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Development of a fuel consumption equation: Test case for a tractor chisel-ploughing in a clay loam soil
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
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ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110
Research Paper
Development of a fuel consumption equation: Test case for a tractor chisel-ploughing in a clay loam soil S.H. Karparvarfard*, H. Rahmanian-Koushkaki Biosystems Engineering Department, College of Agriculture, Shiraz University, Shiraz, Iran
article info
Fuel consumption and tillage draught were measured when chiselling in a clay loam soil in
Article history:
Badjgah Research Station, Shiraz University, Shiraz, Iran. An 81 kW tractor (MF-399)
Received 22 March 2014
instrumented with a data acquisition system was used to measure fuel consumption,
Received in revised form
actual forward speed, theoretical forward speed, slip and implement draught. The effects
18 November 2014
of blade width (5 and 10 cm), tillage depth (10, 15 and 20 cm) and actual forward speed (3, 4
Accepted 25 November 2014
and 5 km h1) upon fuel consumption were investigated. Fuel consumption was assumed
Published online
to be a function of wheel numeric, slip, net traction ratio, rolling resistance ratio, chiseltool aspect ratio and actual forward speed. Collected data were used to model the tractor
Keywords:
fuel consumption using dimensional analysis approach. Results were compared to fuel
Data acquisition
consumption rates as predicted by ASAE Standards (D497.4). The comparisons showed that
Dimensional analysis
the standard overestimates fuel consumption by 26e53%. Results from regression (F-test)
Modelling
between predicted and measured fuel consumption data showed that the slopes for fuel
Massey Ferguson MF-399
consumption with the 5 and 10 cm blade widths were not significantly different from 1:1 line (P 0.05). Consequently, the fuel consumption rate can be successfully predicted by the model with good accuracy. © 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Fuel is the source of energy for the tractor providing for the performance of work and propelling the tractor to overcome implement draught (Smith, 1993). There are many parameters in tillage operation that affect the fuel consumption of a tractor, such as soil texture, climate, relative humidity, tractor
type (two or four wheel drive), tractor size and tractor implement relationship. Therefore, tractor fuel consumption is not constant and varies from one to another situation (Nielsen & Sorensen, 1993). To increase efficiency of agricultural production; it is necessary to increase machine working efficiency. Taylor (1980) estimated that in the U.S. for each 1% improvement in traction efficiency, 284e303 million litres of fuel could be
Abbreviations: MF, Massey Ferguson; ASAE, American Society of Agricultural Engineers; ASABE, American Society of Agricultural and Biological Engineers; PTO, Power Take-off; NRMSE, Normalised Root Mean Square Error; MBE, Mean Bias Error; RNAM, Regional Network for Agricultural Machinery. * Corresponding author. Tel.: þ98 91 7316 0457. E-mail address: [email protected] (S.H. Karparvarfard). http://dx.doi.org/10.1016/j.biosystemseng.2014.11.015 1537-5110/© 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
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Nomenclature Symbols C In-field working capability of chisel plough (ha h1) CI Soil cone index (kPa) D Working depth (m) Overall energy efficiency (%) Eo Tractive efficiency (%) Et f Function FC Experimental fuel consumption (l h1) Predicted fuel consumption (l kW1 h1) FCp Draught force (N) Fd Rolling resistance (N) Fr g Gravitational acceleration (m s2) K Intercept of logarithmic line (constant) L Length (m) M Mass (kg) N Slope of logarithmic line (constant) Drawbar power (kW) Pdb Equivalent PTO power (kW) Peq Fuel consumption per unit area (l ha1) Qf Hourly fuel consumption (l h1) Qi Brake-specific fuel consumption (l kW1 h1) Qs S Driving wheel slip (%) Unloaded overall tyre diameter (m) Td Unloaded tyre section width (m) Tw Actual forward speed (km h1) Va Theoretical forward speed (km h1) Vt W Blade width (m) Dynamic wheel load (N) Wd Static wheel load (N) Ws X Load ratio define as equivalent PTO power required by an operation to the maximum available from the PTO, dimensionless Wheel base (m) Xwb Z Drawbar height (m)
saved annually. Due to increasing world population and limited non-renewable resources, especially fossil fuels, it is necessary to reduce and manage fuel consumption in various agricultural activities. Many studies have been conducted to measure draught, power requirement and fuel consumption of tillage implements (Al-Janobi, 2000; Sahu & Raheman, 2006; Serrano et al., 2003, 2007). Predicting tractor fuel consumption can lead to more appropriate decisions on tractor management. Several studies have been conducted in this area. Khalilian, Batchelder, Self, and Summers (1984) presented the fuel equations corresponding to different diesel engine air intake types. Results showed that fuel efficiency equations more nearly reflect actual data than ASAE equations where predictions were at least 20% higher than experimental data. Raper, Schwab, Balkcom, Burmester, and Reeves (2005) developed an equation to estimate fuel consumption during deep tillage for John Deere 8300 tractors. Power-take-off data was converted to drawbar power using data available from the
Nebraska Tractor Test, and they presented a fuel consumption equation based on drawbar power. Fathollahzadeh et al. (2010) developed a fuel consumption model for a John Deere 3140 tractor at various working depths of mouldboard plough. Their results showed a linear relationship between fuel consumption and working depth of the mouldboard plough. Rahimi-Ajdadi and Abbaspour-Gilandeh (2011) presented models based on artificial neural network and stepwise multiple range regression for prediction of tractor fuel consumption. Fuel consumption was assumed to be a function of engine speed, throttle and load conditions, chassis type, total tested weight, drawbar and PTO powers. Results indicated that the artificial neural network and stepwise regression models gave similar determination coefficients (R2 ¼ 0.98 and R2 ¼ 0.97, respectively) while the artificial neural network provided relatively better prediction accuracy (R2 ¼ 0.93) compared to stepwise regression (R2 ¼ 0.91). Dimensional analysis is a mathematical approach concerning dimensionally homogeneous equations. The form of such equations is independent of the fundamental units used. This is the basis of the theory of dimensional analysis in Buckingham's theorem (Langhaar, 1980). The dimensional analysis is a method by which one can deduce information about a phenomenon from the single premise that the phenomenon can be described by a dimensionally correct equation among pertinent variables. The result of a dimensional analysis of a problem is a reduction in the number of variables in the problem. This results in considerable savings in both cost and labour during the experimental determination of the function (Srivastava, Goering, Rohrbach, & Buckmaster, 2006). Fakhraei and Karparvarfard (2006) developed a general equation for estimating the tractive efficiency of a Universal tractor (U-445, 30 kW) using dimensional analysis. Drawbar force, rolling resistance force of the drive wheels, slip of drive wheels, soil cone index, theoretical and actual velocity and dynamic load on driving wheels were either measured or calculated. This equation can be employed to estimate tractive efficiency of various combinations of tractors and ploughs provided the range of dimensionless terms fall within the limits experienced in the research. By use of this equation and through employing the initial data for tractor and soil, the tractive efficiency could be well predicted. Hosseini and Karparvarfard (2011) developed appropriate equations for predicting draught and vertical forces on a chisel tine using dimensional analysis. The effects of four levels of rake angle (10, 15, 20 and 25 ), three levels of forward speed (1.5, 3 and 4.5 km h1) and three levels of tine aspect ratio (1.5, 2 and 3) on horizontal and vertical forces acting on a chisel plough tine (100 mm wide) were investigated. Results of F-test at 5% probability showed no significant differences between values of slope and intercept of measured values vs. predicted values plot as compared to 1:1 line. Statistical indices NRMSE and MBE emphasise precision of the adopted analytical model. In addition, other results showed an increasing trend of draught force for variation in input parameters. This finding is supported by similar results derived from ASABE general equation. The main objectives of the present study were to develop fuel consumption equation for an 81 kW tractor when carrying implement (chisel plough) in 5 and 10 cm widths.
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Tractor factors were: wheel numeric,1 slip, net traction ratio and rolling resistance ratio. Implement factors were chiseltool aspect ratio and actual forward speed. Modelling of the tractor fuel consumption was conducted using dimensional analysis.
2.
Materials and methods
2.1.
Tillage site
Field experiments were conducted in autumn 2012 at Badjgah Research Station (29 320 N 52 350 E), Shiraz University located in NW Shiraz, Iran. The soil texture at the experimental site was clay loam (35% sand, 30% silt, and 35% clay) with previous wheat crop residue. The plot size was 10 m wide and 50 m long (500 m2). The total number of the plots was 162. The total area used for the experiments was 81,000 m2.The mean soil moisture content (d.b %), bulk density (g cm3) and cone index (kPa) were measured as 8.4 ± 3.8, 1.3 ± 0.2, 2840 ± 710 respectively. These parameters were measured at ten random locations of each plot prior to the tests. Soil core samples for determining moisture content and bulk density were collected using a cylindrical core sampler. These samples were measured for 5 cm increments of depth down to 20 cm. Collected samples were immediately placed in plastic bags to conserve moisture during transfer to the laboratory. The wet samples were weighed, and then put in an oven at 105 C for 24 h. The dry samples were weighed and moisture content and bulk density calculated. Cone index values were obtained by taking penetrometer readings at 5 cm increments to depths of 25 cm at several locations of the plots using a cone penetrometer according to ASAE Standards S313.2 with a cone base area of 130 mm2 (ASAE Standards, 1998b).
