Dynamics Response And Anti-swing Control For Rigid-flexible Coupling Systems Of Gantry And Overhead Crane

China’s modern logistics industries,which include ports and railways for container transport,have been further developed through the promotion of the national strategic "Belt and Road" initiative.However,some key equipment involved in logistics still needs to be made more efficacious and safe so that trade can be maximized,like the gantry cranes that are used in the logistics industries.Currently,the container spreaders on gantry cranes are connected to a trolley via a flexible wire rope,and the payloads tend to swing under the influence of the wind and inertia forces during the work process.This not only makes it difficult to precisely position the containers,but can also cause the containers to collide,thus increasing the security risks,and thus seriously reducing the efficiency of the crane operations.The girder spans of the cranes have also been gradually increased as the trend of container gantry cranes has moved towards large-scale construction,and the crane’s bridge structure,trolley,and payload now consists of a multi-body coupled system.Investigating this complex multi bodied coupling dynamic system and the residual swing of the payloads have become hot topics in China and around the world.This paper,according to the structural characteristics of a container crane,mainly focuses on the following topics: establishing a two degree of freedom model of an elliptical pendulum,the anti-swing characteristics of an inverted triangular structure,a moving mass passing through a bridge model,the multi-body dynamics of a rigid flexible coupling system,and optimizing a two-mode input shaper for the feed forward control and trajectory planning of a trolley.(1)The residual oscillation of a flexible anti-swing system is extremely critical in a rail mounted container gantry crane’s spreader because it is an under-actuated and strongly coupled system.We therefore propose a two-degree of freedom mathematical model constructed according to the physical structure of the crane’s spreader in order to describe the dynamics of the container crane’s spreader.With the calculation of the swing angle of the cable based on the Lagrange theory,the dynamic characteristics of the spreader were assessed and discussed respectively,both when it followed a)the running direction of the trolley and b)the running direction of the crane.(2)The vibration of the crane’s beam and the residual swing of the payload causes fatigue in the crane and affects the precise positioning of the payload.In this paper,the coupled system of an overhead crane was simplified to that of a moving mass passing a bridge and a two degree of freedom elliptical pendulum model.The differential equations that captured the motions of the coupled overhead crane system were derived from and based on the Lagrange equation.The numerical solution was arrived at by using the Newmark-β step by step integral method.The influences of the moving speeds and the structural parameters of the crane on the vibrations of the beam and the payload swing were analyzed.(3)The payload generates residual vibration whenever the overhead crane accelerates or decelerates,due to the forces of inertia that act on the under-actuated payload of the overhead crane.We thus presented an optimized and robust input shaper to reduce the vibration of the payload.To this end,the damped natural frequencies of the payloads were derived according to the dynamic model of an overhead crane.Furthermore,the probability distribution of the payload’s damped natural frequency,which considered any external disturbances,was obtained through using Monte Carlo simulation.An optimal two-mode input shaper was also designed through minimizing the expected level of residual vibration.The optimized two-mode input shaper based on the probability distribution function of the payload’s swing frequency was then used as the feed forward input to increase the frequency robustness.(4)A dynamic model of a crane’s system with damped oscillation was set up and established,and the energy control method was used to dynamically suppress the residual sway of the payload in real time.At the same time,phase plane analysis was used to study the methods for controlling the acceleration curves of the trolley and thus the residual swing of the payloads.Bezier curves were generated through particle swarm optimization to manage the acceleration of the trolley,and thus maximize control in suppressing the residual swing of the payloads.(5)The use of virtual-reality technology based on a 3D graphics rendering engine(OGRE)was proposed to realize the semi-physical simulation of operator training for container cranes.Operator training was needed to overcome the issues of low efficiency and poor security in the field of container handing training.The OGRE renders a 3D virtual scene of a container yard.The crane’s hardware and the virtual reality software communicate and exchanges information through an ethernet.Technologies such as PLC control,image recognition,machine vision,crane position tracking and input shapers were used to suppress any residual swing in the payload.The machine’s visual technology was used to measure the residual swing angle of the payload.The hardware platform of the container crane was built to facilitate real time measurement and control of the trolley’s running position.The location of the container was obtained by using digital image processing,image segmentation,feature matching and object orientation technology.Additionally,the input shaping method was adopted to enable the residual swing of the payloads to be reduced.The amplitude of the payloads was measured via the machine vision method.We established a rigid and flexible multi-bodied coupling dynamics model according to the structural characteristics of a container crane,and got the payload swing and vibration characteristics of the bridge structure through numerical simulations.The residual swing of the payloads was suppressed by designing a feed forward control input shaper for optimal input shaping.Finally,the effectiveness of the feed forward control input was verified through a semi physical simulation experiment and the payload residual swing was suppressed experimentally based on optimized two-mode input shapes.