## Introduction

The impact hammer is a commonly used device for measuring stimulus force in various stimulus tests, often as part of structural test systems. However, the performance of a particular impact hammer is currently in question. To evaluate its performance, we have divided our analysis into two parts: force measurement and resonant frequency analysis. In the first part, we compared the impact force versus time measured by the impact hammer to the values calculated using standard mass and accelerometer measurements. In the second part, we excited a cantilever plate using the impact hammer and analyzed the resulting resonance frequency. To validate our experimental results, we compared them to numerical results obtained from finite element analysis (FEA).

## Equipment

Equipment | Model | Serial Number | Sensitivity | Max. Force | Measuring Range |

Impact hammer A | Kistler Hammer 9726A2000 | 2045105 | 2 mV/N | 2,000 N | N/A |

Impact hammer B | Kistler Hammer 9722A20000 | 2048655 | 0.2 mV/N | 20,000 N | N/A |

Accelerometer | Kistler 8636C10 | 2051077 | 501 mV/g | N/A | ±10g |

Controller | DeweTron Dewe-800 | N/A | N/A | N/A | N/A |

Vibration analysis software | DeweSoft 6.6 | N/A | N/A | N/A | N/A |

Mass | N/A | N/A | N/A | N/A | 893.28 gram |

Cantilever plate | N/A | N/A | N/A | N/A | 5x30x200 mm Al plate |

## Force Measurement

### Experimental Method

To measure the impact force generated by the impact hammer, we used a mass as the target object. The acceleration of the mass was measured using the accelerometer, and the impact force was calculated as the product of the mass and acceleration (F = ma). We compared the resulting impact force measured by the impact hammer to the force calculated from the mass and acceleration measurements.

### Results

The relationships between force and time measured by impact hammer A and acceleration and time measured by the accelerometer are shown in the graph below. We observed that the peak of force measured by impact hammer A corresponds to the peak of acceleration measured by the accelerometer.

Impact forces generated by impact hammer A, as shown in Table 1, were found to be in good agreement with those calculated from the mass and acceleration measurements. Specifically, the average percentage difference was lower than 2%. Therefore, the performance evaluation of impact hammer A using the force measurement method was verified and can be considered reliable.

However, for impact hammer B, the impact forces measured were found to be significantly different from those calculated from the mass and acceleration measurements. Specifically, the average percentage difference was higher than 14%, as shown in Table 2. Therefore, the performance of impact hammer B using the force measurement method cannot be considered reliable.

Table 1. Evaluation of force measurement of impact hammer A

No. | Hammer (N) | Accelerometer (g) | Force from accelerometer (N) | % difference |

1 2 3 4 5 6 7 8 9 10 | 33.4486 53.3549 48.0684 64.3263 47.7379 43.5074 40.0335 71.3639 45.8932 60.1267 | 3.752 5.941 5.439 7.160 5.339 5.041 4.616 8.018 5.103 6.738 | 32.88 52.06 47.67 62.74 46.79 44.18 40.45 70.26 44.72 59.04 | 1.74 2.48 0.84 2.52 2.04 1.52 1.03 1.57 2.63 1.83 |

Table 2. Evaluation of force measurement of impact hammer B

No. | Hammer (N) | Accelerometer (g) | Force from accelerometer (N) | % difference |

1 2 3 4 5 6 7 8 9 10 | 35.21 64.37 27.88 80.7 90.88 70.04 49.25 76.03 73.57 71.53 | 3.547 6.296 2.850 8.313 8.970 6.852 4.785 7.596 7.499 6.932 | 31.08 55.17 24.97 72.85 78.60 60.04 41.93 66.56 65.71 60.75 | 13.28 16.67 11.63 10.78 15.62 16.65 17.45 14.22 11.95 17.75 |

The manufacturer of impact hammer B has recommended a calibration constant of 0.2 mV/N. However, as we observed a significant difference between the impact forces measured by the impact hammer and those calculated from the mass and acceleration measurements, we recommend adjusting the calibration constant. After adjusting the calibration constant from 0.2 mV/N to 0.169 mV/N, we compared the resulting impact forces measured by impact hammer B to those calculated from the mass and acceleration measurements.

