An Approximating Mathematical Model of Interaction Between a Freely Rotating Disk and Soil

A generalized mathematical model of disk interaction with soil was built under general assumptions regarding the mode of the disk knife motion in soil, namely, in a mode of slippage, skidding or rolling without slippage and skidding. Previously constructed models follow from it as particular cases at certain values of parameters. However, because of computational complexity of this model for the case of a freely rotating disk knife consisting in the need for a preliminary numerical solution of a transcendental equation to determine the mode of disk motion, the generalized mathematical model has not found wide application. Therefore, an analytical two-dimensional approximation of a generalized model of disk interaction with soil which is a new model of approximation type was constructed on the basis of a computer experiment using the least squares method.An explicit expression was obtained for the kinematic parameter of a freely rotating disk knife which determines its mode of motion. It was established that this parameter is a rational function of relative depth of the disk penetration and the dimensionless dynamic coefficient characterizing soil properties. Also, explicit expressions were obtained for the projections of the resultant soil reaction forces acting on the blade of the disk knife and its side faces depending on the data of dimensionless parameters. It has been established that the horizontal component of the reaction which determines tractive resistance of the disk is also a rational function of the relative penetration depth and the dimensionless dynamic coefficient. It was established that the magnitude of the kinematic parameter significantly affects the magnitude and direction of the resultant soil reactions to the disk. The expressions obtained make it possible to significantly simplify experiments to determine the resultant soil reaction forces to a freely rotating disk knife and reduce their required number. These expressions make it possible to carry out strength calculations of soil-cultivating working tools with disks and determine their optimal parameters according to the strength criteria and the minimum specific energy consumption with accuracy sufficient for engineering practice. Adequacy of the obtained expressions was confirmed by comparison with experimental data of the disk knife dynamometr

Development of a Criteria­based Approach to Agroecological Assessment of Slope Agrolandscapes

For the forecast and management of erosion processes in order to protect the environment, information is needed on the state of its components and impact factors as well as the results of this impact. The existing methods for assessing the catchment area are mainly descriptive and cannot be used in mathematical prediction problems. The most accurate formulation of the problem of quantitative assessment of the catchment area is carried out during hydrological calculations. It seems expedient to develop theoretical prerequisites for agroecological assessment of slope agrolandscapes on the stability of a network of temporary watercourses by using the Lokhtin criterion.Slope agrolandscapes are erosive dangerous objects. The existence of a continuously changing system of microstreams generated by precipitation on slopes greatly complicates the situation. Criteria are proposed to determine the main trends in the development of watercourses of river systems by washing away or depositing soil. Conclusions about the catchment area as a whole can be obtained by examining a certain area of a microstream flow for a long time and comparing field observations with laboratory experiments. To determine the sustainability of a watercourse, a theoretically reasonable value has been proposed, which allows quantifying the network of temporary streams. When conducting research, data on the catchment area of the Tsivil river (Chuvash Republic, Russia) from 1950 to 2010 were used.A quantitative assessment of the erosion resistance of the microstream system was carried out both for periods of snowmelt and for rains, conventionally divided into summer and autumn. The theoretical background considered is confirmed by the data of long­term observations on the Great Tsivil river for sixty years. The dependences obtained make it possible to compile an adequate forecast of the direction of evolution of the catchment area in relation to the processes of soil deposition or its washing out. The criteria developed are applicable both to a specific catchment area of microstreams and to the catchment area of a river system as a whol

Development of Dimensionally Stable Structures of Multilayer Pipelines and Cylindrical Pressure Vessels From Carbon Fiber Reinforced Plastic

In the framework of the momentless theory of cylindrical thin shells, the elastic deformation of multilayer pipes and pressure vessels is investigated. It is assumed that the pipes and pressure vessels are made by two-way spiral winding of carbon fiber reinforced plastic tape on a metal mandrel.The analysis of the dependences of elastic deformations on the reinforcement angles is performed. The relations for axial and circumferential deformations of the wall, depending on the structure of the layer package, reinforcement angles under static loading are obtained. The separate and combined effect of internal pressure and temperature is considered. For the separate effect of loads, the graphs of deformations against the winding angle are plotted.Composite pipes made of KMU-4L carbon fiber reinforced plastic, as well as composite metal-composite pipes, are investigated. The results obtained for thermal loads are in good agreement with the data of the known experiment and solution. Depending on the load parameters, composite and metal-composite structures with dimensionally stable properties are determined.It is shown that dimensionally stable structures can be used to solve the problem of compensation of elastic deformations of pipelines. For this purpose, using the ASCP software package, the variant analysis of model structures is performed. By the comparative analysis of the three versions of the structure, layer package structures and reinforcement schemes, ensuring a significant reduction of loads on the supporting elements are obtained. On the example of a pipeline with a flowing fluid, it is shown that the use of dimensionally stable multilayer pipes makes it possible to eliminate bending deformations and significantly reduce the level of working forces and stresses.Dimensionally stable composite multilayer pipes open up new approaches to the design of pipelines and pressure vessels. It is possible to create structures with predetermined (not necessarily zero) displacement fields, consistent with the fields of the initial technological displacements, as well as with the displacements of conjugate elastic elements and equipment when the operating mode changes. The scope of such structures is not limited to "hot" pipes. The results can be used in cryogenic engineerin