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Article

Evaluation of the Changes in Dimensions of the Footprint of Agricultural Tires under Various Exploitation Conditions

by
Agata Małecka
*,
Marek Brennensthul
,
Weronika Ptak
,
Jarosław Czarnecki
and
Krzysztof Lejman
Institute of Agricultural Engineering, Wroclaw University of Environmental and Life Sciences, 50-375 Wroclaw, Poland
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(12), 5228; https://doi.org/10.3390/app14125228
Submission received: 6 May 2024 / Revised: 19 May 2024 / Accepted: 21 May 2024 / Published: 17 June 2024
(This article belongs to the Section Agricultural Science and Technology)
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Abstract

:

Featured Application

This work could be applied in agricultural sciences related to soil compaction (to determine the parameters causing the soil compaction). Moreover, this work can be interesting from a practical point of view—especially in agricultural practices, to reduce the risk of soil compaction.

Abstract

This paper presents an innovative method to determine the impact of agricultural wheels on soil. The experiment was conducted under controlled conditions, and the parameters of the tire footprints on the soil were analyzed. The tested parameters were the width, length, and depth of the footprint, the cross-section area of the tire, and the area of the footprint. All parameters were determined using the 3D scanning method. Two types of tires, two levels of vertical load, and three levels of inflation pressure were used. The aim of the research was to demonstrate differences in changes in the footprint parameters as a result of changes in the operational parameters of the tires. It was found the bias-ply tire was less responsive to changes in the width and length of the footprint than the radial tire. Moreover, it was shown that radial and bias-ply tires achieved similar values for the footprint area but in the case of bias-ply tires, there was a much greater footprint depth. This means that the side parts of the footprint of bias-ply tires have a more vertical profile, so they carry the vertical loads to a lesser extent.

1. Introduction

In modern agriculture, there is a tendency to increase efficiency, which has undeniable advantages but may also have negative effects. In order to achieve high efficiency, it is necessary to provide large working widths of machines, which allows for processing a large area with fewer work passes [1]. However, machines with large widths have a high energy requirement, which in turn requires the use of larger tractors [2]. These are characterized by large sizes and weights, which have an impact on the arable soil. In this case, the main negative phenomenon will be soil compaction caused by elements of the chassis of tractors and agricultural machines.
The soil compaction is most often determined as a reduction in the volume of soil pores and the resulting closer proximity of soil particles [3,4]. The consequences of compaction on arable soils include the disruption of water–air relations in the soil, increased mechanical resistance for plant roots, and the need to use more energy to loosen the soil [3,5,6,7]. In order to reduce the compaction of arable soils, methods are used based primarily on increasing the contact surface of the running gear elements with the ground. For this purpose, the following methods are used, among others: the reduction in air pressure in the tires, the use of twin tires, the use of tires with a wider width than standard [8,9,10], and in extreme cases, the installation of tracked systems instead of wheeled systems [11].
Soil compaction is the subject of much scientific research. Research directions include determining changes in parameters describing compaction (density, compactness, maximum shearing stress), describing the geometric parameters of the rut or footprint [2,12,13,14], and formulating mathematical equations describing the impact of operational parameters on the intensity of compaction. The most frequently described changes are those in the compactness or parameters of the rut as a function of the changes in the vertical wheel load or tire inflation pressure [15,16,17,18,19]. Research on compaction can be divided into laboratory and field research. In the first case, soil bins or soil boxes are used. An example of laboratory research is the work of Alkhalif et al. [20], which showed differences in the values of the density and compactness of “artificial” soil at two levels of vertical load and three levels of inflation pressure. Similar results are also described in the work of Jjaghwe et al. [21] (where footprints obtained in a soil bin were modeled) or in the work of Taghavifar and Mardani [22], where the contact surfaces of wheels with the ground in a soil bin were examined. In turn, field tests are performed in real conditions, most often as a result of the impact of full-size agricultural vehicles and machines, and sometimes using special test stands. The works [23,24,25,26] can be taken as examples.
Both in the case of laboratory and field tests, the formulation of mathematical models requires knowledge of many parameters, so it is very important to ensure correct measurement techniques. While there are no major technical problems when measuring tire deformations, they may arise when trying to record what is happening under the soil surface as a result of compaction [15]. There are many studies that attempted to determine stresses in soil and their distribution [27,28,29,30,31,32]. Due to the mentioned technical difficulties related to measuring stresses inside the soil, innovative simulation techniques such as the Finite Elements Method (FEM) are increasingly used—this method was used in the works [33,34,35]. Another innovative technique is the method of scanning a tire rut or footprint to obtain a 3D computer image. This technique was used in the works [14,25,36,37,38,39]. In many studies on the impact of wheels on the ground, the analyzed parameter is the contact area of the wheel with the ground. It has been shown that increases in this surface (e.g., by using wider tires or lower pressure) allow for the obtaining of lower unit pressures and, consequently, less intense compaction [12,22,32,40,41]. However, the analysis of this surface for different operating conditions may give different results. The construction of the tire is of considerable importance here—in the case of bias-ply tires, greater stiffness is maintained than in radial tires [42,43], so the deformation in the front (tread) part may be smaller. In turn, it causes these tires to have a deeper impact on the soil, but the actual contact area will not necessarily be different from that generated by radial tires; the footprint of a bias-ply tire has a more three-dimensional profile, and the footprint area will also include the vertical parts of the profile whereas, on radial tires, the footprint has a flatter profile. It is for these reasons that it seems reasonable to thoroughly analyze not only the surface of the print itself but also its other dimensions. Taking into account the above considerations, the aim of the research was to assess changes in the footprint parameters of two tires with identical dimensions but different construction (bias-ply and radial) under different operating conditions. The analyzed parameters were the width, length, and depth of the footprint, as well as the surface of the footprint and the horizontal cross-sectional area in the place corresponding to the largest transverse deformation of the tire. Variable tire operating conditions were described using three values of inflation pressure and two values of vertical load.

