Optimize Design of Run-Flat Tires by Simulation and Experimental Research - MDPI

materials
Article
Optimize Design of Run-Flat Tires by Simulation and
Experimental Research
Huaqiao Liu, Yiren Pan *, Huiguang Bian and Chuansheng Wang *

 College of Electromechanical Engineering, Qingdao University of Science and Technology, Qingdao 266061,
 China; CM0004@tta-solution.com (H.L.); Bianhuiguang@163.com (H.B.)
 * Correspondence: pyr@qust.edu.cn (Y.P.); wcsmta@qust.edu.cn (C.W.); Tel.: +86-13589345827 (Y.P.);
 +86-13608966169 (C.W.)

 Abstract: In this study, the two key factors affecting the thermal performance of the insert rubber and
 stress distribution on the tire sidewall were analyzed extensively through various performance tests
 and simulations to promote the development of run-flat tires. Four compounds and two structures of
 insert rubber were designed to investigate the effects of heat accumulation and stress distribution
 on durability testing at zero pressure. It was concluded that the rigidity and tensile strength of the
 compound were negatively correlated with temperature. The deformation was a key factor that affects
 energy loss, which could not be judged solely by the loss factor. The stress distribution, however,
 should be considered in order to avoid early damage of the tire caused by stress concentration. On the
 whole, the careful balance of mechanical strength, energy loss, and structural rigidity was the key to
 the optimal development of run-flat tires. More importantly, the successful implementation of the
 simulations in the study provided important and useful guidance for run-flat tire development.

 Keywords: insert rubber; simulation; heat accumulation; stress distribution; run-flat tire

 



 


Citation: Liu, H.; Pan, Y.; Bian, H.; 1. Introduction
Wang, C. Optimize Design of Run-
 Deflated tires on vehicles can potentially have serious safety implications to both
Flat Tires by Simulation and
 the occupants in the vehicle as well to other road users. Statistically, approximately 70%
Experimental Research. Materials
 of traffic accidents on highways were caused by deflated tires, and the mortality rate of
2021, 14, 474. https://doi.org/
 riding on a flat tire was close to 100% at speeds of more than 160 km/h [1,2]. Tire blowout
10.3390/ma14030474
 causes the instantaneous loss of tire pressure, leading to sidewall collapse and support
 to the tire. Subsequently, the center of gravity of the vehicle changes abruptly and the
Received: 1 December 2020
Accepted: 18 January 2021
 vehicle veers out of control. The designing of run-flat tires had undergone many different
Published: 20 January 2021
 iterations of new designs since Chrysler and US Royal introduced a concept of run-flat
 tire in 1958. As early as 1976, several types of run-flat tires have been developed by tire
Publisher’s Note: MDPI stays neutral
 makers in the world since its concept was introduced and the representative ones are the
with regard to jurisdictional claims in
 banded tire introduced [3]. Nowadays, the typical run-flat tires adopt a specially designed
published maps and institutional affil- sidewall support structure, which was able to support the weight of the vehicle even
iations. in the event of lost pressure that the run-flat tire is able to run at zero internal pressure,
 fully loaded, for a maximum 80 km at 80 km/h. Contrary to the sidewall of conventional
 pneumatic tire, the insert rubbers of the sidewall reinforced run-flat tire makes the major
 driving performances such as the riding comfort and the rolling resistance worse than
 the conventional pneumatic tire. However, in consideration of safety, the advantages of
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
 running flat tire are gradually accepted by the market. In 2001, the 4th generation of the
This article is an open access article
 BMW 7 Series launched the market, and was the first model of mass-produced vehicles to
distributed under the terms and be equipped with run-flat tires [4–8], which represents that the run-flat tire has officially
conditions of the Creative Commons entered the original market.
Attribution (CC BY) license (https:// Compared to the traditional tire structure, the additional insert rubber and reinforce-
creativecommons.org/licenses/by/ ment of a run-flat tire inevitably changes the stress state of tire sidewalls during its running
4.0/). process. Many attempts have been made to investigate and optimize the properties of

Materials 2021, 14, 474. https://doi.org/10.3390/ma14030474 https://www.mdpi.com/journal/materials

Compared to the traditional tire structure, the additional insert rubber and reinforce-
 ment of a run-flat tire inevitably changes the stress state of tire sidewalls during its run-
Materials 2021, 14, 474 ning process. Many attempts have been made to investigate and optimize the properties 2 of 14
 of the tire self-supporting reinforced sidewall, based on the structure of the tire and insert
 rubber, including shape, thickness, compound, and flexion heat-generating properties of
 the insert rubber. Unlike traditional sidewall rubber, the properties of the insert rubber
 the tire self-supporting reinforced sidewall, based on the structure of the tire and insert
 required not only higher rigidity for structural support, but also a higher degree of flex-
 rubber, including shape, thickness, compound, and flexion heat-generating properties of
 ural resistance [9,10]. Nevertheless, these two properties were usually contradictory to
 the insert rubber. Unlike traditional sidewall rubber, the properties of the insert rubber
 each other
 required notand
 onlymust
 higherberigidity
 carefullyforbalanced
 structuralto achievebut
 support, thealso
 optimum
 a highercharacteristics.
 degree of flexural
 Generally, harder materials offer greater supporting capacity,
 resistance [9,10]. Nevertheless, these two properties were usually contradictory but sacrifice flexural
 to each
 performance and were prone to higher levels of heat generation.
 other and must be carefully balanced to achieve the optimum characteristics. However, these compar-
 isonsGenerally,
 were usually
 harderbased on the
 materials same
 offer types
 greater of deformation.
 supporting capacity,Ifbut
 a softer rubber
 sacrifice wasper-
 flexural to bear
 the sameand
 formance force, theprone
 were resulttomay
 higherbe levels
 quite of
 theheat
 opposite [11–14].
 generation. Therefore,
 However, thesethe compound of
 comparisons
 the insert
 were usually rubber
 basedmust balance
 on the hardness
 same types and the flexibility
 of deformation. in order
 If a softer rubbertowasachieve
 to bear optimum
 the
 performance.
 same force, theMoreover,
 result may the sidewall
 be quite of traditional
 the opposite [11–14]. tireTherefore,
 was composed of several
 the compound of compo-
 the
 insert
 nents,rubber must beads,
 including balancecarcass
 hardness and and
 piles, the flexibility
 sidewall in order toIt achieve
 chaffer. optimum
 had taken over aperfor-
 hundred
 mance.
 years toMoreover,
 develop athe sidewall
 mature of traditional
 technical system.tire was composed of several components,
 including beads, carcass piles, and sidewall
 Therefore, the rigidity of the insert rubber chaffer.
 mustIt had
 matchtaken
 theover a hundred
 rigidity of otheryears to
 structures
 develop a mature technical system.
 of the tire sidewall to prevent the delamination of the internal components caused by
 Therefore,
 driving with athe rigidity
 deflated of and
 tire the insert
 early rubber
 damage must matchThe
 [15–17]. the development
 rigidity of other of structures
 a run-flat tire
 of
 often requires significant amounts of resources to be invested for testing the tires inby
 the tire sidewall to prevent the delamination of the internal components caused order
 driving with a deflated tire and early damage [15–17]. The development of a run-flat tire
 to achieve the best performance. As such, this work employs mechanical analysis software
 often requires significant amounts of resources to be invested for testing the tires in order to
 to simulate and evaluate the stress state of the sidewall, in order to provide theoretical
 achieve the best performance. As such, this work employs mechanical analysis software to
 support for designing the structure and compound of the run-flat tire insert rubber. In
 simulate and evaluate the stress state of the sidewall, in order to provide theoretical support
 addition,
 for designingmechanical tests and
 the structure werecompound
 carried outofforthetwo structures
 run-flat and rubber.
 tire insert four insert rubber com-
 In addition,
 pounds to further verify the correlation between the simulation
 mechanical tests were carried out for two structures and four insert rubber compounds results and tire perfor-
 to
 mance.verify the correlation between the simulation results and tire performance.
 further