2.2.
Tractor and tillage implement treatments
A front wheel assist, Massey Ferguson tractor (MF-399) (ITM, Tabriz, Iran) with a maximum engine power of 81 kW was used in field evaluation (Table 1). A mounted-type chisel plough (Rau, Germany) with 9 spring curved shanks in 2 rows and 2 gauge wheels was used in this study. Working width of the plough was 225 cm (Fig. 1). Treatments consisted of three levels of actual forward speeds (3, 4 and 5 km h1), three levels of tillage depths (10, 15 and 20 cm), two levels of blade widths (5 and 10 cm) and three replications, giving 3 speeds 3 tillage depths 2 blade widths ¼ 18 experimental cases 3 replications per case ¼ 54 tests.
2.3.
Table 1 e Specifications of MF-399 tractor used. Characteristics Maximum power at 2200 rpm Total weight Front tyres Rear tyres Inflation pressure, front tyre Inflation pressure, rear tyre Wheel base Front axle width Rear axle width Drawbar height Weight on front axle Weight on rear axle
Symbols used in the equations e e e e e Xwb e e Z e e
Unit 81 39.34 14.9e24 18.4/15e34 204 136 2640 1726e2094 1518e2428 433 14.82 24.52
kW kN e e kPa kPa mm mm mm mm kN kN
and tractor are shown in Figs. 2 and 3. The data acquisition system consisted of an electronic board and a portable computer linked via a USB port. Data were sampled at 0.1 s intervals. Rate of fuel consumption was measured with two turbine flow transducers (VISION-1000, Remag, Bern, Switzerland) having a range of 0.1e2.5 l min1. One transducer was accommodated between the fuel filter and the injector pump of the tractor; another was used to measure the excess fuel returning from both injectors and injection pump to the fuel tank. The actual forward speed was measured using a fifth wheel attached to a suitable position underneath the tractor chassis, while the theoretical forward speed was measured on the right rear wheel. Two shaft encoders (Autonics, South Korea) with 500 pulse revolution1 were used in this study. One shaft encoder was mounted on the fifth wheel and used to measure actual forward speed. Another was mounted on the right rear wheel for measuring theoretical forward speed. The speed data were input to a microcontroller to calculate the wheel slip and generate a digital display (Pranav, Pandey, & Tewari, 2010). The following equation was used to calculate the slip percentage: S¼
1
Va Vt
100
Data acquisition system
An instrumentation package for measuring the tractor performance was developed. This package included the data acquisition system and the transducers for measuring fuel consumption, actual forward speed, slip and implement draught. Specifications of the transducers used in the package are listed in Table 2. The general arrangement of transducers 1
Wheel numeric is a dimensionless group which provides an indication of the soiletyre interaction for a given tyre and load.
Fig. 1 e Mounted chisel plough used in this study.
(1)
26
Keli, China Findlay Irvine, Scotland Bisat Electronic, Iran S type, range 0e50 kN, precision grade: C3 Soil penetration resistance at a depth of 50 cm with 1 cm intervals Sampling rate: 0.1 s, Total number of I/O ports: 11 DEE-5t, Traction dynamometer Bush (SP-1000), Penetrometer Electronic board
Measurement of fuel consumption Measurement of actual forward speed and theoretical forward speed Measurement of draught Measurement of cone index Acquisition of data Remag, Switzerland Autonics, South Korea 0.1e2.5 l min (22,000 pulse l ), ±3% 500 pulse revolution1, ±5% Vision-1000, Turbine flow transducer (2 Nos.) E50S8-500-3-N-24, Shaft encoder (2 Nos.)
A traction dynamometer (Keli, China) was used to measure the plough draught according to RNAM2 (1983) method. The plough was mounted on the MF-399 tractor which was used to support the plough but did not provide power. The unit was drawn by another tractor (John Deere 4450) through the traction dynamometer mounted on the tractor hitch. Hence, the plough draught could be calculated once the rolling resistance of the MF-399 tractor was subtracted (Zhang et al., 2003). Dynamic wheel load was calculated using following equation (Diserens, 2010; Moitzi, Haas, Wagentristl, Boxberger, & Gronauer, 2013): Wd ¼ Ws þ Fd
Z Xwb
1 2
(2)
where Wd is the dynamic wheel load in N; Ws is the static wheel load in N; Fd is the draught force in N; Z is the drawbar height in m and Xwb is the wheel base in m. Equation (2) was also used by (Barger, Liljedahl, Carleton, & Mckibben, 1963). The tractor was operated at the respective throttle and gear settings to gain the required forward speed at different operating depths. The tractor was operated in the two-wheel drive mode. During the tests, the tractor's differential lock was kept engaged at all times to ensure equal travel reduction at each of its drive wheels. As indicated in Section 2.2, 54 tests are required for this study. In each test, the data acquisition system collected 250 raw data points for parameters such as fuel consumption, theoretical forward speed, actual forward speed, slip and draught. In the next step, for each raw data point, the values of dependent and independent dimensionless groups were calculated.
2.4.
Data analysis and fuel consumption model
The parameters affecting fuel consumption are represented as an implicit equation (Eq. (3)). As there are too many parameters in Eq. (3) and a thorough study of all would be tedious, it was decided to use dimensional analysis to investigate the experimental data. Accordingly, a basic model was proposed in which all the variables were grouped to produce a number of independent dimensionless ratios. The rank of dimensionless matrix was 3 (M, L, T). Adopting the Buckingham Pi Theorem and combination the terms of Eq. (3), the number of Pi-terms was obtained to be 7. These Pi-terms were arranged into groups of dimensionless dependent and independent quantities. After certain manipulations and transformations, Eq. (4) was obtained. It should be noted that 80 percent of data were used to derive dimensional analysis models and 20 percent of data were used for validation of the models. f ðFC; CI; Tw ; Td ; Wd ; Fd ; Fr ; S; Va ; D; WÞ ¼ 0
(3)
FC Va D CI Tw Td Fd Fr ¼ f 0:5 0:5 ; ; ; ; S; Qi g W W Wd Wd Wd
(4)
where: FC ¼ Qf C
3 4 5
Manufacturer Specification Name of the transducer T. No.
Table 2 e Specification of equipment used.
1
1
Use for
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2
Regional Network for Agricultural Machinery.
(5)
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Fig. 2 e Location of the transducers on the instrumented tractor. 1- Fifth wheel equipped with shaft encoder; 2- Turbine flow transducer, 3- Turbine flow transducer; 4- Shaft encoder; 5- Data acquisition system.
For ease of application, it would also be advisable to select group forms which produce linear relationships with the dependent variable group. The selected model has the following form as: N FC Va D CI Tw Td Fd Fr f3 ¼ K f1 0:5 0:5 f2 f4 f5 ðSÞf6 Qi W g W Wd Wd Wd (6) Taking logarithm of both sides, Eq. (6) can be written as Eq. (7):
Log
found to produce approximately linear relationships. In the preceding analysis the following definitions help avoid unnecessary repetitions: FC Va First residual ¼ Log Log f1 0:5 0:5 (10) Qi g W
Second residual ¼ First residual Log f2
D W
Third residual ¼ Second residual Log f3
CI TW Td Wd
(11)
N FC Va D CI Tw Td Fd Fr f3 ¼ Log K þ Log f1 0:5 0:5 f2 f4 f5 ðSÞf6 Qi W g W Wd Wd Wd
(7)
in which Log K is intercept on the y axis and N is the slope of the logarithmic line. However, these two constants were not calculated until all functional relationships were found. Each of the logarithmic functions has special N and K such as: Va Va (8) Log f1 0:5 0:5 ¼ N1 Log 0:5 0:5 þ K1 g W g W The value of the constant K is different for different values of other functional groups. So for the other functional groups, each one featuring a similar constant, all of the constants could be combined into one value K for the final correlation, containing all functional relations. For the sake of the present discussion, then, the value of K could be neglected or: 1 0 Va D CITw Td þLogf þLogf þC Logf 1 2 3 B W Wd g0:5 W0:5 C B FC C B ¼NB Log C Qi A @ Fd Fr Logf4 þLogf5 ðSÞþLogf6 Wd Wd (9) The quantity of interest here is the value of N which indi cate how the value of all functions change with FC . Qi It is helpful to note that the functional relationships f1 through f6, will be analysed in the same order which was
Fourth residual ¼ Third residual Log f4
Fd Wd
Fifth residual ¼ Fourth residual Log f5 ðSÞ Sixth residual ¼ Fifth residual Log f6
(12)
Fr Wd
(13)
(14) (15)
It should be explained that the first residual, for example, a represents the established values of Log f1 g0:5VW taken from 0:5 the right-hand side of Eq. (9) and subtracted from the corresponding values of the left-hand side of the same equation. In other words the effect of the first function on the fuel consumption term has been removed for the establishment of the next function. The first residual then would be plotted against its corresponding value of the second variable group in this effect. For the other residuals (second residual to sixth residual) this could be repeated. A close look at Eq. (6) indicates that the first and second groups are both functions of the blade width and their effects could easily be separable if one could be held constant while the other is varying. However, considering that the numbers of experimental data points are quite large, it is possible to separate the effects of each group in the following way. In
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To find this function, the vertical shifts could be found and a plotted against the corresponding values of Log g0:5VW in 0:5 Fig. 4. It should be noted that each point on this plot corre a sponds to one line of Fig. 3 or one value ofLog g0:5VW . The 0:5 points of Fig. 4 show a fairly linear relationship with logarithmic scales. The relationship could be shown as: Log f1
D Fig. 3 e A typical graph relating Log FC to Log Qi W consisting a (forming the three lines). of points of fairly equal Log g0:5VW 0:5
together (forming a number of solid lines). The lines contain 3 points. Each data point is the average of 250 raw data points obtained from the data acquisition system. 4 Draw a vertical shift dotted line perpendicular to the 3 solid lines. 5 The distance between each of the three solid lines and the origin is defined as vertical space. The vertical spacing of the a on 3 solid lines is due to the effects of Log g0:5VW 0:5 Va theLog FC Qi , designated as the function off1 g0:5 W0:5 (Fig. 3).
