Modelling of microaccelerations with using of Weierstrass-Mandelbrot
function А.V.Sedelnikov The microaccelerations problem having arisen in 1975 still has
no cardinal solution. It is being got used to and now there is no such
uncompromising struggle as at an initial stage of its development. Space
technologies gave a powerful pulse to manufacture of ultra pure semiconductors,
unique medicines, etc. But a real revolution in manufacture was not
successful - those microaccelerations
interfered which had an absolute value
of less than 10-6g and were completely unperceptive for humans. A number
of researches believed that gravitational and aerodynamic accelerations were
the basic contributors of microaccelerations and
offered their estimations of these contributions to the total microacceleration level. However, these researches were
mainly of theoretical interest. There is rather effective way of struggle
against this part of microaccelerations. It is
launching the space vehicle (SV) into high orbit where the gravitational and
aerodynamic forces can be neglected. Other microaccelerations caused by internal factors can not be
treated like this. For example, for the process of growing the crystals with
perfect structure it is necessary to maintain certain temperature that can
deviate only by several hundredths of degree during three months. Overcooling
or overheating the solution (or melt) is not allowed when SV respectively gets
into Earth shadow or is exposed to the Sun light. The problem of supplying SV with electric power
was solved long ago by mounting the solar arrays (SA). SA operate
efficiently being directed towards the Sun which is implemented by active SV
orientation with help of the engines of position control system (EPCS). Here
the most difficult and almost unsolvable problem occurs: microaccelerations
arise of the order of 10-3 m/s2. This has a pernicious
effect on complicated and subtle technological processes. For example, in case
of crystallization the microacceleration growth leads
to enhancement of convective movements which result in increase of capture of
impurity and crystallization centers. Ordinary polycrystalline structure is
obtained instead of perfect internal structure almost without weak intercrystalline bonds. The start of EPCS excites the oscillations of
SA that represent elastic and rather long structures (up to One should also note that the apparatus for measuring microaccelerations
of the order of 10-6g are the
ultra sensitive ones. The g-forces which they undergo at the SV start may most
probably cause their fault. For example, there are the estimations of microaccelerations obtained with French accelerometers
BETA. Their data on microaccelerations along three
coordinate axes differed more than 20 times though there were no objective
reasons. Perhaps, this was the case when apparatus failed to sustain the start
g-forces. Similar case of approximately 20-fold
discrepancy of microaccelerations possibly takes
place during the experiments on board of "Freedom" with vibration-isolating
device MGIM. Researchers divided all the experimental series into successful
and unsuccessful. Oscillation amplitude in the series also differed
approximately 20 times. In this case the obvious objective reasons were also
not detected. The project ended without results. A number of researches believe that there is
some objective unreliability of full-scale results related to microaccelerations. Construction of adequate mathematical models of
modern SV motion is rather complicated and laborious problem. Many changes,
i.e. possible SV orbit, flight modes, etc., demand construction of new models
taking into account some other disturbing factors. Thus, in the majority of
modern models the microaccelerations are estimated
after SV launch. The problem of microaccelerations
estimation at design stage before SV creation is still unsolved making the
technological projects suffer. For example, the project of SV "Nika-T" was aimed at technological experiments but was not
implemented (the author participated in construction of mathematical model for microaccelerations on board of SV). There is an objective
need in microaccelerations estimation at the stage of
SV design without any additional modeling. The problem is how to construct a
statistical estimation of microacceleration level in
the domain of supposed mounting of technological equipment without SV motion
analysis. This estimation can help to solve some of the accumulated problems. This
paper offers to obtain these estimations using the real part of Weierstrass-Mandelbrot fractal function (WMF). |
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