Methodology for Assessing Tractor Traction Properties with Instability of Coupling Weight

Abstract

The purpose of the study is to increase the efficiency of using the tractor hitch weight in traction mode by reducing the uneven distribution of vertical reactions between the wheels. This work is grounded on a methodology that involves summarizing and analyzing established scientific findings related to the theory of tractors operating in traction mode. The analytical method and comparative analysis were employed to establish a scientific problem, define research objectives, and achieve the goal. The key principles of probability theory were applied in developing the empirical models of the tractor. The main provisions of the methodology for evaluating the traction properties of the tractor with the instability of the coupling weight were formulated. The method of evaluating the vertical reactions on the wheels of the tractor is substantiated, which is based on the measurement of the vertical reaction on one of the four wheels. It was proven that tractors with a center of mass offset to the front or rear axles have the greatest probability of equal distribution of vertical reactions between the wheels of one axle, and tractors with a center of mass in the middle between the axles have the lowest probability. It is theoretically substantiated and experimentally confirmed that when the tractor performs plowing work with uneven distribution of loads on the sides, its operation with maximum traction efficiency is ensured by blocking the front and rear axle drivers.

1. Introduction

The classic approach to the tractor as an object of design and management [1] consists of imagining it as a traction machine that has one connection with the external environment (running gear). Such an idea leads to the setting of tasks for optimizing the properties of the tractor, including traction force and efficiency, movement resistance, load on the axles, etc. These tractor parameters are regulated during their tests in NTTL laboratories [2] in the United States of America and Germany [3].

When the tractor is working in traction mode, its connection with the soil is carried out through two channels (running gear, working implement), which lead to the instability of the traction force of the tractor and the resistance of the aggregated agricultural machine [4,5,6]. At the same time, the reactions between the wheels of the front and rear axles are assumed to be uniform, although due to different rolling resistance of the wheels, for example, when the tractor performs certain tasks, the reactions between the wheels are unevenly distributed [7,8,9]. The movement of the tractor during the execution of the technological process leads to longitudinal, lateral, and vertical oscillations of sprung and unsprung masses and tractor wheels. Longitudinal and lateral oscillations of the tractor lead to an increase in the dynamic tension of the soil due to skidding, which reduces its traction force, and vertical oscillations are the main cause of dynamic soil compaction [10,11]. At the same time, an uneven distribution of vertical reactions between the wheels of the tractor is noted, which affects the efficiency of using the coupling weight in traction mode [12,13]. The essential feature of the tractor’s movement in the traction mode was not adequately covered in the technical literature when evaluating its support and traction properties.

The solution to the problem of the influence of a mobile machine’s center of mass is considered in a number of foreign publications [14], which note the perspective of research in the direction of machine operation in traction mode. It is proposed to determine the energy parameters of the machine by differentiating its mass.

Practice presents science with the need to solve the problem of developing a methodology for assessing the uneven distribution of vertical reactions between the tractor wheels in traction mode.

The efficiency of using the towing weight of the tractor in traction mode is increased by reducing the uneven distribution of vertical reactions between the wheels.

The following tasks were set in this work:

• Justify the dependence of the tractor’s traction properties on the use of the coupling weight of the driving axles.
• Estimate the distribution of vertical reactions between the wheels of one driving axle of a tractor.
• Justify the zone of the most likely reduction in the use of the towing weight of the four-wheel drive tractor.

2. Materials, Method and Results

This work is based on a methodology that summarizes and examines existing scientific findings on the theory of tractors in traction mode. The analytical method and comparative analysis were utilized to formulate the scientific problem, establish research objectives, and achieve the goal. The fundamental principles of probability theory were incorporated in developing the empirical tractor models.

Let us assume that the tractor, being on a flat horizontal surface, moves at a constant speed with the power take-off shaft turned off (Figure 1). Traction efficiency of the tractor can be expressed [1] by the following equation:

$${\eta }_{т}=\frac{N_{т}}{N_e}=\frac{P_{кр}{\upsilon }_{д}}{M_{д}{n}_{д}}\frac{716.2}{270}=2.65\frac{P_{кр}{\upsilon }_{д}}{M_{д}{n}_{д}},$$

(1)

where $N_{т}$—traction power of the tractor, kW; $N_e$—effective engine power, kW; $P_{кр}$—traction force on the hook, kN; ${\upsilon }_{д}$—actual driving speed, km/h.; $M_{д}$—engine torque, kN•m; $n_{д}$—engine crankshaft rotation frequency (engine speed), r/min.