As shown in Table 3, we found that the impact forces measured by impact hammer B with the adjusted calibration constant were in good agreement with those calculated from the mass and acceleration measurements. Specifically, the average percentage difference was lower than 2%. Therefore, we can consider the performance of impact hammer B to be reliable with the adjusted calibration constant.

Table 3. Evaluation of force measurement of impact hammer B

No. | Hammer (N) | Accelerometer (g) | Force from accelerometer (N) | % difference |

1 2 3 4 5 6 7 8 9 10 | 75.1009 60.7991 75.4441 60.7991 87.3446 85.02 62.1543 84.2461 77.6886 84.8321 | 8.408 6.821 8.455 6.821 9.909 9.604 7.018 9.512 8.783 9.619 | 73.68 59.77 74.09 59.77 86.83 84.16 61.5 83.36 76.96 84.3 | 1.93 1.72 1.83 1.72 0.59 1.02 1.06 1.07 0.94 0.64 |

## Resonant Frequency Analysis

### Experimental Method

To analyze the resonant frequency of the cantilever plate, we used the impact hammer to hit the plate, as shown in the diagram below. We used an aluminum tip as the exciter, and the resulting force vs. time data is shown in the graph. We applied Fast Fourier Transform (FFT) to convert the force signal from the time domain to the frequency domain, as shown in the graph.

The -3 dB drop in the force spectrum is generally maintained for very reliable frequencies, while the data are considered to be not sufficiently reliable above a -10 dB drop. Our results show that the impact force generated by the impact hammer can reliably excite the cantilever plate within the frequency range of 0-186 Hz.

We measured the deflection of the cantilever plate as a function of time using an accelerometer, as shown in the graph below. We then converted the deflection data using FFT to obtain the deflection signal in the frequency domain of 0-1000 Hz. We defined the frequency corresponding to the peak of the deflection signal as the resonant frequency. For the present cantilever plate, we identified the second resonant frequency to be 93 Hz and the third mode frequency to be 164 Hz.

To validate our experimental resonant frequency analysis, we compared the results to numerical simulations.

### Numerical method

To overcome the limitations of the analytical closed-form solution method, we used numerical simulations to calculate the resonant frequencies of the aluminum cantilever plate. Specifically, we used Finite Element Analysis (FEA) to conduct 3D simulations. The material properties used in the simulations are Elastic modulus 70 GPa, Poisson' ratio 0.3 and density 2700 kg/m^3.

### Results

The resonant frequencies of the cantilever plate obtained from FEA simulations are shown in the graph below. As the 1st resonant frequency was found to be significantly small (approximately 13 Hz), we neglected it in this work and focused on the 2nd and 3rd resonant frequencies. We compared the resonant frequencies obtained from both experimental and FEA methods and found that they were identical.

To verify the repetitiveness of our resonant frequency analysis, we performed the experiment 5 times. We observed that the percentage difference between the experiment and FEA results was lower than 3%, indicating that the performance evaluation of impact hammer B using the resonant frequency analysis method was reliable.

## Conclusion

In this study, we performed a performance evaluation of impact hammer B used by NRP in two parts: force measurement and resonant frequency analysis. For the force measurement, we compared the impact force measured by impact hammer B to the force calculated from the mass and acceleration measurements. We found that the average percentage difference was higher than 14%. However, after adjusting the calibration constant from 0.2 mV/N to 0.169 mV/N, the impact force measurements became acceptable, as the average percentage difference was lower than 3%.

For the resonant frequency analysis, we used impact hammer B to excite a cantilever plate and analyzed the resulting resonant frequencies. We performed the experiment 5 times and compared the results to those obtained from FEA simulations. We found that the averages of the 2nd and 3rd resonant frequencies obtained from the experiment were similar to those from the FEA simulations, with a percentage difference lower than 3%. Therefore, we can consider the performance evaluation of impact hammer B using the resonant frequency analysis method to be reliable.

In summary, our findings indicate that the performance of impact hammer B used by NRP can be improved by adjusting the calibration constant for the force measurement, and that the resonant frequency analysis method using impact hammer B is a reliable tool for analyzing the resonant frequencies of cantilever plates.