Va g0:5 W 0:5
a to Log g0:5VW . 0:5
Regression equation: y ¼ 0.5704x ¡ 0.9966; R2 ¼ 0.97.
D W
f3 f4
¼ N1 Log
¼
D W
Va W0:5
(16)
g0:5
CI Tw Td Wd Fd Wd
0:0034 where N2 ¼ 0:0034
¼
Fd Wd
¼
3:5072 CI Tw Td Wd
f6
Fr Wd
Fr Wd
¼
where N3 ¼ 3:5072
(18)
(19)
0:0619 where N4 ¼ 0:0619
f5 S ¼ ðSÞ0:1509
where N5 ¼ 0:1509
(20) (21)
1:2637 where N6 ¼ 1:2637
(22)
Similarly, for 10 cm blade width, the following functional relationships could be established: 0:6444 Va Va where N1 ¼ 0:6444 (23) f1 0:5 0:5 ¼ g W g0:5 W0:5 f2
D W
f3
Fig. 4 e Graph relating Log f1
To determine other functional relationships for this replication, the values of the residuals, as defined by Eqs. (10)e(15), were plotted against their corresponding values as shown in Figs. (5)e(9). Final functional relationships can be concluded by averaging from the slopes of three replications as follow: 0:54 Va Va where N1 ¼ 0:54 (17) f1 0:5 0:5 ¼ g W g0:5 W0:5 f2
order to determine the functional relationship for 5 cm blade width, let us use the data of the first replication as follows: plotted against 1 The values of the corresponding Log FC Qi D the values of Log W . a . 2 Each point of Fig. 3 has a value forLog g0:5VW 0:5 a were connected 3 The points of fairly equal Log g0:5VW 0:5
Va W0:5
g0:5
¼
CI Tw Td Wd
D W
0:0226
¼
where N2 ¼ 0:0226 8:8833 CI Tw Td Wd
where N3 ¼ 8:8833
Fig. 5 e Graph relating Log f2
D W
(24)
(25)
D to Log W . Regression
equation: y ¼ 0.0058x þ 0.2632; R2 ¼ 0.82.
29
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Fd Wd
f4
Fd Wd
¼
0:0385
f5 S ¼ ðSÞ0:2774 f6
Fr Wd
¼
Fr Wd
where N4 ¼ 0:0385 where N5 ¼ 0:2774
(26)
The permissible range of each group of variables is given in Table 3.
(27)
4.
0:1115 where N6 ¼ 0:1115
(28)
The final correlation of the data using the model of Eq. (6) was determined. For this purpose, Eq. (6) can be rewritten for 5 cm and 10 cm blade width respectively as:
Discussion
The Nebraska Tractor Test is a recognised standard that constitutes a large body of information on tractor performance (for concrete track). The fuel consumption model by ASAE Standard D497.4 (ASAE Standards, 1998) is given as follows:
" 0:54 0:0034 3:5072 0:0619 1:2637 #N FC Va D CITw Td Fd Fr 0:1509 ¼K ðSÞ Qi W g0:5 W0:5 Wd Wd Wd
(29)
" 0:1115 #N 0:6444 0:0226 8:8833 0:0385 FC Va D CI Tw Td Fd Fr 0:2774 ¼K ðSÞ Qi W g0:5 W0:5 Wd Wd Wd
The values of the quantities in brackets in Eqs. (29) and (30) were plotted against the corresponding values of the fuel consumption ratio for all available data as shown in Figs. 10 and 11. The regression coefficients for 5 cm blade width were found to be: N ¼ 0:5191
(31)
K ¼ 3:5924
(32)
These regression coefficients for 10 cm blade width were found to be: N ¼ 0:3612
(33)
K ¼ 6:0489
(34)
3.
Results
If Eqs. (29) and (30) are rearranged with the values of Eqs. (31)e(34) it takes the following form for 5 and 10 cm blades, respectively:
FC ¼ 103:5924 Qi
FC ¼ 106:0489 Qi
"
Va g0:5 W0:5
"
Va g0:5 W0:5
0:54
D W
0:6444
0:0034
D W
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Qs ¼ 2:64X þ 3:91 0:203 738X þ 173
(37) 1
1
where Qs is the fuel consumption in l kW h and X is the ratio of equivalent PTO power required by an operation to the maximum available from the PTO (load ratio). The equivalent PTO power for any operation can be calculated based on the following equation by ASAE Standard EP391.1 (ASAE Standards, 1984): Peq ¼
Pdb 0:96 Et
(38)
where Peq is the equivalent PTO power in kW, Pdb is the drawbar power and Et is the percent tractive efficiency. By using Eq. (37), fuel consumption was found to be 15% higher than typical Nebraska Tractor Test performance to reflect loss of efficiency for tilled tractive conditions (ASAE Standards D497.4, 1998). Comparison between the predicted outputs by formulated fuel consumption models in this study and the predicted outputs by the ASAE Standard D497.4 is presented in Table 4.
3:5072 0:0619 1:2637 #0:5191 CI Tw Td Fd Fr 0:1509 ðSÞ Wd Wd Wd
0:0226
(30)
0:1115 #0:3612 8:8833 0:0385 CI Tw Td Fd Fr 0:2774 ðSÞ Wd Wd Wd
(35)
(36)
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Fig. 6 e Graph relating Log f3
CI Tw Td Wd
Tw Td to Log CI W . d
Regression equation: y ¼ ¡4.9619x þ 8.2278; R2 ¼ 0.78.
Fig. 7 e Graph relating Log f4
Fd Wd
Fd to Log W . Regression d
equation: y ¼ 0.0028x þ 0.2675; R2 ¼ 0.93. The fuel consumption for the two implements predicted by the ASAE Standard Equation was 26e53% higher than that predicted by the models developed. In this study such discrepancies in magnitudes were expected since the ASAE Standard Equation was developed for tractors of sizes 100 kW or more commonly used in USA as compared to the tractors sizes of 30e80 kW that are more popular in Asia. Furthermore,
Fig. 8 e Graph relating Log f5 ðSÞ to LogðSÞ. Regression equation: y ¼ ¡0.1412x ¡ 1.041; R2 ¼ 0.99.
Fig. 9 e Graph relating Log f6
Fr Wd
Fr to Log W . Regression d
equation: y ¼ 0.6075x þ 0.892; R2 ¼ 0.73.
Fig. 10 e Graph relating Log (FC/Qi) to the dimensionless groups for all experimental test runs for 5 cm blade width. Regression equation: y ¼ 0.5191x þ 3.5924; R2 ¼ 0.87.
the ASAE Standard Equation was formulated based on laboratory operation of tractors taken from the Nebraska Tractor Tests under varying power and fuel consumption settings, while the fuel models developed in this study were formulated based on the field operation of a Massey Ferguson 399 tractor.
4.1.
Validation of the models
The developed fuel consumption models for 5 and 10 cm blade widths were tested against additional field data for validation.
Fig. 11 e Graph relating Log (FC/Qi) to the dimensionless groups for all experimental test runs for 10 cm blade width. Regression equation: y ¼ 0.3612x þ 6.0489; R2 ¼ 0.96.