 2.Materials
 2. MaterialsandandMethods
 Methods
 2.1.
 2.1. Preparation of theTire
 Preparation of the Tireand Simulation
 and Model
 Simulation Model
 The
 Thetwo-dimensional
 two-dimensional(2D) (2D)model
 model used
 usedin in
 thisthis
 simulation waswas
 simulation the 245/45R18 96W96W
 the 245/45R18
 model, and the structural designing of insert rubber was shown in Figure 1.
 model, and the structural designing of insert rubber was shown in Figure 1.

 (a)

 (b)

 Figure 1. Cont.

Materials 2021, 14, 474 3 of 14
Materials 2021, 14, x FOR PEER REVIEW 3 of 15

 (c)
 Figure 1.
 Figure 1. The
 Thestructural
 structuraldesigning
 designingofof insert
 insert rubber
 rubber (unit:
 (unit: mm).
 mm). (a) (a) Run-flat
 Run-flat tire model;
 tire model; (b) (c)
 (b) B-1; B-1; (c)
 B-2.
 B-2. (unit:
 (unit: mm) mm)

 Figure 11 shows
 Figure shows two
 two structures
 structures of of insert
 insert rubber
 rubber which
 which were
 were designated
 designated as as B-1
 B-1 and
 and B-
 2. B-1B-1
 B-2. ladder type
 ladder hadhad
 type a large thickness
 a large transition
 thickness transitionrange, while
 range, B-2B-2
 while waswas a half-moon
 a half-moon shape
 with awith
 shape small thickness
 a small transition
 thickness range.
 transition Compared
 range. Compared withwith
 B-1, B-1,
 the total length
 the total of B-2
 length insert
 of B-2
 insert
 rubberrubber
 was 10 was
 mm 10 smaller,
 mm smaller, the thickness
 the thickness ofmm
 of 11 11 mm at the
 at the middle
 middle points
 points 5 and6 6was
 5 and
 was smaller,
 smaller, and and the thickness
 the thickness at both
 at both endsends
 waswas larger,
 larger, which
 which makes
 makes it more
 it more rigidrigid
 andandstress
 stress concentrated under flexural motion. In order to better research content
 concentrated under flexural motion. In order to better research content of this paper, four of this paper,
 four
 groupsgroups of experimental
 of experimental formulae
 formulae werewere designed
 designed withwith significant
 significant differences
 differences in in heat
 heat gen-
 generation and hardness which were used for simulation analysis and
 eration and hardness which were used for simulation analysis and tire manufacturing tire manufacturing
 with
 with the
 the combination
 combinationofofthe thetwo
 twostructures
 structuresofofinsert
 insertrubber in in
 rubber Figure
 Figure1, and
 1, andthethe
 simulation
 simulation
 model scheme is shown in Table 1.
 model scheme is shown in Table 1.
 Table 1. Simulation model scheme.
 Table 1. Simulation model scheme.
 List Compound Structure
 List Compound Structure
 Model-1 A-1 B-2
 Model-1
 Model-2
 A-1
 A-2 B-2
 B-2
 Model-2
 Model-3 A-2
 A-3 B-2 B-2
 Model-3
 Model-4 A-3
 A-4 B-2 B-2
 Model-5
 Model-4 A-1
 A-4 B-1 B-2
 Model-6 A-2 B-1
 Model-5 A-1 B-1
 (The compounds of A-1/A-2/A-3/A-4 will presented later on).
 Model-6 A-2 B-1
 According to the Smithers FNF report of 225/45
 (The compounds of A-1/A-2/A-3/A-4 will presented later on). R17 HP run-flat tire, the hardness
 of the support rubber of the run flat tire produced by the world-famous tire enterprises
 was generally
 Accordingbetween 71–78, and
 to the Smithers FNFthe rubber
 report material
 of 225/45 R17inHPtherun-flat
 formulatire,wasthe
 mainly cis- of
 hardness
 polybutadiene
 the support rubber (BR) with
 of thenatural
 run flatrubber (NR), such
 tire produced byas theworld-famous
 the support rubber ofenterprises
 tire Bridgestonewas
 was NR/BR
 generally = 30/70,
 between which
 71–78, andwas mainlymaterial
 the rubber considerate theformula
 in the high flexibility
 was mainly of BR. At the
 cis-polybuta-
 same time, other companies also selected natural rubber as the
 diene (BR) with natural rubber (NR), such as the support rubber of Bridgestone main raw material withwas
 cis-polybutadiene, such as Michelin insert rubber used NR/BR = 70/30
 NR/BR = 30/70, which was mainly considerate the high flexibility of BR. At the same time, design, mainly
 considering
 other companies the high
 also physical and mechanical
 selected natural rubber asproperties
 the main raw of nature rubber.
 material Therefore,
 with cis-polybuta-
 based on the two different rigid structures, we designed four groups of different hardness
 diene, such as Michelin insert rubber used NR/BR = 70/30 design, mainly considering the
 insert rubber formulations, the hardness gradients were 78/75/72/68, in which NR/BR
 high physical and mechanical properties of nature rubber. Therefore, based on the two
 = 70/30 was selected for A-2, and NR/BR = 30/70 was selected for the remaining three
 different rigid structures, we designed four groups of different hardness insert rubber for-
 groups. Based on the previous development experience, too low hardness of insert rubber
 mulations, the hardness gradients were 78/75/72/68, in which NR/BR = 70/30 was selected
 was not conducive to the tire’s durability under zero air pressure. Therefore, in this
 for A-2, andA-3
 experiment, NR/BR
 and A-4= 30/70 was combination
 were new selected for designed
 the remaining three groups.
 and developed by us, Based on the
 which will
 previous development experience, too low hardness of insert rubber
 be compared with the previous design. Under the structure of B-1, we only studied A-1 was not conducive
 to the
 and tire's
 A-2 durability
 system underhardness
 with higher zero air pressure.
 while the rawTherefore,
 rubberin this experiment,
 design was just the A-3 and A-4
 opposite,
 were
 so new
 as to combination
 study the balancedesigned
 between andraw developed by us,and
 rubber selection which will be
 hardness compared with the
 design.
 previous
 Otherdesign.
 elements Under the structure
 of structural designing of B-1,
 basedweononly studied
 the tire A-1 and
 simulation model A-2 system
 were shownwith
 higher
 in Tablehardness
 2. while the raw rubber design was just the opposite, so as to study the
 balance between raw rubber selection and hardness design.
 Other elements of structural designing based on the tire simulation model were
 shown in Table 2.

