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Journal of Terramechanics 50 (2013) 99–106
ofTerramechanics
Investigating the effect of velocity, inflation pressure, and verticalload on rolling resistance of a radial ply tire
Hamid Taghavifar ⇑, Aref Mardani
Department of Mechanical Engineering of Agricultural Machinery, Faculty of Agriculture, Urmia University, Iran
Received 14 March 2012; received in revised form 14 January 2013; accepted 17 January 2013Available online 21 April 2013
Abstract
A single-wheel tester facility at Department of Agricultural Machinery of Urmia University was utilized to investigate the effect ofvelocity, tire inflation pressure, and vertical load on rolling resistance of wheel. A Good year 9.5L-14, 6 radial ply tire was used asthe tester wheel on clay-loam soil and was installed on a carriage traversing the length of soil bin. Three inflation pressures of 100,200, and 300 kPa as well as three levels of velocity (i.e. 0.7, 1.4, and 2 m/s) and five levels of vertical load applied on wheel (i.e. 1, 2,3, 4, and 5 kN) were examined. Covariance analysis (ANCOVA) of resulted data revealed that rolling resistance is less effected by appli-cable velocities of tractors in farmlands but is much influenced by inflation pressure and vertical load. An approximate constant rela-tionship existed between velocity and rolling resistance indicating that rolling resistance is not a function of velocity particularly inlower ones. Moreover, it was observed that increase of inflation pressure results in decrease of rolling resistance. Additionally, increaseof vertical load brings about increase of rolling resistance which was estimated to have polynomial relation with order of two. A modelcomprising tested variables was developed with relative high accuracy.� 2013 ISTVS. Published by Elsevier Ltd. All rights reserved.
Keywords: Tire; Soil bin; Rolling resistance; Velocity; Inflation pressure; Vertical load
1. Introduction
The objective of present study was to evaluate the effectsof velocity, tire inflation pressure, and vertical load of trac-tor’s wheel on rolling resistance in a controlled conditionusing a single-wheel tester and a soil bin. Wheel is playingan important role in agricultural and off-road vehicles sinceit is always in contact with farm, nearly all of forces andmoments influencing the motion of vehicle are applied toit, and also it has very noticeable impact on machinedynamics. Hence, soil–wheel interactions should be consid-ered enormously regarding the fundamental role of wheels
0022-4898/$36.00 � 2013 ISTVS. Published by Elsevier Ltd. All rights reserve
http://dx.doi.org/10.1016/j.jterra.2013.01.005
⇑ Corresponding author. Address: Department of Mechanical Engi-neering of Agricultural Machinery, Faculty of Agriculture, UrmiaUniversity, Nazloo Road, Urmia 571531177, Iran. Tel.: +98 441 2770508; fax: +98 441 277 1926.
E-mail address: [email protected] (H. Taghavifar).
in traversing, steering, and traction. As tractor is one ofmajor agricultural vehicles, much more attention shouldbe paid on wheel–soil interactions of tractors. Rolling resis-tance, soil compaction, energy loss, and wheel slip are ofboth crucial and undesirable parameters produced bysoil–wheel interactions. Amongst the mentioned items,rolling resistance has particularly been discussed by manyresearchers as a very influential result of soil–wheel interac-tions, considering its resistive effect while initiating a wheelto roll and also its importance in fuel consumption. Energyloss in agricultural tires because of inaccurate managementwas reported to be about 575 million liters per year in USA[1]. Hence, its reduction to the lowest possible level hasalways been analyzed theoretically, analytically, andexperimentally.
Fundamentally, rolling resistance is a moment appliedto wheel against with the direction of movement, while aforce is required to move the wheel forward [2]. It is
d.
100 H. Taghavifar, A. Mardani / Journal of Terramechanics 50 (2013) 99–106
basically an unwanted force applied to wheel while startingto roll on a surface caused by the energy required for soil orwheel deformation. Hence, rolling resistance is closelyrelated to soil deformation under the wheels and its mea-surement without any proper instrument and in uncon-trolled condition would not provide completely reliableresults. Moreover, its evaluation seems more troublesomewhen the wheel rolls since the condition becomes evidentlyvariable during the movement.