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Table 3 e Range of dimensionless groups considered in the present investigation for the 5 cm and 10 cm blade width. Variable groups FC/Qi Va/g0.5 W0.5 D/W CI Tw Td/Wd Fd/Wd S Fr/Wd
Definition
Range of variation for 5 cm blade width
Range of variation for 10 cm blade width
Ratio of fuel consumption to hourly fuel consumption Ratio of actual forward speed to product of gravitational acceleration and blade width Chisel-tool aspect ratio Wheel numeric Net traction ratio Slip Rolling resistance ratio
0.18e0.36 1.18e1.98
0.23e0.38 0.84e1.40
2.00e4.00 66.32e72.17 0.04e0.59 0.01e0.23 0.06e0.16
1.00e2.00 90.74e96.52 0.10e0.59 0.03e0.28 0.03e0.10
In other words, 80 percent of data had been used to derive the dimensional analysis models and the remaining 20 percent of data were used for validation. Results from regression (F-test) between predicted and measured fuel consumption showed that the resultant slope for the fuel consumption of the 5 and 10 cm blade width were not significantly different from 1:1 line (P 0.05) (Figs. 12 and 13).
4.2.
field working capability of chisel plough in ha h1. Bower (1985) reported that the normal range for Eo is 10-20%, and this can be used as a quick check for the validity of fuel consumption measurements. A tractoreimplement combination having an overall energy efficiency below 10% indicates poor
Power and energy requirements
Summaries of power and energy requirements for the implements are presented in Table 5. Eight parameters were measured or calculated to estimate the power and energy requirements for each implement. It should be noted that fuel consumption depends on tractive efficiency and loading on the tractor, in addition to the drawbar power requirement. Besides the thermal efficiency of the engine, fuel consumption also depends on traction equipment type, soil type and conditions. The overall energy efficiency includes the load matching of the tractor and implement, the tractive efficiency and the engine/power train operating conditions. Overall energy efficiency (Eo) values as presented in Table 5 for two implements were calculated from Eq. (39) by Bower (1985) as follows: 1
1
ð3:6 MJ kW h ÞPdb Eo ¼ 1 38:7 MJ l Qf C
(39)
Fig. 12 e Estimated data versus actual data of tractor fuel consumption for 5 cm chisel blade width. Solid line is the 1:1 relationship; dotted lines are estimated fuel consumption. Regression equation: y ¼ 1.076x ¡ 1.376; R2 ¼ 0.95.
where Eo is the overall energy efficiency in %, Pdb the drawbar power in kW, 38.7 the heating value of the diesel fuel in MJ l1, Qf the fuel consumption rates required in l ha1 and C the in-
Table 4 e Comparisons of implement fuel consumption models with ASAE Standards. Implement Fuel model, Load ratio, ASAE, Qs Error FCpa (l kW1 h1) (%) Xb (l kW1 h1) 5 cm blade width 10 cm blade width
0.29e0.53
0.30e0.89
0.41e0.67
26e41
0.33e0.52
0.20e0.81
0.43e0.80
30e53
Predicted fuel consumption in l kW1 h1. Ratio of equivalent PTO power required by an operation to that maximum available from the PTO. a
b
Fig. 13 e Estimated data versus actual data of tractor fuel consumption for 10 cm chisel blade width. Solid line is the 1:1 relationship; dotted lines are estimated fuel consumption. Regression equation: y ¼ 1.087x ¡ 3.929; R2 ¼ 0.95.
32
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Table 5 e Summary of power and energy requirements for two implements in clay loam soil. In-field Drawbar Tractive Overall energy Draught Fuel consumption Slip (S) Implement Depth Actual (%) capacity (C) Power efficiency (Et) efficiency (Eo) (D) forward force (Fd) per unit area (Qf) (ha h1) (Pdb) (kW) (l ha1) (%) (%) (cm) speed (Va) (kN m1) (km h1) 5 cm blade width
10 cm blade width
10.0 10.0 10.0 15.0 15.0 15.0 20.0 20.0 20.0 10.0 10.0 10.0 15.0 15.0 15.0 20.0 20.0 20.0
3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0
1.9 3.0 3.7 4.3 5.6 8.0 13.0 14.3 16.4 3.4 5.9 8.5 5.6 8.4 11.7 11.2 13.3 15.7
28.6 24.0 18.1 36.5 31.0 25.5 36.7 30.2 27.5 30.5 25.0 22.4 39.1 33.0 27.5 41.2 33.6 29.4
load matching or/and low tractive efficiency, while a value above 20% indicates a good load match or/and high tractive efficiency. The tractive efficiency (Et) has been defined as the ratio of output power to input power of a tractive device.
5.
Conclusions
The fuel consumption rates predicted by ASAE Standards D497.4 were found to be 26-53% higher compared to fuel consumption predicted by models developed. The validation for the fuel consumption models for the two implements was acceptable. Consequently, the fuel consumption rate magnitudes could be successfully predicted by the proposed models with good accuracy. It means that this accuracy (P 0.05) has been in 34-84%. Comparing the developed model with ASAE data, it was determined that the model and the data are in good treatment. The output of this research is recommended for regions with similar soil texture. Noting that the parameters related to traction have been used in a dimensionless equation, the forecast results should not be tractor-specific. The prediction equations are capable of predicting fuel consumption values for this case study in the range of dimensionless groups contained in Table 3.
Acknowledgement The authors wish to thank Research Council of Shiraz University, Shiraz, Iran, for providing necessary funds and research facilities required for this investigation. The authors would also like to express their sincere thanks and appreciation to Prof M. H. Raoufat, Biosystems Engineering Department, College of Agriculture, Shiraz University, Shiraz, Iran for reviewing the manuscript.
2 6 4 14 22 17 13 26 19 6 5 4 23 21 13 29 24 21
0.24 0.43 0.53 0.29 0.37 0.51 0.27 0.41 0.51 0.29 0.40 0.49 0.27 0.37 0.50 0.30 0.40 0.49
1.5 3.4 5.2 3.5 6.2 11.2 11.0 16.0 22.7 2.9 6.5 11.8 4.6 9.4 16.3 9.4 14.8 21.9
21 30 36 32 35 46 56 50 57 33 46 57 35 44 57 44 51 56
2 3 5 3 5 8 10 12 15 3 6 10 4 7 11 7 10 14
references
Al-Janobi, A. (2000). A data-acquisition system to monitor performance of fully mounted implements. Journal of Agricultural Engineering Research, 75, 167e175. ASAE Standards. (1984). EP391.1: Agricultural machinery management. St. Joseph, MI: ASAE. ASAE Standards. (1998a). D497.4: Agricultural machinery management data. St. Joseph, MI: ASAE. ASAE Standards. (1998b). S313.2: Soil cone penetrometer. St. Joseph, MI: ASAE. Barger, E. L., Liljedahl, J. B., Carleton, W. M., & Mckibben, E. G. (1963). Tractors and their power units. New York: Wiley. Bower, C. G., Jr. (1985). Southeastern tillage energy data and recommended reporting. Transactions of the ASAE, 28(3), 731e737. Diserens, E. (2010). Manual for TASC V2.0. Agroscope ART. Fakhraei, O., & Karparvarfard, S. H. (2006). Development of a general equation for estimation of tractive efficiency by dimensional analysis. Iranian Journal of Agriculture Science, 38(3), 447e457 (In Farsi with English abstract). Fathollahzadeh, H., Mobli, H., Rajabipour, A., Minaee, S., Jafari, A., & Tabatabaie, S. M. H. (2010). Average and instantaneous fuel consumption of Iranian conventional tractor with moldboard plow in tillage. ARPN Journal of Engineering and Applied Sciences, 5(2), 30e35. Hosseini, S. A., & Karparvarfard, S. H. (2011). Prediction of acting forces on chisel plow tine by dimensional analysis method. Iranian Journal of Biosystems Engineering, 43(1), 93e103 (in Farsi with English abstract). Khalilian, A., Batchelder, D. G., Self, K., & Summers, J. D. (1984). Revision of fuel consumption equation for diesel tractors. ASAE Paper No. 84e1522. St. Joseph, Mich: ASAE, 49085. Langhaar, H. L. (1980). Dimensional analysis and theory of models. New York: Wiley. Moitzi, G., Haas, H., Wagentristl, H., Boxberger, J., & Gronauer, A. (2013). Energy consumption in cultivating and ploughing with traction improvement system and consideration of the rear furrow wheel-load in ploughing. Soil & Tillage Research, 134, 56e60.
