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

Transcription

1 Agricultural Egieerig Research Joural 3 (1): 01-06, 013 ISSN IDOSI Publicatios, 013 DOI: /idosi.aerj Predictio of Bias-Ply Tire Rollig Resistace Based o Sectio Width, Iflatio Pressure ad Vertical Load Majid Rashidi, Mohammad Gholami ad Mohammad Mohammadi Departmet of Agricultural Machiery, Takesta Brach, Islamic Azad Uiversity, Takesta, Ira Abstract: This study was maily coducted to predict rollig resistace (R) of bias-ply tire based o sectio width (b), iflatio pressure (P) ad vertical load (W). For this purpose, rollig resistace of four bias-ply tires with differet sectio width was measured at three levels of iflatio pressure ad four levels of vertical load. Results of rollig resistace measuremet for bias-ply tires No. 1, ad 3 were utilized to determie regressio model ad three-variable liear regressio model R = b P W with R = 0.97 was obtaied. Also, results of rollig resistace measuremet for bias-ply tire No. 4 were used to verify model. The paired samples t-test results showed that the rollig resistace values predicted by model were statistically less tha the rollig resistace values measured by test apparatus. To check the discrepacies betwee the rollig resistace values predicted by model with the rollig resistace values measured by test apparatus, RMSE ad MRPD were calculated. The amouts of RMSE ad MRPD were kn ad 16.3%, respectively. Ratioal amouts of RMSE ad MRPD cofirmed that the three-variable liear regressio model may be used to predict rollig resistace of bias-ply tire based o sectio width, iflatio pressure ad vertical load. However, to calculate actual rollig resistace values or rollig resistace values measured by test apparatus (R M) based o rollig resistace values predicted by model (R P) the liear equatio R M= R P with R = 0.97 ca be strogly suggested. Key words: Bias-ply tire Rollig resistace Predictio Sectio width Iflatio pressure Vertical load INTRODUCTION It has bee kow i practice that the rollig resistace of a tire icrease both with the vertical load o the tire ad The most importat factor i tractor operatio is with the sikage of the tire ito the soil [4]. Rollig tractio performace. Obtaied data from tractio resistace cosists of three compoets R c, R b ad Rt performace measuremets idicates that gross tractio [3, 5]: ad rollig resistace must be subtracted to achieve the et tractio [1-3]: R = R + R + R () c b t NT = GT - R (1) R c = The rollig resistace compoet related to vertical soil compactio, kn NT = Net tractio, kn R b = The rollig resistace compoet related to GT = Gross tractio, kn horizotal soil displacemet, kn R = Rollig resistace, kn R t = The rollig resistace compoet related to flexig of the tire, kn The rollig resistace of a vehicle is described as a force opposig horizotal motio o a deformable surface For vehicles operatig o a hard surface, R or o flexible tires. Also, rollig resistace ca be costitutes the largest percetage of the rollig resistace cosidered as a rate of eergy loss to the soil ad/or tires. force ad this ca be slightly reduced by icreasig the t Correspodig Author: Dr. Majid Rashidi, Ph.D., Departmet of Agricultural Machiery, Takesta Brach, Islamic Azad Uiversity, Takesta, Ira. 1

