Organizational and engineering models provide a formalized description of the construction process, including a list of operations, their sequence, description of the relationship between the operations, and the features of the work technology. Network models have the most complete mathematical description. However, a number of authors in their works point to serious shortcomings inherent in the network modeling of construction flow. The network model allows displaying accurately enough only the relationship of specialized traffic flows when the object is divided into sections equal in size to interchangeable grips. Such schedules are quite effective in planning and operational management of road works in a short planning period (decade or month). The adequacy of the real construction representation is violated when the network model is enlarged for long-term planning of the flow. The currently developed so-called generalized network models achieve process combination and continuity by introducing links between the operations, characterized by temporal parameters assuming any values, including negative values. However, the complexity of the mathematical description of these models still prevents their use in solving optimization problems. The research aims at developing a mathematical model and an algorithm for calculating the operational control of the groundwork volume during the construction of logging roads. A model of a complex object flow is proposed, where the flow operation time has a discrete nature. This condition is realized in the model by dividing the planned operation period of a complex flow into equal time intervals – scheduling intervals. The below described model of complex road construction flow can be presented on the basis of the scheduling task classification scheme and the analysis of existing economic and mathematical models and methods. The scheduling model developed for the purpose of determining the optimal groundwork for the road construction elements is a deterministic (at the 1st stage), discrete in time, engineering model with variable speeds of operations.

The saw stability in operation defines the ability of the saw blade to resist the forces acting on it in the plane of greatest rigidity. The saw can work reliably only in case of maintaining stable balance, which is achieved through the creation of normalized residual stresses in certain zones of the saw blade by different methods. The stresses balance the forces of external influences. Compressive stresses are created in the central part of the blade to make the circular saw operational. These stresses compensate the forces of centrifugal acceleration, temperature heating of individual zones of the saw blade, external longitudinal and transverse bending forces arising in material processing. In practice, the creation of normalized stresses in the saw disk is traditionally carried out only by local mechanical contact action (forging, rolling) of the saw blade tool on the steel saw blade. It is proposed to form the stressed state of the disk by thermophysical action instead of the traditional mechanical processing of the saw blade. The thermophysical action involves the creation of normalized residual stresses in the saw blade by the concentrated thermal exposure to local differently directed narrow-band zones of straight or deflected shape, mainly radial or along concentric traces, controlling the process in real time. A new approach to the formation of residual stress fields in the saw blade by thermoplastic action enables to radically change the settingup procedure of the circular saw, ensuring its stability in operation.

The working tool of machines with circular cutting units is a circular saw, the condition of which largely determines the quality of material processing. Circular saw blades in the process of operation are subjected to a complex effect of force and temperature factors that cause elongation and deformation of the saw blade, and the occurrence of internal stresses that take it out of the flat form of elastic balance and reduce the tool’s performance. The ability of saws to resist these factors is determined by the rigidity and stability of the saw blade. It is customary to consider a circular saw blade consisting of three zones: peripheral, middle and central. The middle part has the greatest influence on the stability of the saw blade. Initially, after manufacturing, the saw blade has a flat shape of balance, which can be disturbed by any external impact on the saw during the cutting process. The balance disturbance causes the blade and the cutting edge of the saw to deviate from the initial operating condition and reduce the accuracy and quality of wood processing. In order to prevent the influence of external forces, coaxial zones of plastic deformation of a certain width are formed in the middle part of the blade. In this case, under the influence of the created stresses, the effect of web tension appears. In world practice, two methods of forming such zones are used: forging and rolling. The creation of normalized stresses in the circular saw blade is carried out by local mechanical contact action of the working body of the saw tool on the steel saw blade in certain places of the middle zone. Compressive stresses compensating the forces of centrifugal acceleration, the thermal heating of individual zones of the saw blade, the external longitudinal and transverse bending forces that occur in the blade during wood processing are formed in the treated annular zones. The considered methods for creating annular zones of plastic deformation fields involving mechanical action on the saw blade have significant drawbacks, the elimination of which requires fundamentally new technical solutions. It is proposed to form coaxial fields of residual stresses of the saw blade by thermoplastic action consisting in creation of normalized residual stresses in the saw blade by concentrated thermal action on local annular zones coaxially located along the saw blade for the entire thickness of the saw. The formation of coaxial circular fields of residual stresses in the circular saw blade is simulated. The considered method of saw preparation will increase its stability in the process of operation.

The currently available methods for evaluating technical-operational characteristics and conditions of hauling roads are time- consuming. Although, they provide a sufficiently accurate description of the conditions of certain road components. Furthermore, they give the possibilities to identify ways for elimination of the constructional defects and determine the work extent to correct them. A peculiarity of forestry production is the simultaneous exploitation of a branching transport network with different types of subsidiary hauling roads, which depends on weather conditions, change of logging locations, traffic intensity, and other factors. Therefore, the available methods, which clarify the relationships between the traffic resistance and strength of the road construction, are poorly usable for rapid estimation of the technical and operational conditions in renovation planning. The purpose of the study is to improve the methodological fundamentals of traction-operational calculations for timber transportation according to the constructional state of the hauling roads. It has been determined that the calculation of the rolling resistance must include the factor of structural deformation. It is influenced by the modulus of elasticity for the surface structural materials. The resulting relationship makes it possible to increase the accuracy of traction-operational calculations at the project phase of the hauling road building. It can be included into the target function for comparing alternatives in the case of optional project planning. The mathematical aspect in the evaluation of the traffic resistance gives an opportunity to use this parameter as an indirect characteristic of the constructional strength of a road, as well as it can be a comprehensive qualitative indicator of the condition of a pavement. For citation: Prokopets V.S., Kozlov V.G., Skrypnikov A.V., Ponomareva N.G., Levushkin D.M., Borovlev Yu.A. Mathematical Justification of Vehicular Traffic Resistance in Relation to Structural Surface Conditions of Hauling Roads. Lesnoy Zhurnal = Russian Forestry Journal, 2023, no. 2, pp. 106−120. (In Russ.). https://doi.org/10.37482/0536-1036-2023-2-106-120