Prediction of Bias-Ply Tire Contact Area Based on Contact Area Index, Inflation Pressure and Vertical Load

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1 America-Eurasia J. Agric. & Eviro. Sci., 13 (4): , 013 ISSN IDOSI Publicatios, 013 DOI: /idosi.aejaes Predictio of Bias-Ply Tire Cotact Area Based o Cotact Area Idex, Iflatio Pressure ad Vertical Load Majid Rashidi, Mojtaba Mousavi, Siamak Akhtarkavia, Babak Jaberiasab ad Seyyed Mohammad Emadi Departmet of Agricultural Machiery, Takesta Brach, Islamic Azad Uiversity, Takesta, Ira Abstract: This study was coducted to predict cotact area (A) of bias-ply tire based o cotact area idex (CAI), iflatio pressure (P) ad vertical load (W). For this purpose, cotact area of four bias-ply tires with differet cotact area idex were measured at three levels of iflatio pressure ad four levels of vertical load. Results of cotact area measuremet for bias-ply tires No. 1, ad 3 were utilized to determie regressio model ad three-variable liear regressio model A P = CAI P W with R = was obtaied. Also, results of cotact area measuremet for bias-ply tire No. 4 were used to verify model. The paired samples t-test results idicated that the cotact area values predicted by model were more tha the cotact area values measured by test apparatus. To check the discrepacies betwee the cotact area values predicted by model with the cotact area values measured by test apparatus, RMSE ad MRPD were calculated. The amouts of RMSE ad MRPD were 30.4 cm ad 33.1%, respectively. Amouts of RMSE ad MRPD cofirmed that the three-variable liear regressio model may be used to predict cotact area of bias-ply tire based o cotact area idex, iflatio pressure ad vertical load. O the other had, to calculate actual cotact area values or cotact area values measured by test apparatus (A M) based o cotact area values predicted by model (A P) the liear regressio model A M= 0.90 A P with R = ca be strogly recommeded. Key words: Bias-ply tire Cotact area Cotact area idex Iflatio pressure Vertical load Modelig Predictio INTRODUCTION A flexible tire has a smaller cotact area o hard surface tha it dose o soft groud. A rule of thumb which ca be used for estimatio of tire cotact area is show by equatio 1 [1]: A = bl (1) A = Tire cotact area (m ) b = Sectio width of tire (m) L = Cotact legth of tire (m) McKyes [1] gave a approximate method for estimatig cotact legth of tire o hard ad soft surfaces (Fig. 1) as give below i equatios ad 3, respectively: d L = 4 d L = (O a hard surface) () (O a soft surface) (3) d = Overall uloaded diameter of tire (m) From equatios 1, ad 3 it ca be cocluded that sectio width times overall uloaded diameter (bd) ca be cosidered as cotact area idex (CAI). Cotact area is a key parameter ad may equatios have bee developed based o it to evaluate the tractive performace of bias-ply ad radial-ply tires operatig i cohesive-frictioal soils. Gross tractio, motio resistace, et tractio ad tractive Correspodig Author: Dr. Majid Rashidi, Departmet of Agricultural Machiery, Takesta Brach, Islamic Azad Uiversity, Takesta, Ira. 575

2 Am-Euras. J. Agric. & Eviro. Sci., 13 (4): , 013 differet sizes at diverse levels of iflatio pressure ad vertical load. The cotact area measuremet system (Fig. 4) cosisted of teksca sesor (Fig. 5), teksca USB hadle ad computer equipped with I-Sca software (Fig. 6). Fig. 1: Cotact legths of tires o hard ad soft surfaces, adapted from McKyes [1] Experimetal Procedure: Cotact area of four bias-ply tires with differet dimesios was measured at three levels of iflatio pressure ad four levels of vertical load. The dimesios of four bias-ply tires are give i Table 1. Results of cotact area measuremet for bias-ply tires No. 1, ad 3 (Tables, 3 ad 4) were utilized to determie multiple-variable liear regressio models ad results of cotact area measuremet for bias-ply tire No. 4 (Table 5) were used to verify selected model. Regressio Model: A typical three-variable liear regressio model is show i equatio 4: Y = C + C X + C X + C X (4) Y = Depedet variable, for example cotact area of biasply tire X 1, X, X 3 = Idepedet variables, for example cotact Fig. : Tire dimesios, adapted from Brixius [] area idex, iflatio pressure ad vertical load, respectively efficiecy are predicted as a fuctio of soil stregth, tire load, tire slip, tire size, tire deflectio ad tire cotact area C 0, C 1, C, C 3= Regressio coefficiets []. I order to predict cotact area of bias-ply tire based Fig. shows the tire dimesios (b ad d) used. o cotact area idex, iflatio pressure ad vertical load, The tire dimesios ca be obtaied from tire data book a three-variable liear regressio model was suggested or by measurig the tire []. The sectio width (b) is the ad all the data were subjected to regressio aalysis first umber i a tire size desigatio (i.e. omially 18.4 usig the Microsoft Excel 007. iches for a tire). The overall uloaded diameter (d) ca be obtaied from the tire data hadbooks available Statistical Aalysis: A paired samples t-test was used to from off-road tire maufacturers [, 3]. compare the cotact area values predicted by model with As cotact area for a give tire size, iflatio the cotact area values measured by test apparatus. Also, pressure ad vertical load are sigificatly differet to check the discrepacies betwee the cotact area betwee bias-ply ad radial-ply tires, this study was values predicted by model with the cotact area values coducted to predict cotact area (A) of bias-ply tire measured by test apparatus, root mea squared error based o cotact area idex (CAI), iflatio pressure (P) (RSME) ad mea relative percetage deviatio (MRPD) ad vertical load (W). were calculated usig the equatios 5 ad 6, respectively [6-13]: MATERIALS AND METHODS Tire Cotact Area Measuremet Apparatus: A tire cotact area measuremet apparatus (Fig. 3) was desiged ad costructed to measure cotact area of tires with RMSE = i= 1 Pi ( A A ) M i (5) 576