2. Materials and Methods

2.1. The Test Bench

The tests were carried out in controlled conditions using a specialized stand for generating vertical load on the soil placed in a soil box with side lengths of 1000 mm and a height of 600 mm. The experiment was conducted in static conditions—the wheel with tested tires did not roll. Soil samples taken from an arable field were used for the tests. This soil was classified as sandy clay (according to [44]), its moisture content was 25% and its compactness was 0.9 MPa (these values were measured using a Penetrologger device according to [45]). As a first step, the soil compaction was measured in the field. In several repetitions, the values were in the range of 0.84 to 0.96 MPa and the arithmetic mean was 0.90 MPa. Then, the soil moisture was measured—the mean was 25%. These means were used as reference values in experiments in controlled conditions (in the laboratory). Each time the case was filled with the soil, the compaction was measured. When its value was too low, the soil was compacted using the plate loaded with the hydraulic jack. Otherwise, when the compaction was too high, the soil was loosened with the spade. The soil moisture was also controlled—when it was too low, the soil was sprinkled; otherwise, it was set aside to dry.
After this preparation, the footprint was made with the wheel, using a special test stand. A view of the test stand is shown in Figure 1.
In the first stage, the box (4) with intact soil was placed in the lower part of the stand, and then the wheel (1) was moved down using the mechanism (7). Then, in the upper part of the internal frame (3), a hydraulic jack with a load capacity of 5000 kg and a TecSis inductive forcemeter with a measuring range of 0—100 kN and an accuracy of 50 N were installed. Using the hydraulic jack, pressure was exerted on the internal part of the frame together with the wheel. In the initial part of this step, the value of the vertical load was read—two levels were used: 11.8 kN and 19.6 kN. The reference point for the chosen values of the vertical load was the load index formulated by the tire manufacturer. Both for bias-ply and radial tires, it was determined to be 145, which meant the load was 2900 kg. The first level of the vertical load in the experiment was equal to 11.8 kN—after calculations, the mass was found to be 1200 kg—in turn, it was about 40% of the maximum vertical load. In practice, what is recommended is the lower limit of the exploitation of agricultural tires (when the lower loads are often used in exploitation, the farmer should buy the tires with a lower load index). The second level of the vertical load was 19.8 kN, which provides a mass of 2000 kg, which was about 70% of the maximum load. In agricultural practice, it is the upper limit of the load that is recommended for the continuous operation of the tractor. Other (intermediate) levels of the vertical load will be the subject of further research. The selection of inflation pressures was realized based on the recommendation of tire manufacturers. They determined the maximum inflation pressures—for both tires, it was equal to 0.26 MPa but this value is not recommended for continuous operation (it is used just at the assembly of the tire on the rim). For this reason, the maximum value of the inflation pressure was determined to be 0.24 MPa—this value is sometimes used for continuous work at very high vertical loads of tractors, especially in transport operations. Sometimes, this high pressure value is used in field operations by farmers who do not know the principles of inflation pressure selection. Lower levels of inflation pressure (0.16 MPa) are often used for different operations realized by agricultural tractors—it is “universal” pressure both for transport and field operations. It is used especially when the farmer does not have an inflation pressure control system. This medium value of the inflation pressure can obtain low rolling resistance on the road and relatively good traction abilities in the field. The lowest level of inflation pressure (0.08 MPa) is recommended for field operations because it ensures a large area between the tire and soil—in turn, the compaction can be lower. After reaching the set load values and making a footprint, the load was reduced, the forcemeter and hydraulic jack were dismantled, and the wheel was lifted. Then, the soil box was moved out and the footprint was scanned. The tests were performed for three inflation pressures: 0.08 MPa, 0.16 MPa, and 0.24 MPa. Every test was conducted in three replications.
The main limitations of the experiment include the range of pressures at which the tests were carried out and the range of vertical loads. Moreover, the results obtained in real conditions (in the field) with the same operating parameters could differ due to the prior preparation of the soil for tests in controlled conditions. The described experiment was conducted only in the laboratory; however, in further research, field conditions will be taken into account. Then, the comparisons of the results of two types of research will be conducted. Moreover, in further research, the dynamic tests will be realized (the wheel will be rolling on the soil).

2.2. Scanning Process

A Smarttech 3D Universe scanner was used for scanning; the scanner was connected to a computer to enable the continuous visualization of the process. Detailed data regarding the scanner are presented in Table 1 and in Ptak et al. [14]. The scanner was mounted on a tripod, which ensured a constant distance between the scanner and the scanned footprint. Before scanning, markers were placed in the contour of the footprint to clearly separate the scanned area from the background (intact soil). In the first stage of scanning, the so-called triangle mesh was used, from which a three-dimensional (3D) profile of the print was then created in the program. Next, the obtained 3D image was analyzed in a graphic program—a cross-section was made in the vertical plane in the transverse direction (to determine the width and depth of the footprint) and longitudinally (to determine the length of the footprint). In addition, a cross-section was made in the horizontal plane at the height corresponding to the largest transverse deformation—in this case, the aim was to compare the nature of the deformation of a radial and bias-ply tire. The actual surface of the footprint (taking into account vertical deformation) was determined via direct reading in the scanner software (S3Dmeasure v.20). The Smarttech 3D Universe scanner was calibrated for each 50 h of work. The calibration was realized using a special plate with calibration points.
The presented method for the determination of the footprint parameters is innovative, it can simplify the experiment, and it can give high accuracy.