Let us imagine that the traction forces on the hook and the actual speed of movement, which are included in Equation (1) of the traction efficiency of the tractor, are functions of the dimensionless coefficients ${\phi }_{1,2}$ of the use of the coupling weight of the driving axles in the following equation:

$${\phi }_{1,2}=\frac{P_{к1,2}}{Y_{1,2}},$$

(2)

where $P_{к1,2}$—tangential traction force of the driving axle, kN; $Y_{1,2}$—soil reaction, numerically equal to the towed weight of the tractor, which is distributed to the drive axle ($Y_{1,2}=G_{1,2}$), kN. Here, and further, the index “1” refers to the front, and the index “2” refers to the rear axles.

To obtain the dependency $P_{кр}=f({\phi }_1,{\phi }_2)$ we express $P_{кр}=P_{кр1}+P_{кр2}-P_{f1}-P_{f2}$; $P_{к1,2}=G_{1,2}{\phi }_{1,2}$; $P_{f1,2}=G_{1,2}{f}_{1,2}$, where $P_{f1,2}$—force of resistance to rolling of driving axles; $f_{1,2}$—coefficient of resistance to rolling of driving axles.

Taking into account the redistribution of the coupling weight depending on the traction force, we obtain the following equation:

$$P_{кр}=\frac{G\left[A_1\left({\phi }_1-f_1\right)+A_2\left({\phi }_2-f_2\right)\right]}{A_3+h\left({\phi }_1-{\phi }_2\right)},$$

(3)

where $A_1=a-f_2{r}_2$; $A_2=L-a-f_1{r}_1$; $A_3=L-h\left({\phi }_1-f_2\right)+f_1{r}_1-f_2{r}_2$; $G$—the weight of the tractor, kN; $L$—longitudinal base of the tractor, m; $h$—trailer point height, m; $r_1{r}_2$—rolling radii of the wheels, m.

Traction-supporting properties of the tractor depend mainly on its operating weight $G_e$, the conversion of which into traction force $P_{кр}$ is estimated by the coefficient of use of the towing weight ${\phi }_{кр}=P_{кр}/G_e$. When moving a wheeled tractor on a flat agricultural background, with the coefficients of traction of the driving wheels with the soil ${\phi }_{зч}$, rolling resistance $f$, and the share of weight falling on the driving wheels ${\lambda }_{к}$, the support and traction properties of a tractor with one driving axle are estimated according to the dependence ${\phi }_{кр}={\phi }_{зч}{\lambda }_{к}-f$, and for all-wheel drive tractors—${\phi }_{кр}={\phi }_{зч}-f$. An analysis ${\phi }_{кр}$ of tractors with one drive axle and four-wheel drive tractors shows that the greater the coefficient of traction in comparison with the coefficient of rolling resistance, the greater the tractor’s margin of traction force.

In operating conditions, the traction force of the tractor varies from zero to the maximum value $P_{кр}=P_{к{р}_{}\mathit{max}}$, which is determined by the traction properties at $G_e=\mathit{const}$.

Therefore, the coefficient ${\phi }_{кр}$ changes from zero to ${\phi }_{к{р}_{}\mathit{max}}$. The nominal traction force corresponds to a certain value ${\phi }_{к{р}_{} н}$. This statement was confirmed when the John Deere 8335 R tractor was moving in traction mode (Figure 2) [7,9,10,12].

Technical characteristics of the tractor John Deere 8335 R:

Nominal power of the engine, $N_e$, kW—246;

Nominal specific fuel consumption, $g_e$, g/kWh—224;

Engine torque reserve, %—41.4;

Traction power, $N_e$, kW—212;

Operating mass, $m_e$, kg—13,820;

Axle load, front/rear, kg—5528/8292;

Energy saturation, $E=N_e/m_e$—1.81;

Conditional traction efficiency, ${\eta }_{\mathrm{т}}=N_{\mathrm{т}}/N_e$—0.86.