Materials 2021, 14, 474 4 of 14

 Table 2. Other structural designing elements of tires corresponding to structural analysis.

 Structural Features Model
 Structural Designing Features 1 2 3 4 5 6
 Insert Rubber compounds A-1 A-2 A-3 A-4 A-1 A-2
 materials 2 + 2*0.30HT-60EPD
 Belt
 Angle 29◦
 materials 1300D/2-110EPD
 Carcass
 Carcass turn-up low
 Shore A 79
 Apex
 height/mm 40
 Bead materials Φ1.295
 arrange 4-5-6-5-4(ϕ466.8)
 Charfer hardness 73
 Note: EPD, Ends per DM.

 Simulation Mathematical Models and Parameters
 The description methods of mechanical properties of rubber materials can be roughly
 divided into two categories: One is the phenomenological description of rubber as a
 continuous medium, the other is the method based on thermodynamic statistics. At present,
 the polynomial models based on the theory of continuum mechanics are widely used in
 engineering such as Mooney- Rivlin model and Yeoh model. Because the stress-strain
 curve of rubber material had strong nonlinear characteristics, when the strain of rubber
 exceeds 20%, the material would show "hardening" characteristics, while the strain rate
 of insert rubber of run-flat tire was close to 25% at zero pressure. Therefore, in this case,
 the insert rubber appeared hardening. It was necessary to use the material constitutive
 model which can accurately described this characteristic to get the accurate simulation
 results. Mooney-Rivlin model could not reflect the "hardening" characteristics of rubber
 under large deformation, while the Yeoh model with a good fitting of rubber under large
 deformation could accurately reflect the state of the running tire at zero pressure.
 The Yeoh model was used in ABAQUS simulation software to simulate run-flat
 tires. The Yeoh model was suitable for the large deformation behavior of filler-filled
 rubber. This model can predict the mechanical behavior of other deformation by fitting the
 parameters of deformation experimental data, and can reflect the s-shaped stress-strain
 curve under different deformation modes. The deformation range was also relatively wide,
 and the strain energy density function model was as follows:

 N N
 1
 W= ∑ Ci0 ( I1 − 3)i + ∑ d
 (J − 1)2k (1)
 i =1 k =1 k

 J was the volume ratio of after deformation and before deformation. When N = 3,
 the reduced polynomial is Yeoh model, which is a special form of reduced polynomial.
 The typical binomial parameter form can be rewritten as:

 W = C10 ( I1 − 3) + C20 ( I1 − 3)2 (2)

 where N, Cij , and dk were material constants, which were determined by material experi-
 ments, and the initial shear modulus was set as,

 µ = 2C10 (3)

 Rebar embedded unit was used to simulate the composite parts such as the crown
 layer, the band layer, and the body, and the rubber part was simulated by the incompressible
 C3D8H unit.
 The Yeoh model construction equation in origin 8 was as follows:

Materials 2021, 14, 474 5 of 14
Materials 2021, 14, x FOR PEER REVIEW 5 of 15

 y = x )−−(1
 ((1++ )
 = (((1 x )ˆ(−2)) x ((2
 (1++ )^(−2)) 2x c 10 ++44x c 20 x ((((1 )ˆ2 + 2+x (21 (1
 1 ++x )^2 + x+)ˆ(− 1) − 3)−+3)6x+c30
 )^(−1)
 x
 6 ((1 + x )+
 ((1 ˆ2 )^2
 x (1 + x )ˆ(−1) − 3)ˆ2)) + N (4)
 (4)
 + 2 (1 + )^(−1) − 3)^2)) + + 2

 where x andx yand
 where werey were the stress
 the stress and and
 strainstrain
 valuesvalues obtained
 obtained based
 based on the onexperimental
 the experimental
 data
 data
 of rubber compound. The experimental data were imported into the data data
 of rubber compound. The experimental data were imported into the analysis
 analysis soft-
 software
 ware andand fitted
 fitted to to obtain
 obtain C10,C10, C20,C30,
 C20, C30,and andn.n.InInthe
 thedatabase
 database ofof ABAQUS
 ABAQUS simulation
 simulation
 analysis,
 analysis, the rubber material model was established by these four parameters, and finally
 the rubber material model was established by these four parameters, and finally
 used
 used inin the
 the simulation
 simulation analysis.
 analysis.
 The mesh of tire model was shown in Figure 2.
 The mesh of tire model was shown in Figure 2.

 Figure 2.
 Figure 2. The
 The mesh
 mesh of
 of tire
 tire model.
 model.

 In
 In the
 the process
 process of
 of tire
 tire and
 andrim
 rimassembly,
 assembly,the theglobal
 globalboundary
 boundarycondition
 conditionX/Y X/Y axis
 axis was
 was
 set
 set immobility in the global coordinates, and only Z-axis motion was allowed to achieve
 immobility in the global coordinates, and only Z-axis motion was allowed to achieve
 contact
 contact between
 between the bead
 bead andand rim
 rim under
 under inflation
 inflation pressure.
 pressure. In the process of simulation.
 simulation.
 In
 In the
 the simulation
 simulation process,
 process, the
 the X-axis
 X-axis constraint
 constraint was
 was removed
 removed and
 and thethe tire
 tire stress
 stressanalysis
 analysis
 under
 under specific
 specific load
 load and
 and inflation
 inflation pressure
 pressurewaswasstarted.
 started. Therefore,
 Therefore, in
 in order
 order toto simulate
 simulate thethe
 stress of tire under zero pressure, the load is designed to be 80% of the
 stress of tire under zero pressure, the load is designed to be 80% of the tire load.tire load.