2.3. Tested Tires

The tests used two tires with the same external dimensions and identical tread patterns but with different internal structures. This choice was justified by the necessity to verify whether the radial tire remains more flexible and deformable in a wide range of inflation pressures. The tested tires were marked 500/50-17 (bias-ply) and 500/50R17 (radial). In both cases, the tread width was 500 mm, the external diameter was 931.8 mm, and the rim diameter was 431.8 mm. Both tires had a maximum load capacity of 2900 kg (load index of 145).

2.4. Statistical Analysis

The results obtained in the experiment were subjected to a statistical analysis. In order to assess the influence of factors (vertical load, inflation pressure), a two-factor analysis of variance was used at a significance level of α = 0.05. As part of this assessment, post hoc tests (Fisher’s HSD) were also performed to indicate differences between individual factor levels. The next part of the analysis included determining equations describing the relationships between inflation pressure and the analyzed parameters. The data were obtained from the repetitions (3 repetitions each time); from them, the arithmetic means and standard deviations were calculated (for each combination of the factors and for each tire separately). Before performing the analysis of variance (ANOVA), the conditions of its applicability were checked; first, the Shapiro–Wilk test was performed to verify the normality of the distributions and then, the homogeneity of variance test (Levene test) was performed. Due to the fact that the distributions were normal and the variances were homogeneous, there was no need to transform the data. Post hoc tests were performed using the least significant difference (Fisher’s NIR) test. Regression equations describing the relationship between tire inflation pressure and the geometric parameters of the impression were developed using the least squares method. The statistical analysis was performed using the Statistica 13.0 software.