Comparing the values of the loads acting on the front $y_n$ and rear $y_{з}$ wheels of the tractor show that they do not remain constant. If the traction resistance line is parallel to the road surface, then the loads $y_n$ and $y_{з}$ change due to the redistribution of the tractor’s weight between the front and rear wheels. Reducing the load on the front wheels causes the same increase in the load on the rear wheels, and vice versa. The amount $y_n+y_{з}$ is equal to the weight of the tractor $G_{\mathsf{т}}$. Instability in $y_n$ and $y_{з}$ leads to an uneven distribution of vertical reactions between the wheels of the tractor, and a decrease in the efficiency of using its hitch weight in traction mode. At the same time, even when the center of mass of the tractor is located strictly in the longitudinal plane of symmetry, inequality of vertical reactions on the left and right wheels of the same axle is possible. This is due to the static uncertainty of the four-wheeled tractor as a spatial structure that has four supports (connections) and, accordingly, four vertical reactions of the connection. A well-founded methodology for solving this problem is based on the interrelationship of dimensionless (specific) forces on the wheels of the tractor as follows:

$$\begin{gathered} {\gamma }_{\mathit{zi}}=R_{z1}/G; {\gamma }_{z2}=b/L-{\gamma }_{\mathit{zi}}; \\ {\gamma }_{z3}=0.5-{\gamma }_{\mathit{zi}}; {\gamma }_{z4}=\frac{a}{L}-0.5+{\gamma }_{\mathit{zi}}, \end{gathered}$$

(4)

where $R_{z1}$—vertical reaction on the front wheel; $G$—total weight of the tractor; $a$, $b$, $L$—distances from the projection of the center of mass on the horizontal plane to the front and rear axles, the longitudinal wheel base of the tractor.

By specifying and measuring the vertical reaction on one of the four tractor wheels, the vertical reactions on the last three wheels can be accurately determined. Developed at the Kharkiv branch of L. Pogorilyy UkrNDIPVT, the method for determining vertical reactions of tractor wheels involves determining two components: the position of the tractor frame in space and the vertical reaction to any of the four tractor wheels. In this case, the frame of the tractor is taken as a completely solid body and the vertical reaction is determined experimentally; the other three vertical reactions with the known weight of the tractor are determined analytically. For further modeling in this article, it was assumed that the tractor is installed on a perfectly flat surface, that is, the angles of inclination of the frame are equal to zero. In real operation, the position of the frame can be determined using acceleration sensors [15] and calculated analytically or using a digital gyroscope. At the stage of tractor design, it is advisable to imagine the vertical reaction on one of the wheels as a random variable, the distribution of which is subject to a normal law. Let us assume that such an independent random variable will be ${\gamma }_{z2}$, the changes of which are theoretically possible within the limits of $\left[0,b/L\right]$. With a decrease in ${\gamma }_{\mathit{zi}}$ there is a decrease in ${\gamma }_{z4}$, which cannot take negative values, because this leads to a violation of the system equilibrium.

Thus, when ${\gamma }_{\mathit{zi}}=0$ the following must be performed:

$${\gamma }_{z{4}_{}\mathit{min}}=\frac{a}{L-0.5}\ge 0 \mathrm{or} b/L\le 0.5.$$

(5)

Therefore, when $b/L\le 0$, the value ${\gamma }_{\mathit{zi}}$ can vary within the following limits:

$$\frac{b}{L}-0.5\le {\gamma }_{zi}\le 0.5.$$

(6)

With the normal distribution law of vertical reactions on the wheels of the tractor, the density of the distribution of the specific load on one front wheel is estimated by the following equation:

$$f\left({\gamma }_{zi}\right)=\left\{\begin{array}{l}\frac{2394}{b/L}{\mu }_{\sigma }\mathit{exp}\left[-\frac{1}{2}{\left(\frac{6}{b/L}{\gamma }_{zi}-3\right)}^2\right]\mathrm{at}\frac{b}{L}\le 0.5;\\ \frac{2394}{1-b/L}{\mu }_{\sigma }\mathit{exp}\left[-\frac{1}{2}{\left(\frac{6}{1-b/L}{\gamma }_{zi}-\frac{3b/L}{1-b/L}\right)}^2\right]\mathrm{at}\frac{b}{L}>0.5\end{array}\right\}$$

(7)

where ${\mu }_{\sigma }$—the selected scale of the root means square deviation, i.e., the value is conventionally taken as a unit during the analysis.

Figure 3 shows graphs of Function (7) at different positions of the tractor’s center of mass (parameter $b/L$), taking into account the possible range of changes of ${\gamma }_{zi}$.

Analysis of the calculation results shows that tractors with an offset to the front or rear axle of the center of mass have the greatest probability of equal distribution of vertical reactions between the wheels of one axle. Tractors with a center of mass located in the middle between the axles have the lowest probability of equal distribution of vertical reactions at $b/L$ = 0.5, and the largest—at $b/L$ = 0.9 and $b/L$ = 0.1.

