Study of Effect of Contour Design on Radial Tire Performance

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1 Study of Effect of Contour Design on Radial Tire Perforance Guo-Lin WANG, Yan-Tian SUN, Chen LIANG Jiangsu University Zhenjiang,Jiangsu, China Abstract Based on the string balance theory of tire design, taking 205/55R16 and 195/65R15 radial tire as research project, the odified string balance contour design theory was presented, which siplified the belts pressure share ratios as trapeziu. The three-diensional finite eleent odel was established by ABAQUS software to study the coprehensive perforances of tire. The siulation odel is proved reliable in cornering characteristics dru test. The contact perforance, cornering stiffness, abrasion resistance and rolling resistance of existing contour and odified contour were analyzed and copared. In contrast with the existing contour, the results show that the odified contour can increase the contact area between tire and road while decrease the skewness value of contact pressure. It is helpful to enhance tire cornering stiffness. Besides, even though the friction loss increased slightly, the abrasion resistance and the service life of radial tire are iproved. In addition, the rolling resistance of odified contour is decreased contributes to the optiized stress of tread rubber. Keywords - Nuerical siulation, Tire contour design, Cornering stiffness, Rolling resistance I. INTRODUCTION At present, there is no confirable conclusion of the relationship between tire contour and tire perforance. But there is no doubt that the design of carcass contour has a significant influence to the perforance of radial tire. Many researchers proposed theories such as esh odel, thin fil odel, string balance theory odel and so on, which had iproved the design capability to sei quantitative design stage [1]. The cornering characteristics, especially the relationship between cornering force and cornering angle is the fundaental research of the vehicle handing stability [2, 3], it also has indirect effect on the reliability of the vehicle when steering. Refer to the results of dru test, Nikola Korunović et al siulated the tire odel for studying the echanical property of the rolling tire [4]. Based on ABAQUS software, Jiao et al siulated the cornering loading of the triangle equilibriu contour tire, it cae to a conclusion that the triangle equilibriu contour tire can coordinate the rolling resistance with the abrasion resistance of the tire [5]. The Bridgestone Corp proposed the Rolling Contour Optiization Theory (RCOT and Tension Control Optiization Theory (TCOT to iprove the contact perforance, abrasion resistance and the handing stability [6]. The carcass contour has a coplexity relationship with the tire perforance, hence, the research of carcass contour design ethod need to be intensified. In this study, the odified string balance theory for contour design is presented whose belts pressure sharing ratios are siplified to trapeziu. Considering the calculation accuracy and the efficiency of the siulation odel, the 3D siulation tire odel with coplex tread pattern was created to study the relationship between carcass contour and contact perforance, cornering stiffness, abrasion resistance and rolling resistance. The conclusion could be used to iprove the coprehensive perforance of tire in engineering design. II. DESIGN THEORY FOR TIRE CONTOUR A. Modified String Balance Theory for Contour Design The carcass contour of radial tire contributes a lot to the tire perforance. Considering the confining belts force of radial tire, SAKAI Hideo et al proposed the concept of belts pressure sharing ratios [7]. The contact pressure between belts and carcass was used to evaluate the belts sharing ratios of inflation pressure; ζ is the pressure sharing ratios of belt. n (1 p Where n eans the noral stress between belts and carcass, p eans the inflation pressure of radial tire. By the siulation of ABAQUS software, the 205/55R16 and the 195/65R15 tire odels were established. Period research on string balance theory odel considered that the belt s pressure sharing ratios was constant or unifor distributed by two segents. However, it is inconsistent with the actual conditions [8]. The distribution of belt s pressure sharing ratios of 205/55R16 tire and 195/65R15 tire is shown in Fig.1, where one can see that the pressure sharing ratios of belts is distributed by trapeziu for. Besides, the distribution situation is very siilar between two tires. The siplified graph of belts pressure sharing ratios is shown in Fig.2, where one can see the belt s iddle coponent s fluctuation (AB segent is extreely flat while the both ends of the belts(bc segent signally decline, which is caused by the delainating of carcass and belt. DOI /IJSSST.a.16.3B ISSN: x online, print

Figure 1. The belts pressure sharing ratios of two tires Figure 2.

the string balance contour theory odel [9], the feature points were chosen to siplify the carcass contour of inflated tire as Fig.3. Figure 3.

carcass contour; D is the axiu width point of the inner contour; E is the point of the wheel ri s ending which depended on the wheel ri s specification.

