Development of a mathematical model of a force actuator for the opening of a space structure with transformable configuration

Abstract

The prospects for the development of radio astronomy, solar energy, space communications, exploration of the Earth’s surface and other planets from space are currently associated with the creation of fundamentally new large-sized space structures. The inevitable complication of the design schemes of promising large-sized systems due to the increase in their operational functionality requires the development of mathematical models that adequately describe the mechanical properties of structures. When designing large-sized systems, the scheme of which allows for automatic configuration change of the structure, it is necessary to take into account shock loads. They inevitably arise when the working state of the structure fixes in orbit upon completion of the process of its opening. To ensure smooth, reliable and shock-free opening of large-sized space structures, it is proposed to use force actuators with active elements made of titanium nickelide material with a shape memory effect. During the tests of the active elements, the main parameters of the force actuator were determined: the generated force, the actuation time and the length of the working stroke. The length of the working stroke was determined by the change in the relative elongation of the active element of the force actuator during its heating. The conducted experimental and theoretical studies are aimed at developing a mathematical model of the functioning of an active element made of titanium nickelide with a shape memory effect for the opening of a space structure with transformable configuration.

Coefficient estimation of simultaneous equations in the case of stochasticity of exogenous variables

“…The random deviation, one of the elements of the right-hand side of the regression equation, depends on all of its elements: the regression coefficients, values of the dependent and "independent" variables. But the relationship between the dependent variable and the random deviation is determined by the type of the equation itself and with respect to the variables on the right side of the equation, there is one of the main postulates of the least squares method, which is that these independent variables are already predetermined, deterministic and independent of chance [4,5]. Therefore, the error in the minimized target function is determined only by the coefficients.…”

Specificity of modeling the actuator for the deployment of transformable large-scale space structures

“…Since the controlling effect on the active element made of material with SME of a force actuator is a change in its temperature, in the conditions of outer space its actuation can be initiated in several ways: either by passing an electric current through it, or by radiation heating (solar radiation) [16,17]. The heating process of active elements can be described using the heat balance equation based on the law of conservation of energy.…”