Quantitative analysis for the effect of the thermal physical property parameter of adhesive on the thermal performance of the quadrupolar fiber coil

Zhuo Zhang; Fei Yu

doi:10.1364/OE.25.030513

1. Introduction

The fiber optic gyroscope (FOG) is an inertial instrument extensively used in navigation, orientation, and stabilization systems in recent years [1–3]. The performance of FOG has been shown to be sensitive to time-varying temperature present across the fiber coil as described [4–7]. The fiber coil is the core element of the FOG, and it is wound by several kilometers of fiber on basis of quadrupolar winding pattern [8–10], and the adhesive will be used to fasten each loop of the fiber together into a ring solid in Fig. 1. According to the description of shupe effect [11] and elastic-optic effect [12–14], the temperature gradient and thermal stress inside the fiber coil are the main causes of the thermal-induced drift error of the FOG [15–17]. When the environment temperature changes, the thermal physical property parameters of the adhesive(Specific heat, density, thermal conductivity, thermal expansion coefficient, Young’s modulus, Poisson’s ratio, etc) will directly affect the temperature and stress distribution inside the fiber coil, which will further affect the thermal performance of the FOG. However, to the best of authors’ knowledge, no published articles and standards have been studied the influence of property of adhesive material on the performance of fiber coil. However, the selection of adhesive is very important to improve the thermal performance and environmental adaptability of the FOG.

Fig. 1 Fiber coil structure diagram. (a) Relevant dimensions of fiber coil. (b) Schematic diagram of the quadrupolar fiber coil cross section, where the adhesive is filled inside the whole fiber coil.

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The aim of this paper is to quantitative analyze the influence degree of various thermal physical property parameter of adhesive material to the thermal performance of the FOG, ultimately the guiding principle is provided for the choice of adhesive materials used in the fiber coil winding, which can help to improve the thermal performance of the FOG. Firstly, according to the shupe effect and the elastic-optic effect, the influence mechanism of temperature and stress on the non-reciprocal phase difference of the fiber coil is analyzed, and the thermal-induced drift error model of the fiber coil is built. Secondly, the three-dimensional simulation model of fiber coil including fiber core, coating layer, adhesive and various material is built, and the accuracy of the model is verified by simulation and experiment. Finally, based on the simulation model which has already verified, the influence degree of various thermal physical property parameters of adhesive (thermal conductivity, density, specific heat, Young’s modulus, Poisson’s ratio, thermal expansion coefficient, etc) on the thermal-induced drift error of FOG is analyzed.

2. Theory

Fiber coils are commonly wound in a cylindrical quadrupole pattern to reduce errors associated with time-varying temperatur. Winding must start at the center of a fiber length and proceed outwards towards the fiber ends alternately from two feed reels each containing half the length. Half the fiber is wound clockwise(CW) around the coil and the other half counterclockwise(CCW). In Fig. 1(b), the whole fiber coil can be separated into m layer with n loop, every four layers are as one cycle, and each loop of fiber is filled with adhesive to fix the fiber. It can be understood as, the external temperature is passed through the adhesive to each loop of fiber and thermal stress is also applied to the fiber by adhesive, so the property of adhesive will determine the temperature and stress of the fiber directly. This is very important for the thermal performance of the fiber coil.

According to the description of shupe effect and elastic-optic effect [11, 13], when the fiber is subjected to the temperature and stress, the length and refractive index of the fiber will be changed, this is shown in Eqs. (1)–(4).

Δ L_{T} = α \cdot L \cdot Δ T

Δ n_{T} = \frac{\partial n_{0}}{\partial T} \cdot Δ T

Δ L_{P} = - \frac{2 μ}{E} \cdot L \cdot Δ P

Δ n_{P} = - \frac{n_{0}^{3}}{2 E} (p_{11} - μ p_{11} + p_{12} - 3 μ p_{12}) \cdot Δ P

Where L and n₀ indicate the length and effective refractive index of the fiber. ΔL_T and Δn_T indicate the length variation and refractive index variation when the fiber is subjected to temperature change ΔT. α and ∂n₀/∂T are the thermal expansion coefficient and the thermal optical coefficient. ΔL_P and Δn_P indicate the length variation and refractive index variation when the fiber section is subjected to stress change ΔP. The stress is positive when the fiber is stretched and the stress is negative when compressed. E and μ are the Young’s modulus and Poisson’s ratio. p₁₁ and p₁₂ are photoelastic coefficients.