3. Results

The first parameter analyzed was the width of the generated footprint. Figure 2 shows the values of this parameter for both tires used in the tests.
The highest values of the footprint width were found for a radial tire at a lower level of vertical load (19.6 kN). This tendency was observed at all three inflation pressure values—the range of the values was from 467 to 481 mm. In the case of a bias-ply tire with the same vertical load, a different tendency was found. Only at the lowest inflation pressure was the value of the width similar to that observed for the radial tire—it amounted to 477.6 mm, i.e., by approx. 3 mm (0.7%) less than in the case of a radial tire with the same operating parameters. At the other two inflation pressure values, the footprint widths of the bias-ply tire were smaller than those of the radial tire (by 3.7% and 3.8%, respectively). At a lower value of vertical load (11.8 kN), in most cases, the width of the footprint was smaller than at a higher load. The exception was in the case of a radial tire at the lowest inflation pressure—the width was then practically the same as at a higher load level (482 mm for loads 11.8 kN and 481 mm for a load of 19.6 kN).
Analyzing the changes in the width of the footprint as a result of increasing the inflation pressure of the tires, it can be concluded that in most cases, the increase in pressure resulted in a decrease in width. However, the bias-ply tire was characterized by greater stability of these changes. It was probably caused by the greater stiffness of this tire’s structure. With a higher vertical load, the first increase in inflation pressure in the bias-ply tire resulted in a decrease in width of 2% and a following increase of 4%. At lower vertical loads, these changes were approximately 1% and 3%, respectively. In the case of a radial tire with a lower vertical load, increasing the pressure resulted in a significant decrease in the width of the footprint (by 9% and 2%, respectively). However, with a higher vertical load, the changes in the footprint width were much smaller—they amounted to 1% and 2% for the first and second pressure increases, respectively.
In order to demonstrate differences in the nature of changes in the footprint width value at different inflation pressures, a regression analysis was performed, the results of which are presented in Table 2.
It can be concluded that the vertical load determined the differences in the course of changes in the width of the footprint as a result of increasing the tire inflation pressure. With a smaller vertical load, the changes in the footprint values were described using a second-degree polynomial function; meanwhile, with a larger vertical load, a linear function was used.
Figure 3 shows the values of the length of the footprint generated by the tested tires at various values of inflation pressures and vertical loads.
The longest footprints were found for a bias-ply tire with a vertical load of 19.6 kN and the lowest inflation pressure (the value was 518.9 mm). A very similar value was recorded for a radial tire with the same operating parameters (515.2 mm). The lowest values of the footprint length concerned the radial tire with the lowest vertical load and the highest inflation pressure—the length, in this case, was 373.0 mm.
In analyzing the changes in the length of the footprint generated as a result of changes in the inflation pressure, it can be noticed that the dynamics of the changes in the length of the footprint due to changes in the tire operating parameters were greater than in the case of the previously analyzed parameter. This trend was especially visible in the case of the radial tires. At the lowest inflation pressure and with a given vertical load, both tires had similar footprint length values (475–479 mm with a lower vertical load and 515–518 mm with a higher load). Increasing the inflation pressure in a radial tire resulted in a decrease in the footprint length, with a greater rate of decrease occurring at a lower vertical load—the decreases were 15% after increasing the pressure from 0.08 to 0.16 MPa and 9% when increasing from 0.16 MPa to 0.24 MPa (with a higher vertical load, the changes were 3% and 5%, respectively). A different tendency occurred for a bias-ply tire—with a lower vertical load, increasing the inflation pressure resulted in practically no changes in the footprint length values (differences in the range of 1–2%). With a higher vertical load on the bias-ply tire, the first increase in pressure resulted in a decrease in the footprint length of 32 mm (7%). A further increase in inflation pressure resulted in a length increase of 10.7 mm (2% compared to the length corresponding to a pressure of 0.16 MPa). In analyzing the increase in the vertical load, it can be observed that for both tires, increasing the vertical load resulted in an increase in the length of the footprints, but for the radial tire, the differences were higher than for the bias-ply tire. For example, for a bias-ply tire, the largest increase was 9%, and for a radial tire, it was as great as 27%.
Similarly to the previous case, a regression analysis was performed to describe with mathematical equations the changes in the length of the footprint depending on the value of the inflation pressure—the results are presented in Table 3.
Only in the case of a radial tire with a load of 19.6 kN was a linear regression equation used, with a coefficient of determination of 0.97. In the remaining cases (a bias-ply tire with both loads and a radial tire with a load of 11.8 kN), second-degree polynomial equations with determination coefficients of 0.98 were used. This fact was caused by a different type of change in the footprint length of a radial tire with a higher vertical load. There was a continuous decrease in length as a result of increasing the inflation pressure, while in other cases, only the first increase in pressure resulted in a decrease in the footprint length, and subsequent increases resulted in a slight increase.
The next parameter analyzed was the depth of the footprint. The values of this parameter are shown in Figure 4.
In the case of the footprint depth, a tendency can be noticed in which the bias-ply tire generated a significantly deeper footprint compared to the radial tire—this tendency was noticeable at both levels of vertical load. Moreover, it can be stated that for a bias-ply tire, an increase in vertical load resulted in an increase in the value of the analyzed parameter, while for a radial tire, this tendency occurred only at extreme values of inflation pressure. The lowest values were shown for a radial tire at the lowest inflation pressure. In this case, the influence of the vertical load was small—with a lower value (11.8 kN), the depth was 9.7 mm, and with a higher load (19.6 kN), the depth was exactly 1 mm greater. The highest footprint depth values were found at the highest inflation pressure for a bias-ply tire—they were 31.9 and 41.8 for the lower and higher vertical load levels, respectively.
In analyzing changes in depth due to changes in inflation pressure, it can be seen that at a higher level of vertical load, the changes had a more linear character than in the case of a lower load. For a bias-ply tire, the first increase in inflation pressure resulted in an increase in the footprint depth of over 13 mm, which was as much as 71% compared to the initial value of 18.6 mm. The next increase in inflation pressure resulted in an increase of 10 mm, which was 31% compared to the value of 31.8 mm. In the case of a radial tire with a higher vertical load, the first increase in inflation pressure resulted in an increase in the footprint depth by over 7 mm, which was 68%, and the subsequent increase in pressure resulted in an increase in the value of the analyzed parameter by 10 mm (an increase of 56% compared to the value corresponding to the medium pressure). Different types of changes in the depth of footprint were observed at lower vertical loads. Both for radial and bias-ply tires, the largest increases in the footprint depth were observed after the first increase in inflation pressure—they amounted to 15.8 mm for the bias-ply tire (118%) and 11.7 mm for the radial tire (119%). In both cases, a further increase in inflation pressure resulted in a slight increase or even a decrease in the footprint depth value—for the bias-ply tire, an increase of only 2.7 mm (less than 9%) was observed, while for the radial tire, there was a decrease in the footprint depth of 0.7 mm, i.e., 3.2%. In both cases, the second increase in inflation pressure resulted in a change in the character of the increase in the analyzed parameter (the function was no longer linear).
When assessing the impact of changes in the vertical load of a radial tire on the depth value, some tendency can be noticed—the higher the inflation pressure, the higher the increase in the footprint depth as a result of the increase in load. At the lowest pressure, the difference in depth values between loads 11.8 kN and 19.6 kN is 1 mm (9.9%), and at the highest inflation pressure, it is 7.2 mm (34.8%). In the case of a bias-ply tire, load changes had a slightly different impact on changes in the footprint depth. The largest increase in the analyzed parameter as a result of increasing the load (by 5.2 mm, which means 38.7%) was observed at the lowest inflation pressure. At a pressure of 0.16 MPa, the increase in load resulted in an increase in depth of only 2.6 mm (9.0%), while at the highest pressure, an increase of 9.9 mm (31.2%) was achieved.
The results of the regression analysis carried out for the footprint depth as a function of inflation pressure are presented in Table 4. As in the case of the first analyzed parameter (footprint width), it can be seen that at a lower load level, the nature of the footprint depth changes was different than at a higher load level. This tendency was observed for both tires and is confirmed by the different course of the function described with the regression (at a load of 11.8 kN, there is a second-degree polynomial function, and at a load of 19.6 kN, there is a linear function).
One of the parameters that may affect the compaction of the ground by the tractor wheel is the contact pressure. At a given vertical load, its value will depend only on the contact area of the tire with the ground. In turn, this parameter will depend on the size of the tire’s cross-section near its contact with the ground. Based on the literature data, it is known that radial tires will react differently to changes in this cross-section compared to bias-ply tires. For this reason, it becomes justified to analyze both the cross-section of the tire and the footprint areas. The first of these parameters is shown in Figure 5. The cross-sections were made at the height corresponding to the higher transverse deformation of the tires.
Among all the analyzed cases, the smallest changes in cross-section due to the increase in inflation pressure were found for a bias-ply tire with a lower level of vertical load. In this case, the first increase in inflation pressure resulted in an increase in the cross-section area of less than 0.02 m2 (10.0%), while the subsequent increase in inflation pressure did not cause any changes in the cross-section area. In turn, for the same tire with a higher vertical load, the first increase in pressure resulted in a decrease in the cross-section area of 0.03 m2 (12.4%), while a further increase in the inflation pressure resulted in an increase in the cross-section area of 0.02 m2 (8.1%). This tendency may be caused by the fact that when the inflation pressure was first increased, deformation occurred in the radial direction (the effect of “tightening” the side walls), and only when the inflation pressure was increased again did significant transverse deformation occur, resulting in an increase in the cross-section area. In the case of a radial tire with both vertical loads, a decreasing tendency in the cross-section can be seen with increasing inflation pressure. Greater decreases (25% and 11%, respectively, for both inflation pressure increases) were found at lower vertical loads. At higher loads, the decreases in the cross-section area were 7% (first pressure increase) and 8% (second pressure increase). This was probably caused by the fact that the heavier tire became less deformable due to initial deflection.
The regression analysis performed for each tire/load combination (Table 5) showed that only for a radial tire with a higher vertical load was it possible to use linear regression. In other cases, the relationship between the inflation pressure and the cross-sectional area was described with a second-degree polynomial function. This situation was, therefore, similar to that in the case of the footprint length parameter, so the change in the footprint surface is directly related to the change in its length.
As mentioned in the previous section, one of the most important parameters of cooperation between the wheel of an agricultural vehicle and the ground is the surface of the generated footprint. The values of this parameter are shown in Figure 6.
In the case of the last analyzed parameter, the highest values were found at a higher level of vertical load (19.6 kN). For a bias-ply tire, the highest value (0.29 m2) was found at an inflation pressure of 0.24 MPa and the lowest (0.24 m2) at a pressure of 0.16 MPa—therefore, a tendency can be seen that the first increase in inflation pressure caused a decrease in the footprint area (of 0.02 m2, i.e., 8.5%) and subsequent increases to a value higher than the initial value (of 0.04 m2, i.e., 18.2%). A different manner of changes was observed for the radial tire—there was a continuous decrease in the value of the footprint area with increasing inflation pressure (of 5.9% and 4.3%, respectively). At a lower level of vertical load, differences between a radial and a bias-ply tire in terms of changes in the footprint area can also be seen. The radial tire responded by decreasing its surface area with increases in inflation pressure—the first increase in pressure resulted in a decrease of 0.063 m2, which was 24.9%, while the second increase in pressure resulted in a decrease of 0.018 m2 (9.6%). The opposite situation occurred in the case of a bias-ply tire: where the inflation pressure increased, increases in the footprint area were observed (increases of 15.2% at the first increase in pressure and 5.4% at the second increase).
Based on the analysis of changes in the second factor (vertical load), it was shown that for both radial and bias-ply tires, there was an increase in the footprint area as a result of increasing vertical load. In the case of a radial tire, the increase values ranged from 7.9% to 43.0%. For a bias-ply tire, the increases were 35.8%, 7.9%, and 21.1% for inflation pressures of 0.08; 0.16, and 0.24 MPa, respectively.
As in the case of the previous parameters, a regression analysis was performed to describe the relationship between the inflation pressure and the footprint area. The results are presented in Table 6.
It can be stated that in all cases, changes in the analyzed parameter were described via functions with a high level of predictability (R2 values were in the range of 0.96–0.98). Only in the case of a radial tire was a linear function used at a higher vertical load level while in the remaining cases, the changes were described using second-degree polynomial functions.