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Nielsen, V., & Sorensen, C. G. (1993). Technical farm management a program for calculation of work requirement, work capacity, work budget, work. profile (in Danish with English summary). Danish Institute of Agricultural Engineering: Report No. 53 (p. 124). Pranav, P. K., Pandey, K. P., & Tewari, V. K. (2010). Digital wheel slipmeter for agricultural 2WD tractors. Computers and Electronics in Agriculture, 73, 188e193. Rahimi-Ajdadi, F., & Abbaspour-Gilandeh, Y. (2011). Artificial neural network and stepwise multiple range regression methods for prediction of tractor fuel consumption. Measurement, 44, 2104e2111. Raper, R. L., Schwab, E. B., Balkcom, K. S., Burmester, C. H., & Reeves, D. W. (2005). Effect of annual, biennial, and triennial in-row sub soiling on soil compaction and cotton yield in Southeastern US silt loam soils. Applied Engineering in Agriculture, 21(3), 337e343. Regional Network for Agricultural Machinery. (1983). RNAM test codes and procedures of farm machinery. Technical Series No. 12 (p. 129). Bangkok: Thailand. Sahu, R. K., & Raheman, H. (2006). Draught prediction of agricultural implements using reference tillage tools in
33
sandy clay loam soil. Biosystems Engineering, 94(2), 275e284. Serrano, J. M., Pec¸a, J. O., Pinheiro, A., Carvalho, M., Nunes, M., Ribeiro, L., et al. (2003). The effect of gang angle of offset disc harrows on soil tilth, work rate and fuel consumption. Biosystems Engineering, 84(2), 171e176. Serrano, J. M., Pec¸a, J. O., Silva, J. M., Pinheiro, A., & Carvalho, M. (2007). Tractor energy requirements in disc harrow systems. Biosystems Engineering, 98, 286e296. Smith, L. A. (1993). Energy requirements for selected crop production implements. Soil & Tillage Research, 25, 281e299. Srivastava, A. K., Goering, C. E., Rohrbach, R. P., & Buckmaster, D. R. (2006). Engineering principles of agricultural machines (2nd ed.). USA: American Society of Agricultural and Biological Engineers. Taylor, J. H. (1980). Energy savings through improved tractive efficiency. St. Joseph, MI: ASAE Publication 4e81, ASAE, 49085. Zhang, C., Araya, K., Kudoh, M., Liu, F., Jia, H., Zhang, H., et al. (2003). A three-stage soil layer mixing plough for the improvement of meadow soil, part 3: field evaluation. Journal of Agricultural Engineering Research, 79, 47e53.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/issn/15375110
Research Paper
Development of a fuel consumption equation: Test case for a tractor chisel-ploughing in a clay loam soil S.H. Karparvarfard*, H. Rahmanian-Koushkaki Biosystems Engineering Department, College of Agriculture, Shiraz University, Shiraz, Iran
article info
Fuel consumption and tillage draught were measured when chiselling in a clay loam soil in
Article history:
Badjgah Research Station, Shiraz University, Shiraz, Iran. An 81 kW tractor (MF-399)
Received 22 March 2014
instrumented with a data acquisition system was used to measure fuel consumption,
Received in revised form
actual forward speed, theoretical forward speed, slip and implement draught. The effects
18 November 2014
of blade width (5 and 10 cm), tillage depth (10, 15 and 20 cm) and actual forward speed (3, 4
Accepted 25 November 2014
and 5 km h1) upon fuel consumption were investigated. Fuel consumption was assumed
Published online
to be a function of wheel numeric, slip, net traction ratio, rolling resistance ratio, chiseltool aspect ratio and actual forward speed. Collected data were used to model the tractor
Keywords:
fuel consumption using dimensional analysis approach. Results were compared to fuel
Data acquisition
consumption rates as predicted by ASAE Standards (D497.4). The comparisons showed that
Dimensional analysis
the standard overestimates fuel consumption by 26e53%. Results from regression (F-test)
Modelling
between predicted and measured fuel consumption data showed that the slopes for fuel
Massey Ferguson MF-399
consumption with the 5 and 10 cm blade widths were not significantly different from 1:1 line (P 0.05). Consequently, the fuel consumption rate can be successfully predicted by the model with good accuracy. © 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Fuel is the source of energy for the tractor providing for the performance of work and propelling the tractor to overcome implement draught (Smith, 1993). There are many parameters in tillage operation that affect the fuel consumption of a tractor, such as soil texture, climate, relative humidity, tractor
type (two or four wheel drive), tractor size and tractor implement relationship. Therefore, tractor fuel consumption is not constant and varies from one to another situation (Nielsen & Sorensen, 1993). To increase efficiency of agricultural production; it is necessary to increase machine working efficiency. Taylor (1980) estimated that in the U.S. for each 1% improvement in traction efficiency, 284e303 million litres of fuel could be
Abbreviations: MF, Massey Ferguson; ASAE, American Society of Agricultural Engineers; ASABE, American Society of Agricultural and Biological Engineers; PTO, Power Take-off; NRMSE, Normalised Root Mean Square Error; MBE, Mean Bias Error; RNAM, Regional Network for Agricultural Machinery. * Corresponding author. Tel.: þ98 91 7316 0457. E-mail address: [email protected] (S.H. Karparvarfard). http://dx.doi.org/10.1016/j.biosystemseng.2014.11.015 1537-5110/© 2014 IAgrE. Published by Elsevier Ltd. All rights reserved.
24
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Nomenclature Symbols C In-field working capability of chisel plough (ha h1) CI Soil cone index (kPa) D Working depth (m) Overall energy efficiency (%) Eo Tractive efficiency (%) Et f Function FC Experimental fuel consumption (l h1) Predicted fuel consumption (l kW1 h1) FCp Draught force (N) Fd Rolling resistance (N) Fr g Gravitational acceleration (m s2) K Intercept of logarithmic line (constant) L Length (m) M Mass (kg) N Slope of logarithmic line (constant) Drawbar power (kW) Pdb Equivalent PTO power (kW) Peq Fuel consumption per unit area (l ha1) Qf Hourly fuel consumption (l h1) Qi Brake-specific fuel consumption (l kW1 h1) Qs S Driving wheel slip (%) Unloaded overall tyre diameter (m) Td Unloaded tyre section width (m) Tw Actual forward speed (km h1) Va Theoretical forward speed (km h1) Vt W Blade width (m) Dynamic wheel load (N) Wd Static wheel load (N) Ws X Load ratio define as equivalent PTO power required by an operation to the maximum available from the PTO, dimensionless Wheel base (m) Xwb Z Drawbar height (m)
saved annually. Due to increasing world population and limited non-renewable resources, especially fossil fuels, it is necessary to reduce and manage fuel consumption in various agricultural activities. Many studies have been conducted to measure draught, power requirement and fuel consumption of tillage implements (Al-Janobi, 2000; Sahu & Raheman, 2006; Serrano et al., 2003, 2007). Predicting tractor fuel consumption can lead to more appropriate decisions on tractor management. Several studies have been conducted in this area. Khalilian, Batchelder, Self, and Summers (1984) presented the fuel equations corresponding to different diesel engine air intake types. Results showed that fuel efficiency equations more nearly reflect actual data than ASAE equations where predictions were at least 20% higher than experimental data. Raper, Schwab, Balkcom, Burmester, and Reeves (2005) developed an equation to estimate fuel consumption during deep tillage for John Deere 8300 tractors. Power-take-off data was converted to drawbar power using data available from the
Nebraska Tractor Test, and they presented a fuel consumption equation based on drawbar power. Fathollahzadeh et al. (2010) developed a fuel consumption model for a John Deere 3140 tractor at various working depths of mouldboard plough. Their results showed a linear relationship between fuel consumption and working depth of the mouldboard plough. Rahimi-Ajdadi and Abbaspour-Gilandeh (2011) presented models based on artificial neural network and stepwise multiple range regression for prediction of tractor fuel consumption. Fuel consumption was assumed to be a function of engine speed, throttle and load conditions, chassis type, total tested weight, drawbar and PTO powers. Results indicated that the artificial neural network and stepwise regression models gave similar determination coefficients (R2 ¼ 0.98 and R2 ¼ 0.97, respectively) while the artificial neural network provided relatively better prediction accuracy (R2 ¼ 0.93) compared to stepwise regression (R2 ¼ 0.91). Dimensional analysis is a mathematical approach concerning dimensionally homogeneous equations. The form of such equations is independent of the fundamental units used. This is the basis of the theory of dimensional analysis in Buckingham's theorem (Langhaar, 1980). The dimensional analysis is a method by which one can deduce information about a phenomenon from the single premise that the phenomenon can be described by a dimensionally correct equation among pertinent variables. The result of a dimensional analysis of a problem is a reduction in the number of variables in the problem. This results in considerable savings in both cost and labour during the experimental determination of the function (Srivastava, Goering, Rohrbach, & Buckmaster, 2006). Fakhraei and Karparvarfard (2006) developed a general equation for estimating the tractive efficiency of a Universal tractor (U-445, 30 kW) using dimensional analysis. Drawbar force, rolling resistance force of the drive wheels, slip of drive wheels, soil cone index, theoretical and actual velocity and dynamic load on driving wheels were either measured or calculated. This equation can be employed to estimate tractive efficiency of various combinations of tractors and ploughs provided the range of dimensionless terms fall within the limits experienced in the research. By use of this equation and through employing the initial data for tractor and soil, the tractive efficiency could be well predicted. Hosseini and Karparvarfard (2011) developed appropriate equations for predicting draught and vertical forces on a chisel tine using dimensional analysis. The effects of four levels of rake angle (10, 15, 20 and 25 ), three levels of forward speed (1.5, 3 and 4.5 km h1) and three levels of tine aspect ratio (1.5, 2 and 3) on horizontal and vertical forces acting on a chisel plough tine (100 mm wide) were investigated. Results of F-test at 5% probability showed no significant differences between values of slope and intercept of measured values vs. predicted values plot as compared to 1:1 line. Statistical indices NRMSE and MBE emphasise precision of the adopted analytical model. In addition, other results showed an increasing trend of draught force for variation in input parameters. This finding is supported by similar results derived from ASABE general equation. The main objectives of the present study were to develop fuel consumption equation for an 81 kW tractor when carrying implement (chisel plough) in 5 and 10 cm widths.