According to the relevance theory of Sagnac [18] effect, after the length variation and refractive index variation of the fiber is obtained, the thermal-induced drift error model of FOG is as follows:

\begin{array}{l} Ω_{E} = \frac{n_{0}}{L D} {(\frac{\partial n_{0}}{\partial T} + n_{0} α) \int_{0}^{L} (L - 2 s) \dot{T} (s, t) d s + (\frac{n_{0}^{3}}{2 E} (p_{11} - μ p_{11} + p_{12} - 3 μ p_{12}) \\ + \frac{2 μ n_{0}}{E}) \int_{0}^{L} (L - 2 s) \dot{P} (s, t) d s} \end{array}

Let $A_{T} = \frac{n_{0}}{L D} (\frac{\partial n_{0}}{\partial T} + n_{0} α)$ , $A_{P} = \frac{n_{0}}{L D} (\frac{n_{0}^{3}}{2 E} (p_{11} - μ p_{11} + p_{12} - 3 μ p_{12}) + \frac{2 μ n_{0}}{E})$ , and they are respectively defined as the temperature drift influence coefficient and the stress drift influence coefficient, in the case of fixed optical fiber parameters that both parameters are constant.

In accordance with quadrupolar winding pattern, starting from the CW direction and along the length of the fiber, the entire fiber coil is separated into an independent fiber with m layer and n loop per layer (m*n loop in total), and it ends with CCW direction in Fig. 1(b). Equation (5) can be derived as:

\begin{array}{l} Ω_{E} = A_{T} \sum_{i = 1}^{m * n} [\int_{L_{i - 1}}^{L_{i}} (L - 2 s) \dot{T} (s, t) d s] + A_{P} \sum_{i = 1}^{m * n} [\int_{L_{i - 1}}^{L_{i}} (L - 2 s) \dot{P} (s, t) d s] \\ = A_{T} \sum_{i = 1}^{m * n} N (i) \cdot \dot{T} (i) + A_{P} \sum_{i = 1}^{m * n} N (i) \cdot \dot{P} (i) \\ = A_{T} \sum_{i = 1}^{m} \sum_{j = 1}^{n} (N_{i j} \cdot {\dot{T}}_{i j}) + A_{P} \sum_{i = 1}^{m} \sum_{j = 1}^{n} (N_{i j} \cdot {\dot{P}}_{i j}) \\ = A_{T} 〈 N, T 〉 + A_{P} 〈 N, P 〉 \\ N = (\begin{matrix} N_{11} & \dots & N_{1 n} \\ ⋮ & ⋱ & ⋮ \\ N_{m 1} & \dots & N_{m n} \end{matrix}) T = (\begin{matrix} {\dot{T}}_{11} & \dots & {\dot{T}}_{1 n} \\ ⋮ & ⋱ & ⋮ \\ {\dot{T}}_{m 1} & \dots & {\dot{T}}_{m n} \end{matrix}) P = (\begin{matrix} {\dot{P}}_{11} & \dots & {\dot{P}}_{1 n} \\ ⋮ & ⋱ & ⋮ \\ {\dot{P}}_{m 1} & \dots & {\dot{P}}_{m n} \end{matrix}) \end{array}

Where L_i represents the distance from fiber starting point to the ith loop fiber in the fiber coil. All of N, T and P are the m*n dimension matrix, and they respectively represent the weight matrix, temperature field matrix, stress matrix. N_mn,

{\dot{T}}_{m n}

and

{\dot{P}}_{m n}

are respectively represent the weight influence coefficient, temperature gradient and stress gradient of the mth layer with the nth loop fiber in the fiber coil.