3.1. Results of Statistical Analysis—Bias-Ply Tire

Table 7 presents the results of the multivariate analysis of variance for the results obtained for the bias-ply tires. The p-values presented represent the level of probability of accepting the null hypothesis stating that there is no significant impact of the factor on the analyzed parameter.
It can be concluded that in most cases, both factors had a significant impact on the analyzed parameters because the p-values were much lower than the significance level α. The only exception was the influence of inflation pressure on the tire cross-section value—in this case, the statistical analysis did not show any significant differences. As a part of the analysis, post hoc tests were also performed to indicate between which factor levels there were significant differences. In the case of the first factor (vertical load), there were only two levels (11.8 kN and 19.6 kN), so if the analysis showed a significant effect, it meant that there must have been significant differences between the two levels. However, the second factor (inflation pressure) had three levels, so it was justified to perform a homogeneous group test. It showed that only for the footprint depth, each pressure level was a separate, homogeneous group (there were significant differences in the footprint depth values between each of the inflation pressures). For other parameters, the post hoc test identified two homogeneous groups.

3.2. Statistical Analysis Results—Radial Tire

Table 8 presents the results of the multivariate analysis of variance for the results obtained for the radial tires. Similarly to the previous case, p-values indicate the level of probability of accepting the null hypothesis that states there is no significant impact of the factor on the analyzed parameter.
In analyzing the data presented in the table above, it can be concluded that the tire inflation pressure had a significant impact on all analyzed parameters. In the case of the second factor (vertical load of the wheel), there was no significant effect on the depth of the generated footprint (the significance was maintained in the remaining analyzed parameters). Moreover, based on the results of post hoc tests (Fisher’s HSD), it was found that in the case of the impact of vertical load on the depth of footprint, both levels of the factor were classified into the same group (hence, there was no significant effect of this factor). In the case of the second factor, separate groups were found for the length of the footprint, its depth, and cross-section area; meanwhile, two homogeneous groups were found for the width of the footprint and the area of the footprint—in both cases, the inflation pressure levels of 0.16 MPa and 0.24 MPa qualified into the same group.

