Control Systems and Computers, N5, 2016, Article 6
DOI: https://doi.org/10.15407/usim.2016.05.047
Upr. sist. maš., 2016, Issue 5 (265), pp. 47-53.
UDC 007.72; 531.395; 531.553; 621.51/54
Perlov Yevgeniy F., Ph.D. of Technical Sciences, International Research and Training Centre of Information Technologies and Systems of the NAS and MES of Ukraine, Glushkov ave., 40, Kyiv, 03187, Ukraine.
Some Aspects of the Dynamics of the Transient Rotary Operating Element Under the Influence of the Elastic Forces
Purpose. It is vitally necessary to create the mathematical model of the dynamic behavior of the rotary operating element, which is under the influence of inertial forces, the forces of friction and elastic forces in transient regimes of acceleration and deceleration for using the model in robotics, manipulators, etc.
Statement. Due to the mathematical model results of the rotary operating element, working, as a rule, with high angular and linear velocities and accelerations, performing herewith high-precision coordinate orientation, there is the possibility to examine the dynamics of its behavior (movement) in acceleration and deceleration modes. This moving may be realized either by an exponential law, or under the law of damped harmonic oscillations.
Except stated, the rotary working element is considered as a link of the automatic control system (ACS). In this case, the rotary working element can be represented either by the 2nd order link and this link can be replaced by two series-connected inertial links or as an oscillating link.
Method. These results are achieved due to the resulting inhomogeneous differential equation of 2nd order. Depending on the structure of the characteristic equation roots (real or complex roots), transients can be carried out either by an exponential law (real roots), or under the law of damped harmonic oscillations (complex roots). Moreover, the rotary operating element is considered as a link of ACS, that has been made possible by the resulting differential equation, which is presented in a symbolic way by which amplitude-frequency, phase-frequency and amplitude-phase characteristics of the rotary operating element are obtained as a link of the ACS.
Conclusion. At the end of the article there are conclusions that enable the practical use of the results.
Keywords: rotary working element, dynamic, acceleration-deceleration, differential equation, automatic control system.
1. Gritsenko, V.I., Rodionov, A.A., Perlov, Ye.F., 2012. “Nekotoryye aspekty dinamiki perekhodnykh protsessov povorotnogo rabochego elementa, deystvuyushchego bez uprugikh i vyazkouprugikh sil”, Upravlausie sistemy i masiny, 5, pp. 36–45. (In Russian).
2. Korn, G., Korn, T., 1981. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov. M.; Nauka, 720 p. (In Russian).
3. Solodovnikov, V.V., Plotnikov, V.A., Yakovlev, A.V., 1985. Osnovy teorii i elementy sistemy avtomaticheskogo regulirovaniya. M.: Mashinostroyeniye, 536 p. (In Russian).
Received 18.10.2016