From Eqs. (5) and (6), the thermal-induced drift of the FOG is derived from the integral form to the form of the inner product of matrix. The fiber coil of m layer with n loop can correspondingly obtain the weight matrix N, temperature field matrix T and stress matrix P of m*n dimensions, the row and column of these three matrices correspond exactly to the layer and loop in the fiber coil. The thermal-induced error model in this form is not only helpful for understanding the relationship among the four factors of layer number and loop number of the fiber coil, weight coefficient, temperature distribution and stress distribution, but also convenient to improve computational efficiency and reduce the computing time. Where the temperature field matrix T and stress matrix P can be obtained according to the thermal simulation of fiber coil in section 3, and the weight matrix N is related to the design parameters of the fiber coil, as shown below:

C W {\begin{cases} v = ⌊ (i - 1) / n ⌋ + 1 (i = 1 \dots m \times n / 2) \\ m i = m + 1 - 2 v + ((- 1)^{v} - 1) / 2 \\ n i = (- 1)^{v + 1} (\mod (i - 1, n) + 1) + (n + 1) ((- 1)^{v} + 1) / 2 \\ R_{i} = R_{I n} + (m i - 0.5) d \\ L e n g h t i = 2 π R i \\ L_{i} = L_{i - 1} + L e n g h t i (L_{0} = 0) \\ N_{m i, n i} = (L \times L_{i} - L_{i}^{2}) - (L \times L_{i - 1} - L_{i - 1}^{2}) \end{cases}

C C W {\begin{cases} v = ⌊ (i - 1) / n ⌋ + 1 - m / 2 (i = m \times n / 2 + 1 \dots m \times n) \\ m i = 2 v + ((- 1)^{v + 1} - 1) / 2 \\ n i = (- 1)^{v + 1} (\mod (i - 1, n) + 1) + (n + 1) ((- 1)^{v + 1} + 1) / 2 \\ R_{i} = R_{I n} + (m i - 0.5) d \\ L e n g h t i = 2 π R i \\ L_{i} = L_{i - 1} + L e n g h t i \\ N_{m i, n i} = (L \times L_{i} - L_{i}^{2}) - (L \times L_{i - 1} - L_{i - 1}^{2}) \end{cases}

It can be seen from Eqs. (7) and (8), the elements of the weight matrix N(m*n elements in total) are divided into two parts of CW direction(i= 1…m × n/2) and CCW direction(i=m×n/2+1…m×n). mi and ni represent the position of the ith loop fiber located at the mi row and ni column in the fiber coil, Ri represents the bending radius of the ith loop fiber, Lenghti represents its length and N_mi_,_ni represents the elements of the mi row and ni column in matrix N.

3. Simulation model and experimental verification

In order to analyze the influence of adhesive material on temperature distribution and stress distribution in fiber coil, and build three dimensional thermodynamic simulation model of fiber coil containing fiber core layer, coating layer, adhesive and insulation material in Fig. 2, the related parameters of the model are shown in Tables 1 and 2. Where the main thermal physical property parameters of adhesive include: thermal conductivity, density, specific heat, Young’s modulus, Poisson’s ratio and thermal expansion coefficient.

Fig. 2 Finite element simulation model of fiber coil.

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Table 1. Relevant parameter of fiber coil

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Table 2. Material parameter of fiber coil

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In order to verify the accuracy of simulation model and thermal-induced drift model, this paper separately designs two groups of simulation for stress distribution and thermal-induced drift error under temperature varying and two groups of experiment for stress distribution and thermal-induced drift error. The accuracy of the theory is verified by comparing simulation and experimental results.

First of all, in the part of simulation and experiment of stress distribution, the distribution of fiber coil internal strain is calculated respectively under the temperature at 80 °C and − 40 °C, and the distributed brillouin fiber temperature and strain analyzer is used to measure the actual strain inside the fiber coil, the calculation and experiment result is shown in Fig. 3. Where the horizontal axis is distance of fiber coil along the length direction (start from the CW direction to the end of the CCW direction), the vertical axis is the strain. It can be seen in two temperature points of 80 °C and −40 °C, the simulation curves are basically coincide with the experimental curve. The fiber coil expands at 80 °C, the fiber inside the fiber coil is compressed and the strain is negative, and the fiber outside the fiber coil is stretched and the strain is positive. The fiber coil compressed at −40°C, the fiber inside the fiber coil is stretched and the strain is positive, and the fiber outside the fiber coil is compressed and the strain is negative. The simulation curves and experimental curves have some errors in detail which are caused by the uncertain factors in the fiber coil winding process and the inaccuracy of the fiber internal material properties. However, in general, the consistency between simulation and experiment is quite high, and it indicates that the simulation model is accurate; the transient thermal analysis can be further carried out based on this simulation model to calculate the thermal-induced drift of the FOG.

Fig. 3 Simulation and experimental stress distribution results.

