Evaluation of dimensional stability of metering truss structure using built-in laser interferometric dilatometer

The study evaluated the thermal stability of two types of truss struts using the BDMI for axial displacement measuring to demonstrate the basic performance of the proposed technique.

The first one was made of stainless steel (SUS304). The other strut was made of a low thermal expansion ceramic (SiAlON, S110, KROSAKI HARIMA Co.). SiAlON is a solid solution of silicon nitride (Si₃N₄) with aluminum oxide (Al₂O₃) [20]. It is well-known for use in the gas turbine engine because it has high-temperature strength, good fracture toughness, and thermal shock resistance. In addition, it also has superior mechanical properties such as a low CTE, high specific modulus, and non-hygroscopic property. Especially, the CTE of SiAlON, which is equivalent to that of invar alloy, is lower than silicon nitride (Si₃N₄) and silicon carbide (SiC) at room temperature [21–23]. For these reasons, SiAlON is one of the most promising materials for a highly thermo-stable satellite structure.

The struts were 300 mm and 200 mm in length, respectively (figure 3). The truss strut (TS) with the BDMI was constructed of a structural module (STM) and a sensing module (SM), as shown in table 1. The structural module was an ordinary pipe-shaped component. The sensing module was the key part of the proposed system. The interferometric sensor head and the target reflector were built into the flange of each end of the strut as shown in figure 4. The sensing module is designed with a flexible adjusting mechanism for easier optical alignment between the sensor head and the target reflector in the BDMI. The flexure hinges provide 4 degrees of freedom (DOFs); they are in-plane (XY) translation and tip/tilt around X/Y. In addition, the flange part of the sensing module was made of the material having the same or nearly the same CTE as that of the structural module (table 2).

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Table 1. Truss struts specifications.

Truss Strut (TS)		Stainless-steel strut	Ceramic strut
Material of Structural Module (STM)		SUS 304	SiAlON
Material of Sensing Module (SM)		SUS 304	Invar alloy
Flange width, W (Square shape)	mm	84
Pipe outer diameter, ${D}_{outer}$	mm	56
Pipe thickness, t	mm	2.0	3.0
Length, ${L}_{0,STM}$	mm	300	200
STM mass, M	kg	1.71	0.70

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Table 2. Material properties for the truss struts.

Truss strut	Stainless-steel strut		Ceramic strut
Module	Structural module	Sensing module	Structural module	Sensing module
Material	SUS 304		SiAlON	Invar alloy
Material name	—		S110	IC-362A
Manufacturer	—		KROSAKI HARIMA	SHINHOKOKU STEEL
Mass density, $\sigma$	g cm−3	7.93	3.24	8.10
Young's modulus, E	GPa	193	290	141
Mean CTE, $\bar{\alpha }$ at room temperature	10−6/K	17.3	≈1.3	< 2.0
Thermal conductivity, k at room temperature	W m−1 · K	16	21	15

Since the laser optical system, including the sensor head and target reflector, is constructed in the tubular cavity of the truss strut, it is protected from the damage by handling and the fluctuations in the measurement environment (figure 5). Therefore, the BDMI is a far more robust system than a conventional DMI.

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The thermal expansion of the stainless-steel strut was measured simultaneously with the BDMI and with a conventional DMI in a clean room. The DMI needs to assemble some optical components and align them in situ. The DMI used in this experiment consisted of a laser head (5517C, Agilent), a three-axis plane mirror interferometer (Z4399, Agilent), and a laser board with high resolution (N1225, Agilent). The target reflectors had low-distortion kinematic mirror mounts and were attached to the side of the sensing module, one at each end of the strut. The interferometer was installed at a distance from target mirrors and the dimensional change of the strut was determined by the difference in the two measurement beams, which were aligned with both ends of the strut as shown in figure 6. Therefore, the axial displacement of the strut was calculated as in equation (3).

$$\begin{eqnarray}&&{\rm{\Delta }}{L}_{DMI}={\rm{\Delta }}{X}_{A}-{\rm{\Delta }}{X}_{B}\end{eqnarray} \tag{ 3 }$$

Where ${\rm{\Delta }}{L}_{DMI}$ is the axial displacement of the strut, ${\rm{\Delta }}{X}_{A}$ is the displacement between the interferometer and top target reflector A, and ${\rm{\Delta }}{X}_{B}$ is the displacement between the interferometer and bottom target reflector B.