If at $b/L$ = 0.1, this probability is 0.4, then at $b/L$ = 0.5, it is equal to 0.1.

When the tractor is working in the traction mode, the uneven distribution of vertical reactions leads to the deterioration of its traction–speed characteristics, since the total tangential traction force is determined by the wheel, which is in worse grip conditions. If we consider the specific vertical reactions on the wheels (the ratio of the corresponding reaction on the j-th wheel to the total weight of the tractor), taking into account their possible changes within the rms deviation, then the dependencies for their calculation are written in the following form:

$${\gamma }_{z1}=m_{\gamma 1}+{\sigma }_{\gamma 1}; {\gamma }_{z2}=m_{\gamma 2}-{\sigma }_{\gamma 2}; {\gamma }_{z3}=m_{\gamma 3}-{\sigma }_{\gamma 3}; {\gamma }_{z4}=m_{\gamma 4}+{\sigma }_{\gamma 4},$$

(8)

where $m_{\gamma 1}$, $m_{\gamma 2}$, $m_{\gamma 3}$, $m_{\gamma 4}$—mathematical expectation of specific vertical reactions on the corresponding wheels (1, 2—front wheels; 3, 4—rear wheels; 1, 3—left side wheels; 2,4—starboard wheels); ${\sigma }_{\gamma 1}$, ${\sigma }_{\gamma 2}$, ${\sigma }_{\gamma 3}$, ${\sigma }_{\gamma 4}$—root mean square deviations of the specific vertical reactions on the specified wheels.

It is obvious that

$$m_{\gamma 1}=m_{\gamma 1}=\frac{1}{2}\frac{b}{L}; m_{\gamma 3}=m_{\gamma 4}=\frac{1}{2}\left(1-\frac{b}{L}\right).$$

(9)

At $b/L$ $\le$ 0.5 we have

$${\sigma }_{\gamma }={\sigma }_{\gamma 1}={\sigma }_{\gamma 2}={\sigma }_{\gamma 3}={\sigma }_{\gamma 4}=\frac{1b}{6L}.$$

(10)

At $b/L$ > 0.5 we have

$${\sigma }_{\gamma }={\sigma }_{\gamma 1}={\sigma }_{\gamma 2}={\sigma }_{\gamma 3}={\sigma }_{\gamma 4}=\frac{1}{6}\left(1-\frac{b}{L}\right).$$

(11)

The acceleration that occurs when the tractor accelerates in the absence of wheel slippage is determined by the wheel that is in worse grip conditions, that is, having a lower vertical load, as follows:

$$a=g\phi {\phi }_{кр},$$

(12)

where $g$—free fall acceleration, $g$ = 9.81 m/s²; $\phi$—coefficient of adhesion of the wheels to the road; ${\phi }_{кр}$—the coefficient of use of the coupling weight in traction mode for a four-wheel drive tractor.

$${\phi }_{кр}=2\left({\gamma }_{z2}+{\gamma }_{z3}\right)=2\left(m_{\gamma 2}+m_{\gamma 3}-2{\sigma }_{\gamma }\right)=\left\{\begin{array}{l}1-\frac{2b}{3L} at \frac{b}{L}\le 0.5\\ \frac{1}{3}-\frac{2b}{3L} at \frac{b}{L}>0.5\end{array}\right.$$

(13)

Figure 4 presents a graph illustrating the dependence of ${\phi }_{кр}$ on the parameter $b/L$.

Analysis of the graph in Figure 4 shows that the greatest decrease in the coupling weight coefficient of a two-axle four-wheel drive tractor in traction mode occurs when $\frac{b}{L}>0.5$. This decrease can reach 33%.

In case of asymmetric application of the traction force on the tractor hook, for example, the resistance force of the plow, which is characterized by the distance $\alpha$ from the tractor axis to the point of application $P_{nл}$ and different rolling resistance of the wheels $P_{\mathit{fi}}$, the traction force required to overcome $P_{\mathit{fi}}$ will be different for each wheel $P_{кi}$ (Figure 5).

To ensure uniform straight-line movement of the tractor, it is necessary to fulfill the condition $P_{кi}=P_{fi}+P_{кi}^n$, where $P_{кi}^n$—the traction force required to overcome the drag force of the plow.