2 Agric. Egieerig Res. J., 3(1): 01-06, 013 iflatio pressure ad the effective stiffess of the tire. I a off-road situatio, however, the compoets R b ad R c make up the largest proportio of the rollig resistace force [3, 5]. A extesive set of field tests of rollig resistace was performed by McKibbe ad Davidso [6] usig tires of differet sizes. They compared the rollig resistace of differet towed peumatic tires varyig i overall uloaded diameter uder three vertical loads ad five differet field ad road surface coditios. Their results affirm that diameter is a promiet factor goverig the rollig resistace of tires [7]. McKibbe ad Davidso [8] also demostrated that the tire iflatio pressure has a marked effect o rollig resistace, depedig o the type of surface upo which the tire travels. O soft surfaces, a higher iflatio pressure results i a icreased rollig resistace force. O the other had, larger iflatio pressures reduce the rollig resistace of a tire travelig o surfaces which are more firm [3, 5]. A further factor which ca ifluece the effort required to move tires o soil is the arragemet of two or more tires o a vehicle. Aother set of experimets by McKibbe ad Davidso [9] idicated that a differet result is caused by the placig of dual tires, side by side, or a tadem cofiguratio i which oe wheel follows the other. The ivestigators recommeded that field machies should be desiged such that trasport tires follow oe aother ad trailer tires be positioed i the same track as the towig tractor. I this way sigificat ecoomy i rollig resistace eergy could be realized [10]. As rollig resistace for a give tire size, iflatio pressure ad vertical load may be sigificatly differet betwee bias-ply ad radial-ply tires [1], this study was maily coducted to predict rollig resistace (R) of biasply tire based o sectio width (b), iflatio pressure (P) ad vertical load (W). MATERIALS AND METHODS Tire Rollig Resistace Test Apparatus: A three-wheel rollig resistace test apparatus was desiged ad costructed to measure rollig resistace of tires with differet sizes at diverse levels of iflatio pressure ad vertical load. The three-wheel tester, likages, weights, load cell ad data logger are show i Fig. 1. Experimetal Procedure: Rollig resistace of four bias-ply tires with differet sectio width was measured at three levels of iflatio pressure ad four levels of vertical load. The sectio widths of four bias-ply tires are Fig. 1: The tire rollig resistace test apparatus, likages, weights, load cell ad data logger Table 1: Sectio width of the four bias-ply tires used i this study Tire No. Sectio width b (cm) give i Table 1. Results of rollig resistace measuremet for bias-ply tires No. 1, ad 3 (Tables, 3 ad 4) were utilized to determie three-variable liear regressio model ad results of rollig resistace measuremet for bias-ply tire No. 4 (Table 5) were used to verify model. Regressio Model: A typical three-variable liear regressio model is show i equatio 3 [11-14]: Y = C + C X + C X + C X (3) Y = Depedet variable, for example rollig resistace of bias-ply tire X 1, X, X 3 = Idepedet variables, for example sectio width, iflatio pressure ad vertical load C 0, C 1, C, C 3 = Regressio coefficiets I order to predict rollig resistace of bias-ply tire from sectio width, iflatio pressure ad vertical load, a three-variable liear regressio model was suggested ad all the data were subjected to regressio aalysis usig the Microsoft Excel 007.

3 Agric. Egieerig Res. J., 3(1): 01-06, 013 Table : Sectio width, iflatio pressure, vertical load ad rollig resistace (the mea of three replicatios) for bias-ply tire No. 1 Tire No. Sectio width b (cm) Iflatio pressure P (psi) Vertical load W (kn) Rollig resistace R (kn) Table 3: Sectio width, iflatio pressure, vertical load ad rollig resistace (the mea of three replicatios) for bias-ply tire No. Tire No. Sectio width b (cm) Iflatio pressure P (psi) Vertical load W (kn) Rollig resistace R (kn) Table 4: Sectio width, iflatio pressure, vertical load ad rollig resistace (the mea of three replicatios) for bias-ply tire No. 3 Tire No. Sectio width b (cm) Iflatio pressure P (psi) Vertical load W (kn) Rollig resistace R (kn) Table 5: Sectio width, iflatio pressure, vertical load ad rollig resistace (the mea of three replicatios) for bias-ply tire No. 4 Tire No. Sectio width b (cm) Iflatio pressure P (psi) Vertical load W (kn) Rollig resistace R (kn)

