EFFICIENCY IMPROVEMENT OF FOREST MACHINERY EXPLOITATION

The purpose of this work was to develop a model of the interaction process between the wheeled forwarder and the soil of the cutting area, which allows evaluating the influence of soil conditions, the parameters of the wheeled forwarder, as well as load and number of cycles of its application, on the indicators of resistance and adhesion of the forwarder to the traction surface. Modeling results for 3and 4-axle forest machines with different load levels showed that for different soil categories, types of bodies, and tire sizes. The results of the approximation analysis enabled the derive of calculation formulas for estimating the propulsive coefficient and rut depth after the first passage depending on the values of load-bearing capacity, body load coefficient, wheel width, and soil deformation module. The proposed model can be used at laying down the skidding roads and its optimization not only in economic terms but also with respect to the environment as intensive harvesting operations lead to extensive soil destructions. The practical application of the results is expressed in increased performance capacities of wood skidding operations and minimization of costs for restoring the productivity of forest area.


INTRODUCTION
Forest operations are known to cause severe soil disturbance and erosion and have been the subject of numerous studies. In particular, logging with tractors leads to soil compaction [1,2] and rutting, and is a major reason of soil surface degradation caused by human activities [3,4]. The pressure exerted by loaded vehicles moving through the forest is a major factor causing compaction and rut formation [5]. In recent decades, the weight of forest machines has increased, raising new issues of concern in forest soil degradation [6,7]. Skidding trails are usually forest areas subjected to compaction and waterlogging. The roadway in logging areas is usually poorly drained and not subjected to natural compaction, which results in the soil porosity reduction, infiltration of water and gas exchange, as well as increased soil erosion, waterlogging, and mudflows [ 8 , 9 ] . In almost all cases, the timber skidding operation has limited productivity within the whole technological chain of the mechanized harvesting system. Skidding performance depends on a large number of factors. Among others, a key role plays average skidding distance, the traffic load of the skidding equipment, and the speed (velocity) of its movement. Possible traffic load and the speed of skidding machinery depend in turn on the technical characteristics of skidding tractors and operating conditions such as soil, ground, and terrain conditions [10][11][12].
Noteworthy to mention that skidding performed by tractors is the most environmentally harmful operation for the forest ecosystems. Its negative environmental impact is expressed in severe destruction of soil horizons such as rutting and compaction, followed by subsequent processes of waterlogging, ravine formation, and decreased fertility of forest sites [13][14][15]. In this regard, the traffic load and forwarder speed need to be limited not only for operational efficiency reasons -cross-country ability and reliability, but also for ecological efficiency reasons -so that the subsequent costs of restoring the productivity of the forest area (reforestation work) do not exceed the momentary income from high productivity [16][17][18].
With the mechanization of logging operations, numerous studies were performed on improving the performance parameters of the skidding process and in particular forest machines and its trafficability. Enhanced performance of forest machinery and modification of skidding processes in different soil conditions remains a significant concern. One of the most important issues is the interaction between forest mechanized equipment with the forest soils [19][20][21].
Analytical description of the processes related to the movement of machinery on the soil and ground surfaces over the logging sites is much more difficult than that of the roads with a hard surface. Mechanical properties of soil-covered sites are very variable and unstable, the deformation mechanics is complicated, and has not been fully studied so far [22][23][24].
The purpose of this study was mathematical modeling of the interaction process between wheeled forwarder with and the soil of the cutting area. This model allows evaluating the influence of soil conditions, the parameters of the wheeled forwarder, as well as load and number of cycles of its application, on the indicators of resistance and adhesion of the forwarder to the traction surface. The testing of the wheeled forwarder's performance model is performed taking into account the technical characteristics of modern John Deere, Rottne, Ponsse, Komatsu, and Amkador forestry machines and various soil categories. The results of this study allow performing numerical analysis of the wheeled forwarder's traffic capacity and an assessment of the rut depth after the passage under certain conditions that have not only scientific value but also great potential in practical application Translated with www.DeepL.com/Translator (free version)

The methodology for evaluating wheeled forwarder's productivity
Currently, wheeled skidders of several companies are being utilized in Russia. These are John Deere, Rottne, Ponsse, Komatsu, and Amkodor. All models are all-wheels-driving and available with three (six wheels), four (eight wheels), and five (ten wheels) axles.
