Deflection characteristics for radial-ply tractor tyres

Transcription

1 Journal of Parmacognosy and Pytocemistry 218; SP1: E-ISSN: P-ISSN: JPP 218; SP1: Ranjeet Kumar Assistant professor, RMD College of Agriculture and Researc Station, Ambikapur, Cattisgar, India KP Pandey Ret. Professors, IIT Karagpur, West Bengal, India DK Gupta Assoc. Professor, RMD CARS, Ambikapur, Cattisgar, India VK Tewari Researc Scolar, IIT Karagpur, West Bengal, India Satya prakas Scientist, CIAE, Bopal, Madya Prades, India Sanjeev Kumar Researc Scolars, IIT Karagpur, West Bengal, India Deflection caracteristics for radial-ply tractor tyres Ranjeet Kumar, KP Pandey, DK Gupta, VK Tewari, Satya Prakas and Sanjeev Kumar Abstract Te deflection caracteristics of four radial-ply tyres (12.4 R 28, 13.6 R 28, 14.9 R 28 and 16.9 R 28) were studied on a ard surface. Te normal load on te test tyres was varied from 4.91 to kn and inflation pressure from 41 to 27 kpa. Based on te test observations, empirical model was developed to predict deflection of te radial-ply tyres. Tis model was validated and was found to perform well. Te developed deflection model was used to determine te possible combinations of normal load and inflation pressure to acieve te desired deflection of 2, 24 and 28 per cent for eac test tyre. Keywords: Deflection, radial-ply tractor tyres Introduction Te best single indicator of a tyre s ability to perform satisfactorily and deliver normal service life is tyre deflection. Wen a tyre is over deflected as a result of over load and under inflation or a combination of tese, service life will be reduced. Te over deflected tyre bulges excessively at ground contact making it more subject to puncture damage. Tis requires tat te recommended inflation pressure is maintained in all tyres and tat te tyres are not subjected to load more tan te recommended load. It is, terefore, essential to study te deflection caracteristics of a tyre wit a view to arrive at optimum combinations of load and inflation pressure for evaluating its traction performance. Te tyre deflection caracteristics ave extensively been reviewed and presented as follows 2. Materials and metods Te experimental facilities for deflection test included a tyre test carriage (single weel tester), an electronic plate-form balance and deflection measuring device. Te tyre test carriage could accommodate te various sizes of te tyres and could be raised and lowered using a ydraulic cylinder. Te vertical deflection of te tyre was measured wit displacement transducer and recorded by a Data Acquisition System (DAS). Te four different sizes of test tyres (12.4R28, 13.6R28, 14.9R28 and 16.9R28) were selected for te study. Te tyre aspect ratio varied from.812 to.86 and b/d ratio from.2 to.31. Correspondence Ranjeet Kumar Assistant professor, RMD College of Agriculture and Researc Station, Ambikapur, Cattisgar, India 1. Hydraulic cylinder, 2. Displacement transducer, 3. Base plate, 4. Side rail Fig 1: Test set-up for tyre vertical deflection measurement ~ 216 ~

2 Journal of Parmacognosy and Pytocemistry Te tyre wit a given inflation pressure was loaded to te desired vertical load wit te dead weigts on a single weel tester. Te tyre was slowly brougt down and allowed to rest on te ard surface and te transducer output was recorded for deflection measurement. Te transducer was calibrated before conducting te tests. First, initial reading was recorded in a Data Acquisition System (DAS) for a zero position of te displacement. Ten using gauge blocks wit dimensions corresponding to te displacement, te final output was measured in te DAS. Te difference between initial and final readings of te DAS indicated te deflection. Te per cent deflection was calculated using te following formula. Tyredeflection, per cent δ Vertical tyre deflection, Tyresection eigt Flange eigt 1 3. Researc plan Te objective of tis study was to obtain vertical tyre deflection and contact area caracteristics of radial ply tyres at various normal loads and inflation pressure. In order to accomplis te objective four sizes of radial ply tyres were tested at seven different inflation pressures and six different normal loads on ard surface. Independent parameters: T R 28 (321mm 711mm) T R 28 (38mm 711mm) Tyre (radial-ply) 4 T R 28 (4mm 711mm) T R 28 (42mm 711mm) Inflation pressure, kpa (psi) 7 41(6), 69 (1), 97 (14), 124 (18), 2 (22), 179 (26), 27 (3) (), (6), (8), 9.32 (9), (11), (12) - for T1 Normal load, kn (kgf) (6), (8), 9.32 (9), (11), (12), (14) - for T (8), 9.81 (1), (12), (14),.696 (16), (18) - for T (9), (11), (13),.26 (), (17), (19) - for T4 Supporting surface 1 Hard surface Replication 3 Dependent parameters: Vertical tyre deflection, mm 4. Results Calibration of displacement transducer Te displacement transducer was calibrated for measurement of vertical tyre deflection. In order to calibrate te displacement transducer te cange in output voltage was recoded wit respect to cange in deflection. Te calibration curve (Fig. 2) sows a linear relationsip between output voltage and deflection. Te calibration equation was fed to te data acquisition system for real time measurement of vertical tyre deflection. 3 Deflection, mm y = 3.83x R 2 = DAS reading, mv Fig 2: Calibration of displacement transducer for tyre vertical deflection Effect of normal load and inflation pressure on tyre deflection Te relationsip between inflation pressure and tyre deflection ratio at different normal loads is sown in Fig. 3 and tat between normal load and tyre deflection ratio at different inflation pressure in Fig.4. ~ 217 ~

