A Testbench for Measuring the Dynamic Force-Displacement Characteristics of Shockmounts
Abstract
:1. Introduction
2. Materials and Methods
2.1. Investigated Shockmounts
2.2. Description of the Testbench
2.2.1. Shock Test Machine
2.2.2. Displacement Measuring Devices
- Measurement range 250 mm.
- Maximum power supply 60 V
- Displacement speed 10 m/s
- Shock resistance 50 g, 11 ms
- Up to ± 13° tilt
2.2.3. Acceleration Sensors
2.2.4. Improved Guiding System and Loading Mass
2.2.5. Measuring Adapters
2.2.6. Complete Setup
2.2.7. Highspeed Camera
2.2.8. Data Acquisition
2.2.9. Reproducibility
2.3. Advanced Kelvin–Voigt Model and Parameter Identification
2.3.1. Non-Linear Spring Force
2.3.2. Damping Coefficient
2.4. Simulation
2.4.1. State Vectors
2.4.2. Basepoint Excitation
2.4.3. Numerical ODE45 Solver in MATLAB
3. Results and Discussion
3.1. Testbench
- The horizontal traverse of the guiding system, including the housings of the plain bearing bushes, contribute to the loading mass that loads the shockmount. For very soft shockmounts, such as the WSM 175 in shear or roll configurations, almost no additional loading mass is required to displace the shockmount dynamically. In these cases, the mass of the traverse should be as small as possible. Nevertheless, the stiffness of the traverse must be high enough to prevent the bearing housings from oscillating around the middle of the traverse.
- Even if the linear potentiometers in the proposed setup are attached to the guiding traverse, the displacement could be measured, for example, by non-contact evaluation of highspeed camera images. However, the guiding system is required to prevent shockmount-mass combination from tilting. This is especially true for configurations with wire rope shockmounts, which usually show an asymmetric construction, or for configurations with a high center of gravity when using multiple stacked mass modules.
- The linear potentiometers for measuring the displacement have a specified shock capability of only 50 g at 11 ms. In the conducted measurement series, basepoint excitations up to 165 g at 10 ms were applied. As long as the potentiometers were loaded axial to the piston rod, they showed good usability without any failure.
- The intention for using triaxial accelerometers for measuring acceleration of the loading mass was to observe if there is motion of the loading mass in the two directions orthogonally to excitation. Evaluation of measurements showed that there is no significant motion in these directions.
3.2. Exemplary Simulation
3.3. Parameter Sets for the Advanced Kelvin–Voigt Model
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
- Shockmount type (ESM32, ESM40, ESM 55, WSM125, WSM135, WSM175, according to Section 2.1)
- Specimen number (#1, #2, #3) out of three specimens of a shockmount type
- Load directions (compression, tension, shear, roll)
- Drop height (in cm)
Appendix A.1. Elastomer Shockmounts
Appendix A.2. Wire Rope Shockmounts
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Type | Manufacturer and Model | Max. Static Load (kg) | Natural Frequency (Hz) @ Max. Static Load | Max. Displacement (mm) in Direction of | |
---|---|---|---|---|---|
Tension (+) Compression (−) | Shear, Roll | ||||
ESM | Willbrandt KG SES 1500 SH32 | 90 | 5 … 6 | 55 | 55 |
ESM | Willbrandt KG SES 1500 SH40 | 125 | 5 … 6 | 55 | 55 |
ESM | Willbrandt KG SES 1500 SH55 | 260 | 5 … 6 | 55 | 55 |
WSM | Willbrandt KG CAVOFLEX H 63-146-135-175-8 | 22 … 120 | 6.2 … 6.7 | +65/−100 | 86 |
WSM | Willbrandt KG CAVOFLEX H 63-146-110-135-8 | 30 … 150 | 6 … 6.5 | +50/−82 | 65 |
WSM | Willbrandt KG CAVOFLEX H63-146-95-125-8 | 50 … 170 | 7.1 … 7.6 | +45/−67 | 60 |
Signal Name | Sensor Type | Position | Purpose |
---|---|---|---|
a1_z | Triaxial MEMS accelerometer | Loading mass | Measuring vertical acceleration of upper part |
