PSI - Issue 42

Taško Maneski et al. / Procedia Structural Integrity 42 (2022) 1503–1511 T. Maneski at al/ Structural Integrity Procedia 00 (2019) 000 – 000

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the dynamic gain factors for selected excitation-response combinations; measurement of displacement and acceleration dynamics of the support structure, and visual inspection of the condition of the entire structure.

R4 R3

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Robot positions

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Figure 3. Scheme of the supporting structure and photograph of the attached painting robots

Figure 4. Geometry of the theoretical computational model, where x is the longitudinal horizontal axis, y is the vertical axis, and z is the transverse horizontal axis

The entire diagnostic procedure primarily aimed to determine the cause of the unfavorable dynamic and resonant behavior of the support structure. To define the planes and directions of unfavorable dynamic stiffness of the structure, calculations were performed using the finite element method (FEM). The calculations determined the natural oscillations of the support structure and defined the natural oscillation vectors [8]. The painting robots have impulse motion with frequent changes of direction, so they cause excitations at numerous frequencies during operation. However, when the support structure itself has a large number of low natural oscillations, it cannot accept the dynamic inertial forces caused by the robot movement, so relatively large dynamic deformations and resonant behavior occur. In the robot system under study, the support structure behavior had a very unfavorable effect on the operation of the robot motion reducer, and the biggest problems appeared in the zone marked in red in Figure 3. To determine the cause of this support structure failure, the first vibration measurements, performed by an accredited laboratory [9] , determined that the painting robots’ frequencies range between 3.5 Hz and 9.5 Hz. Robot 2 had the highest vibration speeds, as much as 2.33 mm/s in the horizontal transverse direction, while its vibration speed in the vertical direction was slightly lower (RMS about 0.62 to 1.32 mm/s). In order to confirm the theoretical results, appropriate experimental measurements were required. The measured parameters of dynamic behavior should show whether the permitted values were exceeded. Based on comparative analysis of theoretical and experimental results, the causes of the poor performance of the support structure could be determined, and the means to effect remedial repairs and reconstruct individual assemblies could be proposed. Static and dynamic analysis was performed using FEM with the KOMIPS software package developed at the Faculty of Mechanical Engineering, Belgrade, Serbia [8]. 2. Static and dynamic analysis The geometry of the theoretical computational model is shown in Figure 4 in three projections and in isometry. Figure 4 also shows the position of the supports. The first calculation involved theoretical forces of 10 kN in all three directions of the Cartesian coordinate system, at the locations of the robots marked in red in Figure 3. The results obtained, i.e., maximum displacements from individual forces and from all three forces together, are shown in Table 1. Based on maximum displacements, the likely stiffness of the whole system in each coordinate axis direction was then calculated (Table 1). The calculations showed the stiffness in the z direction to be much less than the stiffness in the other two directions. The longitudinal horizontal force ( Fx ) caused large displacement in the x direction, while the vertical force ( Fy ) also would cause significant vertical ( y ) displacement, so the stiffness was calculated as being relatively small.