

F p :

force acting on the tire by the axle, N

M t :

driving torque, N·m

F z :

tire normal force, N

M Y :

tire rolling resistance moment, N·m

F b :

tangential force that the ground acts on the tire, N

F i :

tangential force that the insert acts on the tire, N

E(x i):

elastic modulus after interpolation, MPa

E min :

elastic modulus of material hole, MPa

x i :

unit relative density, kg/m3

p :

penalty factor

E 0 :

elastic modulus of solid part of material, MPa

C(x):

structural strain energy, MPa

{U}:

displacement vector of structure, m

[K]:

stiffness matrix of system

V j :

volume of unit j, m3

\(\bar V\) :

volume value of the set material, m3

S :

safety factor

[δ]:

maximum allowable stress of the material, MPa

δ s :

yield limit of the material, MPa

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Acknowledgement

This research was partly supported by the National Natural Science Foundation of China (Grant No. 51605215), the Open Fund for State Key Laboratory of Automotive Simulation and Control (Grant No. 20210205), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. SJCX22_1049 & SJCX22_1058), and the Research Foundation of Nanjing Institute of Technology (Grant No. CKJA202205).

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Authors and Affiliations

  1. School of Automobile and Rail Transportation, Nanjing Institute of Technology, Nanjing, 211167, China

    Liguo Zang, Tian Lv, Yaowei Li & Xingyu Wang

  2. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130015, China

    Liguo Zang

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  1. Liguo Zang
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  2. Tian Lv
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Correspondence to Liguo Zang.

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Zang, L., Lv, T., Li, Y. et al. Topology Optimization of Inserts Structure of Run-Flat Tire under Zero-Pressure Driving Condition. Int.J Automot. Technol. 24, 311–321 (2023). https://doi.org/10.1007/s12239-023-0026-5

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  • DOI: https://doi.org/10.1007/s12239-023-0026-5

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