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In order to verify the accuracy of the thermal-induced error model, a set of simulation and experiment under variable temperature is designed. The environment temperature is shown in Fig. 4, where the dotted line is the setting temperature of the temperature test chamber, and the solid line is the measurement value of the temperature sensor inside the FOG. The initial temperature of temperature test chamber is set 25°C, temperature speed recording is 1°C/min, and respectively holding 120min at 25°C, −40°C, 60°C and 20°C. It takes some time to transfer the environment temperature to the inside of the FOG, so the measuring temperature generally falls behind the setting temperature of the environment. The fiber coil internal temperature field and stress field distribution are analyzed by using the measuring temperature in Fig. 4 as the boundary condition of the finite element simulation model, the temperature field matrix T and stress matrix P are extracted and introduced to Eq. (6), and the thermal-induced drift of the FOG is obtained and compared with the experimental results. In Fig 5, a dotted line is the thermal-induced drift of the FOG obtained by simulation and the solid line is the output of the FOG obtained by actual measurement, two curves also have high consistency which further proves the accuracy of thermal-induced drift error model in section 2. It is based on this error model and the fiber coil thermal simulation model that we can further analyze the influence of different thermal physical property parameter of the adhesive on performance of the FOG.

Fig. 4 Temperature setting and measurement curve.

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Fig. 5 Simulation curves(dotted line) and experimental curves(solid line) of thermal-induced drift error.

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4. Analysis of different material properties

According to the transient heat transfer equation and thermal stress equation [19], it is known that the main physical property parameters affecting the fiber coil internal temperature and stress distribution include thermal conductivity, density, specific heat, Young’s modulus, Poisson’s ratio and thermal expansion coefficient. For quantitatively analyzing the situation of the thermal-induced error of the FOG by different parameters, and reducing the amount of calculation at the same time, this paper has designed a set of temperature process with a total of 14 minutes in Fig. 6, the temperature rose from 20 °C to 30 °C and temperature gradient kept 1°C/min during the temperature-changing process. Only one physical property parameter of adhesive can be changed during each calculation, the same temperature process was used to do simulation, and the corresponding thermal-induced drift of the FOG was calculated. In the selection of the numerical value of the physical property parameters, total of 5 magnitudes (Table 3) are selected for 0.1 times, 0.5 times, 1 times, 2 times, and 10 times the original parameters (Table 2). Through the calculation results of 30 sets in total, the influence of the physical property parameter of the adhesive on the thermal-induced error of the FOG is analyzed by comparing the error of the FOG with the different magnitude of the same physical property parameter and the same magnitude of different physical property parameter.

Fig. 6 Simulation temperature process(solid line) and temperature gradient(dotted line).

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Table 3. The value of the thermal physical property parameters of the adhesive

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Figure 7, 8 and 9 respectively show the simulation curve of the thermal-induced drift error under specific heat capacity, density and thermal conductivity of different magnitudes. Their common characteristics are that the variation of the parameter magnitude only affects the error curve of beginning and end phase of the temperature change, and it hardly affects the error curve of intermediate phase of temperature change. In general, the thermal-induced drift of the FOG will decrease with the decrease of the heat capacity, the decrease of density and the increase of thermal conductivity. Where the curves of the specific heat capacity and the density are almost identical because of in the transient heat transfer Q = cρVΔT, matter absorbing heat Q is proportional to heat capacity c, densityρ and volumeV. When the relative dimension of the fiber coil is constant, the change of the specific heat capacity and the density of the same magnitude have the same effect on the fiber coil internal temperature field. And the effect of heat capacity and the density with the change of 0.1 times, 0.5 times, 1 times, 2 times on the thermal-induced error is not significant, but the error will suddenly increase at the change of 10 times. In Fig. 9, the thermal conductivity of different magnitudes has an average effect on the thermal-induced error.

Fig. 7 Influence of specific heat capacity on thermal-induced drift error.

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Fig. 8 Influence of density on thermal-induced drift error.

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Fig. 9 Influence of thermal conductivity on thermal-induced drift error.

