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Research Papers

Comparison of Methods for Modeling a Hydraulic Loader Crane With Flexible Translational Links

[+] Author and Article Information
Henrik C. Pedersen

Department of Energy Technology,
Aalborg University,
Aalborg East, DK-9220, Denmark
e-mail: hcp@et.aau.dk

Torben O. Andersen

Department of Energy Technology,
Aalborg University,
Aalborg East, DK-9220, Denmark
e-mail: toa@et.aau.dk

Brian K. Nielsen

Department of Energy Technology,
Aalborg University,
Aalborg East, DK-9220, Denmark
e-mail: briankongsgaard@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 6, 2014; final manuscript received June 4, 2015; published online July 27, 2015. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 137(10), 101012 (Jul 27, 2015) (15 pages) Paper No: DS-14-1456; doi: 10.1115/1.4030801 History: Received November 06, 2014

When modeling flexible robots and structures for control purposes, most often the assumed modes (AMs) method is used to describe the deformation in combination with a floating reference frame formulation. This typically has the benefit of obtaining a low-order, but accurate model of the flexible structure, if the number of modes and AMs are properly chosen. The basis for using this method is, however, that the vibrations (deflections) are time and position independent, i.e., the expression is separable in space and time. This holds for the classic Euler–Bernoulli beam equation, but essentially does not hold for translational links. Hence, special care has to be taken when including flexible translational links. In the current paper, different methods for modeling a hydraulic loader crane with a telescopic arm are investigated and compared using both the finite segment (FS) and AMs method. The translational links are approximated by a single beam, respectively, multiple beam elements, with both one and two modes and using different mode shapes. The models are all validated against experimental data and the comparison is made for different operating scenarios. Based on the results, it is found that in most cases a single beam, low mode order approximation is sufficient to accurately model the mechanical structure and this yields similar results as the FS method.

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Figures

Grahic Jump Location
Fig. 1

Picture of the crane considered

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Fig. 2

Main dimensions, data, and lifting diagram for the crane. The control valves used for each of the 3DOF are Danfoss PVG32 pressure compensated PVGs.

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Fig. 3

Sketch of the system with names of parts

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Fig. 4

System illustration with the used notation. Notice that only the hydraulic system for the jib actuator is shown.

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Fig. 5

Flexible body in the floating reference frame (xi,yi)

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Fig. 6

Sketch of the system in extended configuration

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Fig. 7

Sketch showing how the orientation of the fourth reference frame is determined by ϕ3

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Fig. 8

Considered mode shapes

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Fig. 9

Slack between the translational bodies and how the friction is related to the force couple

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Fig. 10

Sketch showing the segmenting used in the FS method. Notice that all angular rotations are measured absolutely.

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Fig. 11

Connection several segments

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Fig. 12

Pressures in the main cylinder, with the adjusted model parameters and when operating the main cylinder

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Fig. 13

Relative link positions and measured and simulated extension boom positions, when operating the main cylinder and using the 1B2M QS model

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Fig. 14

Operating the main cylinder

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Fig. 15

Operating the jib cylinder, 1B2M QS model

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Fig. 16

Operating the extension system, 1B1M PA model

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Fig. 17

Operating the extension system, FS model

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Fig. 18

Operating all axes simultaneously

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Fig. 19

Response of the 1B2M QS model with flexibility of the nylon pads included. The data series is the same as shown in Sec. 3.2.

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