For this case, the tangent of the traction force of the wheels is written in the following form:

$$\left.\begin{array}{l}{P}_{к1}=P_{nл}\frac{\left(b/2-a\right)}{b}+P_{к3}+{\displaystyle \sum \left(P_{f1,3}+P_{к1,3}^n\right)}\\ P_{к2}=P_{nл}\frac{\left(b/2-a\right)}{b}+P_{к4}+{\displaystyle \sum \left(P_{f2,4}+P_{к2,4}^n\right)}\\ P_{к3}=P_{nл}\frac{\left(b/2-a\right)}{b}+P_{к1}+{\displaystyle \sum \left(P_{f1,3}+P_{к1,3}^n\right)}\\ P_{к3}=P_{nл}\frac{\left(b/2-a\right)}{b}+P_{к2}+{\displaystyle \sum \left(P_{f2,4}+P_{к2,4}^n\right)}\end{array}\right\}$$

(14)

The analysis of this system of equations shows that at P_f1,3 ≠ P_f2,4 caused by different wheel rolling conditions when the tractor plows (P_f2 > P_f4, P_f1 > P_f3, P_f2 > P_f1, P_f4 > P_f3) has P_к2 > P_к4, P_к1 > P_к3, P_к2 > P_к1, P_к4 > P_к3.

In the Kharkiv branch of L. Pogorilyy UkrNDIPVT, in order to evaluate the dependence of the traction force of the tractor on the coupling weight with an uneven distribution of reactions between the axles, experimental studies of the HTZ-17021 tractor when aggregated with a PLN-5.35 plow were carried out. The results of these experimental studies are shown in

Table 1. Torques ($M_{кр}$ ) on the sun gears of the wheel gearboxes of the HTZ-17021 tractor with the PLN-5-35 plow (plowing winter wheat stubble to a depth of 25–27 cm).

y, m	a, m	Mкp, Nm
		Mкp1	Mкp2	Mкp3	Mкp4
0.150	0.36	947	2222	875	2150

y—the distance from the edge of the furrow to the outer edge of the wheel; a—asymmetry of traction load application; M_кp1, M_кp2, M_кp3, M_кp4—torques on the sun gears of the wheel gearboxes of the front left and right wheels, and the rear left and right wheels, respectively.

.

The analysis of this table shows that the front right wheel is the most loaded during plowing of the HTZ tractor, and the rear left wheel is the least loaded. Behind the sides of the tractor, the front wheels are 3–5% more loaded than the rear wheels. Let us take it for simplification that $P_{\mathrm{к}1}^n=P_{\mathrm{к}3}^n$ and $P_{\mathrm{к}2}^n=P_{\mathrm{к}4}^n$. In this case, the load on the wheels of the right $P_{\mathrm{п}}^n$ and left $P_{\mathrm{л}}^n$ sides of the tractor, which is necessary to overcome the resistance of the plow, from the system of Equation (14), is written in the following form:

$$\left.\begin{array}{l}{P}_{\mathrm{п}}^n=P_{\mathrm{п}\mathrm{л}}^{}\left(\frac{1}{2}+\frac{\mathrm{a}}{b}\right),\\ P_{\mathrm{л}}^n=P_{\mathrm{п}\mathrm{л}}^{}\left(\frac{1}{2}-\frac{\mathrm{a}}{b}\right)\end{array}\right\}$$

(15)

The asymmetrical connection of the plow, characterized by parameter a, leads to a greater load on the right side of the tractor compared to the left side. For a tractor of the HTZ type in plowing operations with a PLN-5-35 plow, this excess is 50–60%. In this case, to ensure stable rectilinear movement of the plow unit, it is necessary to fulfill the condition M₂ ≈ 1.5M₁, ω₁ ≈ 1.5ω₂.

For example, Figure 6 shows the universal characteristics of the traction efficiency of the HTZ-170 tractor when plowing winter wheat stubble with a PLN-5-35 plow to a depth of 25–27 cm (operating weight of the tractor 8.0 t, engine power 121.1 kW, speed 2.37 m/s).

The universal characteristics show the traction range of the tractor in the form of a series of straight lines, P_кp = const, on which the graph of the function is plotted φ_п = f(φ_з) at η_т max. This is the optimal combination of coefficients of the use of the driving axles’ coupling weight, which leads to the operation of the tractor with maximum traction efficiency.

The analysis of the universal characteristics shows that η_т max = 0.71 of the KhTZ-17021 tractor during plowing will be in the case of blocked front and rear drive axles. All η_т points are located on the abscissa axis (because φ_п = 0). At the same time, η_т on the universal characteristics will be below η_т max.

According to this characteristic, it is possible to estimate η_T when unlocking the differentials and simultaneously turning on the front and rear axles.