 2.2. Materials
 2.2. Materials
 Natural rubber (NR): TSR20, Thailand 20# Standard Rubber; cis-polybutadiene (short for
 Natural rubber (NR): TSR20, Thailand 20# Standard Rubber; cis-polybutadiene (short
 BR): BR9000, products of Beijing Yanshan Petrochemical Industry Co., Ltd.(Beijing, China);
 for BR): BR9000, products of Beijing Yanshan Petrochemical Industry Co., Ltd.(Beijing,
 carbon black: N330.N550, products of Cabot, America (Cabot, Shanghai, China); zinc oxide
 China); carbon black: N330.N550, products of Cabot, America (Cabot, Shanghai, China);
 (ZnO, white seal) were supplied by Hebei Hongtu Zinc Industry Co., Ltd.(Xingtai, China);
 zinc oxide (ZnO, white seal) were supplied by Hebei Hongtu Zinc Industry Co., Ltd.(Xing-
 stearic acid: Fengyi Oil Technology Co., Ltd. (Suzhou, China); N-(1,3-dimethylbutyl)-
 tai, China); stearic acid: Fengyi Oil Technology Co., Ltd. (Suzhou, China); N-(1,3-dime-
 N0-phenyl-p-phenylenediamine (6PPD), 2,2,4-trimethyl-1,2-dihydroquinoline(TMQ), N-
 thylbutyl)-N0-phenyl-p-phenylenediamine (6PPD), 2,2,4-trimethyl-1,2-dihydroquino-
 tert-butyl-2-benzothiazyl sulfenamide (TBBS), tetra(isobutyl) thioperoxydicarbamicacid
 line(TMQ), N-tert-butyl-2-benzothiazyl sulfenamide (TBBS), tetra(isobutyl) thioperoxydi-
 (TIBTD), and insoluble sulfur (HSOT-20) were purchased from SAN’O Chemical Technol-
 carbamicacid (TIBTD), and insoluble sulfur (HSOT-20) were purchased from SAN’O
 ogy Co., Ltd. (Shanghai, China); paraffin wax was supplied by Shandong Yanggu Huatai
 Chemical Technology Co., Ltd. (Shanghai, China); paraffin wax was supplied by Shan-
 Chemical Co., Ltd. (Liaocheng, China); treated distillate aromatic extract (TDAE) oil was
 dong Yanggu
 obtained Huatai
 from H&R Chemical
 Group from Co., Ltd. (Liaocheng,
 Hamburg, Germany. China); treated distillate aromatic
 extract (TDAE) oil was obtained from H&R Group from Hamburg, Germany.
 Preparation of the Insert Rubber Compounds
 Preparation of the Insert Rubber Compounds
 Table 3 was the compound compounds for experimental.
 Tablesamples
 Four 3 was the
 of compound compounds
 insert rubber for experimental.
 were prepared with the compounds shown in Table 3.
 Measured amounts of the components were mixed as a master batch in an industrial
 Table 3. The
 internal compound
 mixer compounds
 (KOBELCO, (unit:
 BB430, Kobe,parts per hundred
 Japan). rubber; phr).
 A three-stage mixing process for each
 compound wasIngredient
 utilized to ensure the uniform dispersion
 A-1 of
 A-2 carbon black. At the
 A-3 A-4first
 stage, the mixer was filled with rubber to a fill factor of 72%, during which the rubber was
 TSR20 30 80 30 30
 initially masticated for 15 s. Then, 75% of the carbon black was added into the mixture
 BR9000 70 20 70 70
 and mixed for 20 s or until the temperature of the master batch reached 115 ◦ C. Next,
 N330 70 - - -

Materials 2021, 14, 474 6 of 14

 oil was added (just for A-1) and mixed while the temperature of the master batch was
 below 145 ◦ C. The dump temperature of the master batch compound was approximately
 165 ◦ C. In the second stage, the rest of the carbon black was added to the master batch 2
 in the industrial internal mixer and mixed for 20 s. The master batch 2 compounds were
 discharged from the internal mixer at 155 ◦ C. Finally, in stage three, the curatives TBBS,
 TIBTD, and sulfur, were mixed into the master batch 2 in an industrial internal mixer
 (Dalian Rubber & Plastics Machinery Co. Ltd., XM270, Dalian, China). The mixing was
 carried out at a rotor speed of 25 rpm and the mixer was filled to 67%. By controlling the
 time and temperature, the uniformity of rubber mixing can be ensured.

 Table 3. The compound compounds (unit: parts per hundred rubber; phr).

 Ingredient A-1 A-2 A-3 A-4
 TSR20 30 80 30 30
 BR9000 70 20 70 70
 N330 70 - - -
 N550 - 65 60 50
 ZnO 8 4 4 4
 Stearic acid 2 1 1 1
 TDAE 2 - - -
 6PPD 1.5 3 3 3
 TMQ 1 1 1 1
 TBBS 2 2.3 2 2
 TIBTD 0.8 - - -
 HSOT-20 2.8 3 3 3

 The detailed mixing procedures are specified in Table 4.
 Table 4. Mixing procedure.

 Ram Mix Rotor
 Stage Mixer Operation Time/s
 Press/bar Temp/◦ C Speed/rpm
 +Rubber and add. 15 4 - 55
 +CB 20 4 115 50
 MB1 +Oil 15 4 145 45
 Mix 30 4 165 40
 Drop 10 4 - 45
 +MB1 and CB 20 4 125 40
 MB2 Mix 60 4 155 35
 Drop 15 4 - 40
 +MB2 and add 30 4 - 25
 Mix 30 4 - 25
 FB
 Mix 60 4 102 25
 Drop 15 4 - 25
 MB = master batch; FM = final mixing; CB = carbon black; add = additives.

 2.3. Characterization
 The vulcanization of the rubber compounds was carried out in a hydraulic hot press
 at 150 ◦ C based on the optimum cure time measured from the MDR (rotorless curemeter).
 The hardness was determined by using a Shore A durometer (Wallace H17A, UK) according
 to ISO 7619 Part 1. A universal testing machine (Instron 3366 series, Norfolk County, MA,
 USA) following (die type) was used to measure the tensile properties, while the dynamic
 properties were evaluated in tension mode using a dynamic mechanical thermal analyzer
 (DMTA: GABO Qualimeter Eplexor 25N, GABO, Germany). For the temperature sweep
 test, the test conditions were as follows: 7% static strain, 0.25% dynamic strain, frequency
 of 10 Hz, and 2 ◦ C/min heating rate. The temperature was scanned from 40 ◦ C to 160 ◦ C.

Materials 2021, 14, 474 7 of 14

 3. Results and Discussion
 Vulcanization Properties
 The effects of temperature on the mechanical properties of the vulcanizates were
 illustrated in Figure 3, and the mechanical properties including tensile strength and elonga-
 tion at break were summarized in Table 5. Generally, the higher the testing temperature,
 the lower the tensile strength and stress at certain elongation. This causes the damage
 resistance of the compound decrease with temperature increasing, revealing that both the
 thermal accumulation and the actual temperature directly affect the strength of the com-
 pound, and thus the tire performance. The results in Figure 3 also indicate that although
 Materials 2021,the
 14, x stress ofREVIEW
 FOR PEER formulation A-2 at a certain strain was lower than that of formulation A-1, 7 of 15
 its tensile strength and elongation at break were greater than those of A-1. Compared with
 A-3 and A-4, formulation A-2 had greater tensile strength and greater elongation at break.
 The reason for sweep these test, the test conditions
 differences may be thewerehigh
 as follows:
 content7%of static
 NRstrain, 0.25%
 in A-2, as dynamic strain,
 the tensile
 frequency of 10 Hz, and 2 °C/min heating rate. The temperature
 crystallization property of NR made it have stronger mechanical strength than BR. was scanned from 40 °C
 to 160 °C.
 Table 5. Hardness,
 3. tensile
 Resultsstrength, and elongation at break at varying temperatures.
 and Discussion
 Vulcanization
 A-1 Properties
 A-2 A-3 A-4 A-1 A-2 A-3 A-4
 The effects of temperature on the mechanical properties of the vulcanizates were il-
 Hardness 78 75 72 68 - - - -
 lustrated in Figure 3, and the mechanical properties including tensile strength and elon-
 Temperature/◦ C Tensile strength/MPa Elongation at break/%
 gation at break were summarized in Table 5. Generally, the higher the testing tempera-
 23 13.08 18.85 13.59 10.69 131 230 222 225
 ture, the lower the tensile strength and stress at certain elongation. This causes the damage
 30 13.67 18.74 14.12 12.49 151 231 240 237
 resistance of the compound decrease with temperature increasing, revealing that both the
 40 12.55 18.7 12.66 10.95 134 247 216 230
 thermal accumulation and the actual temperature directly affect the strength of the com-
 60 10.25 11.17 10.51 10.38 121 164 177 220
 pound, and thus the tire performance. The results in Figure 3 also indicate that although
 80 9.65 10.88 8.99 8.30 118 174 152 175
 the stress of formulation A-2 at a certain strain was lower than that of formulation A-1, its
 100 8.46 11.71 7.86 7.85 102 179 139 175
 tensile strength and elongation at break were greater than those of A-1. Compared with
 120 8.25 7.32 6.77 6.72 102 115 122 140
 A-3 and A-4, formulation A-2 had greater tensile strength and greater elongation at break.
 140 7.05 8.12 6.49 6.24 91 134 112 136
 The reason for these differences may be the high content of NR in A-2, as the tensile crys-
 tallization property of NR made it have stronger mechanical strength than BR.

