The forces acting on a tractor during field operation play a crucial role in the energy requirement, traction mechanics, stability analysis, and steering control. Three force sensing elements (Fig. 1a) were constructed to measure the draught resistance of agricultural machinery by mounting them to the left, right, and top hitching points. Each sensing element comprised two detachable MS frames (1, 2) and two curved plates (3) with the provision of fixing a commercial S-type force transducer (4). One frame of the sensing element was connected with the tractor linkage (1) while another was connected with the implement hitch (2). Each S-type force transducer had a range and least count of 5000 N and 0.05 kg, respectively for sensing and measuring the forces on a particular linkage. The transducers were packed laterally in between the curved plates perpendicular to the direction of travel in such a way that the magnitude of the imposed force decreased and its nature got reversed consequently at the time of tillage force measurement. When tensile force acted on the sensing element, the curved plates tried to extend, which ultimately imposed compressive force on the force transducer, as also presented in Fig. 1b. Similarly, when the force of compressive nature acted on the sensing element, the curved plates tried to flex and imposed tensile force on the force transducer.

The draught resistance is described as the force needed to drive machinery in the direction of motion (ASAE Standards EP291.3, 2005). The arrangement of fixing the draught sensing elements permits only resultant horizontal force components to act on the force transducer. Thus, the draught was straightaway predicted by deducting the force acting on the top sensing element from the summation of forces acting on lower sensing elements (Eq. 1). The forces measured during the field experiments were acquired for further analysis through a portable DAQ system powered using the tractor battery.

where, D_f is the draught resistance, kN; F_R, F_L, and F_T are measured forces in kN in the right, left, and top link sensing elements, respectively.

The isometric view of the developed draught sensing element with detailed dimensions is shown in Fig. 2. The weight of each developed draught element was 7.5 kg.

Finite element (FE) analysis was performed in ANSYS R15.0 workbench on the designed 3D model of the draught sensing element to check whether its design is safe or not. The prototype model is generally considered to be safe in the static structural analysis if the induced equivalent stress and deformation of components are less than the allowable stress and deformation of the selected material (Karmakar & Kushwaha, 2006; Bentaher et al., 2013; Upadhyay et al., 2017). The results on induced von Mises stresses and deformations were examined, and consequently, the required modifications were made in the 3D design prototype for obtaining optimum components dimensions before the development. The applied forces and boundary constraints on one lower link draught sensing element are shown in Fig. 3a. A horizontal force of 15000 N was applied on the tractor side frame of the draught sensing element (indicated as B), and the implement side frame was fixed (indicated as A). The results of FE analysis are presented in Figs. 3b and 3c in the form of coloured contours indicating degrees of stresses and deformations induced in the prototype. The maximum equivalent stress induced (129.84 MPa) was found to be lower compared to the yield strength of the material (mild steel having a yield strength of 250 MPa) indicating the design of draught sensing elements to be safe.

The dynamometer elements which were fixed to the left and right linkages of the tractor were calibrated under tensile conditions using a mechanical floor crane. The calibration setup used is shown in Fig. 4a. One end of the sensing element was clamped to the bolt of the crane at the bottom, and another end was connected to the crane pulley hook through a certified weighing balance with a digital display having 1000 kg capacity and 0.1 kg least count. The elements were gradually loaded with ratchet pinion of the loading crane from 0 to 900 kg in steps of 50 kg and the resulting force coming on the load cell was logged using an HBM Quantum-X DAQ system.

The top link sensing element was calibrated under compression. The calibration setup (Fig. 4b) consisted of a hydraulic jack placed on a weighing platform. The top link sensing element was mounted between the hydraulic jack and a fixed iron bar. Known force on the element was applied using the hydraulic jack. Because of the fixed bar at the top, the same load was getting transmitted to the weighing platform, and the readings of the force exerted on the weighing platform were displayed on the digital weighing balance.

To validate the developed draught sensing elements, a system comprising instrumented three-point linkage was also developed (Fig. 5), consisting of strain gauges in Wheatstone bridge arrangement for simultaneous determination of draught in the field (Upadhyaya et al., 1985; Sahu, 2005; Roul, 2014; Upadhyay, 2020). The electrical strain gauges (320 Ω, gauge factor 2.6) were fixed on lower linkages to determine the tension and bending. A circular proving ring was fixed on the top linkage to assess the compression. Three rotary position sensors helped to determine the angles of lower linkages in the horizontal and vertical planes, and the angle of the top linkage in the vertical plane.