Morin [3] investigated the effect of rolling resistance onwagons in 1840 and 1841. Theoretical efforts were carriedout in order to survey the problem by Bernstein [4]. Bekkar[5] scientifically studied and established the relationsbetween wheel and soil. Based on his equation (Eq. (1)),amount of rolling resistance is influenced by variety ofparameters may be expressed by:
R ¼ 3w2nþ22nþ1ð Þ
ð3� nÞ2nþ22nþ1ð Þðnþ 1ÞðKC þ bKuÞ
12nþ1ð Þd nþ1
2nþ1ð Þ ð1Þ
KC and Ku have been yielded from pressure sinkage equa-tion (Eq. (2)) as below:
P ¼ KC
bþ Ku
� �Zn ð2Þ
where w is vehicle weight, n is sinkage exponent, b is thesmaller dimension of the rectangular contact area, Z isthe sinkage, and KC and Ku are the soil condition parame-ters. The required energy to compact the soil beneath thewheel during movement for a definite distance is equal witha resistive force against movement multiplied by the dis-tance. This resistive force (i.e. rolling resistance) is sug-gested to be as follows:
R ¼ bw
Z zmax
0
KC
bþ Ku
� �ZndZ ð3Þ
Validity of equation above in order to predict rollingresistance based on soil deformation was offered by Wong[6] for wheel diameters more than 50 cm and sinkage levelsless than 15% of wheel diameter.
Later, Hetherington and Littleton [7] suggested a simpleapproximate equation for calculation of rolling resistancein terms of geometry, load and accepted soil constants asfollows.
The proposed model describing rolling resistance ofwheel over sand is following as:
R ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2W 4
bd2cNq
3
sð4Þ
where R is rolling resistance, W is vertical load acting onwheel, b is width of wheel, d is wheel diameter, c is bulkdensity of sand, and Nq is recognized as Terzaghi’s bearingcapacity solution.
There are numerous parameters affecting rolling resis-tance of them wheel diameter, tire inflation pressure, mul-tipass, soil texture, sinkage, wheel slip, normal load, andvelocity can be included. In 1971, the effect of wheel speed
on rolling resistance was verified by Pope [8]. Elwaleedet al. [9] reported the effect of inflation pressure on motionresistance in their experiments. Way and Kishimoto [10]surveyed soil–wheel interaction and approved the influenceof velocity on rolling resistance especially for high speeds.Zoz and Grisso [11] reported similar results in their exper-iments. McAllister [12] studied reduction in the rollingresistance of wheels determining the values of the coeffi-cient of rolling resistance (CRR) for wheels. The resultsindicated that reductions in CRR can be produced byreducing inflation pressure and vertical load. In 2007, Cou-termarsh [13] claimed that in dry sand, the rolling resis-tance has linear relation with velocity until the tire startsto plane, and then it becomes stabilized or decreases.
With comparison, it is obvious that less attention hassimultaneously been given to effects of velocity, verticalload and tire inflation pressure in rolling resistance usinga single-wheel tester in a soil bin since it prepares con-trolled condition to evaluate the effects precisely and accu-rately. Hence, in this study these effects are discussed topresent exact and accurate results especially for applicableforward wheel velocities of tractors in the farm since mostof previous attempts were conducted for high speeds.
This study will further investigate following intentionsexperimentally using a soil bin and a single-wheel testerproviding absolutely reliable test facility to obtain precisedata:
� Effect of velocity on rolling resistance of tire at varyingconditions of vertical loads and inflation pressures par-ticularly for operational velocities of tractors.� Impact of various inflation pressures on rolling resis-
tance to describe their interrelation at different velocitiesand vertical loads.� The relation between vertical applied load to tire and
rolling resistance for different velocities and inflationpressures.