 (a) (b)

 (c) (d)

 Figure 3. Cont.

Materials 2021, 14, 474 8 of 14
 Materials 2021, 14, x FOR PEER REVIEW 8 of 15

 (e) (f)

Materials 2021, 14, x FOR PEER REVIEW 9 of 15

 due to the inclusion N550 carbon black offering low heat generation and a lower filler
 content in formulation (g) A-2, A-3, A-4. (h)
 Due to the varying loads across different tire applications,
 Figure 3. Temperature-dependent tensile properties of the vulcanizates. (a) tensile stress–strain the performance
 plot at 23 °C; (b) of the
 tensile
 Figure 3. Temperature-dependent tensile properties of the vulcanizates. (a) tensile stress–strain plot
 four compounds
 stress—strain cannot
 plot at 30 °C; (c) be accurately
 tensile stress—strain evaluated
 plot at in
 40 °C; (d) tensilepractical
 stress—strainconditions.
 plot at 60 °C;The tests
 (e) tensile were
 stress—
 strainat 23at◦80
 plot C;°C;
 (b)(f)tensile stress—strain
 tensile stress—strain plotplot 30 ◦ C;
 at°C;
 at 100 (c) tensile stress—strain
 plot at 120 plot 40 ◦ C;
 attensile (d) tensile
 performed based on ideal
 ◦ conditions of (g)
 thetensile
 same stress—strain
 deformation
 ◦ and°C;frequency.
 (h) stress—strain
 This was
 plot atstress—strain
 140 °C. (Color figure can60
 plot at be viewed
 C; (e) in the online
 tensile issue).
 stress—strain plot at 80 C; (f) tensile stress—strain plot at
 understandable as the tire was tested with the same loading. In other words, the tire com-
 100 ◦ C; (g) tensile stress—strain plot at 120 ◦ C; (h) tensile stress—strain plot at 140 ◦ C. (Color figure
 pound was subjected Table to the same
 5. Hardness, force.
 tensile strength, and elongation at break at varying temperatures.
 can be viewed in the online issue).
 To evaluate the performance of the compound A-1 underA-2 real-world
 A-3 A-4 conditions,
 A-1 A-2theA-3 lossA-4
 factorTheof the vulcanizates must
 loss factor (tan δ)Hardness take the actual
 and the dynamic modulus deformation
 78 (E’Mpa)
 75 of the
 of compound
 72 A-168 and A-4 into consid-
 - in -dynamic - -
 eration.
 mechanical Thus, energy temperature
 analysis dissipation
 Temperature/°C △E was used
 scanning were to presented
 evaluate
 Tensile a in
 strain
 strength/MPa Tableperiod, Anand
 5. Elongation was
 analysis ex-
 at break/%
 of
 pressed
 the resultsin Equation
 indicates(5). that the23dynamic modulus 13.08tends 18.85 13.59 10.69
 to decrease with131 230 222
 increasing test225
 temperature. From Figure 4, the 30 reduction in dynamic13.67 modulus
 18.74 14.12 12.49
 can be seen151 231 greatly
 to vary 240 237
 40ΔE =πσ0 γ0sin δ12.55
 ≈ πσ0γ0 tan
 18.7δ 12.66 10.95 134 247 216 (5)
 at the two key temperature points of 100 C and 160 C, while only small variations were230
 ◦ ◦
 where σ0 was the maximum 60
 amplitude In 10.25
 of contrast,
 stress andthe 11.17
 γ0loss 10.51
 wasfactor 10.38
 the maximum 121 164
 amplitude 177 of 220
 observed between those temperatures. was found to decrease
 80 9.65 10.88 8.99 8.30 118 174 152 175
 strain.
 with increasing temperature,100 and the rate of change was relatively consistent. As expected,
 8.46 11.71 7.86 7.85 102 179 139 175
 Subsequently,
 the dynamic modulusfourand
 compounds
 loss
 120 factorof
 of insert rubber
 formulation
 8.25
 with
 A-1, different
 A-2, A-3,
 7.32 6.77 6.72
 modulus
 and A-4 and heat-
 102 decreased
 115 122in140
 generation
 turn, due towere designedN550
 the inclusion to140
 investigate
 carbon black theoffering
 roles
 7.05 and
 lowimpacts
 heat of deformation
 generation
 8.12 6.49 6.24 91 and a and112
 lower
 134 loss136
 filler
 factor
 contentof in
 a tire which was
 formulation shown
 A-2, in Figure 4.
 A-3, A-4.
 The loss factor (tan δ) and the dynamic modulus (E’Mpa) of A-1 and A-4 in dynamic
 mechanical analysis temperature scanning were presented in Table 5. An analysis of the
 results indicates that the dynamic modulus tends to decrease with increasing test temper-
 ature. From Figure 4, the reduction in dynamic modulus can be seen to vary greatly at the
 two key temperature points of 100 °C and 160 °C, while only small variations were ob-
 served between those temperatures. In contrast, the loss factor was found to decrease with
 increasing temperature, and the rate of change was relatively consistent. As expected, the
 dynamic modulus and loss factor of formulation A-1, A-2, A-3, and A-4 decreased in turn,

 (a) (b)
 Figure 4. The
 Figure dynamic
 4. The mechanical
 dynamic characteristics
 mechanical of the
 characteristics vulcanizates.
 of the (a)(a)
 vulcanizates. Dynamic
 Dynamicmodulus
 modulus (E’); (b) loss
 (E’); (b) lossfactor
 factor(tan
 (tan
 δ).δ).

 Table 6 was the summarize of dynamic modulus (E’) and loss factor (tan δ) of the
 vulcanizates at various temperatures

Materials 2021, 14, 474 9 of 14

 Due to the varying loads across different tire applications, the performance of the
 four compounds cannot be accurately evaluated in practical conditions. The tests were
 performed based on ideal conditions of the same deformation and frequency. This was
 understandable as the tire was tested with the same loading. In other words, the tire
 compound was subjected to the same force.
 To evaluate the performance of the compound under real-world conditions, the loss
 factor of the vulcanizates must take the actual deformation of the compound into con-
 sideration. Thus, energy dissipation 4E was used to evaluate a strain period, and was
 expressed in Equation (5).

 ∆E =πσ0 γ0sin δ ≈ πσ0γ0 tan δ (5)

 where σ0 was the maximum amplitude of stress and γ0 was the maximum amplitude
 of strain.
 Subsequently, four compounds of insert rubber with different modulus and heat-
 generation were designed to investigate the roles and impacts of deformation and loss
 factor of a tire which was shown in Figure 4.
 Table 6 was the summarize of dynamic modulus (E’) and loss factor (tan δ) of the
 vulcanizates at various temperatures.
 Table 6. Dynamic modulus (E’) and loss factor (tan δ) of the vulcanizates at various temperatures.

