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

1506

4

Table 1. Calculated deformations and likely stiffness depending on the load i Load Fi Deformation [mm]

Stifness [kN/mm]

fx

fy

fz

Fi/fx

Fi/fy

Fi/fz

1 2 3 4

Fx = -10 kN Fy = -10 kN Fz = -10 kN

-0.664

0

0

15





0 0

-0.524 -0.247 -0.771

0.247

19

40.5

 

2.93

40.5

3.4

Fx=Fy=Fz= -10kN

-0.667

-3.177

15

13

3.15

Within the dynamic analysis, the eigenfrequencies and maximum amplitudes of the main oscillation forms were determined. In addition to the mass of the support structure, the masses of the robots were introduced into the calculation, and the results obtained are shown in Table 2.

Table 2. Eigen-frequencies fi and maximal amplitudes Ai of the main oscillation forms calculated

No.

fi [Hz]

Ai [mm]

No.

fi [Hz]

Ai [mm]

No.

fi [Hz]

Ai [mm]

No.

fi [Hz]

Ai [mm]

1 2 3 4 5

2,2

6,6

6 7 8 9

10

47

11 12 13 14 15

14

47 19

16 17 18 19 20

15,3 16,1 16,2 16,9

36,4 20,8 18,7 47,5 24,2

4

10 12

10,7 12,1 12,8 13,7

10,6

14,2 14,5

7,6 8,6 9,3

50

29,5 42,7 57,2

11,7

13,1 19,4

14,58 14,64

9,3

10

17

Dynamic analysis showed that 20 natural frequencies were below 17 Hz, of which the first seven were below 11 Hz. In order to determine the behavior of the support structure, the appropriate fields of amplitudes were determined, i.e., the deformation during oscillation was analyzed. This analysis was performed on the model as shown in Figure 4, with concentrated masses being introduced in all three directions at the robot locations. Figure 5 shows selected modes of structure oscillation. Analysis of the amplitude field during oscillation led to the conclusion that in the first four modes, the translation of the support structure in the z -axis direction (transverse displacement) was dominant. In mode 5, sliding in the longitudinal ( x -axis) direction also occurred. Modes 6-8 indicated only local movement of some peripheral parts within the support structure (outside the space where the robots are located). Modes 9 and 10 showed bending occured in the longitudinal and transverse horizontal girders.

Model

Third mode

Second oscillation pattern

Ninth oscillation pattern

Figure 5. Scheme of selected oscillation modes

FEM analysis showed the behavior of the support structure was extremely unfavorable because as many as 20 natural oscillations had a frequency less than 17 Hz, and of them, only five were local oscillations of peripheral parts