3 Am-Euras. J. Agric. & Eviro. Sci., 13 (4): , 013 Table 1: Dimesios of the four bias-ply tires used i this study Sectio width b (cm) Overall uloaded diameter d (cm) Cotact area idex bd (cm ) Table : Cotact area idex, iflatio pressure, vertical load ad cotact area (three replicatios) for bias-ply tire No Cotact area idex CAI (cm ) Iflatio pressure P (MPa) Vertical load W (kn) R1 R R Table 3: Cotact area idex, iflatio pressure, vertical load ad cotact area (three replicatios) for bias-ply tire No Cotact area idex CAI (cm ) Iflatio pressure P (MPa) Vertical load W (kn) R1 R R Table 4: Cotact area idex, iflatio pressure, vertical load ad cotact area (three replicatios) for bias-ply tire No Cotact area idex CAI (cm ) Iflatio pressure P (MPa) Vertical load W (kn) R1 R R

4 Am-Euras. J. Agric. & Eviro. Sci., 13 (4): , 013 Fig. 5: Teksca sesor, adapted from Teksca [5] Fig. 3: Tire cotact area measuremet apparatus Fig. 4: Cotact area measuremet system, i.e. teksca sesor, teksca USB hadle ad computer equipped with I-Sca software, adapted from Aderso [4] Fig. 6: I-Sca software screeshot for tire cotact area measuremet Table 5: Cotact area idex, iflatio pressure, vertical load ad cotact area (three replicatios) for bias-ply tire No Cotact area idex CAI (cm ) Iflatio pressure P (MPa) Vertical load W (kn) R1 R R

5 MRPD = Mea relative percetage deviatio, % RESULTS AND DISCUSSION Three-variable liear regressio model, p-value of idepedet variables ad coefficiet of determiatio (R ) of the model are show i Table 6. I this model cotact area of bias-ply tire ca be predicted as a fuctio of cotact area idex (CAI), iflatio pressure (P) ad vertical load (W). The p-value of idepedet variables (CAI, P ad W) ad R of the model were , 1.99E-7, 1.1E-48 ad 0.901, respectively. Based o the statistical results, the three-variable liear regressio model was iitially accepted, which is give by equatio 7: Am-Euras. J. Agric. & Eviro. Sci., 13 (4): , 013 Cotact area of bias-ply tire No. 4 was the predicted RMSE = Root mea squared error (cm ) at three levels of iflatio pressure ad four levels of A mi = Cotact area measured by tire cotact area vertical load usig the three-variable liear regressio measuremet apparatus (cm ) model. The cotact area values predicted by model were A pi = Cotact area predicted by three-variable liear compared with the cotact are values measured by test regressio model (cm ) apparatus ad are show i Table 7. The paired samples t-test results idicated that the cotact area values AM i A predicted by model were more tha the cotact area Pi 100 A (6) values measured by test apparatus. The average cotact i= 1 Mi MRPD = area differece betwee two methods was 9.9 cm (95% cofidece iterval for differece i meas: 6.5 cm ad 33.4 cm ; p-value =1.0000). The stadard deviatio of the cotact area differece was 5.37 cm (Table 8). To check the discrepacies betwee the cotact area values predicted by model with the cotact area values measured by test apparatus, RMSE ad MRPD were calculated. The amouts of RMSE ad MRPD were 30.4 cm ad 33.1% respectively. Amouts of RMSE ad MRPD cofirmed that the three-variable liear regressio model A P = CAI P W with R = may be used to predict cotact area of bias-ply tire based o cotact area idex, iflatio pressure ad vertical load. O the other had, as it is idicated i Fig. 7, our attempts to relate cotact area values predicted by three-variable liear regressio model (A ) to cotact P area values measured by test apparatus (A M) usig a liear equatio resulted i very good agreemets (R = 0.916) as equatio 8: A = CAI P W (7) P A M= 0.90 A P (8) Table 6: Three-variable liear regressio model, p-value of idepedet variables ad coefficiet of determiatio (R) p-value Model CAI P W R A = CAI P W E-7 1.1E Table 7: Cotact area idex, iflatio pressure, vertical load ad cotact area for bias-ply tire No. 4 used i evaluatig three-variable liear regressio model Cotact area idex CAI (cm ) Iflatio pressure P (MPa) Vertical load W (kn) Measured by test apparatus Predicted by model

