A numerical model-based non-metallic material parameter analysis method for fiber-optic gyroscope

Abstract

The application belongs to the technical field of inertial navigation, and discloses a fiber-optic gyroscope nonmetal material parameter analysis method based on a numerical model. Specifically, the method comprises the following steps: constructing a high-precision finite element model of a fiber-optic ring of a fiber-optic gyroscope core device according to an actual product; establishing a nonmetal material thermal viscoelastic constitutive equation of the fiber-optic ring of the fiber-optic gyroscope core device and testing related parameters; setting a temperature load consistent with a service environment, giving the nonmetal material attribute parameters of the fiber-optic ring of the fiber-optic gyroscope, writing and calling a thermal viscoelastic constitutive equation subroutine, and simulating and analyzing the creep characteristics of the fiber-optic ring in the finite element simulation model; and screening out the most critical material parameters of the fiber-optic ring creep by using sensitivity analysis and summarizing the influence law. The application quantitatively evaluates the influence of the material parameters of the fiber-optic ring of the fiber-optic gyroscope on the creep characteristics under a temperature field environment based on a digital model, provides theoretical guidance for subsequent optimization of the material of the fiber-optic ring and process control, and improves the precision of the fiber-optic gyroscope.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, and specifically to a method for analyzing the parameters of non-metallic materials in fiber optic gyroscopes based on numerical models. Background Technology

[0002] Inertial navigation systems (INS) are crucial airborne / missile-borne equipment systems that utilize inertial elements to measure the motion information of a carrier, enabling autonomous navigation. Angular velocity sensors are the core components of INS, primarily used to measure the angular motion of a moving carrier relative to inertial space. Fiber optic gyroscopes, a rapidly developing type of angular velocity sensor in recent years, differ from traditional electromechanical gyroscopes in that they do not require a rotor and have no internal moving parts. They offer advantages such as small size, shock resistance, long lifespan, short start-up time, fast instantaneous response, and high sensitivity, and are widely used in key national sectors such as aviation, aerospace, navigation, and weaponry. Fiber optic gyroscopes and their associated airborne or missile-borne equipment operate under consistent conditions, with a working temperature range of -55 to 85°C. Temperature performance is a crucial indicator for evaluating product accuracy and reliability. With the continuous development of inertial navigation technology in China, the performance accuracy and requirements for inertial devices are becoming increasingly stringent. Currently, the environmental adaptability of fiber optic gyroscopes has become a key factor restricting their development towards higher precision, particularly the significant impact of temperature on their performance. Therefore, it is necessary to conduct research on the temperature performance of fiber optic gyroscopes and improve their output stability under temperature variations, which is of great significance for improving the accuracy of fiber optic gyroscopes and the performance of inertial navigation systems.

[0003] In temperature-varying environments, the internal optics of fiber optic gyroscopes experience thermal stress, affecting optical signal transmission and causing temperature drift errors. Accumulated errors over time can lead to significant shifts in the gyroscope's detection accuracy, consequently impacting the overall navigation system's precision. Simultaneously, the fiber optic ring, a core component of the gyroscope, is primarily composed of non-metallic materials. In temperature-changing environments, the internal thermal stress significantly affects the refractive index of the optical signal. However, due to the complex viscoelastic properties of these materials, the mechanism of stress variation within the fiber optic ring remains unclear, severely hindering performance improvements. Currently, few studies have delved into the mechanical models of fiber optic rings under time-varying temperatures. While a few scholars have explored and researched the mechanical properties of non-metallic materials in fiber optic gyroscope rings, the characterization of these materials is relatively simple and fails to consider the stress coupling effects between various structural materials, making it impossible to quantitatively reveal the mechanical evolution mechanism and process of the fiber optic ring under time-varying temperatures. Furthermore, the fiber optic ring involves coupling effects from multiple nonlinear materials in temperature-varying environments, and the impact of key mechanical parameters on performance has not been summarized, leaving the direction for product optimization unclear and presenting technical challenges for performance improvement. Summary of the Invention

[0004] This invention discloses a numerical model-based method for analyzing the parameters of non-metallic materials in fiber optic gyroscopes. It innovatively constructs a fiber optic ring model for fiber optic gyroscopes that considers the coupling of nonlinear mechanical properties of various non-metallic materials, which effectively reveals the evolution of stress and strain inside the fiber optic ring under temperature load. Based on this, the most critical material names for fiber optic ring creep are selected based on the digital model, and their influence laws are summarized, providing direction for product performance improvement and optimization.