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Figure 10, 11 and 12 respectively show simulation curve of the thermal-induced drift error which corresponding the thermal expansion coefficient, Young’s modulus and Poisson’s ratio of different magnitudes. All of these three coefficients affect the thermal stress distribution inside the fiber coil and further affect the drift error, so their error curves are similar. Unlike the first three parameters (specific heat capacity, density and thermal conductivity), the change of last three parameters will affect the error curve in the whole temperature change process. In general, the thermal-induced drift error can be obviously reduced by reducing thermal expansion coefficient, increasing Young’s modulus and reducing Poisson’s ratio. The influence of the expansion coefficient on the error is the most obvious in Fig. 10. When the thermal expansion coefficient increases to 10 times the original, the error of FOG will have a very large increase. While in Fig. 12, when Poisson’s ratio increases to 2 times and 10 times the original, the thermal-induced error hardly changes, and it is indicating that the Poisson’s ratio in this change interval has no influence on the output error of the FOG.

p = (Ω_{\max} - Ω_{\min}) / Ω_{\min}

Fig. 10 The influence of thermal expansion coefficient on thermal drift error.

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Fig. 11 The influence of Young’s modulus on thermal drift error.

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Fig. 12 The influence of Poisson’s ratio on thermal drift error.

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The quantitative influence degree of the six thermal physical property parameters of adhesive on the thermal-induced error of the FOG is shown in Tables 4 and 5. According to the influence trend of different parameters on the thermal-induced error, this paper respectively calculates the root-mean-square (RMS) error of the FOG error and the maximum rate of change(MRC) in the two cases of 1–3min and whole temperature processes. Where the maximum rate of change is calculated based on Eq. (9). According to the numerical value of maximum rate of change, it can be seen intuitively that the thermal expansion coefficient has the most obvious effect on the thermal-induced error in 1–3min, it can be described as thermal expansion coefficient > Young’s modulus > specific heat capacity = density > Poisson’s ratio > thermal conductivity. In the whole temperature processes that the thermal expansion coefficient also has the most obvious effect, and it can be described as thermal expansion coefficient > Young’s modulus> Poisson’s ratio > specific heat capacity = density > thermal conductivity. Whether in 1–3min or the whole temperature process, the influence of different thermal physical property parameters of the adhesive on the thermal-induced drift of the FOG is basically consistent. In six thermal physical property parameters of adhesive, the thermal conductivity, density and specific heat mainly affect the distribution of temperature field inside the fiber coil; Young’s modulus, Poisson’s ratio and thermal expansion coefficient mainly affect the distribution of stress field. So to a certain extent, comparing with the temperature field distribution, the thermal stress distribution inside the fiber coil is more important to improve the thermal performance of the FOG.

Table 4. The thermal-induced error of the FOG with different parameter magnitude in 1–3min (°/h)

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Table 5. The thermal-induced error of the FOG with different parameter magnitude in the whole temperature process(°/h)

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5. Conclusion

This paper based on the shupe effect and elastic-optic effect, the theoretical model and simulation model of the thermal-induced error of the FOG are set up considering both the temperature field and the thermal stress field at the same time and through experimental verification, and the influence degree of the six thermal physical property parameters of adhesive materials on the thermal performance of FOG was quantitatively analyzed. Results show that aiming at the thermal physical property parameters for adhesive, decreasing the thermal expansion coefficient, improving the Young’s modulus, reducing the Poisson’s ratio, reducing the specific heat capacity, reducing the density and increasing the thermal conductivity within a certain range will be beneficial to improve the thermal performance of FOG. It is proved that the thermal expansion coefficient of the adhesive has the greatest influence on the thermal-induced drift error, others in turn is Young’s modulus, Poisson’s ratio, specific heat capacity, density and thermal conductivity. And it further found that the thermal stress distribution inside the fiber coil has more influence on the thermal performance of the FOG than the temperature field distribution. The above findings will provide an extremely meaningful help for the selection and production of adhesive material for the fiber coil and help to find ways to further improve the thermal performance of FOG. In the next study, the material properties of the fiber coating layer will be considered, and searching the best matching scheme for the adhesive material and fiber coating layer material.

Funding

National Natural Science Foundation of China (No. 51509049 and 51679047); Postdoctoral Foundation of Heilongjiang Province (No.LBH-Z16044).