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In contrast, since the BDMI is integrated into the strut in advance, it is available by only installing the strut in situ and connecting optical fiber to the end of the structure. Figure 7 shows the optical layout of the BDMI and the DMI.

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These measurement systems were installed in a clean room that had a highly stable air conditioning control system (< ± 0.5 °C, < ± 0.9%RH). The specimen temperature was controlled in steps of 5 °C from 15 °C to 30 °C by the air conditioner of the clean room. Each temperature interval was maintained until the temperature reached the steady-state temperature. The thermal expansion was measured during two ways that were cooling from 30 °C to 15 °C and heating from 15 °C to 30 °C. The specimen temperature was measured with high-precision NTC type thermistors (N550 probe sensor with N820 DAQ system, Nikkiso-Thermo Co.). Besides, the conditions of the test environment in the clean room (such as air temperature, relative humidity, and air pressure) were also monitored to compensate for fluctuations in the air refractive index. The air temperature and humidity were measured with an NTC thermistor and capacitive humidity sensor (testo176P1, Testo Co.). The air pressure was measured using a barometer (F4711, YOKOGAWA Denshikiki Co.). Figure 8 shows the experimental setup. These tests were performed on a thermostable optical bench with a vibration isolation mechanism to reduce the ground vibrations.

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The axial displacement of the SUS304 strut due to the temperature changes was measured simultaneously with the BDMI and the DMI as shown in figure 9. Both measurements detected precisely the displacement associated with the set temperature changes. The temperature represents the mean value of the measurement of the thermistors attached to the surface of the strut. These displacements were compensated for the air refractive index fluctuation using Edlen's equation [24]. Figure 10 shows a blow-up of the measured displacement associated with the temperature fluctuation at the steady-state temperature attained during heating. The slight temperature fluctuation was caused by the control period of the air conditioning system. The graph indicates that the displacement behavior measured with the BDMI and DMI matched well at the steady-state condition. Figure 11 shows the difference between the measurements with the BDMI and the DMI. It is assumed that the spike noise was caused by a difference in the stability of the air in each measurement path during the transient-state condition. The evidence that points to this is that the displacement measured with DMI has a significant deviation that is not associated with temperature in the transient state (figure 12). Since the measurement path of the BDMI travels inside the strut, contrasted with the path of the DMI that travels outside the pipe, the influence of measurement error caused by the fluctuation of the air conditioning could be small. It is the advantage of the BDMI as having the measurement path inside the structures, compared with other interferometry systems. Hence, displacement measured with the BDMI matched well with the temperature fluctuation even in transition.

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Including the transient-state temperature, the RMS (Root-Mean-Square) of the difference between the BDMI and the DMI measurements was 0.20 μm during the cooling condition and 0.14 μm during the heating condition. Therefore, the BDMI had a measurement precision equal to that of the conventional DMI and had good reproducibility.

The thermal expansion and CTE of the ceramic truss strut were measured with the BDMI and were compared with those of the material sample.

The material sample was manufactured from the same production lots as the strut (figure 13). The temperature-dependent CTE of the sample was measured with a commercial dilatometer (LIX-2, ADVANCED RIKO Inc.), a duplex-passed Michelson interferometric dilatometer, from −50 °C to 100 °C in high-purity He gas under low pressure.

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The thermal displacement of the ceramic strut was measured in the vacuum chamber at less than 2 Pa to reduce the environmental errors due to the air refractive index fluctuation (figure 14). The temperature was changed by a heatsink installed in the chamber. The heatsink was connected by a feed-through to the circulating heater bath unit (PRESTO A80, Julabo) to carry chiller oil. The temperature was controlled in steps from 0 °C to 50 °C in increments of 5 °C or 10 °C, depending in the temperature region. Each temperature interval was maintained until the specimen temperature reached the steady-state temperature. The specimen temperature was measured with high-precision NTC type thermistors (N550 probe sensor with N820 DAQ system, Nikkiso-Thermo Co.). The optical fiber for the BDMI and the thermistors for temperature measurement were connected by using the feed-through to the electronics outside of the vacuum chamber. The vacuum chamber was installed on an optical bench with a vibration isolation mechanism to reduce the ground vibrations.