[0005] Specifically, this patent proposes a method for analyzing the parameters of non-metallic materials in fiber optic gyroscopes based on a numerical model. This method includes the following steps:

[0006] Step 1: Construct a finite element analysis model with the same dimensions as the actual fiber optic gyroscope fiber optic ring structure used in production;

[0007] Step 2: Establish the thermoviscoelastic constitutive equation of the non-metallic material of the fiber optic gyroscope ring based on the finite element analysis model and test the relevant non-metallic material parameters;

[0008] Step 3: Based on the actual service environment temperature, set the temperature load consistent with the service environment, assign material property parameters, write and call the non-metallic material thermoviscoelastic constitutive equation subroutine, and perform simulation analysis on the fiber ring creep characteristics in the finite element simulation model.

[0009] Step 4: Post-process and analyze the finite element simulation results, select the names of the non-metallic materials that are most critical to fiber ring creep, and summarize their influence laws.

[0010] Furthermore, in step 1, the finite element analysis model imposes constraints on the inner coating, outer coating, wrapping adhesive, and bonding adhesive structure of the fiber optic ring and performs mesh generation, with a minimum mesh size of 0.02 mm.

[0011] Furthermore, step 2 also includes the following steps:

[0012] Step 21: Based on the actual service environment of the fiber optic gyroscope, derive the thermoviscoelastic constitutive equation of the non-metallic material of the fiber optic ring considering temperature and time factors.

[0013] Step 22: Test the relaxation modulus of the non-metallic material of the fiber optic ring at different temperatures, obtain the master curve at the reference temperature point, and fit it into a multi-order Prony series.

[0014] Step 23: Combine the non-metallic materials corresponding to the fiber optic ring structure of the fiber optic gyroscope and test their Poisson's ratio and coefficient of thermal expansion.

[0015] Furthermore, in step 21, the thermoviscoelastic constitutive equation for the nonmetallic material is:

[0016]

[0017] In the formula, σ ij S represents the stress tensor. ij Denotes the deviatoric stress tensor; δ ij Representing the Kronecker symbol, and when i = j, δ ij =1; when i≠j, δ ij =0; σ kk Let represent the stress sphere tensor, v represent Poisson's ratio, E(t) represent the relaxation modulus, and e represent the stress sphere tensor. ij Denotes the strain partial tensor, ε kk Let represent the strain sphere tensor, α represent the coefficient of thermal expansion, ΔT be the temperature difference between the real-time ambient temperature and the reference temperature, t represent time, τ represent the time integration variable, and ζ(t) represent the converted time. ζ(t) can be written as:

[0018]

[0019] In the formula, a T Let ψ[T] represent the time-temperature equivalence factor at temperature T, where ψ[T] is zero time at temperature T.

[0020] Furthermore, in step 22, the master curve at the reference temperature point is obtained and fitted into a multi-order Prony series as follows:

[0021]

[0022] In the formula, E(t) is the modulus at time t under the reference temperature, E0 is the constant term in the Prony series, and E i and τ i Let n be the relaxation modulus and relaxation time corresponding to the i-th Maxwell model, and n be the order of the Prony series.

[0023] Furthermore, in step 3, the temperature load conditions of the finite element simulation model are set to be consistent with the actual service conditions of the fiber optic gyroscope fiber optic ring.

[0024] The fiber optic gyroscope is assigned non-metallic material property parameters to the fiber optic ring. A user subroutine is written for the viscoelastic constitutive equation of the non-metallic material of the fiber optic ring. The subroutine is then called through finite element software to simulate and analyze the creep characteristics of the fiber optic ring under temperature load conditions.

[0025] Furthermore, in step 4, based on the creep of the fiber core position in the high-temperature isothermal section of the fiber ring during temperature cycling in the digital simulation model of the fiber ring, multiple sets of modeling simulations are performed by changing the modulus parameters of different non-metallic materials to screen out the names of non-metallic materials that have the most critical impact on creep.

[0026] The beneficial effects achieved by this invention are:

[0027] This invention provides a numerical model-based method for analyzing the parameters of non-metallic materials in fiber optic gyroscopes. It innovatively constructs a fiber optic ring model for fiber optic gyroscopes that considers the coupling of nonlinear mechanical properties of various non-metallic materials, enabling accurate assessment of the temperature stress of the fiber optic ring. In existing publicly available materials, there is no such in-depth modeling analysis and stress-strain evolution study on fiber optic rings for fiber optic gyroscopes. This invention patent supplements this part of the research.

[0028] This invention uses sensitivity analysis technology based on digital simulation models to obtain the most critical material parameters for fiber optic ring creep and summarize their influence laws, thereby improving researchers' understanding of product performance mechanisms and providing theoretical guidance for subsequent optimization of fiber optic ring component material selection, so as to improve the accuracy and survival rate of fiber optic gyroscopes.

