In this article, based on the Lagrange principle, the fundamental elements of the mechanics of continuous media with moving boundaries in relation to hydraulic drive systems of hydrostatic transmissions of combine harvesters are developed, which allows to expand the field of research and modeling diagnostics of these systems. The elements of the theory, the method of calculation of nonstationary processes of one - dimensional motions of uncompressed liquid media with moving media boundaries in hydraulic channels of complex geometric shapes of hydrostatic transmissions of combine harvesters are developed in the article. The analysis of methods of numerical solution of systems of ordinary differential equations with discontinuous coefficients is performed. It is shown that the Bless method is a more effective method of numerical solution of such systems of equations in the studied area. It is shown that for one-dimensional motions of uncompressed liquid media moving in the channel and bounded by moving boundaries, the calculation is reduced to solving the equation a a(x,t)ẍ= b(x, t)ẋ 2 + c(x, t). Here x = x (t) is the coordinate of the front or rear boundary of the liquid medium moving in the channel. It is shown that this equation is a generalized Bernoulli equation in the case of the motion of incompressible liquid media with moving boundaries. This equation is similar to the equation of motion of bodies with variable mass, and is convenient for use in CAD. The theory and method of calculation of processes of incomplete hydraulic shock arising at filling of liquid or gas-liquid environments of channels with local hydraulic support of difficult geometrical forms, for example, the centrifugal pump of hydrostatic transmissions of combine harvesters are created.The method of engineering calculation is obtained, which allows to determine the coefficient ε of compression of the liquid jet and the value of ∆p̅ = (p1 − p0 )/p0 relative shock pressure increase with incomplete hydraulic impact on local hydraulic resistance of complex geometric shape of hydrostatic transmissions of combine harvesters. Thus, the elements of the theory are created, as well as the method of calculating non-stationary processes of movement of uncompressed liquid media in the channels of complex geometric shapes of hydrostatic transmissions of combine harvesters. The method is used in the calculation of the dynamics of the start of the ampouled hydraulic system of the drive of hydrostatic transmissions of combine harvesters with minimum volumes of 1...10% of gas cavities for storage of the working fluid of the drive. The elements of the theory described above and the created calculation methods allow to expand the field of research of dynamic modes of operation of hydraulic systems of power drive of hydrostatic transmissions of combine harvesters in the process of filling working fluid channels of hydraulic systems with branches and hydraulic supports. Their application has allowed to increase the accuracy and reliability of diagnosing real processes characteristic of hydraulic drive systems of hydrostatic transmissions of combine harvesters, especially in difficult conditions of their amputation
methodology, transmission, hydrostatics, efficiency, combine
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