Experimental Investigation of the VibrationInduced Heating of Polyetheretherketone for HighFrequency Applications
Abstract
:1. Introduction
2. Materials and Methods
2.1. Specimen Preparation
2.2. Experimental Setup and Procedure
 1.
 For the beam’s vibrational behavior (natural frequencies ${f}_{n}$, loss factors $\mathrm{tan}{\delta}_{n}$), a voltage sweep according to Equation (2) with a duration of the sweep of ${t}_{\mathrm{e}}$ = 12.8 s, a sampling frequency of 163.84 kHz, an initial sweep frequency of ${f}_{\mathrm{e},1}$ = 1 kHz, a final sweep frequency of ${f}_{\mathrm{e},2}$ = 16 kHz and a frequency resolution of 78.125 mHz was used as the actuator’s excitation signal ${U}_{\mathrm{e}}\left(t\right)$. Fast Fourier transform (FFT) and a rectangular window function without filtering of the time signals were applied to obtain the average frequency spectrum ${\widehat{u}}_{2}\left({x}_{i},f\right)$ and the transfer function $H\left({x}_{i},f\right)$, which represents the complex relationship between output signals ${u}_{2}\left({x}_{i},t\right)$ and input signals ${u}_{2,e}\left(t\right)$ as a function of frequency (Figure 2). Using this transfer function, the natural frequencies ${f}_{n}$ as well as the loss factors $\mathrm{tan}{\delta}_{n}=\mathsf{\Delta}{f}_{n}/f\_n$ were determined. The loss factors were calculated by means of the halfpower bandwidth method, where $\mathsf{\Delta}{f}_{n}$, ${f}_{n}$ and $\varphi \left({x}_{3}\right)$ are the 3 dB bandwidth, the associated resonance frequency (see, e.g., [56]) and the corresponding mode shapes (see Figure 3), respectively.
 2.
 To quantify changes in mechanical and the related thermal phenomena, the resulting temperature increase $\mathrm{max}\left\{\mathsf{\Delta}\vartheta \left(t\right)\right\}$ of the whole specimen and the change in the velocity amplitude $\widehat{u}\left({x}_{i}={\tilde{x}}_{i}\right)$ at the position $[{\tilde{x}}_{i}]$ = [2.5 mm, 0, 4.7 mm] (sampling frequency 128 kHz, frequency resolution 7.8 mHz) were measured for different input voltage amplitudes of ${\widehat{U}}_{\mathrm{e}}$ in the range between 11 V and 54 V (Figure 4). Therefore, the specimen was sinusoidally excited with a voltage signal ${U}_{\mathrm{e}}\left(t\right)$ as shown in Equation (1) and the natural frequencies were chosen for excitation so that the relationship ${f}_{\mathrm{e}}={f}_{n}$ was fulfilled.
 3.
 The mode shapes $\varphi \left({x}_{3}\right)$ (see Figure 3) and the beam’s real physical velocity distribution ${u}_{2}\left({x}_{3}\right)$ were determined by means of additional measurements with a monofrequent sinusoidal voltage signal according to Equation (1) at the given natural frequencies ${f}_{n}$. Therefore, a sinusoidal excitation with an input voltage amplitude of ${\widehat{U}}_{\mathrm{e}}$ = 11 V was carried out with a sampling frequency of 128 kHz, a frequency resolution of 7.8 mHz and a measuring time of 512 ms.
 4.
 Additional measurements of the temperature increase $\mathsf{\Delta}\vartheta \left(t\right)$ for a duration of $t$= 32.8 s and the different natural frequencies ${f}_{n}$ were performed using an input voltage amplitude of ${\widehat{U}}_{\mathrm{e}}$ = 54 V. Due to the application of the highest investigated voltage amplitude ${\widehat{U}}_{\mathrm{e}}$, sufficient heating should be generated.
3. Results and Discussion
3.1. Vibration Characteristic
3.2. Influence of Excitation Amplitude on Temperature Increase
3.3. Resulting Temperature Distribution and its Correlation with Vibrational Mode Shapes
3.4. Implications for the Design of Dynamically Loaded PEEK Structures
3.5. Limitations of the Experimental Approach
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Property  Test Method  Unit  Value 

