Bifurkace rovnovážných stavů pohonových soustav

Bifurcation of drive systems steady states

journal article - other

Czech

Předkládaný příspěvek se zabývá problematikou chování pohonových soustav na hranicích oblastí stability, kdy může docházet buď ke vzniku reálné nebo komplexní bifurkace rovnovážného stavu, které se projevují kvalitativními změnami v chování dané pohonové soustavy.

Presented contribution deals with detailed qualitative analysis in steady states. Results of this analysis shows that considering dynamical properties of drive motor represented by time constant of the motor the number of stability conditions of the drive system steady state increases into two stability conditions, while: a) stability condition (7b) binds static properties of drive engine and working machine in such a way that slope of the tangent to the torque characteristic of working machine must be higher than slope of the tangent to the static torque characteristic of the drive. When this condition is broken the real bifurcation of the steady state can occur which develops to the drive system transition to the different steady state, b) stability condition (7a), not shown in literature, binds static and dynamical properties of drive engine, represented by the slope of the tangent to the torque characteristic of drive in steady state and time constant of the drive, together with global characteristic of drive system, represented by reduced moment of inertia of the whole drive system. When this stability condition is broken the complex (Hopf) bifurcation of the steady state always occur which develops to the branch of stable or unstable periodic solutions, which results in creation of intensive selfexcited oscillations in drives. From above mentioned conclusions is clear that ignoring dynamical properties of the drive engine in drive system can lead to the results essentially different from reality, which is particularly clear mainly in the micro-drive area, when reduced moments of inertia reach the same or even smaller values than time constant of the drive and there is high probability that parameters of given drive will be close to the boundary of the stability area, defined by stability condition (7a), which was not considered so far.

Pohonová soustava, rovnovážný stav, stabilita rovnovážného stavu, reálná bifurkace, komplexní bifurkace.

Driving system, steady state, stability of steady state, real bifurcation, complex (Hopf) bifurcation.

PROCHÁZKA, F.

30. 6. 2003

1210-2717

Inženýrská mechanika - Engineering Mechanics

10

3

Czech Republic

199

218

20