3 Journal of Parmacognosy and Pytocemistry Tyre T 1 (12.4 R 28) 4.9 kn kn kn 9.32 kn kn kn Tyre T 2 (13.6 R 28) kn kn 9.32 kn kn kn kn Tyre T 3 (14.9 R 28) kn 9.81 kn kn kn.696 kn kn Tyre T 4 (16.9 R 28) 9.32 kn kn kn.26 kn kn kn Fig 3: Relationsip between inflation pressure and tyre deflection at different normal loads for test tyres Te general trend sows tat tyre deflection decreased nonlinearly wit increase in inflation pressure from 41 to 27 kpa, wile it increased linearly wit increase in normal load for different test tyres. A similar trend was also observed by Abeel (1976), Fujimoto (1977), Yong et al. (1978), Plackett (1983), Sarma and Pandey (1996) and Tiwari (26). It is also noticed tat te rate of increase of deflection wit normal load is iger at lower values of inflation pressure tan at iger ones. Tis may be due to te fact tat carcass stiffness is not a constant value but canges wit inflation pressure. Tis finding is supported by Karafait and Nawatzki (1978). He suggested tat tyre carcass stiffness is influenced by its inflation pressure and it reduces wit inflation pressure. Tyre T 1 (12.4 R 28) Tyre T 2 (13.6 R 28) kpa 27 kpa kpa 27 kpa ~ 218 ~

4 Journal of Parmacognosy and Pytocemistry Tyre T 3 (14.9 R 28) 2 kpa 27 kpa Tyre T 4 (16.9 R 28) 2 kpa 27 kpa Fig 4: Relationsip between normal load and tyre deflection at different inflation pressures for test tyres Te relationsip between tyre deflection ratio and inflation pressure is represented by C 2 1 pi C2 pi C3 and tat between tyre deflection ratio and normal load by C W 4 C were, = deflection ratio, percent; p i = inflation pressure, kpa; W = normal load, kn; and C 1 to C = constants. It is clear from te curves tat due to iger stiffness, te larger tyres yielded smaller deflection compared to smaller tyres at te same inflation pressure and normal load. Deflection models Te deflection of agricultural tyres depends on teir normal load, air inflation pressure and b/d ratio. Te experimental data were analyzed to develop two deflection models based on regression analysis approac and dimensional analysis approac to predict deflection of agricultural tyres at different inflation pressures and normal loads. Regression analysis approac A second degree-regression equation was found to best fit te experimental data as given below. b b b 2 b C1 C2 W C3 pi C4 C Wpi C6 W C7 pi C8 pi C 9 d d d d were, b d = deflection ratio, per cent; = widt to diameter ratio of tyre, p i = inflation pressure, MPa; W = normal load, kn; and C 1 to C 9 = regression coefficients (Table.1). 2 Table 1: Coefficients of te developed deflection model based on regression approac Constants Coefficients Std. Error C C C C C C C C C R 2 =.98 A ig value of R 2 sows tat te experimental data fit te regression very well. Tis model was used to calculate te load-pressure combinations to get te desired level of 2, 24 and 28 per cent tyre deflection for eac test tyre. Tese values are given in Table 2 and te same were adopted to study te traction performance of test tyres under different soil conditions. ~ 219 ~

