# Resonant Fatigue Tests on Drill Pipe Connections with Different Geometries and Sizes
## 2 Materials and Methods
### Control System to Regulate the Test Rig during the Test  
The control system to operate the test rig is shown in Figure 5. The boxes of Figure 5a briefly summarize the logic behind the control system. In the first part of the tests, the objective was to reach the imposed alternating stress at the pin and at the box designed locations, and the voltage signals to perform this task were extracted from the strain gauges. The previously introduced calibration constants for the strain gauges are used during the dynamic run. Given that the experimental stress at the pin and at the box could be slightly different, the average between these two quantities was generally controlled. Once the target value of the alternating stress \(\sigma_{\text{a,ref}}\) was reached, the control was kept on the strain gauge acquisition or switched either to the connection strain gauge, or alternatively to the laser displacement signal whenever the strain gauge started to be unreliable. The reference value of the alternating laser displacement \(\delta_{\text{a,ref}}\) was registered at the laser position once the alternating stress reached the target value during the initial minutes of the run. The voltage signals obtained from the strain gauges and the lasers were converted to digital and, through the calculated scale factors, the corresponding values of the alternating stress \(\sigma_{\text{a}}\) and alternating laser displacement \(\delta_{\text{a}}\) were then obtained. In both situations, the alternating signals were compared with the corresponding desirable values obtaining the related prediction error \(e\), and a Proportional Integrative (PI) control continuously produced a pulse-width modulation (PWM) voltage signal. Given that the inverter was set to work with an analog voltage input, a conversion of the PWM voltage signal to a fixed averaged signal to dialogue with the inverter was required. This last conversion was conducted considering that, generally, during these tests, a small portion of the available scale of the inverter was exploited, so the converted voltage quantity directly fell into this interval in order to enhance the resolution. The inverter output was a power alternating current with a frequency \(f\). However, the working frequency of the motor (\(f^{\prime}\)) scaled from that at the inverter (\(f\)) by the sliding factor (\(k\)), so the excitation frequency of the eccentric mass eventually was \(f^{\prime}\). In Figure 5b, there is an overview of some of the electronic devices employed during the tests. An ARDUINO card provided the analog-to-digital conversion and vice versa, whereas the ethernet cable allowed to send the information to the control software (on a PC and managed with MATLAB R2021b), where the PI controller was implemented. Finally, on the right of the figure it is shown the card to enhance the resolution of the voltage signal before entering into the inverter.  
In Figure 6a, the qualitative trends of the stress obtained at the pin, at the box, and at the connection during a test are reported, whereas in Figure 6b, the qualitative trends of the horizontal and vertical displacements at the laser position are shown, and a phase shift of \(\pi/2\) is evident. In Figure 6c the recorded alternating amplitudes during a particular test are presented, and