## 4 Validation of MD Calculation Scheme for Lifter Operation
### Mechanical Effect of Artificial Damage on Vibration Characteristics of Lifter  
The acceleration waveforms of the unloaded lifter under three different conditions are shown in Figure 13: operating in the normal state (Figure 13(a1)), operating with a damaged belt  
(Figure 13(a2)), and operating with a damaged guide wheel (Figure 13(a3)). All of these results were measured by receiver R1. In this study, the lifter carriage continuously moved up and down in the range between 0.3 and 2.8 m above the ground. Each round trip of the carriage took 8.6 s. Thus, the carriage made 418 trips per hour or 10,046 trips per day. As can be seen in Figure 14, the vibration waveforms during the rising and descending phases of operation are slightly different. In this study, only the vibration waveform for the rising phase was used. Looking at the waveforms shown in Figure 13(a1)-(a3), it can be seen that they are quite different depending on the type of damage. The spectrograms obtained from the time waveforms are shown in Figure 13(b1)-(b3), respectively. When the carriage rises, it first starts to move, then accelerates, reaches maximum speed, then decelerates, and finally stops at the top. As can be seen from these spectrograms, the eminent frequency of the main frequency component of vibration begins to rise at the start of operation, then begins to fall as deceleration starts. Although the spectrogram of the respective conditions has slightly different features, it is difficult to determine the effect of each type of damage on the time-frequency response. Consequently, the results of FFT processing of the waveforms in Figure 13(a1)-(a3) are shown in Figure 15. As can be seen in Figure 15a, the frequency characteristics of the peaks and dips when operating in the normal condition differ from those associated with operating with a damaged belt. Figure 15b also shows some differences between operating in the normal condition and operating with a damaged guide wheel. Figure 12: Artificially damaged conditions: (**A**) damage to belt, (**B**) damage to guide wheel, and (**C**) damage to bearings. Figure 16 shows the time waveforms and spectrograms obtained by R2 under the normal condition and under the condition of damaged (impeded) bearings. The differences between the normal and damaged conditions observed in the time waveform and spectrogram are relatively small compared to those shown in Figure 13. Figure 17 shows the frequency characteristics in these conditions. In these results, the characteristic difference in the peak-dip tendencies shown in Figure 15 is not observed; however, in the damaged-bearing condition, the energy level is approximately 5 dB lower than under the normal condition over the entire frequency range. Figure 13: Acceleration waveforms and their spectrograms for the lifter (**a1,b1**) operating in normal state, (**a2,b2**) operating with a damaged belt, and (**a3,b3**) operating with a damaged guide wheel. As shown in Figure 13(**a1**) and (**b1**), the waveform starts to sweep up after around 0.9 s when the lifter starts to accelerate; after that, the waveform starts to sweep down after 1.8 s; then finally, the large fluctuation of the waveform finishes at around 2.8 s when the lifter stops. Figure 16: Acceleration waveforms and their spectrograms for the lifter (**a1,b1**) in the normal state and (**a2,b2**) operating with a damaged bearing: As shown in Figure 16**(a1**)** and (**b1**), the waveform starts to sweep up after around 0.9 s when the lifter starts to accelerate; after that, the waveform starts to sweep down after 1.8 s; then finally, the large fluctuation of the waveform finishes at around 2.8 s when the lifter stops. The differences between the normal and damaged conditions observed in the time waveform and spectrogram are relatively small compared to those shown in Figure 13.  
Figure 14: Example of the acceleration waveform for the lifter when rising and descending: These vibration waveforms during the rising and descending phases of operation are slightly different.