4 Statistical Aalysis: A paired samples t-test was used to compare the rollig resistace values predicted by model with the rollig resistace values measured by test apparatus. Also, to check the discrepacies betwee the rollig resistace values predicted by model with the rollig resistace values measured by test apparatus, root mea squared error (RSME) ad mea relative percetage deviatio (MRPD) were calculated usig the equatios 4 ad 5, respectively [15-0]: Agric. Egieerig Res. J., 3(1): 01-06, 013 RMSE = i= 1 Pi ( R R ) Mi (4) RMSE = Root mea squared error, kn R MI = Rollig resistace measured by test apparatus, kn R Pi = Rollig resistace predicted by model, kn Fig. : Curve of rollig resistace values measured by test apparatus (R M) based o rollig resistace RM i R values predicted by model (R P) for bias-ply tire Pi 100 R (5) No. 4 i= 1 Mi MRPD = The paired samples t-test results idicated that the rollig resistace values predicted by model were statistically MRPD = Mea relative percetage deviatio, % less tha the rollig resistace values measured by test apparatus. The average rollig resistace differece RESULTS AND DISCUSSION betwee two methods was kn (95% cofidece itervals for the differece i meas: kn ad Three-variable liear regressio model, p-value of kn; p-value = ). The stadard deviatio of the idepedet variables ad coefficiet of determiatio rollig resistace differece was 0.01 kn (Table 8). (R ) of the model are show i Table 6. I this model To check the discrepacies betwee the rollig resistace rollig resistace of bias-ply tire ca be predicted as a values predicted by model with the rollig resistace fuctio of sectio width (b), iflatio pressure (P) ad values measured by test apparatus, RMSE ad MRPD vertical load (W). The p-value of idepedet variables were calculated. The amouts of RMSE ad MRPD were (b, P ad W) ad R of the model were 1.44E-06, 1.6E-11, kn ad 16.3%, respectively. Ratioal amouts of 5.00E-5 ad 0.97, respectively. Based o the statistical RMSE ad MRPD cofirmed that the three-variable results, the three-variable liear regressio model was liear regressio model R = b P iitially accepted, which is give by equatio 6: W with R = 0.97 may be used to predict rollig resistace of bias-ply tire based o sectio width, R = b P W (6) iflatio pressure ad vertical load. As it is idicated i Fig., our attempts to relate rollig resistace values Rollig resistace of bias-ply tire No. 4 was the predicted by model (R P) to rollig resistace values predicted at three levels of iflatio pressure ad four measured by test apparatus (R M) usig a liear equatio levels of vertical load usig the three-variable liear resulted i very good agreemets (R = 0.97) as equatio regressio model. The rollig resistace values predicted 7: by model were compared with the rollig resistace values measured by test apparatus ad are show i Table 7. R = R (7) M P 4

5 Agric. Egieerig Res. J., 3(1): 01-06, 013 Table 6: Three-variable liear regressio model, p-value of idepedet variables ad coefficiet of determiatio (R ) p-value Model b P W R R = b P W E E E Table 7: Sectio width, iflatio pressure, vertical load ad rollig resistace (the mea of three replicatios) for bias-ply tire No. 4 used i evaluatig the model Rollig resistace R (kn) Sectio width b (cm) Iflatio pressure P (psi) Vertical load W (kn) Measured by test apparatus Predicted by model Table 8: Paired samples t-test aalysis o comparig rollig resistace determiatio methods Determiatio methods Average differece (kn) Stadard deviatio of differece (kn) p-value 95% cofidece itervals for the differece i meas (kn) Test apparatus vs. model , Therefore, actual or measured rollig resistace (R M) compariso of radial ad cross-ply carcass ca be computed i two steps. At first step, predicted costructio. J. Agric. Eg. Res., (4): rollig resistace (R P) is calculated based o sectio width. ASAE, 003. Agricultural machiery maagemet (b), iflatio pressure (P) ad vertical load (W) usig the data. ASAE Stadard D ASAE Stadards, St. three-variable liear regressio model. At secod step, Joseph, Mich.: ASAE. actual or measured rollig resistace (R M) is calculated 3. Rebati, J. ad M. Loghavi, 006. Ivestigatio ad based o predicted rollig resistace (R P) usig the liear evaluatio of rollig resistace predictio models for equatio 7. peumatic tires of agricultural vehicles. Ira Agric. CONCLUSIONS 4. Res., 5(1): McKyes, E., Soil Cuttig ad Tillage. Elsevier Sciece Publishig Compay Ic., New York, USA. It ca be cocluded that actual or measured rollig 5. Packett, C.W., A preview of force predictio resistace (R M) of bias-ply tire ca be computed i two methods for off-road wheels. J. Agric. Eg. Res., steps. At first step, predicted rollig resistace (R P) is 31: calculated based o sectio width (b), iflatio pressure 6. McKibbe, E.G. ad J.B. Davidso, (P) ad vertical load (W) usig the three-variable liear Trasport wheels for agricultural machies IV. Effect regressio model R = b P W of outside ad cross-sectio diameters o the rollig with R = At secod step, actual or resistace of peumatic implemet tires. Agric. Eg., measured rollig resistace (R M) is calculated based o 1 (): predicted rollig resistace (R P) usig the liear equatio 7. Gee-Clough, D., Selectio of tire sizes for R M= R P with R = agricultural vehicles. J. Agric. Eg. Res., 4(3): REFERENCES 8. McKibbe, E.G. ad J.B. Davidso, Trasport wheels for agricultural machies III. Effect of iflatio 1. Gee-Clough, D., M. McAllister ad D.W. Everde, pressure o the rollig resistace of peumatic Tractive performace of tractor drive tires, II. A implemet tires. Agric. Eg., 1(1):