2 Figure 1. The belts pressure sharing ratios of two tires Figure 2. The trapeziu for of belts pressure sharing ratios of 205/55R16 tire The pressure sharing ratios of AB segent: 1 C (2 The pressure sharing ratios of BC segent: kx b (3 k C 2 Cx B,b C (4 xb xb Based on the string balance contour theory odel [9], the feature points were chosen to siplify the carcass contour of inflated tire as Fig.3. Figure 3. The siplified odel of carcass contour of inflated tire Where A is the vertex of the tire tread; BC is the transition point between AB segent and BC segent; C is the apping point of belts ends to carcass contour; D is the axiu width point of the inner contour; E is the point of the wheel ri s ending which depended on the wheel ri s specification. The Y-coordinate point was generally given by the existing tire. The existing string balance theory odel was odified by the practical pressure sharing ratios of belts, the odified string balance theory contour can be written as: dy dx (5 sin 2 Where sin is the sine of the points noral angle. The inner contour of 205/55R16 tire was segented to four segents for partition convolution. The integral equations of each segent s contour are: The integral equation of AB segent: x A yab ya dx (6 x 2 sin The integral equation of BC segent: x B ybc yb dx (7 x 2 sin The integral equation of CD segent: x C ycd yc dx (8 x 2 sin The integral equation of DE segent: x D yde yd dx (9 x 2 sin Where the sine of noral angle of four segents is: The sine of AB segent: xa x (1 1 C (10 The sine of BC segent: x C (1 2 C (11 The sine of CD segent: x C (12 The sine of DE segent: x C sin C 2 ( x x ( 1 ( x x ( 1 ( x x 2 C D 1 A B 2 B C (13 (14 The pressure sharing ratios 1 and 2 were put into the forula to get the new forula of string balance theory odel. The x A was found to be the defect point when it was calculated. Since the segent of xa has little influence on carcass contour, the sall fraction of the segent surrounded with the A point was consistent with the current contour. B. Carcass Contour Design The MATLAB software was used to prograing the odified string balance contour. The inner contour of DOI /IJSSST.a.16.3B ISSN: x online, print

205/55R16 tire designed by progra is show in the Fig.4, while the key points of tire contour are shown in Table 1. TABLE Ⅰ.

Modelling and Mesh Generating The study of 205/55R16 odel was based on the CAD odel developed by the author. The two-diensional tire section odel was created by CAD software.

The surface boundary between tread pattern and tread was created by the Tie coand of ABAQUS. The eleents were rotated 120 segents with 3 angle per segent.

3 205/55R16 tire designed by progra is show in the Fig.4, while the key points of tire contour are shown in Table 1. TABLE Ⅰ. THE KEY POINTS OF TIRE 205/55R16 CONTOUR Coordinate( Key points Y-axis X-axis Italic A B C D E III. THE ESTABLISHING OF FINITE ELEMENT MODEL A. Modelling and Mesh Generating The study of 205/55R16 odel was based on the CAD odel developed by the author. The two-diensional tire section odel was created by CAD software. HYPERMESH software was used to generate the esh, while ABAQUS/Standard odule was used to generate the esh of three-diensional odel. The surface boundary between tread pattern and tread was created by the Tie coand of ABAQUS. The eleents were rotated 120 segents with 3 angle per segent. The tire odel with coplex tread pattern is shown in Fig.6. Figure 6. Tire odel with coplex tread pattern Figure 4. The odified string balance contour of 205/55R16 tire Figure 5. The coparison between existing and odified contour of radial tire Copared with the existing contour, the odified contour enlarging the curvature of the tire shoulder while reducing the curvature of the bead. The odified contour is soother than the existing one. B. Establishent of Material Model and Boundary Conditions Tire is a coplex construction with kinds of aterials, for instance, rubber, steel code and coposite aterial of rubber and code. The nonlinear constitutive odel YEOH was used to siulate the echanical properties of rubber s stress and strain. The C3D8R and C3D6R type eleents were used to fit the rubber s incopressibility and nonlinear echanical property [10]. The type of rebar eleent was used to siulate the rubber code coposite aterial. The tire and the ri were interference fit and the loading of the tire was 4000N. When calculating the rolling resistance, the speed of the tire was set as 80 K/h. C. The Tire s Steady-state Lateral Rolling Model Euler-Lagrange equation was used to analyze the steady state of tire. In the odel, the rolling tire was siulated with iobile nodes and reovable aterials. The rotator inertia was in consideration. The Coulob friction odel was used to analyze the nonlinearity contact boundary condition between tire and road [11]. Based on the prograing by FORTRAN language, the user subroutine was established to calculate iteratively by ABAQUS. The operating condition of siulation odel was set as: the tire s speed was 10K/h; the lateral angle of tire was set as -5 ~5. The realization ethod of tire odeling process is shown in Fig.7. DOI /IJSSST.a.16.3B ISSN: x online, print