25
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Tractor factors were: wheel numeric,1 slip, net traction ratio and rolling resistance ratio. Implement factors were chiseltool aspect ratio and actual forward speed. Modelling of the tractor fuel consumption was conducted using dimensional analysis.
2.
Materials and methods
2.1.
Tillage site
Field experiments were conducted in autumn 2012 at Badjgah Research Station (29 320 N 52 350 E), Shiraz University located in NW Shiraz, Iran. The soil texture at the experimental site was clay loam (35% sand, 30% silt, and 35% clay) with previous wheat crop residue. The plot size was 10 m wide and 50 m long (500 m2). The total number of the plots was 162. The total area used for the experiments was 81,000 m2.The mean soil moisture content (d.b %), bulk density (g cm3) and cone index (kPa) were measured as 8.4 ± 3.8, 1.3 ± 0.2, 2840 ± 710 respectively. These parameters were measured at ten random locations of each plot prior to the tests. Soil core samples for determining moisture content and bulk density were collected using a cylindrical core sampler. These samples were measured for 5 cm increments of depth down to 20 cm. Collected samples were immediately placed in plastic bags to conserve moisture during transfer to the laboratory. The wet samples were weighed, and then put in an oven at 105 C for 24 h. The dry samples were weighed and moisture content and bulk density calculated. Cone index values were obtained by taking penetrometer readings at 5 cm increments to depths of 25 cm at several locations of the plots using a cone penetrometer according to ASAE Standards S313.2 with a cone base area of 130 mm2 (ASAE Standards, 1998b).
2.2.
Tractor and tillage implement treatments
A front wheel assist, Massey Ferguson tractor (MF-399) (ITM, Tabriz, Iran) with a maximum engine power of 81 kW was used in field evaluation (Table 1). A mounted-type chisel plough (Rau, Germany) with 9 spring curved shanks in 2 rows and 2 gauge wheels was used in this study. Working width of the plough was 225 cm (Fig. 1). Treatments consisted of three levels of actual forward speeds (3, 4 and 5 km h1), three levels of tillage depths (10, 15 and 20 cm), two levels of blade widths (5 and 10 cm) and three replications, giving 3 speeds 3 tillage depths 2 blade widths ¼ 18 experimental cases 3 replications per case ¼ 54 tests.
2.3.
Table 1 e Specifications of MF-399 tractor used. Characteristics Maximum power at 2200 rpm Total weight Front tyres Rear tyres Inflation pressure, front tyre Inflation pressure, rear tyre Wheel base Front axle width Rear axle width Drawbar height Weight on front axle Weight on rear axle
Symbols used in the equations e e e e e Xwb e e Z e e
Unit 81 39.34 14.9e24 18.4/15e34 204 136 2640 1726e2094 1518e2428 433 14.82 24.52
kW kN e e kPa kPa mm mm mm mm kN kN
and tractor are shown in Figs. 2 and 3. The data acquisition system consisted of an electronic board and a portable computer linked via a USB port. Data were sampled at 0.1 s intervals. Rate of fuel consumption was measured with two turbine flow transducers (VISION-1000, Remag, Bern, Switzerland) having a range of 0.1e2.5 l min1. One transducer was accommodated between the fuel filter and the injector pump of the tractor; another was used to measure the excess fuel returning from both injectors and injection pump to the fuel tank. The actual forward speed was measured using a fifth wheel attached to a suitable position underneath the tractor chassis, while the theoretical forward speed was measured on the right rear wheel. Two shaft encoders (Autonics, South Korea) with 500 pulse revolution1 were used in this study. One shaft encoder was mounted on the fifth wheel and used to measure actual forward speed. Another was mounted on the right rear wheel for measuring theoretical forward speed. The speed data were input to a microcontroller to calculate the wheel slip and generate a digital display (Pranav, Pandey, & Tewari, 2010). The following equation was used to calculate the slip percentage: S¼
1
Va Vt
100
Data acquisition system
An instrumentation package for measuring the tractor performance was developed. This package included the data acquisition system and the transducers for measuring fuel consumption, actual forward speed, slip and implement draught. Specifications of the transducers used in the package are listed in Table 2. The general arrangement of transducers 1
Wheel numeric is a dimensionless group which provides an indication of the soiletyre interaction for a given tyre and load.
Fig. 1 e Mounted chisel plough used in this study.
(1)
26
Keli, China Findlay Irvine, Scotland Bisat Electronic, Iran S type, range 0e50 kN, precision grade: C3 Soil penetration resistance at a depth of 50 cm with 1 cm intervals Sampling rate: 0.1 s, Total number of I/O ports: 11 DEE-5t, Traction dynamometer Bush (SP-1000), Penetrometer Electronic board
Measurement of fuel consumption Measurement of actual forward speed and theoretical forward speed Measurement of draught Measurement of cone index Acquisition of data Remag, Switzerland Autonics, South Korea 0.1e2.5 l min (22,000 pulse l ), ±3% 500 pulse revolution1, ±5% Vision-1000, Turbine flow transducer (2 Nos.) E50S8-500-3-N-24, Shaft encoder (2 Nos.)
A traction dynamometer (Keli, China) was used to measure the plough draught according to RNAM2 (1983) method. The plough was mounted on the MF-399 tractor which was used to support the plough but did not provide power. The unit was drawn by another tractor (John Deere 4450) through the traction dynamometer mounted on the tractor hitch. Hence, the plough draught could be calculated once the rolling resistance of the MF-399 tractor was subtracted (Zhang et al., 2003). Dynamic wheel load was calculated using following equation (Diserens, 2010; Moitzi, Haas, Wagentristl, Boxberger, & Gronauer, 2013): Wd ¼ Ws þ Fd
Z Xwb
1 2
(2)
where Wd is the dynamic wheel load in N; Ws is the static wheel load in N; Fd is the draught force in N; Z is the drawbar height in m and Xwb is the wheel base in m. Equation (2) was also used by (Barger, Liljedahl, Carleton, & Mckibben, 1963). The tractor was operated at the respective throttle and gear settings to gain the required forward speed at different operating depths. The tractor was operated in the two-wheel drive mode. During the tests, the tractor's differential lock was kept engaged at all times to ensure equal travel reduction at each of its drive wheels. As indicated in Section 2.2, 54 tests are required for this study. In each test, the data acquisition system collected 250 raw data points for parameters such as fuel consumption, theoretical forward speed, actual forward speed, slip and draught. In the next step, for each raw data point, the values of dependent and independent dimensionless groups were calculated.
2.4.
Data analysis and fuel consumption model
The parameters affecting fuel consumption are represented as an implicit equation (Eq. (3)). As there are too many parameters in Eq. (3) and a thorough study of all would be tedious, it was decided to use dimensional analysis to investigate the experimental data. Accordingly, a basic model was proposed in which all the variables were grouped to produce a number of independent dimensionless ratios. The rank of dimensionless matrix was 3 (M, L, T). Adopting the Buckingham Pi Theorem and combination the terms of Eq. (3), the number of Pi-terms was obtained to be 7. These Pi-terms were arranged into groups of dimensionless dependent and independent quantities. After certain manipulations and transformations, Eq. (4) was obtained. It should be noted that 80 percent of data were used to derive dimensional analysis models and 20 percent of data were used for validation of the models. f ðFC; CI; Tw ; Td ; Wd ; Fd ; Fr ; S; Va ; D; WÞ ¼ 0
(3)
FC Va D CI Tw Td Fd Fr ¼ f 0:5 0:5 ; ; ; ; S; Qi g W W Wd Wd Wd
(4)
where: FC ¼ Qf C
3 4 5
Manufacturer Specification Name of the transducer T. No.