Density  DIN EN ISO 11831  g cm^{−3}  1.31 
Yield stress  DIN EN ISO 527  MPa  110 
Tensile modulus of elasticity  DIN EN ISO 527  MPa  4000 
Melting temperature  ISO 113573  °C  343 
Thermal conductivity  DIN 526121  W m^{−1} K^{−1}  0.25 
Thermal capacity  DIN 52612  kJ kg^{−1} K^{−1}  1.34 
Coefficient of linear thermal expansion  DIN 53752  K^{−1}  50 × 10^{−6} 
Service temperature, longterm    °C  −60…250 
Service temperature, shortterm    °C  310 
Heat deflection temperature  DIN EN ISO 75  °C  152 
$$\mathrm{Order}n$$
 5  6  7  8  9  10  11  12  13  14  15  16  17 

$$\mathrm{Frequency}{\mathrm{f}}_{\mathrm{n}}\mathrm{in}\mathrm{kHz}$$
 1.1  1.7  2.4  3.2  4.1  5.1  6.2  7.4  8.7  10.1  11.7  13.3  15.0 
$$\mathrm{Loss}\mathrm{factor}\mathrm{tan}\mathsf{\delta}$$
 0.011  0.014  0.009  0.010  0.010  0.010  0.011  0.011  0.011  0.012  0.012  0.012  0.013 
$$\mathit{n}$$

$${\mathit{f}}_{\mathbf{n}}\phantom{\rule{0ex}{0ex}}\mathbf{in}\mathbf{kHz}$$

$${\widehat{\mathit{u}}}_{\mathbf{2}}\mathbf{at}\phantom{\rule{0ex}{0ex}}{\mathit{U}}_{e}\mathbf{=}\mathbf{11}{\mathbf{V}}^{\mathbf{a}}\phantom{\rule{0ex}{0ex}}\mathbf{in}\mathbf{m}{\mathbf{s}}^{1}$$

$${\widehat{\mathit{u}}}_{\mathbf{2}}\mathbf{at}\phantom{\rule{0ex}{0ex}}{\mathit{U}}_{e}\mathbf{=}\mathbf{54}{\mathbf{V}}^{\mathbf{b}}\phantom{\rule{0ex}{0ex}}\mathbf{in}\mathbf{m}{\mathbf{s}}^{\mathbf{1}}$$

$${\mathit{\tau}}^{\mathbf{c}}\phantom{\rule{0ex}{0ex}}\mathbf{in}\mathbf{s}$$

$${\mathbf{max}\left\{\Delta {\vartheta}_{\infty}\right\}}^{\mathbf{c}}\phantom{\rule{0ex}{0ex}}\mathbf{in}\mathbf{K}$$
 MTRS ^{d} in mK s^{−1}  VHR ^{e} in mK m^{−1} 
$${c}_{PCC,1}\phantom{\rule{0ex}{0ex}}\mathbf{in}{\mathbf{m}}^{\mathbf{2}}{\mathbf{s}}^{\mathbf{2}}{\mathbf{K}}^{\mathbf{2}}$$

$${c}_{PCC,2}\phantom{\rule{0ex}{0ex}}\mathbf{in}{\mathbf{m}}^{\mathbf{2}}{\mathbf{s}}^{\mathbf{2}}{\mathbf{K}}^{\mathbf{2}}$$


5  1.1  0.006  0.018    <0.2         
6  1.7  0.015  0.046    <0.2         
7  2.4  0.029  0.088    <0.2         
8  3.2  0.026  0.080    <0.2         
9  4.1  0.028  0.089    <0.2         
10  5.1  0.032  0.103    <0.2         
11  6.2  0.091  0.300  10.6  0.7  21  70.2  0.2  0.6 
12  7.4  0.022  0.076    <0.2         
13  8.7  0.034  0.120    <0.2         
14  10.1  0.044  0.164  7.9  0.4  11  65.7  0.1  0.5 
15  11.7  0.066  0.261  21.4  0.9  29  110.6  0.2  0.7 
16  13.3  0.241  1.047  13.2  6.4  194  185.3  −0.1  0.7 
17  15.1  0.076  0.347  18.7  2.5  77  221.1  −0.1  0.8 
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Kucher, M.; Dannemann, M.; Peyrow Hedayati, D.; Böhm, R.; Modler, N. Experimental Investigation of the VibrationInduced Heating of Polyetheretherketone for HighFrequency Applications. Solids 2023, 4, 116132. https://doi.org/10.3390/solids4020008
Kucher M, Dannemann M, Peyrow Hedayati D, Böhm R, Modler N. Experimental Investigation of the VibrationInduced Heating of Polyetheretherketone for HighFrequency Applications. Solids. 2023; 4(2):116132. https://doi.org/10.3390/solids4020008
Chicago/Turabian StyleKucher, Michael, Martin Dannemann, Davood Peyrow Hedayati, Robert Böhm, and Niels Modler. 2023. "Experimental Investigation of the VibrationInduced Heating of Polyetheretherketone for HighFrequency Applications" Solids 4, no. 2: 116132. https://doi.org/10.3390/solids4020008