3. Discussion

The results of this research are mainly aimed at solving the scientific problem of increasing the efficiency of using the tractor hitch weight in traction mode by reducing the uneven distribution of vertical reactions between the wheels. New dependencies of the traction properties of the tractor on the use of its drawbar weight and a method of estimating the vertical reactions on the tractor’s wheels from its drawbar weight are proposed. It was proven that the greatest efficiency of using the hitch weight of an all-wheel drive tractor in traction mode is achieved when its center of mass is located between the driving axles. At the same time, during plowing operations, the most energy-intensive technological process ensures its operation with maximum traction efficiency when the front and rear axle drivers are blocked.

Domestic and foreign scientists pay attention to the fact that the efficiency of tractors significantly depends on the position of its center of mass and the distribution of vertical reactions between the wheels. Domestic regulatory documents and methods of testing tractors according to the OECD Code 2 procedure in NTTL laboratories [2] in the United States of America and in Germany [3] do not provide for evaluating the efficiency of the tested tractors from the position of the center of its masses during the execution of the technological process. This is mainly a consequence of the lack of methods and instrumentation for evaluating the traction properties of the tractor during its unsteady movement.

The solution to this problem is possible using the method of partial accelerations [10], which is implemented at the standard L. Pogorilyy UkrNDIPVT, and the measuring and registration complex developed at the Kharkiv branch of L. Pogorilyy UkrNDIPVT, who has no analogues in the world. The presence of a solid underlying layer in the form of permafrost and the heavy precipitation typical of this period drastically reduce the load-bearing capacity of soils [16,17,18,19,20]. The increase in the tractor’s weight under these conditions results in breaking of the upper layer of the soil down to permafrost, degradation of traction, and coupling properties and slippage, which, in turn, causes the increase in the man-made (technogenic) impact, and bad flotation even with small hook loads [21,22,23,24]. Numerous scientists worldwide have investigated this problem and proposed various solutions. One such study [2] examines the relationship between the load-carrying capacity and the speed of transport aggregate movement. The optimal ratio of these two factors helps to reduce the vertical load on the soil. The sustainable dead weight loading is also an efficient way to reduce the impact of the ground drive system on the soil when the tractor is in motion [25,26,27,28]. However, the dead weight loading increases metal consumption, fuel consumption, and the cost of the tractor. After analyzing both the foreign and domestic scientific literature, it was found that the established techniques used to enhance the traction and coupling properties of wheeled tractors [29,30] are not efficient when one needs to reduce the man-made (technogenic) impact of the ground drive system on the soil and simultaneously achieve sufficient traction properties of the machine-tractor units (MTA) or tractor-transport units (TTA). Therefore, the aim of this research is to determine new methods of improving the traction and coupling properties and reducing the anthropogenic (technogenic) impact on the arable soil of the drive system of a moving wheeled tractor, which are important components of increasing the productivity and efficiency of labor and mechanized work, as well as the rational use of natural resources and long-term conservation of soil horizons [11,31]. In their research, the authors of [16] determined that the optimal way to achieve this goal is to rationally distribute the weight of the coupling to the tractor propellers. For non-wheel drive modifications, the weight is redistributed from the non-driving front wheels to the driving rear wheels, with the front wheels pre-loaded to provide longitudinal stability if necessary.

4. Conclusions

Based on the results of this research, the methodology for evaluating the impact of the position of the tractor’s center of mass on its traction properties is substantiated. The results of this research made it possible to form the main theoretical and scientific-practical conclusions:

• The formulated methodology for evaluating the traction properties of a tractor with instability of the vertical reactions on its wheels. It was proven that when the tractor’s center of mass is located in the longitudinal plane of symmetry, an uneven distribution of vertical reactions on the wheels of one axle of the tractor is possible.
• The method of evaluating the vertical reactions on the wheels of the tractor, which is based on the measurement of the vertical reaction on one of the four wheels, is substantiated.
• It was proven that tractors with the center of mass shifted to the front or rear axle have the greatest probability of equal distribution of the vertical reactions between the wheels of one axle, and tractors with the center of mass in the middle, between the axles, have the lowest probability.
• It is theoretically substantiated and experimentally confirmed that when the tractor performs plowing work with an uneven distribution of the load on the sides, it is ensured that it works with maximum traction efficiency with the front and rear axles locked.
• The issue of evaluating the influence of the tractor’s center of mass on its traction properties when aggregated with mounted, trailed, and combined agricultural machines remains open. It is necessary to carry out theoretical and experimental research in this direction.