[0029] This invention provides a numerical model-based method for analyzing the parameters of non-metallic materials in fiber optic gyroscopes. The analysis method and process constructed in this invention have strong versatility and can provide reference and guidance for the performance optimization and consistency improvement of other types of precision instruments. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the actual fiber optic ring product structure provided in the embodiments of the present invention;

[0031] Figure 2 This is a fitting diagram of the relaxation modulus of four non-metallic materials for an optical fiber ring at different temperatures provided in an embodiment of the present invention.

[0032] Figure 3 This is a schematic diagram illustrating the application of temperature field load in the fiber optic ring simulation model provided in this embodiment of the invention.

[0033] Figure 4 This is a temperature-stress curve of the fiber optic ring extracted from a simulation model, provided in an embodiment of the present invention.

[0034] Figure 5 This is a temperature-displacement curve of the optical fiber ring extracted from the simulation model, provided in this embodiment of the invention.

[0035] Figure 6 This is a graph showing the change of optical fiber core displacement with the modulus parameters of various non-metallic materials during the high-temperature temperature cycling stage, as provided in an embodiment of the present invention. Detailed Implementation

[0036] The present invention will be further described below with reference to specific embodiments, and the advantages and features of the present invention will become clearer as a result. However, these embodiments are merely exemplary and do not constitute any limitation on the scope of the present invention. Those skilled in the art should understand that modifications or substitutions can be made to the details and form of the technical solutions of the present invention without departing from the spirit and scope of the present invention, but all such modifications and substitutions fall within the protection scope of the present invention.

[0037] This invention discloses a numerical model-based method for analyzing the parameters of non-metallic materials in fiber optic gyroscopes. It innovatively constructs a fiber optic ring model for a fiber optic gyroscope that considers the coupling of nonlinear mechanical properties of various non-metallic materials. This model effectively reveals the evolution of stress and strain within the fiber optic ring under temperature loads. Based on this, the most critical material names for fiber optic ring creep are selected using the digital model, and their influence laws are summarized, providing direction for product performance improvement and optimization. The specific steps include:

[0038] Step 1: Construct a finite element analysis model with the same dimensions as the actual fiber optic gyroscope fiber optic ring structure used in production;

[0039] A finite element analysis model is constructed based on the physical structural dimensions of the fiber optic gyroscope's fiber optic ring, such as... Figure 1 As shown, constraints are applied to the fiber optic ring structure (inner coating, outer coating, wrapping adhesive, and bonding adhesive) and meshing is performed; in this embodiment, the minimum mesh size is 0.02 mm, and the number of meshes is approximately 8.27 million.

[0040] Step 2: Establish the thermoviscoelastic constitutive equation of the non-metallic material of the fiber optic gyroscope ring and test the relevant parameters;

[0041] Specifically, it also includes the following steps:

[0042] Step 21: Based on the actual service environment of the fiber optic gyroscope, derive the thermoviscoelastic constitutive equation of the non-metallic material of the fiber optic ring considering temperature and time factors.

[0043] The constitutive equation for the thermoviscoelasticity of nonmetallic materials is:

[0044]

[0045] In the formula, σ ij S represents the stress tensor. ij Denotes the deviatoric stress tensor; δ ij Representing the Kronecker symbol, and when i = j, δ ij =1; when i≠j, δ ij =0; σ kk Let represent the stress sphere tensor, v represent Poisson's ratio, E(t) represent the relaxation modulus, and e represent the stress sphere tensor. ij Denotes the strain partial tensor, ε kkLet represent the strain sphere tensor, α represent the coefficient of thermal expansion, ΔT be the temperature difference between the real-time ambient temperature and the reference temperature, t represent time, τ represent the time integration variable, and ζ(t) represent the converted time. ζ(t) can be written as:

[0046]

[0047] In the formula, a T Let ψ[T] represent the time-temperature equivalence factor at temperature T, where ψ[T] is zero time at temperature T.

[0048] Step 22: Test the relaxation modulus of the non-metallic material of the fiber optic ring at different temperatures, obtain the master curve at the reference temperature point, and fit it into a multi-order Prony series.

[0049] The relaxation modulus of the nonmetallic fiber optic ring material at different temperatures was measured using a DMA thermomechanical analyzer. The master curve at the reference temperature was obtained using the time-temperature equivalence principle and fitted with a multi-order Prony series, which can be expressed as:

[0050]

[0051] In the formula, E(t) is the modulus at time t under the reference temperature, E0 is the constant term in the Prony series, and E i and τ i Let n be the relaxation modulus and relaxation time corresponding to the i-th Maxwell model, and n be the order of the Prony series.