To determine the lower linkage forces under tension, four active gauges (T1, T2, T3, and T4) were installed on the imaginary neutral axis. For neglecting the effect of temperature, four dummy gauges (D1, D2, D3, and D4) were fixed on a separate metal piece. The arrangement of strain gauges on the lower linkages is given in Fig. 6a. Active gauges were configured such that they were only responsive to tension and irresponsive to bending. Lateral force compensation was accomplished by arranging T1 and T3 gauges opposite to T2 and T4. With these gauges, a Wheatstone bridge circuit (Fig. 6b) was configured to measure the tensile force.

For determining the bending in lower linkages, eight active strain gauges (B1, B2, B3, B4, B1’, B2’, B3’, and B4’) were installed on the upper and lower faces of the lower links (Fig. 6a). The gauges B2, B4, B2’, and B4’ were installed between the implement hitch point and the lifting rod; and B1, B3, B1’, and B3’ were installed behind the lifting rod. Bending causes tension in B1, B1’, B2, and B2’ and compression in B3, B3’, B4, and B4’. Since all the eight gauges were strained to the same amount when subjected to a tensile force; the output of the Wheatstone bridge circuit was not affected due to a tensile force. Thus, all active gauges were sensitive to bending force only. Utilizing these gauges, a circuit (Fig. 6b) was configured to measure the bending force.

To measure the force on the top linkage, mild steel proving circular ring was fitted at the position of the turnbuckle. The ring was fabricated as per the standard design methodology (Godwin et al., 1993; O’Dogherty, 1996). A S-type force transducer having 1000 kg range was fitted inside the proving ring such that the compressive stress in the top linkage induced tension in the force transducer and vice versa.

Calibrations of the instrumented three-point links were carried out under both tension and bending for lower linkages and under tension for top linkage. For calibrating under tension, the lower linkages were held vertically by fixing one side of the linkage and attaching the other side to the hook of the crane with a certified digital weighing balance in-between having 1000 kg capacity and 0.1 kg least count (Fig. 7a). For calibrating under bending, the lower linkages were placed horizontally under the base frame of the mechanical crane. The end sections of both the lower linkages were held together and the load was applied at the centre position (Fig. 7b). For each calibration, the linkages were loaded up to 900 kg with step load increments of 50 kg, and the respective bridge outputs were logged using a data acquisition (DAQ) system. For calibration of the top linkage, a compressive load was applied on the proving ring from 0 to 950 kg in steps of 50 kg following the similar procedure as used for calibration of the top link draught sensing element (Fig. 7c). The bridge output of the force transducer was logged using a DAQ system.

A 10k ohms rotary position sensor was mounted on a fabricated frame attached to the tractor above PTO for determining the vertical inclination of the top linkage. Besides this, two other rotary position sensors each of 10k ohms were used for measuring the vertical and horizontal inclinations of the lower link. Out of these rotary position sensors, one was fixed on the rocker arm of the tractor hydraulic system to assess the vertical inclination of the lower link, and the other one was fixed on the fabricated frames attached to the tractor on one side of PTO to gage the horizontal angle made by the lower link. The knobs of the position sensors rotated freely with the actuation of the three-point linkage. Calibrations of the rotary position sensors were conducted using a digital protractor. Bridge outputs with respect to different linkage angles were logged using the DAQ system.

Knowing the magnitude of forces acting on both lower links, top link, and the angles made by these links in horizontal and vertical planes, the draught of the implement was computed using the following expression (Eq. 2) according to the vector geometry (Upadhyaya et al., 1985; Sahu, 2005; Kumar et al., 2016; Upadhyay, 2020):

where, D_r is the draught resistance; T_fl and B_fl are the tension and bending forces in lower linkages; C_ft is the compression force in top linkage; α and β are the angles of lower linkages in the horizontal and vertical plane; θ and ϕ are the angles of top linkage in the horizontal and vertical plane.