6 Am-Euras. J. Agric. & Eviro. Sci., 13 (4): , 013 Table 8: Paired samples t-test aalyses o comparig cotact area determiatio methods Average Stadard deviatio 95% cofidece itervals for Determiatio methods differece (cm ) of differece (cm ) p-value the differece i meas (cm ) Test apparatus vs. model , Brixius, W.W., Tractio predictio equatios for bias ply tires. ASAE Paper No St. Joseph, Mich.: ASAE. 3. Goerig, C.E., M.L. Stoe, D.W. Smith ad P.K. Turquist, 006. Off-Road Vehicle Egieerig Priciples. St. Joseph, Mich.: ASABE. 4. Aderso, J., 006. Asphalt pavemet pressure distributios usig teksca measuremet system. M.Sc. Thesis, Uiversity of Ketucky, December. 5. Teksca, 006. Teksca idustrial sesor catalog itroductio, Accessed: November 13, Rashidi, M. ad K. Seyfi, 007. Field compariso of differet ifiltratio models to determie the soil Fig. 7: Curve of cotact area values measured by test ifiltratio for border irrigatio method. Am-Euras. J. apparatus (AM) based o cotact area values Agric. & Eviro. Sci., (6): predicted by three-variable liear regressio model 7. Rashidi, M. ad K. Seyfi, 008. Comparative studies (AP) for bias-ply tire No. 4 o Bekker ad Upadhyaya models for soil pressuresikage behaviour predictio. Am-Euras. J. Agric. & It meas that actual or measured cotact area (A M) Eviro. Sci., 3(1): ca be computed i two steps. At first step predicted 8. Rashidi, M. ad M. Gholami, 008. Modelig of soil cotact area (A P) ca be calculated based o cotact area pressure-sikage behaviour usig the fiite elemet idex (CAI), iflatio pressure (P) ad vertical load (W) method. World Appl. Sci. J., 3(4): usig the three-variable liear regressio model, i.e. 9. Rashidi, M. ad M. Gholami, 008. Multiplate equatio 7. Secod step is calculatig actual or measured peetratio tests to predict soil pressure-sikage cotact area (A M) based o predicted cotact area (A P) behaviour. World Appl. Sci. J., 3(5): usig the liear model, i.e. equatio Rashidi, M., M. Gholami, I. Rajbar ad S. Abbassi, 010. Fiite elemet modelig of soil sikage by CONCLUSIONS multiple loadigs. Am-Euras. J. Agric. & Eviro. Sci., 8(3): It ca be cocluded that actual or measured cotact 11. Rashidi, M., M. Fakhri, M.A. Sheikhi, S. Azadeh ad area (A M) of bias-ply tire ca be computed i two easy S. Razavi, 01. Evaluatio of Bekker model i steps. At first step, predicted cotact area (A P) ca be predictig soil pressure-sikage behaviour uder calculated based o cotact area idex (CAI), iflatio field coditios. Middle-East J. Sci. Res., pressure (P) ad vertical load (W) usig the three-variable 1(10): liear regressio model A P = CAI Rashidi, M., M. Fakhri, S. Azadeh, M.A. Sheikhi ad P W with R = Secod step is calculatig S. Razavi, 01. Assessmet of Upadhyaya model actual or measured cotact area (A M) based o predicted i predictig soil pressure-sikage behaviour cotact area (A P) usig the liear equatio A M= 0.90 A P- uder field coditios. Middle-East J. Sci. Res., 0.08 with R = (9): Rashidi, M., M. Fakhri, S. Razavi, S. Razavi ad REFERENCES M. Oroojloo, 01. Compariso of Bekker ad Upadhyaya models i predictig soil pressure- 1. McKyes, E., Soil Cuttig ad Tillage. Elsevier sikage behaviour uder field coditios. Am-Euras. Sciece Publishig Compay Ic. New York, USA. J. Agric. & Eviro. Sci., 1(1):

Prediction of Bias-Ply Tire Rolling Resistance Based on Section Width, Inflation Pressure and Vertical Load

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