References and links

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4. E. V. Dranitsyna, D. A. Egorov, A. A. Untilov, G. B. Deineka, I. A. Sharkov, and I. G. Deineka, “Reducing the effect of temperature variations on FOG output signal,” Gyroscopy Navigation 4(2), 92–98 (2013). [CrossRef]

5. Y. L. Wang, L. Y. Ren, J. T. Xu, J. Liang, M. H Kang, K. L. Ren, and N. B. Shi, “The compensation of y waveguide temperature drifts in fog with the thermal resistor,” Adv. Mater. Res. 924, 336–342 (2014). [CrossRef]

6. F. Mohr, “Thermooptically induced bias drift in fiber optical Sagnac interferometers,” J. Lightwave Technol. 14(1), 27–41 (1996). [CrossRef]

7. C. Zhang, S. Du, J. Jin, and Z. Zhang, “Thermal analysis of the effects of thermally induced nonreciprocity in fiber optic gyroscope sensing coils,” Optik 122(1), 20–23 (2011). [CrossRef]

8. M. Sardinha, J. Rivera, A. Kaliszek, and S. Kopacz, “Octupole winding pattern for a fiber optic coil,” EP2075535 (2009).

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Parameters	Values
Fiber diameter d	165μm
Fiber core diameter	80μm
Inner radius R_In	81.7mm
Number of winding layer m	44
Number of loop per layer n	84
Speed of light c	3×10⁸m/s
Average wavelength of light source λ₀	1550nm
effective refractive index n₀	1.456
Thermo-optic coefficient ∂n₀/∂T	8.11×10⁻⁶/K
Thermal expansion coefficient α	5.5×10⁻⁷/K
Photoelastic coefficients P₁₁ and P₁₂	0.121 and 0.27
Length of fiber coil L	1035.03338m
Winding pattern	QAD

Parameters	Core	Coating	Adhesive	Insulation material
Specific heat J/(kg * K	703	1400	1600	2200
Density kg/m³	2203	1190	970	1370
Thermal conductivity W/(m * k)	1.38	0.21	0.21	0.25
Thermal expansion coefficient 1/K	0.55 ×10⁻⁶	67.1 ×10⁻⁶	110×10⁻⁶	6×10⁻⁶
Young’s modulus Pa	80×10⁹	1.56×10⁸	1.434×10⁹	4×10⁷
Poisson’s ratio	0.17	0.4	0.499	0.39

Parameters	0.1 times	0.5 times	1 times	2 times	10 times
Specific heat J/(kg * K)	160	800	1600	3200	16000
Density kg/m³	97	485	970	1940	9700
Thermal conductivity W/(m * k)	0.021	0.105	0.21	0.42	2.1
Thermal expansion coefficient 1/K	11 10⁻⁶	55×10⁻⁶	110×10⁻⁶	220×10⁻⁶	1100×10⁻⁶
Young’s modulus Pa	0.1434×10⁹	0.717×10⁹	1.434×10⁹	2.868×10⁹	14.34×10⁹
Poisson’s ratio	0.0499	0.2495	0.499	0.998	4.99

Parameters	0.1 times	0.5 times	1 times	2 times	10 times	MRC
Specific heat	0.0299	0.0305	0.0312	0.0327	0.0431	44.22%
Density	0.0299	0.0305	0.0312	0.0327	0.0431	44.22%
Thermal conductivity	0.0334	0.0321	0.0312	0.0302	0.0287	16.33%
Thermal expansion coefficient	0.0174	0.0232	0.0312	0.0482	0.1896	987.51%
Young’s modulus	0.0357	0.0343	0.0312	0.0275	0.0215	66.43%
Poisson’s ratio	0.0240	0.0265	0.0312	0.0312	0.0312	30.16%

Parameters	0.1 times	0.5 times	1 times	2 times	10 times	MRC
Specific heat	0.0309	0.0311	0.0313	0.0317	0.0356	15.01%
Density	0.0309	0.0311	0.0313	0.0317	0.0356	15.01%
Thermal conductivity	0.0319	0.0315	0.0313	0.0310	0.0307	4.11%
Thermal expansion coefficient	0.0119	0.0196	0.0313	0.0560	0.2584	2068.26%
Young’s modulus	0.0374	0.0356	0.0313	0.0259	0.0173	115.97%
Poisson’s ratio	0.0208	0.0245	0.0313	0.0313	0.0313	50.53%

Quantitative analysis for the effect of the thermal physical property parameter of adhesive on the thermal performance of the quadrupolar fiber coil

Abstract

1. Introduction

2. Theory

3. Simulation model and experimental verification

4. Analysis of different material properties

5. Conclusion

Funding

References and links

Cited By

Figures (12)

Tables (5)

Equations (9)

Optics Express