# Determination of Clamping Force Using Bolt Vibration Responses during the Tightening Process
## 3 Estimation of Clamping Force from Vibration Measured in the Clamped Parts
### Test Results with Accelerometer Attached to the Nutrunner  
For the experiments on the load cell, the vibration was measured directly on the clamped part. For application during assembly, the acceleration response was measured in the nutrunner to ensure minimal influence on the parts or the manufacturing process. The bolt was rotated using the nutrunner, and strong attachment to the bolt was expected. Four main motions occur when a manual nutrunner is used by an operator [48]. In the fastening step, the vibrations at relatively high frequencies are generated with large amplitude. In the case of idling, the constant frequency components from motor rotations are generated with relatively low amplitude. When an operator holds the nutrunner in his hand, there is an out-of-work signal generated by the hand. Both the amplitude and frequency are relatively low when vibrations are measured during walking. Therefore, the vibration measured on the nutrunner in the fastened state is distinguished from the vibration in the idling state. As the fastening of the bolt proceeds, the vibration characteristic of the bolt changes. The cepstral coefficient was derived using the LFCC to distinguish the changing vibration characteristics. Since the rotational speed of the nutrunner is identical, the fastening components become the significant components. The k-means clustering and Euclidean distance were used to classify the clamping force.  
The accelerometer was attached to the head of the nutrunner as close as possible to the bolt, as shown in Figure 7. The accelerometer measured the fastening characteristics, which changed according to the clamping force. Experiments using the accelerometer on the nutrunner were also performed using 500 bolts in the load cell to investigate the applicability. Fastening was performed using the same torque as in the actual production line. Accelerometers were attached to both the load cell and the nutrunner. Compared to the responses measured in the load cell, the vibration of the nutrunner was influenced by the rotating elements, especially below 4 kHz, as shown in Figure 8. In addition, the high-frequency components above 12 kHz were not effectively measured due to attenuation during transfer from the bolt to the nutrunner. The resonant frequency band of the bolt in which the clamping force has influence was measured. Band-pass filtering was applied from 4 to 20 kHz. The k-means clustering algorithm was used to exclude the components below 4 kHz, which include the contribution from rotating elements of the nutrunner. The same parameters of the k-means algorithm as in the experiment of clamping on the load cell were applied. In total, 400 training sets were constructed from 500 vibration measurements to generate fitting curves, and the results were applied to 100 test sets.  
In the experiment in which the accelerometer was attached to the nutrunner, the distribution of the clamping force was narrower than that of the previous load-cell experiment, as shown in Figure 4, in which the tightening torque was varied. Figure 9 shows that the clamping forces were in the 35 to 45 kN ranges. The maximum scatter measured by each method is compared in Table 1. The result of estimating the clamping force using the Euclidean distance was confirmed, showing that the estimation is linearly obtained according to the clamping force. Extrapolation is also possible in addition to the measured range. For bolt tightening experiments, only discrete data was considered. It is possible to predict the clamping force sufficiently by using the continuous clamping force diagram.  
Figure 7: Vibration measurement with the accelerometer attached to the head of the nutrunner (red circle).