 Screening A-1 A-2 A-3 A-4 A-1 A-2 A-3 A-4
 Temperature (◦ C) Loss Factor (tan δ) E’(MPa)
 40 0.102 0.090 0.033 0.026 27.0 16.2 11.1 8.7
 60 0.103 0.078 0.029 0.025 23.4 14.8 11.0 8.7
 80 0.093 0.064 0.027 0.016 20.3 13.8 11.0 8.8
 100 0.080 0.053 0.019 0.015 18.5 13.2 11.1 8.8
 120 0.067 0.051 0.020 0.016 17.5 12.9 11.2 9.0
 140 0.058 0.043 0.020 0.014 17.1 12.9 11.5 9.3

 Strictly speaking, the fatigue failure of rubber is a kind of mechanical process. The stress
 relaxation process produced in the material was often too late to complete in the defor-
 mation cycle under the repeated cyclic deformation of rubber. As a result, the internal
 generated stress could not be dispersed in time, and it might be concentrated in some
 defects (such as cracks, weak bonds, etc.), which caused fracture failure.
 Figure 5 shows the simulation results of six tire models (size = 245/45/R18 96W)
 based on Table 1. The results of stress distribution of tire sidewall show that the stress
 was mainly concentrated in the insert compound in both the B-1 and B-2 structures which
 was shown in Figure 2. Surprisingly, using the A-1 compounds with the B-1 structure
 resulted in a more uniform stress distribution of the tire sidewall. This was because in
 the flexure test of the tire side adhesive, the stress was mainly concentrated on the insert
 support with high hardness, as shown in model 5. At the same time, compared with B-2,
 B-1 structure had a longer supporting compound, a larger amount of padding between
 the tread and the bead apex, and a better rigid transition with the tire sidewall, that was
 why the deformation of model 5 and model 6 on tire sidewall was greater than that of
 model 1, model 2, and model 3. Model 3 and model 4 used similar insert compound
 with soft hardness under the structure of B-2, the rigidity of the tire sidewall was weak,
 and the stress was concentrated on the weakest point of rigidity during flexion, which can
 be clearly seen from Figure 5a,b. The results of Table 6 also indicated that the actual
 stresses of the different compounds at the same part of the tire were different during the
 actual movement of the tire. This demonstrates why the loss factor cannot be directly used
 under the same deformation in the dynamic mechanical analysis test to evaluate the tire’s
 thermal performance.

the tire. This demonstrates why the loss factor cannot be directly used under the same
 deformation in the dynamic mechanical analysis test to evaluate the tire’s thermal perfor-
 mance.
 Strain energy density of bead apex and insert rubber of tire were also shown in Figure
Materials 2021, 14, 474 5c. Compared to model 5 and model 6, the strain energy density distribution10of other
 of 14
 models were more concentrated, suggesting a greater likelihood for the formation of a
 failure point.

 Model 1 Model 2 Model 3

 Materials 2021, 14, x FOR PEER REVIEW 11 of 15
 Model 4 Model 5 Model 6
 (a)

 Model 1 Model 2 Model 3

 Model 4 Model 5 Model 6
 (b)

 Model 1 Model 2 Model 3

 Model 4 Model 5 Model 6
 (c)
 Figure 5. Figure
 Simulation results of the
 5. Simulation models.
 results of(a)
 theStress distribution
 models. of tire
 (a) Stress section; (b)of
 distribution stress
 tire of bead apex
 section; and insert
 (b) stress rubber
 of bead
 of tire section; (c) strain energy density of bead apex and insert rubber of tire.
 apex and insert rubber of tire section; (c) strain energy density of bead apex and insert rubber of tire.
 Table 7 shows the summary of the analytical and quantitative results of the groups
 of analysis models. It is generally considered that the maximum stress and strain energy
 density at the bead apex rubber and support compound are the most important indexes
 related to the zero pressure durability of tire. The maximum stress and strain energy den-

Materials 2021, 14, 474 11 of 14

 Strain energy density of bead apex and insert rubber of tire were also shown in
 Figure 5c. Compared to model 5 and model 6, the strain energy density distribution of
 other models were more concentrated, suggesting a greater likelihood for the formation of
 a failure point.
 Table 7 shows the summary of the analytical and quantitative results of the groups
 of analysis models. It is generally considered that the maximum stress and strain energy
 density at the bead apex rubber and support compound are the most important indexes
 related to the zero pressure durability of tire. The maximum stress and strain energy
 density of model 5 and model 6 under structure B-1 were smaller than those of other
 schemes,
 Materials 2021, 14, x FOR which indicates that the influence of structural rigidity is greater than that of
 PEER REVIEW 12 of 15
 the hardness of insert rubber. At the same time, under the same structure, the higher the
 hardness of the insert rubber, the smaller the stress and strain energy density, which can be
 found7.from
 Table the comparison
 Summary of and
 of the analytical the quantitative
 previous four models.
 results of the groups of analysis models.
 Table 7. Summary of the analytical and quantitative results of the groups of analysis models.
 Model Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
 Maximum
 Model stress distribution of
 Model 1 4.405
 Model 2 5.777Model 3 3.893Model 4 3.617Model 5 4.065Model 6 4.063
 tire section/MPa
 Maximum stress distribution of
 4.405 5.777 3.893 3.617 4.065 4.063
 tireMaximum
 section/MPa stress of bead apex and
 1.924 3.179 2.822 3.322 1.662 1.744
 insert rubber
 Maximum stress of bead apex and of tire section/MPa
 1.924 3.179 2.822 3.322 1.662 1.744
 insert rubber Maximum strain energy density
 of tire section/MPa
 Maximum strain energy
 of bead apexdensity of rubber of
 and insert 3.420 4.944 4.965 5.577 3.000 3.060
 bead apex and insert rubber
 tire of tire
 section J/m 3 3.420 4.944 4.965 5.577 3.000 3.060
 section J/m 3

 Figure 6 shows the shear stress distribution of the six models. There were no obvious
 Figure benefits
 6 showsofthe shear stress distribution of the six models. There were no obvious
 reducing the length of the insert compound with respect to the direction of the
 benefits of reducing the
 shear force on length of theofinsert
 each part compound
 the tire sidewall, with respectbetween
 particularly to the direction of rubber
 the insert the and
 shear force on each part of the tire sidewall, particularly between the insert rubber
 bead apex. Delamination was easily induced by applying different directions of shear and bead
 apex. Delamination was damage
 stress, causing easily induced
 points andby premature
 applying different directions with
 damage. Compared of shear stress,
 the first four mod-
 causing damage points and premature damage. Compared with the first four models,
 els, model 5 and model 6 use B-1 structure, which had a longer contact surface with bead
 model 5 and model
 apex 6 use
 rubber, B-1 effectively
 which structure, avoids
 whichthe had a longer
 shear stress contact surface
 of relative with bead
 slip between the two in-
 apex rubber, whichdue
 terfaces effectively
 to unevenavoids
 stress. the shear3stress
 In model of relative
 and model 4, due toslip
 thebetween the rubber
 use of insert two with
 interfaces due
 lowerto uneven
 hardness,stress. In model
 the shear 3 and model
 stress between 4, due parts
 the various to theofuse of insert
 sidewall wasrubber
 small, mainly
 with lower concentrated
 hardness, the in shear stress
 the inner sidebetween the
 of the tire at various parts
 the center of sidewall was small,
 of sidewall.
 mainly concentrated in the inner side of the tire at the center of sidewall.