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Figure 15 shows the CTE of SiAlON (S110), material sample, measured with the laser interferometric dilatometer, confirming the temperature-dependent CTE. Especially, the CTE in the temperature range from 0 °C to 50 °C appeared to be linear. Thermal expansion of many ceramics is known that it can be approximated by a quadratic function under the limited temperature range except for high temperature [25–27]. However, the CTE of these ceramics at around room temperature is a linear approximation for practical applications.

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Figure 16 shows the axial displacement of the ceramic strut with the BDMI as a function of time during the temperature cycle. Each temperature interval was maintained until the specimen temperature reached the steady-state temperature. For a long measurement over a week, a temperature change was operated every 24 h, and the 6 h was available as the steady-state condition of each temperature interval. The standard deviations of displacement and temperature at the steady-state temperature are less than 10 nm and 0.03 °C, respectively. Figure 17 shows the measured displacement as a function of temperature. The data points represent the mean value of the experimental data in the steady-state temperature. The dotted curve is a second-order polynomial fit obtained from measurement points with the BDMI. The solid curve is the analytical curve of the thermal expansion that was assumed to be a function of the CTEs of the constituents of the structural module and the sensing module, as shown in figure 18 and following equation (4).

$$\begin{eqnarray}&&{\rm{\Delta }}{L}_{TS}={\rm{\Delta }}{L}_{STM}+{\rm{\Delta }}{L}_{SM1,SM2}\end{eqnarray} \tag{ 4 }$$

Where

$$\begin{eqnarray*}&&{\rm{\Delta }}{L}_{STM}=\displaystyle \int {\alpha }_{Sialon\_Material}\left(T\right)\cdot {L}_{0,STM}dT\end{eqnarray*}$$

and

$$\begin{eqnarray*}&&{\rm{\Delta }}{L}_{SM}={\rm{\Delta }}{L}_{SM1,SM2}=\displaystyle \displaystyle \sum _{i}\displaystyle \int {\bar{\alpha }}_{i}\cdot {L}_{0,i}dT\end{eqnarray*}$$

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The CTE of the SiAlON was an actual measurement result, but the other CTEs were assumed to be constant over the temperature range, according to manufacture specifications (table 3). The analytical value closely matched with the experimental data points. The RMS of difference between the polynomial fit curve and the analytical curve was 202 nm during the wide temperature range (from 5 °C to 45 °C). The RMS was 100 nm during the limited temperature range (from 15 °C to 30 °C). There is a remarkable difference in the wide temperature range, caused by some constituent parts not having a constant CTE over the temperature. Thus, to identify the thermal behavior of the sensing module, the displacement of the sensing module ${\rm{\Delta }}{L}_{SM1,SM2}$ associated with the temperature change was measured without the structural module. The chained curve is the analytical curve of the thermal expansion with compensation of the thermal behavior of the sensing module. The RMS of difference between the polynomial fit curve and analytical curve with compensation of sensing module was 145 nm during the wide temperature range (from 5 °C to 45 °C). The RMS was 69 nm during the limited temperature range (from 15 °C to 30 °C). Therefore, the analytical value with compensation of the sensing modules matched well with the experimental data points.

Table 3. Specifications of the constituents of the structural module.

Parts name	Material	Mean CTE at room temperature ${\bar{\alpha }}_{i},$ 10−6 K−1	Initial length ${L}_{0,i},$ mm
Sensing module housing	Invar alloy	1.9	21
Sensor head	Titanium	8.8	3.5
Lens holder	Super invar alloy	0.29	8
Retroreflector	Fused silica	0.55	6

Next, the CTE of the SiAlON of the structural module was also evaluated by the BDMI measurement data and was compared with that of the material sample. Figure 18 shows the CTE of SiAlON obtained from the measurements of the truss strut subtracted by the thermal behavior of the sensing modules according to equation (5).

$$\begin{eqnarray}&&{\bar{\alpha }}_{STM}\left({T}_{2},\,{T}_{1}\right)\equiv \displaystyle \frac{1}{{L}_{0,STM}}\cdot \displaystyle \frac{{L}_{2,STM}\left({T}_{2}\right)-{L}_{1,STM}\left({T}_{1}\right)}{{T}_{2}-{T}_{1}}\end{eqnarray} \tag{ 5 }$$

and

$$\begin{eqnarray*}&&{L}_{i,STM}\left({T}_{i}\right)={L}_{i,TS}\left({T}_{i}\right)-\,{L}_{i,SM1,SM2}\left({T}_{i}\right)\end{eqnarray*}$$

The data points represent the experimental data in the steady-state temperature. The dotted line is a fitting line determined from the polynomial fit curve of displacement as shown in figure 19. The solid curve indicates the measurements of the material sample which is the same production lot as the strut. The uncertainty budgets of the CTE measurement with the BDMI are shown in table 4. The combined standard uncertainty ${u}_{c}$ was calculated from equation (6).