a2_z | Uniaxial MEMS accelerometer | Basepoint | Measuring vertical acceleration of lower part |
aBase_z | Uniaxial MEMS accelerometer | Seismic base | Measuring vertical acceleration of base |
deltaA | Linear potentiometer | Between rod and traverse of guide system | Measuring displacement between basepoint and loading mass |
deltaB | Linear potentiometer | Between rod and traverse of guide system | Measuring displacement between basepoint and loading mass |
Parameter | ||||||
---|---|---|---|---|---|---|
Value | − | − |
Parameter | ||||
---|---|---|---|---|
Value | 3.449 |
Compr. | Tension | Shear | Roll | Damp. | Stiffness from Parameter Identification | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
SM | H | M | L | H | M | L | H | M | L | H | M | L | |||||||
ESM32#1 | X | 2.6 | −2.67 × 102 | 1.34 × 10−1 | −1.60 × 10−4 | −2.09 × 10−5 | 7.86 × 10−8 | 3.66 × 10−9 | |||||||||||
#2 | X | 3.2 | −1.07 × 10−2 | 1.29 × 10−1 | −8.51 × 10−5 | −1.84 × 10−5 | 5.22 × 10−8 | 2.83 × 10−9 | |||||||||||
#3 | X | 2.2 | 5.15 × 10−3 | 7.76 × 10−2 | 1.07 × 10−5 | −8.85 × 10−6 | −4.94 × 10−9 | 1.22 × 10−9 | |||||||||||
ESM40#1 | X | 2,6 | −4.40 × 10−2 | 1.47 × 10−2 | −1.98 × 10−4 | −2.44 × 10−5 | 9.96 × 10−8 | 4.34 × 10−9 | |||||||||||
#2 | X | 2.6 | −3.01 × 10−2 | 1.44 × 10−1 | −1.27 × 10−4 | −2.16 × 10−5 | 7.63 × 10−8 | 3.23 × 10−9 | |||||||||||
#3 | X | 2.3 | −8.73 × 10−3 | 8.96 × 10−2 | 6.21 × 10−6 | −1.01 × 10−5 | −2.55 × 10−9 | 1.37 × 10−9 | |||||||||||
ESM55#1 | X | 4.2 | −5.85 × 10−2 | 2.2 × 10−1 | −3.03 × 10−4 | −5.09 × 10−5 | 2.08 × 10−7 | 1.34 × 10−8 | |||||||||||
#2 | X | 4.6 | −2.21 × 10−2 | 2.41 × 10−1 | 5.45 × 10−5 | −4.74 × 10−5 | 3.21 × 10−8 | 1.17 × 10−8 | |||||||||||
#3 | X | 4.1 | −1.67 × 10−2 | 1.37 × 10−1 | 3.18 × 10−5 | −1.92 × 10−5 | −2.54 × 10−8 | 3.77 × 10−9 | |||||||||||
WSM125#1 | X | 5.0 | 1.27 × 10−2 | 1.28 × 10−2 | 9.97 × 10−6 | 4.91 × 10−7 | 1.50 × 10−7 | 2.44 × 10−9 | |||||||||||
#2 | X | 4.3 | 1.23 × 10−2 | 1.58 × 10−2 | 3.35 × 10−5 | −6.05 × 10−6 | 1.42 × 10−7 | 6.07 × 10−9 | |||||||||||
#3 | X | 9.8 | −5.03 × 10−3 | 2.94 × 10−3 | 2.81 × 10−5 | 1.01 × 10−6 | −5.11 × 10−8 | 7.55 × 10−10 | |||||||||||
WSM135#1 | X | 6.9 | 8.92 × 10−3 | 1.04 × 10−2 | 5.99 × 10−5 | 1.93 × 10−6 | 8.90 × 10−8 | 1.03 × 10−9 | |||||||||||
#2 | X | 5.0 | −1.11 × 10−2 | 1.38 × 10−2 | 2.16 × 10−4 | −1.14 × 10−5 | −1.01 × 10−7 | 8.91 × 10−9 | |||||||||||
#3 | X | 9.6 | −2.34 × 10−4 | 2.52 × 10−3 | 5.50 × 10−6 | 2.80 × 10−7 | −4.80 × 10−9 | 1.32 × 10−10 | |||||||||||
WSM175#1 | X | 6.4 | 9.12 × 10−3 | 5.16 × 10−3 | 1.18 × 10−7 | −3.09 × 10−7 | 2.02 × 10−8 | 2.84 × 10−10 | |||||||||||
#2 | X | 5.0 | 3.84 × 10−3 | 6.15 × 10−3 | −3.78 × 10−6 | −1.23 × 10−6 | 2.14 × 10−8 | 4.90 × 10−10 | |||||||||||
#3 | X | 11.3 | 3.68 × 10−4 | 9.26 × 10−4 | 1.72 × 10−6 | 1.34 × 10−7 | −1.70 × 10−9 | 2.03 × 10−11 |
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Heinemann, B.; Simanowski, K.; Clasen, M.; Dreesen, J.; Sachau, D. A Testbench for Measuring the Dynamic Force-Displacement Characteristics of Shockmounts. Vibration 2024, 7, 1-35. https://doi.org/10.3390/vibration7010001
Heinemann B, Simanowski K, Clasen M, Dreesen J, Sachau D. A Testbench for Measuring the Dynamic Force-Displacement Characteristics of Shockmounts. Vibration. 2024; 7(1):1-35. https://doi.org/10.3390/vibration7010001
Chicago/Turabian StyleHeinemann, Bernhard, Kai Simanowski, Michael Clasen, Jan Dreesen, and Delf Sachau. 2024. "A Testbench for Measuring the Dynamic Force-Displacement Characteristics of Shockmounts" Vibration 7, no. 1: 1-35. https://doi.org/10.3390/vibration7010001
APA StyleHeinemann, B., Simanowski, K., Clasen, M., Dreesen, J., & Sachau, D. (2024). A Testbench for Measuring the Dynamic Force-Displacement Characteristics of Shockmounts. Vibration, 7(1), 1-35. https://doi.org/10.3390/vibration7010001