# Determination of Clamping Force Using Bolt Vibration Responses during the Tightening Process
## 3 Estimation of Clamping Force from Vibration Measured in the Clamped Parts
### Clamping on a Load Cell  
Experiments were performed to fasten bolts to the load cell, as shown in Figure 3. The bolt was made of SCM435 and galvanized GEOMET(r). The length of the bolt was 70 mm and the diameter was 10 mm. The standard bolted pitch was 1.25 mm. An accelerometer PCB 352A21/NC was attached to the load cell to measure the vibration of the bolt during fastening. The bolts were fastened at a constant speed using an electric Atlas Copco nutrunner. The data acquisition system (NI cDAQ-9178 and NI 9234) was used to receive the vibration signal from the accelerometer and the data processing was performed with MATLAB.  
When the bolt was excited during the fastening process using a nutrunner, a dynamic characteristic that changes according to the fastening force was measured by an accelerometer. Figure 4 shows the short-time Fourier transform (STFT) of the measured vibrations of the load cell. The vibration responses show the change in the resonance frequency with the clamping of the bolt. The bolt started to rotate after 1.2 s. The seating occurred after 1.9 s when the vibration components of the bolt were observed in the vibration responses. The resonant responses occurred in the 8 kHz band in the above experiment. This frequency is similar to the natural frequency of the bolt when clamped at both ends. This suggests that the bolt flexural vibration occurs during the bolt assembly process and that this influences the acceleration measurements. The frequency of the resonant responses increased steadily until about 3.6 s during the fastening process.  
For this experiment, bolt tightening was performed with the nutrunner to induce different torques ranging from 50 Nm to 90 Nm. As shown in Figure 5, the bolts were tightened with clamping forces ranging from 15 kN to 50 kN. When the clamping force of each torque was measured, up to 35% error occurred in order to reach the desired clamping force. The distribution of the clamping force was very large when the fastening was performed by controlling the torque. For better estimation, classification was performed using the reference function of Equation (3), using the k-means clustering algorithm. The measured responses and evaluated variables were used. The test set was evaluated in the same manner as for the training detailed in Section 2. The vibration responses measured with the highest clamping force were selected as the references among the variations. The maximum value was obtained when the distance between the reference data and the cluster of each data point was derived using Euclidean distance. The maximum squared Euclidean distance was derived as a comparison method for each vibration response. Figure 6 shows the estimated clamping force from the Euclidean distance. The derived results were curve-fitted using a linear function, and the error between the actual clamping force and the predicted value was compared. The average error was about 5%, which was much smaller than that estimated by the torque. The maximum error was less than 15%. The bolt yielded when tightened with the clamping force larger than 35 kN. It can be seen that the inflection of the data occurred in this vicinity. The proposed clamping force estimation by measurement of the vibration response and its cepstrum allowed precise estimation, which was not possible with torque control methods.  
Figure 4: Short-time spectrum of the bolt fastening signal.  
Figure 5: The influence of the applied torque on the resulting clamping force. When the same torque was applied, the clamping force showed more than 30% deviations.  
Figure 3: Experimental setup for bolt tightening to the load cell using a nutrunner. The load cell vibration was measured by the accelerometer (PCB, 352A21/NC).  
Figure 6: (a) Scatter of estimated clamping forces using accelerometer on load cell compared to the actual value, and (b) relative deviations.