Dynamic analysis of machine (FEA)
The two parts ‘spindle’ and ‘table’ were considered for harmonic testing. Fig. 10 shows the FEA results of harmonic testing on both production and new machines for the X-axis. The peaks show the dynamic stiffness of the two beds. The solid blue curve shows the ‘spindle,’ and the solid brown shows the ‘table’ of the production machine, while the dashed red and blue curves show the ‘table’ of the new machine. Table 3 shows the excitation frequencies of the Y and Z axes, too.
As for the production machine shown in Fig. 10, ‘spindle’ mode 1 is at 23 Hz, mode 2 at 37 Hz, mode 3 at 52 Hz, and mode 4 at 71 Hz. The first two modes are tool changer frequencies, which are very small on the ‘spindle.’ Nevertheless, these two modes in case of jerk motion can create a ripple or texture mark on the side wall of the test cut. Mode 3 at 52 Hz and mode 4 at 71 Hz are actual main modes of machine casting/frame, and the new machine should have higher dynamic stiffness than the production one at the above-mentioned frequencies since the dashed red curve is smaller than the solid blue curve of the production machine. The production machine ‘table’ mode 1 is at 52 Hz and mode 2 at 71 Hz. The new machine should have higher dynamic stiffness than the production machine at the frequencies mentioned above since the dashed green curve is smaller than the solid red curve of the production machine. Important to note that the ‘spindle’ and ‘table’ frequencies match entirely. The frequency overlap is a potential bottleneck for any machine. The excitation frequencies of other axes are presented in Table 3.
Modal (Hammer) Test on ‘spindle’ and ‘table’
This test was done on both the production and the new machines. A hammer was used to exert a force on ‘spindle’ and ‘table’ and measured the vibrations along the same axis the force was exerted. Fig. 11 illustrates the transfer function graphs for the modal test on both ‘spindle’ and ‘table.’
The production machine spindle’s first 3 modes occur at frequencies of 12, 16, 37, and 59 Hz at amplitudes of 1.6, 4.1, 1.3, and 1.2 x 10-3 g/lbf, respectively. The new machine spindle’s first 4 modes occur at 11, 14, 19, 37, and 60 Hz at 1.1, 1.9, 0.9 and 1.9 x 10-3 g/lbf, respectively. The values of amplitude in 3-axes for both ‘spindle’ and ‘table’ are given in Table 4.
The amplitudes of all modes of the new machine ‘spindle’ up to the frequency of interest (50 Hz) are smaller compared to those of the production machine. As it was mentioned earlier, transfer function magnitude is inversely proportional to the dynamic stiffness; the smaller the magnitude, the larger the dynamic stiffness. In Fig. 11b, it is clear that the first two modes have shorter amplitude while the third one has a higher amplitude, overall better because usually, the first two modes are the most important for machine structural stability.
To verify the performance of the new machine, cutting test was applied under the same conditions including rpm, feed rate (in/min), and tool path, which define the final shape. In this test, the production and the new machines were used to cut identical parts, and observed the surface finish and texture qualities of the machined parts for any differences. The final results portrayed no noticeable differences at all. It is important to note that in a simulation study, by adding ribs at suitable locations, 1.5% weight reduction was achieved (11), and in yet another study, using cross and horizontal ribs with hollow bed, the results indicated 4% weight reduction (6), but in this study, the weight reduction was 9.3% and it was experimentally verified. It was earlier mentioned that in a similar MPF simulation study, the weight of the bed was reduced by 4.8% (16).