When determining the maximum volume of skidded timber, the following points should be considered [25]: 1. Load capacity limit of the machine. 2. Tangential traction force limit of the machine (tractive resistance of the vehicle should not exceed the maximum pulling force of the forwarder). 3. The limit of the forwarder's adhesion to the ground (tangential traction force should not exceed the force of the forwarder's adhesion to the soil of the harvesting area). Moreover, it is recommended to set the weight limits for the skidder loading based on the allowable track depth after the first passage of the forwarder [26], which is considered to be no deeper than 10 cm. This statement is supported by the studies on track development at the cyclic operation of grapples, i.e., multiple passes of the forwarder over the same trail sections. This raises the question of the forwarder's performance in skidding operations concerning the track depth limit.
The output per shift for each forwarder is determined by a formula: where φ 1 is the coefficient of operations per shift, T S is the shift duration, Q is the volume of a bunch skidded by the forwarder, l AV is an average skidding distance, t M is maneuvering time in the harvesting area, t WT is the time for changing the equipment from transport to operational mode vice versa, Q P is the volume of wood taken and loaded into the load box by a harvesting arm at one go, t CD is the time for clam delivery to wood assortment, their capture and stacking into the forming device, U U is the speed of an unloaded skidder, and U L is the speed of a loaded skidder.
The ability of the vehicle to move with the limit of tractive force is determined from a well-known ratio [27]: where T is the traction force; F R is the total tractive resistance force. In technical calculations, the tractive resistance force is determined as follows [27]: = where φ R is the traction resistance coefficient of the vehicle, G is the weight of the vehicle, ρ is bulk density of the wood, and g is a free-fall acceleration.
The speed and productivity of forest machinery is commonly calculated based on approximate values of traction resistance. These values are presented in Tables 1 and 2.
Noteworthy, the values of the traction resistance are given in Tables 1 and 2 regardless of the machinery weight. At that, some studies [27,30] describe the nonlinear nature of the change in the traction resistance force of the machine depending on its weight. This indicates that the given coefficient is not a constant value for a particular terrain type. With a known value of the traction resistance φ R , the speed of machine U U and U L can be calculated as follows: where η is the transmission efficiency, N is engine power, F LF and F UF are the values of the traction resistance force of loaded and unloaded forwarder, respectively.
The adhesion limit is defined as follows [27]: The adhesion force for all-wheel-drive forwarders is accepted to calculate as: = ⋅ ( + ), where φ AD is the coefficient of the forwarder's adhesion to the surface of movement. This coefficient is believed to vary within the range 0.3-0.6 for wheeled vehicles [27].

Evaluation of the forwarder's traction resistance force
The influence of soil conditions on the performance of wheeled forwarders was examined based on soil classification by its mechanical properties offered in [32]. According to this classification, physical and mechanical properties of the soil can be expressed with satisfactory accuracy through the deformation module E as follows:  (12) where E is the soil deformation module, C 0 is internal adhesion, φ 0 is internal friction angle, γ is volume weight of soil in natural compaction, H is the thickness of the deformed layer (depth of compression strain expansion), and ν is Poisson's coefficient of the soil.
Considering that the shear module E 1 is calculated by formula [34]: (13) and using equation (12), follows that: The deformation module follows by default as [28]: where σ is the normal operational stress and ε is the relative deformation. Relative deformation ε is the sum of reversible (elastic) and irreversible (plastic) deformations.
The variability of compression stress by soil depth is described by the quadratic equation [28]: (16) where J is the coefficient of the contact area, q is the stress on the contact surface of the forwarder with the soil, a is the stress attenuation constant by the depth of the soil, and b is the average width of the contact area approximately equal to the width of the wheel.