 Model 1 Model 2 Model 3

 Model 4 Model 5 Model 6
 Figure 6. Shear stress distribution.
 Figure 6. Shear stress distribution.
 Based on the six simulation models, six actual tires under the structure of Table 2
 were produced for testing, named as T-1, T-2, T-3, T-4, T-5, and T-6. Tables 8 and 9 show
 the basic characteristics of the tires under a conventional static load and a zero-pressure
 static load. The static radius was most heavily influenced by the subsidence and subsid-

Materials 2021, 14, 474 12 of 14

 Based on the six simulation models, six actual tires under the structure of Table 2 were
 produced for testing, named as T-1, T-2, T-3, T-4, T-5, and T-6. Tables 8 and 9 show the basic
 characteristics of the tires under a conventional static load and a zero-pressure static load.
 The static radius was most heavily influenced by the subsidence and subsidence rate under
 static load, and the structure of the insert rubber which provide structural rigidity to the
 tire. Further, it can be seen that under the same structure, the static load radius and sinkage
 of the tire were directly proportional to the rigidity of the insert rubber. Especially under
 the condition of zero pressure load, the stiffness of the insert rubber directly affects the
 static load radius and sinkage representing the tire deformation. Therefore, in comparison
 with
 Materials 2021, 14, x T-5 and REVIEW
 FOR PEER T-6, the greater deformation of T-1, T-2, T-3, and T-4 may lead to increases in
 13 of 15
 heat generation.

 rectly
 Table 8. Conventional affects
 static thetest.
 load static load radius and sinkage representing the tire deformation. There-
 fore, in comparison with T-5 and T-6, the greater deformation of T-1, T-2, T-3, and T-4 may
 List lead to increases inT-1 T-2
 heat generation. T-3 T-4 T-5 T-6
 Static radius under load/mm 319 316 315 316 318 317
 Table 8. Conventional static load test.
 Sinkage/mm 18.9 20.9 20.6 20.9 18.6 20.0
 Sinkage/% 17.4
 List 19.3 T-119.2 T-2 19.4
 T-3 17.2
 T-4 T-518.5 T-6
 Imprint long axis/mm 200 load/mm
 Static radius under 200 319201 316 203
 315 199
 316 318200 317
 Imprint minor axis/mm Sinkage/mm 133 135 18.9151 20.9 145
 20.6 141
 20.9 18.6144 20.0
 Sinkage/% 17.4 19.3 19.2 19.4 17.2 18.5
 Imprint
 Table 9. Zero pressure static load long
 test. axis/mm 200 200 201 203 199 200
 Imprint minor axis/mm 133 135 151 145 141 144
 List T-1 T-2 T-3 T-4 T-5 T-6
 Table 9. Zero pressure static load test.
 Static radius under load/mm 311 309 307 307 314 310
 Sinkage/mm 23.2
 List 25.0 27
 T-1 T-2 27 T-3 21.5
 T-4 T-524.4 T-6
 21.9 load/mm
 Sinkage/% Static radius under 23.7 25.6 309 25.6307
 311 20.0
 307 31423.0 310
 Imprint long axis/mm Sinkage/mm 222 231 250 25.0 247 27
 23.2 219
 27 21.5232 24.4
 Imprint minor axis/mm Sinkage/% 215 217 218
 21.9 219
 23.7 25.6 215
 25.6 20.0216 23.0
 Imprint long axis/mm 222 231 250 247 219 232
 The curves of temperature riseaxis/mm
 Imprint minor of the tire sidewall
 215 and
 217bead218
 during219
 the zero-pressure
 215 216
 durability test were shown in Figure 7. The sidewall and bead temperatures of T-1, T-2, T-3,
 and T-4 increase to aThehigher
 curvesvalue over time,
 of temperature risecompared to T-5 and
 of the tire sidewall andbead
 T-6.during
 This was mainly
 the zero-pressure
 due to the weakerdurability
 structuraltestrigidity
 were shown in and
 of B-2 Figurethe7. larger
 The sidewall
 sinkageandofbead
 the temperatures of T-1,
 tire, in addition to T-2,
 higher energy lossT-3, and T-4 increase
 according to a higher
 to the energy lossvalue over time,
 formula. compared
 Moreover, the to T-5 and
 results in T-6. This7 was
 Figure
 mainly due to the weaker structural rigidity of B-2 and the larger sinkage of the tire, in
 reveal that although the loss factor of A-2 was lower than that of A-1, the difference in heat
 addition to higher energy loss according to the energy loss formula. Moreover, the results
 generation at theinsidewalls of T-1
 Figure 7 reveal and
 that T-2 was
 although theminimal,
 loss factor mainly
 of A-2 wasdue to the
 lower thanlarger
 that ofsinkage
 A-1, the dif-
 and the greater deformation
 ference in heatof T-2, which
 generation ledsidewalls
 at the to higher energy
 of T-1 loss.
 and T-2 wasThe comparison
 minimal, data
 mainly due to the
 of T-5 and T-6 with stronger
 larger sinkagetire
 andstructure candeformation
 the greater also proveof this
 T-2,conclusion.
 which led toThe results
 higher further
 energy loss. The
 comparison
 prove that the loss factor and datadeformation
 of T-5 and T-6 should
 with stronger tire structure
 be considered can also prove this conclusion.
 comprehensively in the
 energy loss of theThe resultscompound.
 rubber further prove that the loss factor and deformation should be considered com-
 prehensively in the energy loss of the rubber compound.

 (a) (b)
 Figure 7. Temperature curve of tire testing. (a) Temperature curve of the tire sidewall; (b) temperature curve of tire bead.
 Figure 7. Temperature curve of tire testing. (a) Temperature curve of the tire sidewall; (b) temperature
 curve of tire bead. Table 10 summarizes the zero-pressure durability test results of the tires. It was evi-
 dent that under the same rubber conditions, the results of the zero-pressure durability test
 were directly related to the rate of temperature rise of the tire sidewall. As the temperature
 increases, the resistance to damage of the compound decreases, which was clearly proven
 by the test results. At the same time, the stress distribution of tire sidewall was also found

Materials 2021, 14, 474 13 of 14

 Table 10 summarizes the zero-pressure durability test results of the tires. It was evident
 that under the same rubber conditions, the results of the zero-pressure durability test were
 directly related to the rate of temperature rise of the tire sidewall. As the temperature
 increases, the resistance to damage of the compound decreases, which was clearly proven
 by the test results. At the same time, the stress distribution of tire sidewall was also found
 to directly affect results of the zero-pressure durability test. Although the difference of
 heat generated at the sidewall between T-1 and T-2 was minimal, an analysis of the strain
 energy density of bead apex and insert rubber of tire shown in Figure 5 suggested that the
 stress concentration in T-2 may lead to early tire failure. The test results of T-5 and T-6 can
 also prove this point. In addition, the zero pressure durability of T-5 and T-6 was better
 than that of T-1 and T-2 under the strong structural rigidity of B-1, which can also prove
 the effect of strain energy density. Compared with A-1 and A-2, the rigidity of A-3 and A-4
 was lower. Although it can be seen from Table 6 that the loss factor of A-3 and A-4 was
 lower, the sidewall shape of the tire changed greatly, and the temperature rise in Figure 7
 was faster, which led to the faster damage of the insert rubber.
 Table 10. Durability test results at zero pressure.