The validation tests were conducted with a 46 horsepower 2WD tractor having a rated engine speed of 2500 rpm. The soil type was sandy clay loam (57.1% sand, 19.9% silt, and 23.0% clay) with soil water content, cone index (CI), and bulk density of the upper 120 mm layer varying in the range of 10.50-12.13% (db), 546-975 kPa, and 1420-1680 kg m^-3, respectively. The speed of the tractor engine was adjusted by the hand throttle before initiating each experimental run. Proper tyre pressures were maintained in the front and rear wheels. The standard oven-drying technique (IS: 2720, 1973) was used for determining the soil water content under which the test samples have to be put in an oven for 24 hours at 105 ºC. The core cutter technique (IS: 2720, 1975) was followed for the measurement of the soil bulk density. The soil penetration resistance was determined using a sensor-based hydraulic cone penetrometer device designed by Upadhyay & Raheman (2020) having cone base and rod dimensions as per ASABE Standards S313.3 (2001). The depth of operation was determined by recording the distance between furrow sole and ground level along the furrow wall at an interval of about 5 m along the length of the test run and at least three locations along the width of cut of the implement. The loose soil was removed carefully up to the firm furrow sole before taking measurement. Hall effect sensors were installed on the front and rear tyres to determine the forward speed of operation following the procedures of Rasool et al. (2017) and Nataraj et al. (2021).

For performing experimental validation in the test plots, data on draught were measured simultaneously using both developed draught sensing elements and instrumented three-point links by varying tillage depth and forward speed between 80-120 mm and 3.50-7.00 km h^-1, respectively. The implement used was a mounted offset type disk harrow equipped with six cut-away concave disks mounted on the front arbor bolt and six plain concave disks at the rear. Each of the disks used had an outer circle radius of 28 cm, thickness of 0.4 cm, and centre concavity of 7 cm. Each cut-away disk had eleven notches (width 8.2 cm and depth 3.2 cm) at equal intervals. The data from both draught measurement systems were taken at 50 Hz set frequency in each channel of the HBM Quantum-X logging system (Darmstadt, Germany). Each trial was performed for a straight test run of 50 m without using the foot accelerator. The statistical investigation was accomplished in SPSS software.

The statistical indices considered for validation were: mean absolute percentage deviation (MAPD), root mean square deviation (RMSD), and maximum absolute deviation (MAD) (Upadhyay & Raheman, 2019b; Nataraj et al., 2021). MAPD was calculated for comparing the draught resistance accuracy of the measurement system in percentage. RMSD denotes the measurement capacity of the developed draught sensing elements in terms of residuals standard deviation. MAD helped to assess the maximum variation in draught resistance values measured with the sensing elements and the instrumented three-point linkages of the tractor.

An instrumentation system involving three force sensing elements was designed to measure the draught resistance of any tillage and seeding tools during field operation. The draught measurement capacity of the sensing elements was 10 kN along with an accuracy of 93.40%. Non-linearity was observed to be 1.95%, 1.44%, and 1.63% for the left link (tensile force), right link (tensile force), and top link (compressive force), respectively. The hysteresis and non-repeatability were found to be 1.50% and 0.23%, 1.58% and 0.24%, and 1.75% and 0.19% for left, right, and top links, respectively.

A system involving instrumented three-point linkages was also developed and calibrated consisting of strain gauges in Wheatstone bridge arrangement for simultaneous measurement and validation of the draught in the field. The results of field testing indicated that the developed elements were capable of providing reliable draught results with reasonable accuracy. The draught measured using developed sensing elements was also corroborated by comparing the values with the output from models developed by previous researchers at different combinations of soil cone indices, operating speeds, and depths. The average and maximum absolute variations between the estimated draught from Roul (2014) model and the developed system were observed to be 8.17% and 19.45%, respectively. The corresponding variations between Upadhyay & Raheman (2019b) model and the developed system were found to be 8.59% and 22.89%, respectively.

The developed instrumentation system is simple, reliable, and could be useful in database generation, implement design, and matching for effective utilization of tractor engine power. The uniqueness of this sensing device is its ease of construction, least changes in the hitching geometry, lower cost, and capability of quick hitching. Because of the separate use of sensing elements for all the hitching points, the different lower hitch point spread and the mast height provided in different implements are not a concern.