Compression of elementary soil layer with thickness of the elemental layer in deformable state dz is determined by Eq. [28]: ℎ 0 = ( − ) ⁄ (17) Then the total compression strain of the soil array is determined after integration ratio (17) and considering Eq. (16) and accepting that E >> σ: The disproportionate increase in compression strain with the acting stress approaching the bearing capacity of the soil is considered by coefficient k S . At that, the actual value of subsidence h is determined by the formula [28]: where q S is the bearing capacity of the soil. From Eqs. (18) and (19) follows: (20) Equation (20) has no analytical solution concerning subsidence value h, thus, further calculations were made based on numerical methods. A special program has been compiled to implement the calculations. The values J and a included in equation (20) are determined by known formulas [28]: where l is the average length of the forwarder's contact area with the soil surface.
where G W is the load on one wheel of the machine and F is the contact area of the wheel and the soil surface.
The shape of the contact area of the wheeled forwarder and the soil varies from elliptical for solid soil to rectangular-like for soft soil ( Figure 1). The area of an ellipse is defined by multiplying the lengths of axes by 0,25π and the area of a rectangle is calculated by multiplying the lengths of sides. If the average width b and the average length l of the contact area is taken as the ellipse axis when operating on solid soils (E = 3 MPa according to the accepted classification) and as side lengths when operating on solid soils (E = 0.4 MPa according to the accepted classification), the contact area can be generally expressed as follows: where k F is a coefficient of a form that depends on the soil condition.
Assuming an exponential deviation of the form coefficient from the soil deformation module, the form coefficient k F is defined as follows: = 0.8766 0.1199 (25) Formula (25) is illustrated as a graph in Fig. 2. Using Eqs. (24) and the ratio (25), the contact area can be defined as follows: = 0.8766 0.1199 (26) The length of the contact area is calculated by a known ratio [28]: (27) where d is the wheel diameter, h Z is axial deformation of the wheel.
The value of deformation h Z depends on the tire modification, the inner pressure in tire tube p W , the load on the wheel G W , and soil deformation. Several simple ratios are offered for determining the value h Z , which allow reaching high accuracy in practical calculations. One of the most common ratios is called the Heidekel formula. It can be expressed as follows: (28) It should be noted that the bearing capacity value q S used in the Eq. (20) is not constant for the soil value [30]. It varies depending on geometrical parameters of a contact area and depth of press tool immersion. The bearing capacity of the soil can be determined by the following formula [30]: (29) where q S0 is the bearing capacity of the soil layer with unlimited thickness and α Z is the thickness coefficient of the compressible soil layer.
At that, the bearing capacity value of the soil with unlimited thickness q S0 is defined as [29]: where N 1 , N 2 , N 3 , and S are auxiliary coefficients, J 1 and J 2 are geometrical parameters of the press tool, which can be calculated as [30]: where l is the length of the press tool and b is the width.
The coefficients N 1 , N 2 , N 3 , and S can be calculated as follows [36]: The thickness of deformable layer of the soil is calculated by the formula: where H* and ε are auxiliary values and are determined in the formula [29]: = 0.75 0 (38) From the analysis of dependencies (20)- (38) follows that based on Eqs. (8)- (13), which determine physical and mechanical properties of the soil depending on the deformation module E, and at known values of internal pressure in the tire tube p W , wheel width b, wheel diameter d, and wheel load G W , the equation (13)  The resistance force of the soil to deformation, i.e., the force of soil to withstand the rolling of the wheel, is determined by the formula [36]: Recurrence of the applied load is important to consider by studying the interaction of wheeled forwarders with the soil in the logging sites. Taking into account the number of axes of wheel forwarders, there are 3-4 consecutive passes of the wheel with a short time interval over one track by one machine passage.
The following empirical formula [32] was used to determine the recurrence of applied load: where h (1) is the track depth after the passage of first axis wheels, n is the number of forwarder's axes, and a is an empirical coefficient that depends on properties and condition of the soil.
General experimental observations [37] are presented in Table 3. When associating the deformation module values for different soil categories in with the soil quality characteristics based on Table 3, the dependence of the average coefficient a on the deformation module E can be presented in the form of a graph (Figure 3).
The total resistance force of the machine's passage will be determined as follows. First, by solving the equation (20), the depth of the track should be calculated that corresponds to the given load on the wheel G W . The track depth corresponding to the pass of the machine is determined by the formula (70) using the resulting value h (1) . Afterward, the ratio q = G W /F within the variability of track depth from 0 to h is defined based on (69), which integration by any numerical method gives the required value of the traction resistance force of the machine.