4. Discussion

In accordance with the assumed aim of the research, differences in the values of the footprint parameters generated by tires of different internal structures, at different inflation pressures, and vertical loads were assessed. The research was carried out in controlled conditions using a 3D scanning technique. In this way, the deformation characteristics of both tires due to inflation pressure changes were determined. When comparing the method used with other techniques described in the literature, some analogies can be found. Very similar techniques were used in studies [21,37]—in these works, a three-dimensional model of the footprint was obtained in static conditions on soil placed in a soil bin. In turn, in works [22,25,26], a 3D image of the footprint was also obtained but this took place in dynamic conditions while rolling the wheel on the soil in long soil bins. In works [12,40], the parameters of the footprint were also assessed but this took place in field conditions.
One of the relationships observed in the research was the fact that a tire with a higher inflation pressure is characterized by higher stiffness and, therefore, a potentially more negative impact on agricultural soil. This tendency is also confirmed by works [12,46]. In the first of these references, the authors concluded that the tire with dimensions similar to the tires used in the discussed results can obtain a width of footprint in the range of 0.38–0.54 m while in the presented results, this range was from 425 mm to 481 mm. However, the tire structure and its possible impact on the tire’s deformability at various pressures and vertical loads should also be taken into account. The relationship most often described in the literature is that radial tires are more sensitive to pressure changes than their bias-ply tires [42,47,48]; however, in the studies performed, the obtained relationships also depended on the operational parameters. For a bias-ply tire, it was shown that, with low vertical load, the footprint area increases with increasing pressure faster than the horizontal cross-section area of the tire. This increase, however, was caused by an equally dynamic increase in the depth of the footprint—this situation is not favorable at all, because the total surface of the footprint also includes its vertical parts, which do not carry the loads resulting from the weight of the vehicle. With a higher vertical load, a similar tendency was shown for the bias-ply tire, but it was most visible after the second increase in inflation pressure (from 0.16 MPa to 0.24 MPa). In this case, it was clearly demonstrated that the increase in the actual surface of the footprint was correlated with the increase in the footprint depth—this is consistent with the results obtained in [49]. In this work, the difference in footprint depth generated by the radial tire at the minimum and maximum inflation pressures was about 21%, while in current research, this difference was 29.4%. Moreover, for the bias-ply tires, there were small changes in the width and length of the footprint as a result of changing the inflation pressure, which only further confirms the hypothesis that the inflation pressure has a large impact on increasing the stiffness of the tire and, consequently, on its deeper impact. Slightly different relationships were demonstrated in work [27], where a bias-ply tire was inflated to three pressures (0.10, 0.16, and 0.32 MPa), and with the increase in pressure, a decrease in the actual footprint area was observed each time. In this case, the maximum difference in values of the actual footprint area at extreme inflation pressures (0.100 MPa vs. 0.325 MPa) was 86%, while in the current results, this difference does not exceed 44%. However, in those studies, tires with a less aggressive tread design were used, so its in-depth impact was probably smaller. In turn, work [28] showed some analogies to the results obtained in this study—the lowest contact area values were achieved at the middle value of the inflation pressure.
The radial tire responded to the increase in inflation pressure differently than the bias-ply tire. Reducing the inflation pressure resulted in an increase in the tire footprint and cross-section area. This trend was visible for both vertical load levels. At the same time, it was found that the inflation pressure had a greater impact on the changes in the linear dimensions of the footprint (especially the width). Such relationships seem to be reflected in work [25], in which a radial tire was tested at normal pressure (70 kPa), underinflated, and overinflated. It has been shown that reducing the pressure allows for a larger contact surface and lower contact pressures. A similar observation was presented in work [50], where the influence of inflation pressure on the value of tire penetration in the soil was analyzed, and in each case, the best operating conditions concerned the lowest inflation pressure. Works [17,51] also showed that a radial tire responds better to lowering the inflation pressure by having a larger contact surface with the ground.
In analyzing the influence of vertical load, it was found that in the case of a bias-ply tire, it had an impact on all analyzed parameters. In each case, an increase in parameter values was observed as a result of the increase in vertical load, with the largest changes observed in the tire footprint and cross-section area and the smallest changes in the footprint width. This tendency is similar to the results presented in the literature—for example, in works [3,17,31], it was shown that an increase in vertical load results in an increase in rut parameters (especially the vertical depth). In turn, for a radial tire, a significant impact of the vertical load was found only on the size of the footprint surface and the cross-section of the tire and on the footprint length and width. However, there was no effect on the footprint depth, which may indicate the better adaptation of the tire to the ground as a result of vertical load changes (the footprint area increased so much that the tire had a larger contact area; so, there was no tendency to sink the tire into the soil). This tendency seems to be consistent with the results obtained in [2,32].
It is very important that the practical aspects of tire research be taken into account in addition to the scientific aspects. In the case of analyzing the impact of wheels on the soil, the main practical aspect is the necessity to reduce compaction by indicating such factor values that result in the greatest width of the rut length and the largest contact area of the wheels with the ground. This results in the least deep impact of the wheels on the soil, and as a result, better soil aeration, better moisture conditions, and lower mechanical resistance to the roots of the plants. It means that properly selected tire operating conditions can give higher yields and lower energy consumption via agricultural equipment. Many economic benefits can be achieved when farmers control operational parameters. First of all, by selecting the tire pressure and vertical load, you can ensure the optimal adjustment of the tires to the ground and, as a result, reduce pressure and compaction. This, in turn, allows for lower mechanical resistance that the soil will pose to agricultural machinery elements. This, in turn, has a positive impact on energy use (reduction in fuel consumption). These changes become visible especially after a longer time—after a larger number of treatments. Practical activities based on obtained results can be integrated into existing agricultural work management systems. This applies especially to tire inflation pressure management systems because this parameter can be changed quite quickly even while driving a tractor. Combined with the work management system, this can operate continuously, adapting the pumping pressure to the current operating conditions of the tractor, thus ensuring less soil compaction.