2. Materials and methods
A long soil bin was built in 2010 in the Faculty of Agri-culture, Urmia University, Iran. This soil bin has 23 mlength, 2 m width and 1 m depth [14]. This long channelhad the ability to hold a wheel carriage, a single-wheel tes-ter, and different tillage tools to be moved altogether in thelength of the soil bin. The facility to fill the channel withvarious soil textures and different moisture contents pro-vided higher advantage in comparison with uncontrolledconditions. A three-phase electromotor of 30 hp was usedto move a carriage through the length of soil bin by meansof chain system along with the wheel-tester when the car-riage had the ability to traverse at the speed of about20 km/h. The output shaft of the electromotor was con-nected to the drive shaft of the chains that pull the carriageforward or reverse. An inverter providing variable frequen-cies was used to supply power of electromotor in order to
Fig. 1. Soil bin system set up and including carriage and a single wheel-tester.
Fig. 3. Single-wheel tester installed on the carriage traversing the length ofsoil bin.
H. Taghavifar, A. Mardani / Journal of Terramechanics 50 (2013) 99–106 101
reach varying velocities. Another advantage of this systemis the facility of adjusting braking and starting accelerationof electromotor which results in decrease of inertia forces.Four S-shape transducers with the capacity of 200 kg werecalibrated and then were placed at proper places horizon-tally in parallel pattern between carriage and single-wheeltester and these transducers were interfaced to data acqui-sition system included a data logger, enabled monitoringthe data on a screen and simultaneously, the data were sentto a computer with frequencies of around 30 Hz. A single-wheel tester was assembled to the carriage system with fourS-shape transducers to measure the rolling resistance alter-ations caused by motion of wheel in various treatmentsbeing tested. The utilized driven tire was Good year9.5L-14, 6 radial ply agricultural tractor tire which is usedin John Deere tractors. The system set up is shown in Fig. 1and schematic diagram of designed soil bin is shown inFig. 2.
The measured volume of soil bin was assessed to be46 m3 and consequently was filled with soil. To initiate theprocess, the electromotor generated power for the carriagemovement based on adjusted velocity by an inverter by con-nection between the shafts of electromotor and chain sys-tem. An optic tachometer was used to measure the speedof carriage while an inverter could produce variety of veloc-ities for the carriage. This system is equipped to railroadsinside which are two rolling wheels to carry and bear theweight of carriage. Hence there was no load entering to
Fig. 2. Procedure of power transmission
wheel tester from the carriage. Also, the vertical load couldbe adjusted by a power bolt which was connected to wheelframe from one end and to the carriage from another end.By turning the power bolt, vertical displacement of wheeloccurred in proportion with the amount of loading. Thegenerated load was measured by a vertical load cell thatwas placed between power bolt and the wheel frame. Themeasured load was then transmitted to digital indicatorenabling to reading the value. Loading could stop or con-tinue in order to reach the desired value.
The movement of carriage by chain system generatedtraction of single-wheel tester in the soil bin and accord-ingly, transducers sent signals to the data acquisition sys-tem which were indicators of rolling resistance of wheeland eventually, data acquisition system enabled monitoringthese data and also transferring them to the computer.Microsoft Office Excel was used to process, evaluate anddetermine the relation between velocity and rolling resis-tance. Fig. 3 illustrates the single wheel-tester installed onthe carriage through four parallel and horizontal load cellstraversing the length of soil bin.
This experiment was conducted with the different veloc-ities of 0.7, 1.4, and 2 m/s at three inflation pressure ofwheel at three levels of 100, 200, and 300 kPa and five dif-ferent normal loads of 1, 2, 3, 4, and 5 kN on wheel tester.Summary of treatments being tested is shown in Table 1.
The soil bin was filled with clay-loam soil to simulate thereal condition of farms that exists in most of regions inUrmia, Iran. Particular equipments were used to organize
and schematic diagram of soil bin.
Table 1Summary of experiment conducted.
Normal load (kN) Independent parameters Dependent parameter
Inflationpressure (kP)
Velocity(m/s)
1 100 0.72 200 1.43 300 2 Rolling resistance45
Table 2Soil constituents and its measured properties.
Item Value
Sand (%) 34.3Silt (%) 22.2Clay (%) 43.5Bulk density (kg/m3) 2360Frictional angle (�) 32Cone index (kPa) 700
Fig. 4. Contact area of tire with soil in variety of treatments along soil binchannel.
Fig. 5. Taken image in RGB space (a) and processed image (b).