Determination of the forwarder's adhesion to the soil surface
Besides soil resistance to deformation, the adhesion of the wheeled forwarder to the surface of traction is one more important factor affecting the performance capacity of the forwarder.
The adhesion sufficient for movement without slipping is provided if following ratios are fulfilled (diagrams of restrictions are presented on Fig. 4) [28]: where k S is the saturation coefficient of a tirethread, φ Р is the friction coefficient of the wheels on the soil, and Q S is the allowable load on the soil limited by its bearing capacity. The allowable load Q S is determined by the formula [33], [34]: where q Sβ is the bearing capacity of the soil considering the deviation of the resulting load vector from the movement surface normal, β is the angle of the resulting load application versus the movement surface normal.
The application angle of the resulting load β is determined based on the value of normal load G W and tangential reaction of the soil R T: Thus, the tangential reaction of R T must therefore be determined in order to estimate the adhesion of the forwarder to the soil. This can be fulfilled using the scheme shown in Figure 5.
where r R is the rolling radius of the wheel: where r is the wheel radius, δ is the coefficient of slipping. Therefore: On the site AB: On the site BC: The values of angles α 1 and α 2 are determined using the scheme in Figure 6 by the following equations [28]: The direct tangential force R T is determined by integrating the dependence of the shear stress τ on the shear strain j 1 and j 2 on the sites by any numerical method: The actual shear strain is determined considering its increase when the shear stress τ approaches the limit of the soil shear strength τ SH by the formula [28]: where j 0 is the shear strain without taking into account its possible increase by the shear stress approaching the limit of the soil shear strength.
The soil deformation j 0 enclosed between the wheel lugs is related to the shear stress as follows: where t WL is the distance between the wheel lugs.
Substituting the (60) into the formula (59) results in: The limit of the soil shear strength can be calculated as follows:  (61) and transformations in relation to τ, the following ratio τ(j) can be defined: The ratio (63) for three soil categories is graphically depicted in Figure 6 (tg = 0.14 m, q = 50 kPa).
After calculating the tangential reaction R T by formula (58), it is possible to determine the angle of the resulting load application β. Thus, the solution of condition whether the forwarder's adhesion to the soil surface is fulfilled can be checked according to formulas (42) and (43).
This equation allows estimating the height of the threshold unevenness (i.e., the maximum height of the unevenness, which the wheels of the machine can overcome), by the following formula [28]: where R is the wheel radius, φ P is the propulsive coefficient.
The last two equations form another limit on the volume of a skidded bunch of wood.
The data [33]  The performance capacity of the forwarders was estimated for the following soil categories: • Category I -sand, sand loam, light (wet) loam, soil of plant layer, peat; • Category II --loam, small and medium gravel, light and clay; • Category III -clay medium or heavy, loosened, dense loam;

Assessment of the forwarder's productivity
The influence of soil conditions on the forwarder's productivity was examined based on 8x8 vehicles used Eq.(1)- (7), with the following initial data [19,31,32]: φ 1 = 0.8; T СМ = 7 h, T ML = 90 s, T RT = 30 s, t DZU = 200 s, Q = 1.5 m3, ρ = 850 kg/m3, η =0. 8. The values of φ R . were taken from Tables 1 and 2. The weight of the machine, the engine capacity by the equation, and the maximum tractive force are determined based on the analysis data [33]. The volume of skidded timber logs is limited only by the load-carrying capacity of the vehicle. Figure 7 depicts the ratio of maximum traction force T versus forwarder's traction resistance F S depending on the traction resistance coefficient φ R . At that, by varying the coefficient within 0.1-0.5, the value F R does not exceed the maximum traction force. Thus, limiting the volume of skidded timber to the maximum traction force is a matter of low importance for modern wheeled vehicles. Fig. 7. Maximum traction force T versus forwarder's traction resistance force F R As a first approximation, the adhesion coefficient φ AD changes linearly depending on the traction resistance coefficient φ R . At that, the value φ AD = 0.6 and φ AD = 0.3 correspond to φ R = 0.1 and φ R = 0.4, respectively. In this case, the adhesion force F AD versus the traction force F R can be presented as a diagram in Figure 8. It depicts that a limit on the weight of loaded forest machinery is applicable to operation on relatively soft soil. Current knowledge on how the adhesion coefficient changes depending on soil condition is not sufficient and requires additional studies in this sphere.  