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{{u}_{c}\left(\alpha \right)}{\alpha }\equiv \left[{{\left(\displaystyle \frac{u\left({\rm{\Delta }}L\right)}{L}\right)}_{RMS\_fit}}^{2}+{\left(\displaystyle \frac{u\left(L\right)}{L}\right)}^{2}\right.\\ \,+{\left.{\left(\displaystyle \frac{u\left({\rm{\Delta }}L\right)}{{\rm{\Delta }}L}\right)}^{2}+{\left(\displaystyle \frac{u\left({\rm{\Delta }}T\right)}{{\rm{\Delta }}T}\right)}^{2}+{\left(\displaystyle \frac{u\left({\rm{\Delta }}\lambda \right)}{\lambda }\right)}^{2}\right]}^{\displaystyle \frac{1}{2}}\end{array}\end{eqnarray} \tag{ 6 }$$

Where

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Table 4. Uncertainty budget of the CTE of SiAlON measurement using the BDMI.

Term	Factor, ${x}_{i}$	Standard uncertainty, ${\rm{u}}\left({x}_{i}\right)$		Probability distribution	Divisor, D	Sensitivity coefficient, ${C}_{i}$	Type
$u\left({\rm{\Delta }}\lambda \right)$	Wavelength stability	50	Ppb	Rectangular	$\sqrt{3}$	1	B
$u\left({\rm{\Delta }}L\right)$	Sensor resolution	1	Pm	Rectangular	$\sqrt{3}$	$\tfrac{1}{{\rm{\Delta }}L}$	B
	Sensor repeatability Working distance: 200 mm	8.3	Nm	Rectangular	$\sqrt{3}$	$\tfrac{1}{{\rm{\Delta }}L}$	B
	Signal stability $(2\sigma )$ Working distance: 200 mm	2.7	Nm	Gaussian	$2$	$\tfrac{1}{{\rm{\Delta }}L}$	B
$u\left(L\right)$	Length uncertainty	0.005	Mm	Rectangular	$\sqrt{3}$	$\tfrac{1}{L}$	B
$u\left({\rm{\Delta }}T\right)$	Temperature uncertainty	0.01	K	Rectangular	$\sqrt{3}$	$\tfrac{1}{{\rm{\Delta }}T}$	B

${\rm{\Delta }}T:$ Temperature change in °C

${\rm{\Delta }}L:$ Measured displacement in nm

${x}_{i}:$ Factor (Input value)

$u\left({x}_{i}\right):$ Standard uncertainty

${u}_{c}\left({x}_{i}\right):$ Combined standard uncertainty

The RMS deviation of fitting residual ($u\left({\rm{\Delta }}L\right)=57\,{\rm{nm}}$) is added to the combined measurement uncertainty of the CTE [28]. In addition, the expanded measurement uncertainty ${U}_{95 \% }$ for a level of confidence of approximately 95% is obtained by multiplying the combined standard uncertainty ${u}_{c}\left(\alpha \right)$ by a coverage factor ${k}_{95 \% }=2.$ Therefore, the CTE measured using the BDMI and using the LIX-2 system are $\left(1.213\pm 0.063\right)\times {10}^{-6}$/K and $\left(1.294\pm 0.040\right)\times {10}^{-6}$/K at room temperature, respectively. The errors indicated the measurement uncertainties of the BDMI (for $\lambda =1530\,{\rm{nm}},$ ${\rm{\Delta }}T=5\,^\circ {\rm{C}}$ and $L=199.950\,{\rm{mm}}$) and the LIX-2 (for ${\rm{\Delta }}T=5\,^\circ {\rm{C}}$ and $L=14.191\,{\rm{mm}}$). The CTE of the fitting value of the BDMI measurement agreed with that of the material sample measured within $1.0\times {10}^{-7}$/K. The slight difference in CTE was caused by CTE inhomogeneity (Specimen size dependence), the uncertainty of each measurement system, the residual error of the sensing module compensation, and the data fitting process.