5. Conclusions

This paper presented the results of the research regarding the parameters of tire footprints; the experiment was conducted in controlled conditions using an innovative 3D scanning method. The analyzed parameters were the width of the footprint, the length of the footprint, the depth of the footprint, the area of the cross-section of the tire, and the actual area of the footprint.
Based on the results of the conducted research, the following conclusions were formulated:
  • A bias-ply tire subjected to changes in operating parameters reacts to a lesser extent to changes in footprint parameters compared to a radial tire. Due to the stiffer structure confirmed through small changes in the cross-section, increasing the inflation pressure and vertical load causes the tire to sink into the ground significantly. The observed large increase in the footprint area after increasing the vertical load and pressure is caused by the large footprint effect—the footprint area also includes its vertical parts that do not carry vertical loads.
  • A bias-ply tire is more susceptible to deformations caused by inflation pressure changes. Pressure reduction results in a large increase in the width of the footprint and a slightly smaller increase in its length. Therefore, it is of a different deformation character than in a radial tire. At the same time, as a result of inflation pressure reduction, increases are observed both in the cross-section area of the tire and in the footprint area. This first increase means the greater flexibility of a radial tire compared to a bias-ply one. As for the increase in the footprint area, it was more intense than the increase in depth, which indicated that the tire adapted to the ground better. Increasing the vertical load resulted in an increase in all analyzed parameters except the footprint depth, which confirms the theory that the radial tire adapts better to the ground.
  • A correct analysis of the impact of agricultural tires on the soil should take into account not only the footprint area but also changes in parameters such as the width, length, and depth of the rut. Additionally, a parameter related to the tire’s deformability should be taken into account. The analysis of the footprint itself may lead to erroneous conclusions because the surface also includes parts with a more vertical profile that carry loads to a small extent. As a result, with a large footprint area and a simultaneous large depth, the actual surface carrying vertical loads is smaller than the measured footprint area.
In the experiments, there were the following limitations: a specified range of vertical loads and inflation pressures and one type of soil and static conditions. In further research, the range of the factors should be extended. For this reason, there are plans to determine the impact of rolling wheels on different agricultural soils under field conditions. These experiments will be conducted in a wide range of vertical loads and inflation pressures.

Author Contributions

Conceptualization, A.M. and W.P.; methodology, J.C.; software, M.B. and A.M.; validation, A.M. and M.B.; formal analysis, J.C. and K.L.; investigation, A.M., W.P. and M.B.; resources, A.M. and W.P.; data curation, M.B.; writing—original draft preparation, A.M. and M.B.; writing—review and editing, M.B.; visualization, W.P.; supervision, J.C.; project administration, J.C. and K.L.; funding acquisition, J.C. and K.L. All authors have read and agreed to the published version of the manuscript.

Funding

The article processing charge was financed by the Wroclaw University of Environmental and Life Sciences.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of the data; in the writing of the manuscript; or in the decision to publish the results.