5 Journal of Parmacognosy and Pytocemistry Table 2: Inflation pressure required to acieve 2, 24 and 28 per cent deflection at different normal loads for te test tyres Tyre T1 (12.4R28) T2 (13.6R28) T3 (14.9R28) T4 (16.9R28) Inflation pressure, kpa (psi) Load, kn (kgf) At tyre deflection, % (7) 8 (12.3) 63 (9.1) 44 (6.4) 9.32 (9) 121 (17.) 92 (13.4) 71 (1.3) (11) 171 (24.8) 126 (18.3) 99 (14.4) 9.32 (9) 94 (13.7) 7 (1.1) (7.2) (11) 127 (18.4) 97 (14) 74 (1.7) (13) 171 (24.8) 12 (18.1) 98 (14.2) (11) 13 (14.9) 76 (11) (8) (14) 139 (2.2) (.3) 81 (11.8) (16) 194 (28.2) 137 (19.8) 18 (.6) (14) 1 (16.7) 87 (12.6) 66 (9.) (17) 14 (21) 111 (16.1) 87 (12.6) (19) 17 (2.4) 134 (19.4) 18 (.6) Dimensional analysis approac A matematical relationsip between tyre deflection and ground pressure was formulated using dimensional analysis approac as discussed in section Te experimental data of all te tyres were fitted to tis model and te values of te constants C 1 and C 2 were determined. Te generalized deflection model takes te following form, Pg C1 W d b C2 were, / = deflection ratio, per cent b = widt of te tyre, m; d = diameter of te tyre, m; W = normal load, kn; P g = (p i + p c), = ground pressure (W/A), kpa; A = tyre-surface contact area, m 2 and C 1 and C 2 = constants (Table.3). Tis model can be used to determine te tyre deflection in terms of ground pressure and normal load for radial-ply tyres aving b/d ratio in te test range of.2 to.31. Te nonlinear regression summary statistics and te coefficients of te developed deflection model is given in Table 3. Table 3: Nonlinear regression summary statistics for te deflection model based on dimensional analysis approac Source Sum of Squares DF Mean Square F Regression * Residual Total % Confidence Interval Parameter Estimate Std. Error Lower Upper C C * Significant at per cent level R 2.97 Te average ground pressure P g for a specific tyre at given normal load and inflation pressure can be derived from te so called generalized deflection cart, normally available from tyre manufacturers. However, P g can also be determined using a model developed in te present study. Validation and comparison of te developed model Te developed model based on regression analysis as 9 coefficients wile tat based on dimensional analysis as only 2 coefficients. Even toug te coefficient of determination of te model based on dimensional analysis is lower, but it is more compact and andy. Terefore, tis model is finally recommended to predict te deflection caracteristics of te radial-ply tyres. Te developed model was validated wit te test data wic were not included for developing te model of four test tyres. Te predicted and te experimental deflection ratio were plotted against te dimensionless term. From te curve (Fig. ) it can be found tat te model predicts te deflection ratio very well. Te statistical analysis for te validation and comparison of te developed model is sown in Table 4. Deflection ratio Experimental data developed model {(Pg/W)(b.d)} Fig : Comparison of te developed deflection model based on dimensional analysis approac wit te test data ~ 22 ~

6 Journal of Parmacognosy and Pytocemistry Table 4: Statistical analysis for model validation and comparison Mean Models RMSE % Model Effi. Bias % Deviation % R Obs. Sim. 2 Developed to R 2 = Correlation coefficient, Obs. = Observed, Sim. = Simulated. It was noticed from te analysis tat te model based on dimensional analysis was suitable to predict deflection of agricultural tyres as tis model gives a ig value of coefficient of determination (.948) wit a per cent deviation of -7.6 to 8.6 %. Te model efficiency of.989 indicates tat te developed model was acceptable. Te root mean square error (RMSE) of te developed model was 1.8 % and per cent bias was -2.2 also supported te acceptability of te developed model. 1. Tiwari VK. Te deflection and contact area caracteristics of bias-ply tyres, unpublised PD tesis, 26.. Conclusions Te test results sowed tat te tyre deflection increased nonlinearly wit decrease in inflation pressure from 27 to 41 kpa, wile it increased linearly wit increase in normal load for all te test tyres. It was also noticed tat te rate of increase of deflection wit normal load was iger at lower values of inflation pressure tan at iger ones. Te following models were developed to predict deflection of te tyres on a ard surface P 1.7 g db W were b = widt of te tyre, m; d = diameter of te tyre, m; = deflection ratio, per cent; W = normal load, kn; and P g = ground pressure (W/A), kpa. References 1. Abeels PJF. Tyre deflection and contact studies. Journal of Terra mecanics. 1976; 13(3): Abeels PJF. Tyre testing: Automatic recording of te tyre deformability. ASAE paper No. 89-1, St. Josep, MI, Anonimous. Yearbook. Tyre and Rim Association, ASAE Standards. ASAE S296.4 DEC9. General terminology for traction of agricultural tractors, selfpropelled implements, and traction and transport devices. St. Josep, Micigan: ASAE, ASAE Standards. ASAE EP496.2 DEC99. Agricultural macinery management. St. Josep, Micigan: ASAE, Burt EC, Bailley AC. Load and inflation pressure effects on tyres. Transactions of te ASAE. 1982; 2(4): Komandi G. Te determination of te deflection, contact area dimensions and load carrying capacity for driven pneumatic tyres operarting on concrete pavement. Journal of Terra mecanics. 1976; 13(1): Lyasko MI. Te determination of deflection and contact caracteristics of a pneumatic tyre on a rigid surface. Journal of Terra mecanics. 1994; 31(4): Sarma AK, Pandey KP. Te deflection and contact caracteristics of some agricultural tyres wit zero sinkage. Journal of Terra mecanics. 1996; 33(6): ~ 221 ~