Figure 9. It can be seen that the traction resistance force significantly influences the speed of the vehicle. At the same volume of skidded timber, the traction speed of the machine varies by 4-5 times depending on the skidding conditions. Thus, the necessity to examine the interaction between grapple skidders and the soil of logging sites remains of great interest. The last statement is supported by diagrams in Figure 10, which shows the share of traction time T T (movement time of the loaded vehicle versus that of the unloaded) in total duration of the skidding cycle T C depending on the average skidding distance l AV at forwarder's load-carrying capacity of 10 tons.   The analysis of charts in Figs. 11-13 shows a noticeable effect of the forwarder's traction coefficient on its output per shift. This effect is more visible by forwarders with low carrying capacity, often used for skidding on relatively weak soils.   For example, track depth after the passage of the first-axles-wheels will amount to h (1) = 0.127 m employing a 4-axes-forwarder with a load capacity of 20 t on the soil of II category with deformation module E = 1 MPa. The load on the wheel, in this case, is 50 kN and b = 0.7 m. Then, the total track depth after the forwarder's passage is h=0.19 m, according to (39). The resistance force is determined by integrating the q(h) dependence (Fig.  18) within the h limits from 0 to 0.19 m and multiplying the obtained value by the wheel width b = 0.7 m. The calculation value of the forwarder's resistance force to rolling will amount to 7.819 kN.

Assessment of the forwarder's productivity with respect to soil conditions
Input data for the calculation are presented in Table 4. The wood density was assumed to be 0.85 t/m3. Load on the wheel was determined by dividing the total weight of the loaded forwarder by the number of wheels. The movement speed and speed of unloaded forwarder were calculated by formulas (4), (5). The output capacity was determined by Eq. (1). When implementing the model, the physical and mechanical properties of the soil were expressed through the deformation module by expressions (8)- (11), (14). The basic equation of track depth and pressure relation is represented by formula (20), in which auxiliary coefficients are defined by formulas (21) and (22), pressure and contact area are defined by formulas (23), (26)- (28), and bearing capacity of the soil is estimated by formulas (29)- (38).
The rolling resistance force of the wheel caused by the soil resistance is calculated by the formula (39). The impact of transfer number (i.e., the number of forwarder's axles) on process indicators is estimated by formulas (40) and (41). The propulsor's adhesion force to the soil is determined according to (47) by the allowable load on the soil limited by its bearing capacity with (44)-(46), (53)-(58), and (63). The height of the threshold unevenness, which the machine can overcome, is calculated by formulas (64) and (65). An example of the model implementation results is presented in Table 5.  The results of the analysis are summarized in Tables 6 and 7. When working on the soils of the I and II category, the adhesion force of the forwarder with the surface is sufficient to move without slipping on all types of soils, i.e., soft, medium, and solid (Table 6). Lightweight 3-axle forwarders with normal tires width and at 50% body load, 4-axle forwarders with 50 and 75% body load, as well as medium-weight forwarders with 50% body load can operate without slipping on soils of category III. Lightweight 3-axle forwarders with 50 and 75% body load and medium forwarders with 50% body load as well as lightweight 4-axle forwarders with 50 and 75% body load, medium forwarders with 50% body load, and heavy forwarders with 50% body load are suitable for movement without slipping and at larger tire widths.   II,II  I  I,II  I,II   I,II,II  I   I,II,II  I  I,II   15  I,II  I,II  I,II   I,II,II  I  I,II  I,II   20  I,II  I,II  I,II  I,II  I,II  I,II   0.  8   10   I,II,II  I   I,II,II  I  I,II   I,II,II  I   I,II,II  I  I,II   15   I,II,II  I  I,II  I,II   I,II,II  I  I,II  I,II   20  I,II  I,II  I,II   I,II,II  I  I,II  I,II   Table 7. Soil categories with the track depth not more than 0.1 m 50  75  100  50  75  100   0.7   10 I, II  I,II  I,II I, II  I,II  I,II   15 I, II  I,II  I  I, II  I,II  I,II   20 I, II  I  I  I, II  I,II  I   0.8   10 I, II  I,II  I,II I, II  I,II  I,II   15 I, II  I,II  I  I, II  I,II  I,II   20 I, II  I,II  I  I, II  I,II  I,II The data in Table 7 shows that regardless of the weight of a forwarder and at full-body load, the track depth cannot exceed the value of more than 0.1 m when working on the soils of the I category.