102 H. Taghavifar, A. Mardani / Journal of Terramechanics 50 (2013) 99–106
soil bed including leveler and harrow since it is very impor-tant to have well-prepared soil inside soil bin for acquiringreliable and precise results from this experiment. Soil afterprocessing was cultivated and leveler and roller wereutilized up to reaching the desired cone index. It shouldbe noted that owing to the capacious dimensions of soilbin, only with two times preparation of soil in soil bin,all the experimentations were conducted in similarconditions.
The cone index of soil was measured by a RIMIK digitalpenetrometer device (CP20) with tip cone angle of 30�, astandard bar, a load cell and chipset according to ASAEStandards S313.2 and the penetration into the soil was per-formed with 0.02 m/s constant velocity. Soil constituentsand its properties are defined in Table 2.
2.1. Image processing method for contact area determination
White powder was spread on periphery of tire–soil inter-face at each of the treatments in order to determine thecontact area of wheel. The tests were replicated three timesfor higher accuracy. Fig. 4 illustrates the contact area oftire with soil in variety of treatments. This phase consistedof a digital camera, a glass plane to put the camera on andMATLAB� software to process the images. The imageswere taken from constant and fix distance on a glass planeattached to the carriage while moving alongside the soil binchannel. The images were taken at RGB space. Fig. 5aillustrates a taken image and its color components. Utiliz-ing s component in HSV space as well as b in Lab space, anexcellent separation of tire track and the image backgroundwas obtained. Pixel intensities of both components werenormalized at the range of 0–1. The two components werethen added and the result was again normalized at the samerange.
X 1 ¼ ðsþ bÞ ð5ÞTo achieve more enhanced separation of image back-
ground and tire track, Gamma Transform was used asfollows:
X 2 ¼ ðX 1Þa ð6Þwhere in the case of this investigation, the optimal a wasobtained to be 2. Afterwards, in order to separate tire trackand background a threshold level was required which Ottsumethod was utilized to gain optimum level. Binary imagewas obtained using the resulted image of dilation and thres-holding. Fig. 5b demonstrates the binary image in whichwhite pixels indicate the tire track. The colorful image ta-ken with digital camera is shown in figure in which tiretrack is signified with black pixels.
Eventually, the objects were extracted from binaryimages and their qualifications such as pixel area (numberof pixels in the object region) and calibrated area (number
Fig. 6. Effect of contact area on rolling resistance at three inflationpressure levels and under five vertical loads.
Fig. 7. Effect of velocity on rolling resistance at three inflation pressures of(a), (b), and (c) at 100, 200, and 300 (kPa), respectively.
H. Taghavifar, A. Mardani / Journal of Terramechanics 50 (2013) 99–106 103
of pixels in the object region � ratio of actual to predictedvalues) were measured in cm2. An index with the pre-defined dimensions was used beside each image to calibratethe determinations and yielding contact area.
3. Results and discussion
3.1. Effect of velocity on rolling resistance
The obtained data were processed for five levels of ver-tical load, three levels of inflation pressure, and three levelsof velocity in order to determine the effect of velocity onrolling resistance. Fig. 6 illustrates the effect of velocityon rolling resistance at three different inflation pressuresof 100, 200, and 300 kPa, respectively when vertical loadsapplied on wheel varied at five diverse levels.
Given that contact area of the tire is needed to discussthe rolling resistance with the velocity, contact area wasmeasured prior to each run of treatments under differentloads and inflation pressures. Rolling resistance as a func-tion of contact area was investigated and the results signi-fied increase of rolling resistance due to increase of contactarea (Fig. 7). At each of three inflation pressures, increaseof vertical load caused increase of contact area. Basicallyincrease of vertical load at constant value of inflation pres-sure results in increase of tire deflection and deformationwhich in its turn, provides increase of rolling resistance.
Analyzing the acquired data, amount of rolling resis-tance at all of treatments is observed to be approximatelyconstant indicating that change of velocity is not effectiveparameter to modify rolling resistance. Results of the pres-ent study showed there were no significant differences ofrolling resistance at the velocities varying in the range of0.7–2 m/s (P < 0.01) as presented in Table 3. W1, W2,W3, W4, and W5 in Fig. 7 are representatives of 1, 2, 3,4, and 5 kN, respectively. It should be mentioned that foreach run of tests in Fig. 6, neither contact area nor rollingresistance were changed in the range of tested velocities.Additionally it is inferred that at each constant inflationpressure, increase of rolling resistance under higher verticalloads indicates increase of tire–soil contact area.
