Calculation of shearing stress for nonstationary fluid friction
DOI:
https://doi.org/10.33216/1998-7927-2022-272-2-67-81Keywords:
Fluid friction, shearing stress, equation of motion, Laplace transform, transfer functionAbstract
The important parameter in the calculation of hydromechanical processes is the force of viscous fluid friction, which is characterized by shearing stress arising in the working environment, which comes into contact with the surface of the moving element of the actuator, control, distribution or auxiliary hydraulic device. In the presence of a gap between the surfaces of the elements, the shearing stresses occur during the relative motion of these surfaces and the movement of the medium under the influence of the pressure drop. Traditional approaches to the construction of mathematical models of nonstationary hydromechanical processes are largely based on the fact that real flows are replaced by a sequence of time-varying flows with a quasi-stationary distribution of hydrodynamic quantities over the section. This allows you to enter into the calculation of the coefficients and characteristics obtained for stationary flows.In fact, the structure of the nonstationary flow differs from the quasi-stationary one, and it is not always known how and under what conditions such a difference can affect the change of hydrodynamic characteristics. Therefore, the nonstationary plane laminar motion of incompressible fluid in the gap between the moving and a fixed elements in the Cartesian coordinate system is considered. The solution of the equation of motion in partial derivatives is fulfilled using the Laplace transform. The dependence in the operator form for the shearing stress for nonstationary fluid friction is obtained. The transfer functions for the shearing stress of the velocity of the moving element and the pressure gradient are determined. Based on the analysis of amplitude-frequency characteristics, the boundaries of a quasi-stationary approach are established for calculating the forces of nonstationary viscous friction on the moving elements of hydraulic devices. The solution of the equation of motion in partial derivatives is fulfilled using the Laplace transform. The approximate transfer functions for the nonstationary shearing stress are obtained, which allow to establish the connection between the originals in the form of ordinary linear differential equations. The dependence for the shearing stress under nonstationary fluid friction is proposed, which takes into account the moving surface acceleration, which makes it possible to increase the accuracy of calculating the dynamic characteristics for hydraulic systems.
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