At the normal width of the tire, the depth of the track goes below 0,1 m while operating on soils of II category with 3-axle medium-weight forwarders with 100% body load and with heavy forwarders with more than 75% body load. By larger tire widths, medium and heavy 3-axle forwarders with 100% body load leave a track of more than 0.1 m, as well as do 4-axle heavy forwarders with normal tire width.
The propulsive coefficient can be calculated as follows (R 2 = 0.9504): Formula (75) allows estimating the track depth after the first pass of the forwarder by varying the load capacity, body load coefficient, wheel width, and soil deformation module. At a given value of allowable track depth, the formula (75) can be used to set the forwarder's load factor based on its maximum load-carrying capacity, wheel width, and soil deformation module.

Results and Discussion
Currently, physical parameters of the soil are generally considered to be the most useful for assessing impacts on soil from vehicle movements [38]. For this reason, the bulk density, subsidence resistance, shear resistance, and soil porosity of soil were applied to measure soil compaction. According to previous studies [39,40], the results of this research showed that the investigated physical soil parameters were significantly influenced mainly by the first passes of a vehicle. Similar results concerning the impact of the forwarder on the soil were recorded for the same wood extraction parameters in Italian Alps [41]. Other studies, however, report the opposite results. Gondard et al. [42] assessed the impact of logging in the Aleppo pine forests (Pinus halepensis) in southern France using both forwarders and skidders and reported deep soil disturbance, i.e., removal of topsoil and exposure of lower layers, according to proposed methods and classification [43] only when using a skidding tractor without track formation. Deconchat [44] has noted the same results for mixed oak groves (Quercus robur, Q. petraea and Q. pubescens) in southern France in an oceanic climate. This study focuses mainly on soil disturbance by skidders rather than forwarders, although skidders accounted for less than 1% of the skidding operations. However, both studies were performed based on methods developed to assess the disturbance of the soil surface by simply observing the condition of the soil after felling so that less noticeable effects such as soil compaction cannot be immediately detected.
Besides, the first research was carried out in dry soil conditions with high compaction resistance, where only scratching of timber logs can have any impact. The current study focuses, among others, on frozen soils of the high latitude of low density and high water content. Although obtained in this study results show the significant extent of soil disturbance by forwarders, there is more potential to soften negative consequences specifically for forwarders by optimizing their routes and load capacity and selecting more suitable modification of the forwarder for particular landscape and soil type.

CONCLUSIONS
Based on the obtained results, the following conclusions can be drawn. The comprised model of the interaction process between the wheeled forwarder and the soil is based on the physical theories considering the complex influence of soil and terrain conditions, the parameters of the wheeled propulsor, as well as load and cycles number of its application on the indicators of resistance and adhesion of the forwarder with the traction surface. The presented 75 equations in this model contain accounts of the physical processes of forest soil deformation, rut depth and wheel pressure, bearing capacity and strength of soil resistance, adhesion force, etc. The analysis of technical characteristics of modern wheeled forwarders John Deere, Rottne, Ponsse, Komatsu, and Amkador revealed that the links between the load capacity of machines and their weight, engine power and their weight, maximum propulsion force with load capacity are described for 4-axle and 3axle forwarders with the accuracy satisfactory for practical calculations. Testing results of the developed model, body load levels for 3-and 4-axle forwarders were defined depending on the type of the loading body, tire size, and soil category. The assessment of adhesion and traction and force without slipping was made. Besides, the depth of the wheel immersion at 100% loading for different types of bodies was estimated. Based on calculation results, the practice applicable equations were derived to estimate the traction coefficient of the rut depth after first passage depending on the values of load-bearing capacity, body loading coefficient, wheel width, and deformation module of soil. The approach chosen in this paper can serve as a basis for application in skidding roads projection, soil damage assessment, and another research in this field in future.