Fig. 8 represents that despite of reported results signify-ing increase of rolling resistance for speeds varying from40 m/s to higher ones, rolling resistance has negligiblychanged in this study when velocity increased from 0.7 to2 m/s. Monitoring Fig. 7 it is inferred that for higher verti-cal loads in concern with each treatment, rolling resistanceincreases significantly.
In similar studies, Pope [8] reported that based on theo-retical investigation rolling resistance was predicted todecrease from 24 to 20 lb in the velocity range of 2–15 ft/min and wheel load of 124 lb, however, two tested wheelsindicated even less variation in the similar range of velocityand wheel load. Similarly, in case of wheel load 204 lb, thepredicted difference in rolling resistance between theextreme wheel speeds was 8.1 lb (0.036 kN) and the mea-sured values were 6.5 lb (0.028 kN) and 7.3 lb (0.032 kN)for tested wheels. Way and Kishimoto [10] reported anincreasing linear relation between velocity and rolling resis-tance. This experiment was conducted for high velocitiesvarying from 11 m/s and upper ones which are notfrequently used as operational speeds of tractors in the
Table 3Results of variance analysis of factorial test with variables of velocity (V), inflation pressure (P) and vertical load (W).
Variation source Degrees of freedom Sum of squares Mean square Fs
Repetition 2 10232.6 5116.3 0.20ns
Treatment 44 4780267.1 108642.4 4.45**
P 2 674956.8 337478.4 13.83**
V 2 11362.6 5681.3 0.23ns
W 4 1862375.9 465,594 19.09**
P � V 4 17313.7 4328.4 0.17ns
P �W 8 981193.5 122649.2 5.03**
V �W 8 27069.4 3383.6 0.13ns
P � V �W 16 1205995.1 75374.7 3.09**
Error 88 24387.5Total 134 4814887.1
ns – not significant.** P < 0.01.
Fig. 8. Effect of tire inflation pressure on rolling resistance at three levels of velocity.
104 H. Taghavifar, A. Mardani / Journal of Terramechanics 50 (2013) 99–106
farmlands. Unlikely, the results of this study is validated bythe results reported by Zoz and Grisso [11] describing slighteffect of velocity on rolling resistance in regular runningvelocities of tractors. The results reported by Coutermarsh[13] strengthens the results of present study while states atvarious inflation pressures, increase of velocity up to about20 miles/h (8.9 m/s) does not seem to be effective althoughfor higher speeds, rolling resistance commences to rise.
3.2. Effect of inflation pressure on rolling resistance
During this experiment to obtain information aboutimpact of inflation pressure on rolling resistance, five levelsof vertical load (1, 2, 3, 4, and 5 kN) and three levels ofvelocity (0.7, 1.4, and 2 m/s) varied to investigate the roleof inflation pressure on rolling resistance at diversity of ver-tical loads and velocities. Fig. 8 clearly illustrates eachtreatment and obtained results.
It is obvious that for higher inflation pressures rollingresistance is likely to decrease particularly when higher val-ues of vertical loads are applied to the wheel. Consideringthe fact that reduction of rolling resistance is relativelydependent function of vertical load and inflation pressure
and regarding the fact that modification of inflation pres-sure seems much more practical, increase of inflation pres-sure is influential parameter to reach this purpose.
In similar studies reduction of tire inflation pressure by55 kPa caused increased rolling resistance by 9.9% whichfurther supports the experimental results obtained fromthe current investigation [9]. Based on presented results,decrease of rolling resistance at higher inflation pressuresis absolutely distinct while rapidly decreases at higher ver-tical loads. This phenomenon is possible to be interpretedregarding the important impact of tire deformation on roll-ing resistance since continuous tire deformation duringrolling under high vertical loads require greater energy.Accordingly, increasing inflation pressure and decreasingtire deformation result in reduction of energy loss. Theresult is spotlighted considering that energy loss becauseof incorrect management in agricultural tires is about575 million liters per year in USA [1].