Table 2 e Specification of equipment used.
1
1
Use for
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
2
Regional Network for Agricultural Machinery.
(5)
27
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Fig. 2 e Location of the transducers on the instrumented tractor. 1- Fifth wheel equipped with shaft encoder; 2- Turbine flow transducer, 3- Turbine flow transducer; 4- Shaft encoder; 5- Data acquisition system.
For ease of application, it would also be advisable to select group forms which produce linear relationships with the dependent variable group. The selected model has the following form as: N FC Va D CI Tw Td Fd Fr f3 ¼ K f1 0:5 0:5 f2 f4 f5 ðSÞf6 Qi W g W Wd Wd Wd (6) Taking logarithm of both sides, Eq. (6) can be written as Eq. (7):
Log
found to produce approximately linear relationships. In the preceding analysis the following definitions help avoid unnecessary repetitions: FC Va First residual ¼ Log Log f1 0:5 0:5 (10) Qi g W
Second residual ¼ First residual Log f2
D W
Third residual ¼ Second residual Log f3
CI TW Td Wd
(11)
N FC Va D CI Tw Td Fd Fr f3 ¼ Log K þ Log f1 0:5 0:5 f2 f4 f5 ðSÞf6 Qi W g W Wd Wd Wd
(7)
in which Log K is intercept on the y axis and N is the slope of the logarithmic line. However, these two constants were not calculated until all functional relationships were found. Each of the logarithmic functions has special N and K such as: Va Va (8) Log f1 0:5 0:5 ¼ N1 Log 0:5 0:5 þ K1 g W g W The value of the constant K is different for different values of other functional groups. So for the other functional groups, each one featuring a similar constant, all of the constants could be combined into one value K for the final correlation, containing all functional relations. For the sake of the present discussion, then, the value of K could be neglected or: 1 0 Va D CITw Td þLogf þLogf þC Logf 1 2 3 B W Wd g0:5 W0:5 C B FC C B ¼NB Log C Qi A @ Fd Fr Logf4 þLogf5 ðSÞþLogf6 Wd Wd (9) The quantity of interest here is the value of N which indi cate how the value of all functions change with FC . Qi It is helpful to note that the functional relationships f1 through f6, will be analysed in the same order which was
Fourth residual ¼ Third residual Log f4
Fd Wd
Fifth residual ¼ Fourth residual Log f5 ðSÞ Sixth residual ¼ Fifth residual Log f6
(12)
Fr Wd
(13)
(14) (15)
It should be explained that the first residual, for example, a represents the established values of Log f1 g0:5VW taken from 0:5 the right-hand side of Eq. (9) and subtracted from the corresponding values of the left-hand side of the same equation. In other words the effect of the first function on the fuel consumption term has been removed for the establishment of the next function. The first residual then would be plotted against its corresponding value of the second variable group in this effect. For the other residuals (second residual to sixth residual) this could be repeated. A close look at Eq. (6) indicates that the first and second groups are both functions of the blade width and their effects could easily be separable if one could be held constant while the other is varying. However, considering that the numbers of experimental data points are quite large, it is possible to separate the effects of each group in the following way. In
28
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
To find this function, the vertical shifts could be found and a plotted against the corresponding values of Log g0:5VW in 0:5 Fig. 4. It should be noted that each point on this plot corre a sponds to one line of Fig. 3 or one value ofLog g0:5VW . The 0:5 points of Fig. 4 show a fairly linear relationship with logarithmic scales. The relationship could be shown as: Log f1
D Fig. 3 e A typical graph relating Log FC to Log Qi W consisting a (forming the three lines). of points of fairly equal Log g0:5VW 0:5
together (forming a number of solid lines). The lines contain 3 points. Each data point is the average of 250 raw data points obtained from the data acquisition system. 4 Draw a vertical shift dotted line perpendicular to the 3 solid lines. 5 The distance between each of the three solid lines and the origin is defined as vertical space. The vertical spacing of the a on 3 solid lines is due to the effects of Log g0:5VW 0:5 Va theLog FC Qi , designated as the function off1 g0:5 W0:5 (Fig. 3).
Va g0:5 W 0:5
a to Log g0:5VW . 0:5
Regression equation: y ¼ 0.5704x ¡ 0.9966; R2 ¼ 0.97.
D W
f3 f4
¼ N1 Log
¼
D W
Va W0:5
(16)
g0:5
CI Tw Td Wd Fd Wd
0:0034 where N2 ¼ 0:0034
¼
Fd Wd
¼
3:5072 CI Tw Td Wd
f6
Fr Wd
Fr Wd
¼
where N3 ¼ 3:5072
(18)
(19)
0:0619 where N4 ¼ 0:0619
f5 S ¼ ðSÞ0:1509
where N5 ¼ 0:1509
(20) (21)
1:2637 where N6 ¼ 1:2637
(22)
Similarly, for 10 cm blade width, the following functional relationships could be established: 0:6444 Va Va where N1 ¼ 0:6444 (23) f1 0:5 0:5 ¼ g W g0:5 W0:5 f2
D W
f3
Fig. 4 e Graph relating Log f1
To determine other functional relationships for this replication, the values of the residuals, as defined by Eqs. (10)e(15), were plotted against their corresponding values as shown in Figs. (5)e(9). Final functional relationships can be concluded by averaging from the slopes of three replications as follow: 0:54 Va Va where N1 ¼ 0:54 (17) f1 0:5 0:5 ¼ g W g0:5 W0:5 f2
order to determine the functional relationship for 5 cm blade width, let us use the data of the first replication as follows: plotted against 1 The values of the corresponding Log FC Qi D the values of Log W . a . 2 Each point of Fig. 3 has a value forLog g0:5VW 0:5 a were connected 3 The points of fairly equal Log g0:5VW 0:5
Va W0:5
g0:5
¼
CI Tw Td Wd
D W
0:0226
¼
where N2 ¼ 0:0226 8:8833 CI Tw Td Wd
where N3 ¼ 8:8833
Fig. 5 e Graph relating Log f2
D W
(24)
(25)
D to Log W . Regression
equation: y ¼ 0.0058x þ 0.2632; R2 ¼ 0.82.
29
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Fd Wd
f4
Fd Wd
¼
0:0385
f5 S ¼ ðSÞ0:2774 f6
Fr Wd
¼
Fr Wd
where N4 ¼ 0:0385 where N5 ¼ 0:2774
(26)
The permissible range of each group of variables is given in Table 3.
(27)
4.
0:1115 where N6 ¼ 0:1115
(28)
The final correlation of the data using the model of Eq. (6) was determined. For this purpose, Eq. (6) can be rewritten for 5 cm and 10 cm blade width respectively as:
Discussion
The Nebraska Tractor Test is a recognised standard that constitutes a large body of information on tractor performance (for concrete track). The fuel consumption model by ASAE Standard D497.4 (ASAE Standards, 1998) is given as follows:
" 0:54 0:0034 3:5072 0:0619 1:2637 #N FC Va D CITw Td Fd Fr 0:1509 ¼K ðSÞ Qi W g0:5 W0:5 Wd Wd Wd
(29)
" 0:1115 #N 0:6444 0:0226 8:8833 0:0385 FC Va D CI Tw Td Fd Fr 0:2774 ¼K ðSÞ Qi W g0:5 W0:5 Wd Wd Wd
The values of the quantities in brackets in Eqs. (29) and (30) were plotted against the corresponding values of the fuel consumption ratio for all available data as shown in Figs. 10 and 11. The regression coefficients for 5 cm blade width were found to be: N ¼ 0:5191
(31)
K ¼ 3:5924
(32)
These regression coefficients for 10 cm blade width were found to be: N ¼ 0:3612
(33)
K ¼ 6:0489
(34)
3.
Results
If Eqs. (29) and (30) are rearranged with the values of Eqs. (31)e(34) it takes the following form for 5 and 10 cm blades, respectively:
FC ¼ 103:5924 Qi
FC ¼ 106:0489 Qi
"
Va g0:5 W0:5
"
Va g0:5 W0:5
0:54
D W
0:6444
0:0034
D W
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Qs ¼ 2:64X þ 3:91 0:203 738X þ 173
(37) 1
1
where Qs is the fuel consumption in l kW h and X is the ratio of equivalent PTO power required by an operation to the maximum available from the PTO (load ratio). The equivalent PTO power for any operation can be calculated based on the following equation by ASAE Standard EP391.1 (ASAE Standards, 1984): Peq ¼
Pdb 0:96 Et
(38)
where Peq is the equivalent PTO power in kW, Pdb is the drawbar power and Et is the percent tractive efficiency. By using Eq. (37), fuel consumption was found to be 15% higher than typical Nebraska Tractor Test performance to reflect loss of efficiency for tilled tractive conditions (ASAE Standards D497.4, 1998). Comparison between the predicted outputs by formulated fuel consumption models in this study and the predicted outputs by the ASAE Standard D497.4 is presented in Table 4.
