Abstract
The results of analytical and numerical modeling of dynamic characteristics of linear and non-linear mathematical models of the “trolley-load” system of bridge and container cranes are presented. KiDyM software complex is used for numerical modeling, which, based on the use of the apparatus of structural matrices and the built-in computer algebra system, allows the construction of ordinary differential equations of motion of the class of systems under consideration at the analytical level. Recommendations on the possible use of the considered mathematical models of the “trolley-load” system in various regular and forced operation modes of bridge and container cranes are given on the basis of the analysis. The ratio of the results of calculations for various design models of regular and forced operation of the bridge crane has been established. The magnitude of the distribution of the maximum values of the dynamic characteristics of motion of the container crane has been designed by calculating the forced operation mode using various mathematical models.
Highlights
Increasing the efficiency of the use of lifting machines requires the improvement of the design as a whole and its individual units, as well as improving the control of the truck crane movement
Practice has proved that the calculated dynamic characteristics of the trolley-load system can differ by more than 2.5 times, depending on the chosen approach
In paragraphs 2.5, 2.6, we consider two more mathematical models of the crane-load system, in which the crane equation is replaced by an equation similar to the N.S
Summary
Increasing the efficiency of the use of lifting machines requires the improvement of the design as a whole and its individual units, as well as improving the control of the truck crane movement. Introduction of the optimal automatic control is a rather challenging task This can be explained by the relatively small number of operating systems on real cranes compared with the numerous scientific developments on this problem that have been accumulated in the world for decades since its appearance. The search for ways of simplification has involved mathematical models - the basis for constructing the laws of optimal movement of the trolley-load system [3]. The simplification of the mathematical model may not always be acceptable, for example, for container cranes, where optimality of control is one of the main requirements, and the deviation of load positioning should not exceed 10-20 mm at high speeds of movement of the trolley (up to 240 m/min.), a significant length of the suspension (up to 40 m) and a large weight of the load with a spreader. Practice has proved that the calculated dynamic characteristics of the trolley-load system can differ by more than 2.5 times, depending on the chosen approach
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