Mathematical model of the dynamics change departure of the jib system manipulator with the simultaneous movement of its links

Abstract

An equation of motion of the manipulator is obtained taking into account the influence of the inertial component of each link of the boom system and the effect of the oscillatory movement of the cargo on the dynamic loads of the metalware elements and hydraulic drive elements. The influence of the simultaneous movement of the first jib section, the second jib section and the telescopic jib section on cargo oscillation, as well as the effect of cargo oscillation on dynamic loads that occur in the boom system and manipulator hydraulic drive elements, is determined.

Drive power minimization of outreach change mechanism of tower crane during steady-state slewing mode

“…The joint movement dynamics of the outreach change and crane slewing mechanisms is considered in the research paper [11], and the joint movement mode of the outreach change and load lifting mechanisms was determined in [12,13]. The kinematic, force and energy characteristics of the outreach change, load lifting and crane slewing mechanisms were determined on the basis of these studies.…”

“…The variational problem (11) and ( 9) with expressions ( 6) and ( 7) is linear, the solution of which is presented in the next form 4, 41522 C   were found. We will obtain the final solution of the linear variation problem (11) and ( 9) by substituting the found constants 1,..., 12 C in (12). This will ensure the rootmean-square value minimization of the drive moment of the load outreach change mechanism during the steady-state crane slewing.…”

“…We will use the analytical solution of the linear variational problem (11) and ( 9), as the initial approximate solution of the nonlinear variational problem (8) and (9). In order to obtain approximate solution of the variational problem ( 8) and ( 9), we add the next polynomial to the known solution (12):…”

“…Diagrams in black correspond to the case of the initial iteration, i.e. function (12), and in gray -the found approximate solution to problem ( 8) and ( 9). The next notations are accepted in Fig.…”

“…In addition, the main parameters of the movement characteristics were calculated, which correspond to the found approximate solution of the problem (8) and ( 9) according to the root-mean-square value criterion of the power and the known solution (12) according to the root-mean-square value criterion of the driving moment (Table 1).…”