3:5072 0:0619 1:2637 #0:5191 CI Tw Td Fd Fr 0:1509 ðSÞ Wd Wd Wd
0:0226
(30)
0:1115 #0:3612 8:8833 0:0385 CI Tw Td Fd Fr 0:2774 ðSÞ Wd Wd Wd
(35)
(36)
30
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Fig. 6 e Graph relating Log f3
CI Tw Td Wd
Tw Td to Log CI W . d
Regression equation: y ¼ ¡4.9619x þ 8.2278; R2 ¼ 0.78.
Fig. 7 e Graph relating Log f4
Fd Wd
Fd to Log W . Regression d
equation: y ¼ 0.0028x þ 0.2675; R2 ¼ 0.93. The fuel consumption for the two implements predicted by the ASAE Standard Equation was 26e53% higher than that predicted by the models developed. In this study such discrepancies in magnitudes were expected since the ASAE Standard Equation was developed for tractors of sizes 100 kW or more commonly used in USA as compared to the tractors sizes of 30e80 kW that are more popular in Asia. Furthermore,
Fig. 8 e Graph relating Log f5 ðSÞ to LogðSÞ. Regression equation: y ¼ ¡0.1412x ¡ 1.041; R2 ¼ 0.99.
Fig. 9 e Graph relating Log f6
Fr Wd
Fr to Log W . Regression d
equation: y ¼ 0.6075x þ 0.892; R2 ¼ 0.73.
Fig. 10 e Graph relating Log (FC/Qi) to the dimensionless groups for all experimental test runs for 5 cm blade width. Regression equation: y ¼ 0.5191x þ 3.5924; R2 ¼ 0.87.
the ASAE Standard Equation was formulated based on laboratory operation of tractors taken from the Nebraska Tractor Tests under varying power and fuel consumption settings, while the fuel models developed in this study were formulated based on the field operation of a Massey Ferguson 399 tractor.
4.1.
Validation of the models
The developed fuel consumption models for 5 and 10 cm blade widths were tested against additional field data for validation.
Fig. 11 e Graph relating Log (FC/Qi) to the dimensionless groups for all experimental test runs for 10 cm blade width. Regression equation: y ¼ 0.3612x þ 6.0489; R2 ¼ 0.96.
31
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Table 3 e Range of dimensionless groups considered in the present investigation for the 5 cm and 10 cm blade width. Variable groups FC/Qi Va/g0.5 W0.5 D/W CI Tw Td/Wd Fd/Wd S Fr/Wd
Definition
Range of variation for 5 cm blade width
Range of variation for 10 cm blade width
Ratio of fuel consumption to hourly fuel consumption Ratio of actual forward speed to product of gravitational acceleration and blade width Chisel-tool aspect ratio Wheel numeric Net traction ratio Slip Rolling resistance ratio
0.18e0.36 1.18e1.98
0.23e0.38 0.84e1.40
2.00e4.00 66.32e72.17 0.04e0.59 0.01e0.23 0.06e0.16
1.00e2.00 90.74e96.52 0.10e0.59 0.03e0.28 0.03e0.10
In other words, 80 percent of data had been used to derive the dimensional analysis models and the remaining 20 percent of data were used for validation. Results from regression (F-test) between predicted and measured fuel consumption showed that the resultant slope for the fuel consumption of the 5 and 10 cm blade width were not significantly different from 1:1 line (P 0.05) (Figs. 12 and 13).
4.2.
field working capability of chisel plough in ha h1. Bower (1985) reported that the normal range for Eo is 10-20%, and this can be used as a quick check for the validity of fuel consumption measurements. A tractoreimplement combination having an overall energy efficiency below 10% indicates poor
Power and energy requirements
Summaries of power and energy requirements for the implements are presented in Table 5. Eight parameters were measured or calculated to estimate the power and energy requirements for each implement. It should be noted that fuel consumption depends on tractive efficiency and loading on the tractor, in addition to the drawbar power requirement. Besides the thermal efficiency of the engine, fuel consumption also depends on traction equipment type, soil type and conditions. The overall energy efficiency includes the load matching of the tractor and implement, the tractive efficiency and the engine/power train operating conditions. Overall energy efficiency (Eo) values as presented in Table 5 for two implements were calculated from Eq. (39) by Bower (1985) as follows: 1
1
ð3:6 MJ kW h ÞPdb Eo ¼ 1 38:7 MJ l Qf C
(39)
Fig. 12 e Estimated data versus actual data of tractor fuel consumption for 5 cm chisel blade width. Solid line is the 1:1 relationship; dotted lines are estimated fuel consumption. Regression equation: y ¼ 1.076x ¡ 1.376; R2 ¼ 0.95.
where Eo is the overall energy efficiency in %, Pdb the drawbar power in kW, 38.7 the heating value of the diesel fuel in MJ l1, Qf the fuel consumption rates required in l ha1 and C the in-
Table 4 e Comparisons of implement fuel consumption models with ASAE Standards. Implement Fuel model, Load ratio, ASAE, Qs Error FCpa (l kW1 h1) (%) Xb (l kW1 h1) 5 cm blade width 10 cm blade width
0.29e0.53
0.30e0.89
0.41e0.67
26e41
0.33e0.52
0.20e0.81
0.43e0.80
30e53
Predicted fuel consumption in l kW1 h1. Ratio of equivalent PTO power required by an operation to that maximum available from the PTO. a
b
Fig. 13 e Estimated data versus actual data of tractor fuel consumption for 10 cm chisel blade width. Solid line is the 1:1 relationship; dotted lines are estimated fuel consumption. Regression equation: y ¼ 1.087x ¡ 3.929; R2 ¼ 0.95.
32
b i o s y s t e m s e n g i n e e r i n g 1 3 0 ( 2 0 1 5 ) 2 3 e3 3
Table 5 e Summary of power and energy requirements for two implements in clay loam soil. In-field Drawbar Tractive Overall energy Draught Fuel consumption Slip (S) Implement Depth Actual (%) capacity (C) Power efficiency (Et) efficiency (Eo) (D) forward force (Fd) per unit area (Qf) (ha h1) (Pdb) (kW) (l ha1) (%) (%) (cm) speed (Va) (kN m1) (km h1) 5 cm blade width
10 cm blade width
10.0 10.0 10.0 15.0 15.0 15.0 20.0 20.0 20.0 10.0 10.0 10.0 15.0 15.0 15.0 20.0 20.0 20.0
3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0 3.0 4.0 5.0
1.9 3.0 3.7 4.3 5.6 8.0 13.0 14.3 16.4 3.4 5.9 8.5 5.6 8.4 11.7 11.2 13.3 15.7
28.6 24.0 18.1 36.5 31.0 25.5 36.7 30.2 27.5 30.5 25.0 22.4 39.1 33.0 27.5 41.2 33.6 29.4
load matching or/and low tractive efficiency, while a value above 20% indicates a good load match or/and high tractive efficiency. The tractive efficiency (Et) has been defined as the ratio of output power to input power of a tractive device.
5.
Conclusions
The fuel consumption rates predicted by ASAE Standards D497.4 were found to be 26-53% higher compared to fuel consumption predicted by models developed. The validation for the fuel consumption models for the two implements was acceptable. Consequently, the fuel consumption rate magnitudes could be successfully predicted by the proposed models with good accuracy. It means that this accuracy (P 0.05) has been in 34-84%. Comparing the developed model with ASAE data, it was determined that the model and the data are in good treatment. The output of this research is recommended for regions with similar soil texture. Noting that the parameters related to traction have been used in a dimensionless equation, the forecast results should not be tractor-specific. The prediction equations are capable of predicting fuel consumption values for this case study in the range of dimensionless groups contained in Table 3.
Acknowledgement The authors wish to thank Research Council of Shiraz University, Shiraz, Iran, for providing necessary funds and research facilities required for this investigation. The authors would also like to express their sincere thanks and appreciation to Prof M. H. Raoufat, Biosystems Engineering Department, College of Agriculture, Shiraz University, Shiraz, Iran for reviewing the manuscript.
2 6 4 14 22 17 13 26 19 6 5 4 23 21 13 29 24 21
0.24 0.43 0.53 0.29 0.37 0.51 0.27 0.41 0.51 0.29 0.40 0.49 0.27 0.37 0.50 0.30 0.40 0.49
1.5 3.4 5.2 3.5 6.2 11.2 11.0 16.0 22.7 2.9 6.5 11.8 4.6 9.4 16.3 9.4 14.8 21.9
21 30 36 32 35 46 56 50 57 33 46 57 35 44 57 44 51 56
2 3 5 3 5 8 10 12 15 3 6 10 4 7 11 7 10 14
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