DECREASING OF MECHANISMS DYNAMIC LOADING AT THE TRANSIENT STATE
DOI:
https://doi.org/10.15802/stp2015/57031Keywords:
optimal control, terminal criterion, dynamical programming, variation calculation, boundary problemAbstract
Purpose. It is necessary to select modes of motion to reduce the dynamic loads in the mechanisms. This choice should be made on optimization basis. The purpose of research is to study methods of synthesis regimes of mechanisms and machines motion that provide optimal modes of movement for terminal and integral criteria. Methodology. For research the one-mass dynamic model of the mechanism has been used. As optimization criteria the terminal and comprehensive integral criteria were used. The stated optimization problem has been solved using dynamic programming and variational calculation. The direct variation method, which allowed finding only approximate solution of the original problem of optimal control, has been used as well. Findings. The ways of ensuring the absolute minimum of terminal criterion have been set for each method of problem solving. The stated characteristics show softness changes of kinematic functions during braking of mechanism. They point to the absolute minimum of adopted terminal criterion in the calculation. Originality. It is necessary to introduce new variables in the system equations during the solving of optimal control problems using dynamic programming to achieve an absolute minimum of terminal criteria. In general, to achieve a minimum of n-order terminal criterion an optimization problem should find relatively (n+1)-th order function. When optimization problems is solving by variational calculation in order to ensure a minimization of n-th order terminal criterion by selecting the appropriate boundary conditions, it is necessary to solve the Euler-Poisson 2(n+1)-th order equation (subject to symmetric setting boundary conditions). It is a necessary condition for an extremum of the functional with the (n+1)-th order integrant. Practical value. Minimizing of adopted terminal criterion in the calculation allows eliminate the brunt in kinematic gearing of mechanisms, which increases their operational life. In addition, the reducing of the acceleration increasing intensity of system driving mass (for example, rotor of electric motor) allows reducing undesirable energy losses in a drive.
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