 Tyre Compound Structure Durability at Zero Pressure
 T-1 A-1 B-2 57 min
 T-2 A-2 B-2 54 min
 T-3 A-3 B-2 44 min
 T-4 A-4 B-2 39 min
 T-5 A-1 B-1 3h
 T-6 A-2 B-1 1 h 50 min

 4. Conclusions
 According to the study, a successful attempt was made to employ simulation methods
 to study the key factors to be considered in the development of run-flat tires. The effects
 of heat and stress concentration on the zero-pressure durability of tires were studied by
 designing different components with different stiffness, heat generation and shape to
 change the stiffness of tire sidewall. The results revealed that the tensile strength and
 modulus of the insert compound decreased with the increase of temperature. The heat
 generation of the insert rubber was not only dependent on the loss factor, but also related
 to the deformation. By using the insert rubber with higher hardness or improving the
 structural stiffness of the tire, the deformation of the support rubber could be reduced and
 the heat storage of the support rubber could be reduced, which can significantly improve
 the sinking rate of the tire under zero pressure. In addition, the maximum strain energy
 density at the top of the bead and the maximum strain energy density of the cross-section
 insert rubber were significantly related to the durability of the zero pressure run flat tire
 and the initial failure point of the insert rubber. In conclusion, the balanced design of
 formula and structure was the key to tire development. At the same time, the potential of
 numerical simulation technology in tire development is verified. The application of these
 technologies could shorten the tire development process and improved the success rate of
 tire development.

 Author Contributions: Conceptualization, H.L. and C.W.; data curation, Y.P.; formal analysis, H.L.
 and C.W.; funding acquisition, H.B. and C.W.; methodology, Y.P. and H.B.; resources, Y.P.; writing—
 original draft, H.L. All authors have read and agreed to the published version of the manuscript.
 Funding: This research was funded by Key Technology and Equipment for Intelligent Green Man-
 ufacturing of Rubber Products, grant number ZR2016XJ003; Natural Science Foundation of Shan-
 dong Province, grant number ZR2019BEE056; Polymer Material Intelligent Manufacturing Inno-
 vation Team, grant number 2019KJB007; Key R & D Plan of Shandong Province, grant number
 2019GGX102018; Shandong Provincial Natural Science Foundation, grant number ZR2020QE207.
 The funders contributed to the work.

Materials 2021, 14, 474 14 of 14

 Data Availability Statement: The data was basically presented in the article.
 Acknowledgments: We would like to thank the support of the key Laboratory of Shandong Province
 for this experiment.
 Conflicts of Interest: The authors declare no conflict of interest.

References
1. Martin, J.L.; Laumon, B. Tire blow-outs and motorway accidents. Traffic Inj. Prev. 2005, 6, 53–55. [CrossRef] [PubMed]
2. La Clair, T.J. Rolling resistance. In The Pneumatic Tire; Brewer, H.K., Clark, S.K., Gent, A.N., Eds.; US Department of Transportation,
 National Highway Traffic Safety Administration: Washington, DC, USA, 2006; pp. 475–532.
3. Martini, M. A run-flat future. Automot. Eng. Int. 2005, 113, 74–75.
4. Wang, F.; Chen, H.; Guo, K.; Cao, D. A novel integrated approach for path following and directional stability control of road
 vehicles after a tire blow-out. Mech. Syst. Signal Process. 2017, 93, 431–444. [CrossRef]
5. Wilson, G.N.; Ramirez-Serrano, A.; Sun, Q. Geometric-based tyre vertical force estimation and stiffness parameterisation for
 automotive and unmannedvehicle applications. Veh. Syst. Dyn. Int. J. Veh. Mech. Mobil. 2017, 55, 168–190.
6. Park, N.; Seo, J.; Kim, K.; Sim, J.; Kang, Y.; Han, M.; Kim, W. Sidewall-insert compound based on ZnO-treated aramid pulp fibers
 for run-flat tires. Compos. Interfaces 2016, 23, 781–796. [CrossRef]
7. Bwereket, Z.; Blower, D.F.; MacAdam, C. Blowout Resistant Tire Study for Commercial Highway Vehicles; UMTRI Technical Report;
 DTRS57-97-C-0005; National Technical Information Service: Springfield, VA, USA, 2000.
8. Wang, H.; Al-Qadi, I.L.; Stanciulescu, I. Simulation of tyre-pavement interaction for predicting contact stresses at static and
 various rolling conditions. Int. J. Pavement Eng. 2012, 4, 310–321. [CrossRef]
9. Cho, J.R.; Lee, J.H.; Jeong, K.M.; Kim, K.W. Optimum design of run-flat tire insert rubber by genetic algorithm. Finite Elem.
 Anal. Des. 2012, 52, 60–70. [CrossRef]
10. Leister, G.; Hein, H.R. The Tire Stiffness Index TSI and How to Calculate It: A Test Method for New Passenger Car Tires with Run-Flat
 Properties; Tire Technology Expo: Cologne, Germany, 2012.
11. Bae, J.J.; Suh, J.B.; Kang, N. Structural stiffness of tire calculated from strain energy. In Proceedings of the International Design
 Engineering Technical Conferences and Computers and Information in Engineering Conference, Boston, MA, USA, 2–5 August
 2015.
12. Schuring, D.J. A new look at the definition of tire rolling loss. In SAE Conference Proceedings of Tire Rolling Losses and Fuel
 Economy—An R&D Planning Workshop; SAE International: Warrendale, PA, USA, 1977; Volume 74, pp. 31–37.
13. Schuring, D.J. The rolling loss of pneumatic tires. Rubber Chem. Technol. 1980, 53, 600–727. [CrossRef]
14. Hall, D.E.; Moreland, J.C. Fundamentals of rolling resistance. Rubber Chem. Technol. 2001, 74, 525–539. [CrossRef]
15. Hunt, J.D.; Walter, J.D.; Hall, G.L. The effect of tread polymer variations on radial tire rolling resistance. In Tire Rolling Losses
 and Fuel Economy—An R&D Workshop Cambridge, MA; Society of Automotive Engineers: Warrendale, PA, USA, 1977; Volume 18,
 pp. 161–168.
16. Klamp, W.K. Power consumption of tires related to how they were used. In Tire Rolling Losses and Fuel Economy—An R&D
 Workshop, Cambridge, MA; Society of Automotive Engineers: Warrendale, PA, USA, 1977; pp. 5–11.
17. Ju, J.; Ananthasayanam, B.; Summers, J.D.; Joseph, P. Design of cellular shear bands of a non-pneumatic tire-investigation of
 contact pressure. SAE Int. J. Passeng. Cars Mech. Syst. 2010, 3, 598–606. [CrossRef]