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Figure 1. View of the test stand used in the tests: 1—tested wheel, 2—main frame, 3—internal frame with wheel mounting system, 4—box with tested soil, 5—scanner, 6—computer with scanner software, 7—lifting mechanism wheels, and 8—installation site of the inductive forcemeter and hydraulic actuator.
Figure 1. View of the test stand used in the tests: 1—tested wheel, 2—main frame, 3—internal frame with wheel mounting system, 4—box with tested soil, 5—scanner, 6—computer with scanner software, 7—lifting mechanism wheels, and 8—installation site of the inductive forcemeter and hydraulic actuator.
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Figure 2. The values of the width of the footprint with different inflation pressures and vertical loads.
Figure 2. The values of the width of the footprint with different inflation pressures and vertical loads.
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Figure 3. The values of the length of the footprint with different inflation pressures and vertical loads.
Figure 3. The values of the length of the footprint with different inflation pressures and vertical loads.
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Figure 4. The values of the depth of the footprint with different inflation pressures and vertical loads.
Figure 4. The values of the depth of the footprint with different inflation pressures and vertical loads.
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Figure 5. Values of the cross-section area of the tires with different inflation pressures and vertical loads.
Figure 5. Values of the cross-section area of the tires with different inflation pressures and vertical loads.
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Figure 6. Values of tire footprint area, depending on inflation pressure and vertical load.
Figure 6. Values of tire footprint area, depending on inflation pressure and vertical load.
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Table 1. Parameters of the Smarttech 3D Universe scanner [14].
Table 1. Parameters of the Smarttech 3D Universe scanner [14].
ParameterDescription
Scanning technologyWhite structural light—LED
Dimensions (XYZ) of measuring volume (mm)400 × 300 × 230
Distance between points (mm)0.156
Accuracy (mm)0.08
Power consumption during measurement (W)200
Total mass (kg)4.40
Working temperature (°C)20 ± 0.5
Table 2. Results of the regression analysis between the width of the footprint and the tire inflation pressure.
Table 2. Results of the regression analysis between the width of the footprint and the tire inflation pressure.
Tire/Vertical Load Regression EquationCoefficient of DeterminationCoefficient of Correlation (r-Pearson)
Bias-ply, 11.8 kNy = 890.6x2 − 375.5x + 478.20.980.99
Radial,
11.8 kN		y = 2631.2x2 −1185.1x + 560.10.980.99
Bias-ply 19.6 kNy = −168.4x + 489.30.950.97
Radial,
19.6 kN		y = −81.5x + 487.90.980.99
Table 3. Results of the regression analysis between the footprint length and tire inflation pressure.
Table 3. Results of the regression analysis between the footprint length and tire inflation pressure.
Tire/Vertical Load Regression EquationCoefficient of DeterminationCoefficient of Correlation (r-Pearson)
Bias-ply, 11.8 kNy = 979.7x2 − 277.1x + 491.30.980.99
Radial,
11.8 kN		y = 2688.3x2 − 1527.3x + 584.80.980.99
Bias-ply 19.6 kNy = 3343.7x2 − 1202.7x + 593.80.980.99
Radial,
19.6 kN		y = −260.31x + 537.80.970.98
Table 4. Results of the regression analysis between the footprint depth and tire inflation pressure.
Table 4. Results of the regression analysis between the footprint depth and tire inflation pressure.
Tire/Vertical Load Regression EquationCoefficient of DeterminationCoefficient of Correlation (r-Pearson)
Bias-ply, 11.8 kNy = −1025.0x2 + 443.4x − 15.50.980.99
Radial,
11.8 kN		y = −964.1x2 + 377.1x − 14.30.980.99
Bias-ply 19.6 kNy = 145.1x + 7.530.980.99
Radial,
19.6 kN		y = 107.8x + 1.620.980.99
Table 5. Results of the regression analysis between the tire cross-section area and its inflation pressure.
Table 5. Results of the regression analysis between the tire cross-section area and its inflation pressure.
Tire/Vertical Load Regression EquationCoefficient of DeterminationCoefficient of Correlation (r-Pearson)
Bias-ply,
11.8 kN		y = −1.26x2 + 0.51x + 0.140.980.99
Radial,
11.8 kN		y = 2.83x2 − 1.36x + 0.310.970.98
Bias-ply
19.6 kN		y = 3.49x2 − 1.20x +0.300.980.99
Radial,
19.6 kN		y = −0.21x + 0.260.980.99
Table 6. Results of the regression analysis between the tire footprint area and its inflation pressure.
Table 6. Results of the regression analysis between the tire footprint area and its inflation pressure.
Tire/Vertical Load Regression EquationCoefficient of DeterminationCoefficient of Correlation (r-Pearson)
Bias-ply,
11.8 kN		y = −1.37x2 + 0.70x + 0.150.980.99
Radial,
11.8 kN		y = 3.48x2 − 1.62 + 0.360.980.99
Bias-ply
19.6 kN		y = 5.24x2 − 1.54x + 0.360.980.99
Radial,
19.6 kN		y = −0.17x + 0.280.960.98
Table 7. Results of the statistical analysis of experimental data for the bias-ply tire; the significance level α = 0.05; SD—standard deviation.
Table 7. Results of the statistical analysis of experimental data for the bias-ply tire; the significance level α = 0.05; SD—standard deviation.
Footprint ParameterFactorFactor LevelArithmetic Mean±SDp-Value
Width of the footprint, mmVertical load11.8 kN444.87 A7.990.000001
19.6 kN462.12 B12.31
Inflation pressure0.08 MPa465.75 A13.330.000004
0.16 MPa449.69 B10.20
0.24 MPa444.92 B6.86
Length of the footprint, mmVertical load11.8 kN476.09 A5.330.000015
19.6 kN500.90 B14.52
Inflation pressure0.08 MPa497.03 A14.040.006526
0.16 MPa479.02 B8.65
0.24 MPa489.44 A9.37
Depth of the footprint, mmVertical load11.8 kN24.80 A0.870.000006
19.6 kN30.72 B1.01
Inflation pressure0.08 MPa15.94 A2.85<0.000001
0.16 MPa30.51 B1.49
0.24 MPa36.83 C3.48
Cross-section area of the tire, m2Vertical load11.8 kN0.179 A0.0190.000006
19.6 kN0.217 B0.019
Inflation pressure0.08 MPa0.199 A0.0340.456757
0.16 MPa0.194 A0.009
0.24 MPa0.202 A0.017
Tire–soil contact area, m2Vertical load11.8 kN0.220 A0.0180.000002
19.6 kN0.266 B0.019
Inflation pressure0.08 MPa0.232 A0.0370.000828
0.16 MPa0.234 A0.010
0.24 MPa0.263 B0.027
The letters at arithmetic means (A,B,C) denote separate homogenous groups.
Table 8. Results of the statistical analysis of experimental data for the radial tire; the significance level α = 0.05; SD—standard deviation.
Table 8. Results of the statistical analysis of experimental data for the radial tire; the significance level α = 0.05; SD—standard deviation.
Footprint ParameterFactorFactor LevelArithmetic Mean±SDp-Value
Width of the footprint, mmVertical load11.8 kN449.15 A25.310.000220
19.6 kN474.76 B6.59
Inflation pressure0.08 MPa481.77 A12.610.000275
0.16 MPa456.57 B21.13
0.24 MPa447.53 B21.83
Length of the footprint, mmVertical load11.8 kN420.80 A36.87<0.000001
19.6 kN496.09 B18.31
Inflation pressure0.08 MPa497.41 A19.640.000007
0.16 MPa454.49 B39.36
0.24 MPa423.45 C34.96
Depth of the footprint, mmVertical load11.8 kN17.27 A2.650.198806
19.6 kN18.88 A2.56
Inflation pressure0.08 MPa10.21 A0.61<0.000001
0.16 MPa19.66 B0.89
0.24 MPa24.36 C2.02
Cross-section area of the tire, m2Vertical load11.8 kN0.177 A0.032<0.000001
19.6 kN0.224 B0.014
Inflation pressure0.08 MPa0.229 A0.0120.000002
0.16 MPa0.195 B0.033
0.24 MPa0.177 C0.032
Tire–soil contact area, m2Vertical load11.8 kN0.207 A0.0340.000002
19.6 kN0.257 B0.012
Inflation pressure0.08 MPa0.261 A0.0110.000051
0.16 MPa0.222 B0.036
0.24 MPa0.212 B0.035
The letters at arithmetic means (A,B,C) denote separate homogenous groups.
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Małecka, A.; Brennensthul, M.; Ptak, W.; Czarnecki, J.; Lejman, K. Evaluation of the Changes in Dimensions of the Footprint of Agricultural Tires under Various Exploitation Conditions. Appl. Sci. 2024, 14, 5228. https://doi.org/10.3390/app14125228

AMA Style

Małecka A, Brennensthul M, Ptak W, Czarnecki J, Lejman K. Evaluation of the Changes in Dimensions of the Footprint of Agricultural Tires under Various Exploitation Conditions. Applied Sciences. 2024; 14(12):5228. https://doi.org/10.3390/app14125228

Chicago/Turabian Style

Małecka, Agata, Marek Brennensthul, Weronika Ptak, Jarosław Czarnecki, and Krzysztof Lejman. 2024. "Evaluation of the Changes in Dimensions of the Footprint of Agricultural Tires under Various Exploitation Conditions" Applied Sciences 14, no. 12: 5228. https://doi.org/10.3390/app14125228

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