the lateral angle. FCP E. The Analysis of Experient The siulation analysis was set as the sae condition of experient. The coparison between siulation and experient result is shown in Fig.9. Figure 7.

The Experient of Radial Tire Cornering Stiffness Cornering stiffness is a very iportant evaluation index of tire perforance; it also influences the handing stability of driving [12~13].

4 change per second. The experient was retested for three ties and the cornering stiffness of the tire is calculated by: dfcp GCP d (15 Where GCP eans the cornering stiffness of the tire, eans the lateral force and θ is the lateral angle. FCP E. The Analysis of Experient The siulation analysis was set as the sae condition of experient. The coparison between siulation and experient result is shown in Fig.9. Figure 7. The establishent of tire odel D. The Experient of Radial Tire Cornering Stiffness Cornering stiffness is a very iportant evaluation index of tire perforance; it also influences the handing stability of driving [12~13]. The precision of siulation odel was verified by the test bench as Fig.8, where the echanics capability of side slip was tested. The technological paraeters of test bench are shown in Tab Ⅱ: Figure 9. The coparison between siulation and experient result As is shown in Fig.9, the unifority of siulation and experient result is good. There is a siple linear relationship between the lateral force and the lateral angle when the lateral angle is within the scope of -3 ~3. The cornering stiffness of the experient is N/, while the siulation result is N/. The relative error is 15.6%, so the siulation odel is proved to be correct. IV. THE COMPREHENSIVE PERFORMANCE ANALYSIS AND CALCULATION OF RADIAL TIRE Figure 8. The test bench of tire dynaic perforance TABLE Ⅱ. THE TECHNOLOGICAL PERFORMANCE OF TIRE S TEST BENCH Technological perforance Type of test bench:md Diaeter of dru 1599 Diaeter of tire Loading Scope of slip angle Scope of caber angle kN, 25Hz ±18,0.1 precision ±8, 0.1 precision Data collection syste Data Translation 9800 PC Before the experient started, tire was required to run 30 inutes on 30K/h speed with 4000N loading and 240kPa air pressure to ake sure that the tire s situation is steady. The slip angle was within the scope of -8 ~8 with 1 degree A. The Analysis of Contact Perforance The contact perforance is the basic perforance of tire because it influences the cornering characteristics, abrasion resistance, rolling resistance etc. of tire. The contact area and the skewness value of contact pressure are used to evaluate the contact perforance. The equation for the skewness value of contact pressure α is: 1 n 2 ( P i 1 i P (16 n 1 Where P i is the contact pressure of point I, P is the average pressure of all nodes which contact the road, n is the nodes total nuber which contact the road. Based on the definition of the cornering stiffness, the contact for of the steady-state rolling tire was studied of 0/ slip angle; the siulation results of the odified and the existing contour are as shown in Fig.10: DOI /IJSSST.a.16.3B ISSN: x online, print

There is a siple linear relationship between the Figure 11.

The grounding for of odified and existing contour As is shown in the Fig.

The odified tire s skewness value of contact pressure is reduced copared with the existing one as is shown in Tab Ⅲ. TABLE Ⅲ.