6 Agric. Egieerig Res. J., 3(1): 01-06, McKibbe, E.G. ad J.B. Davidso, Trasport 16. Rashidi, M., M. Mousavi, S. Akhtarkavia, B. wheels for agricultural machies V. Effect of wheel Jaberiasab ad S.M. Emadi, 013. Predictio of arragemet o rollig resistace. Agric. Eg., bias-ply tire cotact area based o cotact area idex, 1(3): iflatio pressure ad vertical load. Am-Euras. J. 10. McAllister, M., Reductio i the rollig Agric. & Eviro. Sci., 13(4): resistace of tires for trailed agricultural machiery. 17. Rashidi, M., M. Mousavi, S. Razavi, P. Fatehirad ad J. Agric. Eg. Res., 8(1): A. Lotfi-Aski, 013. Predictio of bias-ply tire cotact 11. Azadeh, S., M. Rashidi ad M. Gholami, 013. area based o overall uloaded diameter, iflatio Modelig of bias-ply tire deflectio based o tire pressure ad vertical load usig liear regressio dimesios, tire iflatio pressure ad vertical load model. Middle-East J. Sci. Res., 14(11): o tire. Middle-East J. Sci. Res., 14(1): Rashidi, M., S. Azadeh, B. Jaberiasab, 1. Mousavi, M., M. Rashidi, I. Rajbar, M.S. Garmroudi S. Akhtarkavia ad M. Nazari, 013. Predictio of ad M. Ghaebi, 013. Modelig of bias-ply tire bias-ply tire deflectio based o overall uloaded cotact area based o tire dimesios, tire iflatio diameter, iflatio pressure ad vertical load. Middlepressure ad vertical load o tire usig liear East J. Sci. Res., 14(10): regressio models. Am-Euras. J. Agric. & Eviro. 19. Rashidi, M., S. Azadeh, P. Fatehirad, S.M. Emadi ad Sci., 13(5): A. Lotfi-Aski, 013. Predictio of bias-ply tire 13. Oroojloo, M., M. Rashidi ad M. Gholami, 013. deflectio based o cotact area idex, iflatio Modelig of radial-ply tire cotact area based o tire pressure ad vertical load usig liear regressio dimesios, tire iflatio pressure ad vertical load model. World Appl. Sci. J., (7): o tire. Middle-East J. Sci. Res., 17(7): Rashidi, M., S. Azadeh, S. Amii, A. Niazkhai ad 14. Sheikhi, M.A., M. Rashidi ad M. Gholami, 013. M. Fayyazi, 013. Predictio of bias-ply tire Modelig of radial-ply tire deflectio based o tire deflectio based o tire size, iflatio pressure ad dimesios, tire iflatio pressure ad vertical vertical load. Am-Euras. J. Agric. & Eviro. Sci., load o tire. Am-Euras. J. Agric. & Eviro. Sci., 13(5): (): Mousavi, S.M., M. Rashidi, I. Rajbar, M.S. Garmroudi ad S.S. Garmroodi, 013. Predictio of bias-ply tire cotact area based o sectio width, iflatio pressure ad vertical load. Middle-East J. Sci. Res., 15(11):