3.3. Effect of vertical load on rolling resistance
Normal load applied on wheel was investigated as aneffective parameter to assess its impact on value of rolling
Fig. 10. Predicted values with respect to measured values utilizingproposed equation.
H. Taghavifar, A. Mardani / Journal of Terramechanics 50 (2013) 99–106 105
resistance. Fig. 9 clearly depicts these variations at threeinflation pressures of 100, 200, and 300 kPa as (a), (b),and (c), respectively.
It is noticeable that increase of vertical load is approxi-mately polynomial with order of two function of rollingresistance and as it was stated in Section 3.1, rolling resis-tance is not a function of velocities conducted in this study.
Ineffectiveness of velocity on rolling resistance is obvi-ous in Fig. 9. Although Fig. 9 suggests a linear relationbetween vertical load and rolling resistance but in contrast,it seems more reasonable to describe their relation as aquadratic equation while rolling resistance is function ofvertical load. In this study Eq. (7) was obtained by multipleregression method comprising the tested variables. Thisequation was evaluated against experimental resultsobtained indicating relative high correlation and reason-able accurate predicting rolling resistance (RR) (Fig. 10).
RR ¼ 10W 2 þ 3:2W� 0:37P� 25Vþ 103:56 ð7Þwhere W is vertical load (kN), P is inflation pressure (kPa),and V is velocity (m/s).
The experimental results obtained from the presentstudy further indicate that the relation between rolling
Fig. 9. Effect of vertical load on rolling resistance at three inflationpressures of (a), (b), and (c) at 100, 200, and 300 (kPa), respectively.
Fig. 11. Theoretical relation between vertical load and rolling resistanceusing Wismer and Luth suggested equation.
resistance and vertical load can be described by polynomialwith order of two with higher correlation rather than poly-nomial with degree of 4/3 suggested by Hetherington andLittleton [7].Of conventional empirical models, Wismerand Luth [15] equation can be exemplified based on wheelnumerics as follows (Eq. (4)):
R ¼ 1:2� W 2
CI � b � d þ 0:04W ð8Þ
where W is vertical load (kN), CI is cone index (kPa), b iswidth of tire (m), and d is wheel diameter (m).
Fig. 11 demonstrates the relation between vertical loadand rolling resistance using Eq. (8) where CI is 700 kPa,b is 0.2 m, and d is 0.7 m.
Obviously, the results of current study expressing inter-relation between vertical load and rolling resistance suggestan acceptable correlation. Reliability of this investigation isapparently validated by Eq. (8) and Fig. 11.
Table 3 demonstrates the results of variance analysis(ANCOVA) utilizing factorial test.
106 H. Taghavifar, A. Mardani / Journal of Terramechanics 50 (2013) 99–106
4. Conclusion
Single wheel-tester in a soil bin was utilized to investi-gate the influence of prominent parameters like velocity,inflation pressure, and vertical load on rolling resistanceaccurately. The conducted levels consisted of three levelsof velocity (i.e. 0.7, 1.4, and 2 m/s), three levels of inflationpressure (i.e. 100, 200, and 300 kPa), and five levels ofvertical load (i.e. 1, 2, 3, 4, and 5 kN). Each treatmentwas performed for the wheel passing through the lengthof soil bin while transferring data to the computer by fourtransducers. Covariance analysis of resulted data revealedsignificant consequences follows:
1. The rolling resistance of wheel is increasingly influencedby inflation pressure and vertical load than velocitiesbeing investigated in this study.
2. The rolling resistance has approximately constant rela-tion with low velocities (0.7, 1.4, and 2 m/s). Basically,operational speeds of tractors in the farm cannot exceedto high levels, Hence these velocities were investigated ina soil bin indicating no considerable effect on rollingresistance.
3. Based on obtained results of this study, increase of infla-tion pressure suggests reverse relation with rollingresistance particularly at higher values of vertical load.
4. Vertical load applied on wheel has considerable impacton rolling resistance and its increase results inpolynomial with order of two increase of rollingresistance.
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