5 There is a siple linear relationship between the Figure 11. The coparison of cornering stiffness between existing and odified contour (athe grounding for of existing contour tire (bthe grounding for of odified contour tire Figure 10. The grounding for of odified and existing contour As is shown in the Fig.10, the grounding area of odified contour tire is larger than the existing one in the tire shoulder coponent and the tread coponent, while the atrix CPRESS is reduced. The odified tire s skewness value of contact pressure is reduced copared with the existing one as is shown in Tab Ⅲ. TABLE Ⅲ. THE GROUNDING FORM COMPARISON BETWEEN MODIFIED AND EXISTING CONTOUR TIRE Skewness value of contact Progras Grounding area ( pressure (MPa Modified contour E E-01 Existing contour E E-01 B. The Analysis of Cornering Stiffness The ground connection perforance is iproved by the odified contour of tire, it is also beneficial to the cornering stiffness of tire, which influence deeply to the aneuverability of autoobile [13~14]. The coparison of cornering stiffness between existing contour and odified contour as is shown in Fig.11. existing cornering stiffness and the odified cornering stiffness when the lateral angle is within the scope of -3 ~3. The cornering stiffness of odified contour noticeable increase to N/, while the existing one is N/, which eans the odified contour s cornering stiffness is 4.75% higher than the existing one. It is obvious that the odified ethod of tire contour design iprove the cornering stiffness of the tire. C. The Analysis of Abrasion Resistance The wearing of tire is caused by the cobined action of tangential stress and lateral stress, which eans the abrasion resistance perforance can be evaluated by the speed of tread s wearing and the unifority of wearing. The wearing speed of tire can be evaluated by the friction loss of tread and the unifority of wearing can be assessed by the skewness value of contact pressure [15]. The friction loss of tire is ineluctable while the tire is rolling. Under the preise of considering tread deforation and friction loss, the equation for the energy loss E [16]: E S u q 0 i 1 p n k s j 0 l 1 lj a lj A ( x P A ( x y y lj (17 Where a eans the tangential stress of adhesive area; S eans the slip radio; u s eans the friction coefficient between tire and road; P eans the contact pressure of slip area nodes; A eans the grounding area of tire when rolling; p eans the nuber of adhesive area nodes; k eans the nuber of adhesive area nodes which contact the road; eans the nuber of slip area nodes; n eans the nuber of slip area nodes which contact the road; x eans the X-axle slip distance of tread nodes; y eans the Y-axle slip distance of tread nodes. The energy loss of friction is calculated by forula 17. The friction loss of the existing contour is J while the odified contour s friction loss is J. The skewness value of contact pressure is shown in Tab Ⅲ. Due to the larger grounding area and the flatter contour, the wearing DOI /IJSSST.a.16.3B ISSN: x online, print

6 speed of odified contour is increased slight than the existing one. However, the decrease of skewness value of contact pressure can avoid the uneven wear of the tread, which benefit obviously to the service life of tire. It coes to the conclusion that the tire s contour based on the odified string balance theory can iprove the abrasion resistance perforance. D. The Analysis of Rolling Resistance The rolling resistance is the basic perforance of tire, it influence the fuel consuption of the vehicle directly. The rolling resistance is caused by the hysteresis energy loss of the rubber. The Fourier expansion is used to describe the distribution of strain and stress of whole tire as: 0 1n 2n sin( n t n n 1 0 1n 2n sin( n t n n 1 (18 (19 Where eans the equivalent stress of eleents; eans the equivalent strain of eleents; φ eans the phase angle of stress and strain, eans the ters of Fourier expansion. The equation for the rolling resistance of tire: n sin V n 1 n n i FR (20 2 r G'' tan (21 G' Where FR eans the rolling resistance; Vi eans the volue of rubber eleents, G' ' and G' are respectively called the storage odulus and the loss odulus, which coes fro the experient [10]. The energy loss of the tire coponents is shown in Tab Ⅳ. Progras TABLE Ⅳ. THE ENERGY LOSS OF THE TIRE COMPONENTS The energy loss of tire coponents (J Tread Under treadcarcassbelt/plyapexsidewallabrasioninner Existing contour Modified contour Due to the flatter tread, the tread rubber s deforation of odified contour is reduced, which contributes to the less energy loss of tread while raised the energy loss of under tread and carcass slightly. The rolling resistance of existing contour and the odified contour is calculated as Table 4. TABLE Ⅴ. THE ROLLING RESISTANCE OF EXISTING AND MODIFIED Progras CONTOUR Rolling resistance(n Existing contour Modified contour Copared with the existing contour, the odified designed contour reduced 4.78N of rolling resistance, which eans 4.43% higher perforance of rolling resistance. It can be concluded that the tire s contour based on the odified string balance contour theory can iprove the rolling resistance perforance. V. CONCLUSIONS In this paper, the tire s contour design ethod based on the new odified string balance contour theory is proposed. The paper analyzes the influences of tire contour to ground connection properties, cornering stiffness, abrasion resisting perforance and rolling resistance perforance. (1 The pressure sharing ratios of belt is distributed by trapeziu in practice. Based on the belts pressure sharing ratios, the odified tire contour design ethod of string balance contour theory is proposed. (2 The 3D siulation tire odel with coplex tread pattern is established. Based on the experient of the test bench, the siulation odel proved to be accurate and reliably. (3 Copared with the existing design contour, the odified contour increases the grounding area and decreases the skewness value of contact pressure of the tire. Besides, the odified contour s cornering stiffness increases 34.7N/, which eans 4.75% higher perforance than the existing one. (4 Even through the wearing speed of odified contour increase slightly than the existing one, the uneven wear of tread is avoided; which is beneficial to the abrasion resisting perforance. (5 The odified string balance tire contour optiize the distribution of stress and strain. Coparing with the existing contour, the odified contour reduce 4.78 N resistance, which eans 4.43% higher perforance of rolling resistance. ACKNOWLEDGMENT This article is supported by the National Natural Science Foundation of China ( , and China Postdoctoral Science Foundation (2014M REFERENCES [1] Frank F, hofferberth W, Mechanics of the pneuatic tire, Rubber Cheistry and Technology, vol. 40, pp , [2] XU Yonggong, Research on the atch of vehicle and tire based on handling and stability, Changchun: Jilin University, [3] BAFFET G, CHARARA A, and Daniel Lechner, Estiation of vehicle sideslip, tire force and wheel cornering stiffness, Control Engineering Practice, vol.17, pp , [4] Korunović N, Trajanović M, Stojkoviéć M, et al, Finite eleent analysis of a tire steady rolling on the dru and coparison with DOI /IJSSST.a.16.3B ISSN: x online, print

7 experient, Journal of Mechanical Engineering, vol. 57, pp , [5] JIAO Zhiwei, ZHAO Peng, LIU Yuexing, et al, Finite eleent analysis for echanical properties of a new section contour tire, Key Engineering Materials, vol. 561, pp , [6] YU Qi, DING Jianping, Structure design and anufacturing technology of radial tire, Beijing: Cheical industry press, [7] SAKAI Hideo, Tire engineering, Tokyo: Grand Prix of Corporation Publication, [8] WANG Guolin, WAN Zhijun, LIANG Chen, et al, Structural design of radial tire based on nonbalance outline theory, Journal of Mechanical Engineering, vol. 48, pp , [9] LI Wei, Study of radial tire finite eleent analysis and design rules, Hefei: University of Science and Technology of China, [10] J. R. Cho, H. W. Lee, W. B. Jeong, Nuerical estiation of rolling resistance and teperature distribution of 3-D periodic patterned tire, International Journal of Solids and Structures, vol. 1, pp , [11] LIU Wenwu, HU Changsheng, LU Nianli, ANSYS enabled analysis and investigation into contact between tires and roads for engineering vehicles, Chinese Journal of Construction Machinery, vol. 10, pp , [12] YU Fan, LIN Yi, Vehicle syste dynaics, Beijing: Machinery Industry Press, [13] ZHUANG Jide, Autoobile tire technology, Beijing: Beijing Institute of Technology Press, [14] Nakajia Y, Kadowaki H, Kaegawa T, et al, Application of a Neural Network for the Optiization of Tire Design, Tire Science and Technology, vol. 27, pp , [15] YAO Wei, Genetic algorith iproved strategy and tire structure ultiobjective optiization research, Harbin: Harbin Institute of Technology, [16] FANG Qinghong, LU Jinlin, The finite eleent calculation odel research of ground of energy loss in the tyre wear analysis, Journal of Shenyang institute of cheical industry, vol. 16, pp , DOI /IJSSST.a.16.3B ISSN: x online, print

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