[0052] In this embodiment, considering the actual service environment temperature of the fiber optic gyroscope fiber optic ring, the isothermal relaxation modulus of four non-metallic materials of the fiber optic ring at -55℃, -35℃, -15℃, 0℃, 20℃, 40℃, 60℃, and 85℃ was tested using a DMA thermomechanical analyzer. Some measurement results are shown below. Figure 2 As shown in (a) to (d), the master curves of relaxation modulus at different reference temperatures were obtained using the time-temperature equivalence principle and fitted into multi-order Prony series. The master curves of relaxation modulus for the outer coating and the wrap-around adhesive are as follows:

[0053] (1) Master curve of relaxation modulus of outer coating at reference temperature:

[0054]

[0055] (2) Master curve of relaxation modulus of the wrapping rubber at reference temperature:

[0056]

[0057] Step 23: Combine the specific non-metallic materials used in the actual production of the fiber optic gyroscope fiber optic ring, and test its parameters according to relevant testing standards to construct a finite element model corresponding to the parameters.

[0058] Based on the specific non-metallic materials used in the actual production of fiber optic gyroscope fiber optic rings, the Poisson's ratio and coefficient of thermal expansion of the non-metallic materials were tested using a high and low temperature universal testing machine and a thermomechanical analyzer, respectively. The test results are shown in Table 1 and Table 2.

[0059] Table 1 Summary of Poisson's Ratio Test Results for Non-metallic Materials in Fiber Optic Gyroscope Fiber Rings

[0060]

[0061] Table 2 Summary of Test Results for Thermal Expansion Coefficient of Non-metallic Materials in Fiber Optic Gyroscope Fiber Optic Ring

[0062]

[0063] Step 3: Based on the actual service environment temperature, set a temperature load consistent with the service environment, assign material property parameters, write and call the UMAT subroutine of the non-metallic viscoelastic constitutive equation, and perform simulation analysis on the fiber ring creep characteristics.

[0064] Based on the actual service conditions of the fiber optic gyroscope's fiber optic ring, its service environment temperature is -55 to 85℃. Consistent temperature load conditions are set in the finite element simulation model, such as... Figure 3 As shown. The relaxation modulus, Poisson's ratio, and coefficient of thermal expansion, as tested in step 2, are assigned parameters. A program is written based on the FORTRAN programming language to derive the viscoelastic constitutive equation of the non-metallic fiber ring derived in step 2. The ABAQUS finite element software is then used to call this program to simulate and analyze the creep characteristics of the fiber ring under temperature load conditions. The stress and strain variations at the fiber core with temperature and time are extracted and compared with the properties of linear elastic materials, such as... Figure 4 , Figure 5 As shown.

[0065] Step 4: Post-process and analyze the finite element simulation results, select the names of the non-metallic materials that are most critical to fiber ring creep, and summarize their influence laws.

[0066] In the actual production and performance evaluation of fiber optic gyroscopes, the high-temperature isothermal section of the fiber optic ring ( Figure 3 The displacement change of segment AB in the fiber core characterizes the product's stability performance and is one of the important indicators for evaluating the product's temperature performance. Therefore, when processing the simulation results, the focus is on analyzing the displacement change of segment AB of the fiber core during temperature cycling (referred to as creep, the same throughout). Based on the digital simulation model of the fiber ring, multiple sets of modeling simulations were conducted by changing the modulus parameters of different non-metallic materials. The names of the non-metallic materials that have the most critical impact on creep were identified, and the analysis results are as follows: Figure 6 As shown in (a) to (d).

[0067] In this embodiment, analysis of the data in the figure reveals that: (1) the modulus of the inner coating has the greatest impact on the displacement change of the high-temperature isothermal section of the optical fiber ring, followed by the outer coating and the wrapping adhesive, while the adhesive has the least impact; (2) reducing the modulus of the inner coating, increasing the modulus of the outer coating, and increasing the modulus of the wrapping adhesive are all beneficial to reducing the displacement change of the high-temperature isothermal section and improving product stability. Furthermore, since the inner coating has the most significant impact on displacement change, the preparation process and storage environment of the inner coating should be strictly controlled to improve product performance and consistency.

[0068] The above are merely specific steps of the present invention and do not constitute any limitation on the scope of protection of the present invention; all technical solutions formed by equivalent transformation or equivalent substitution fall within the scope of protection of the present invention; the parts of the present invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A numerical model-based non-metallic material parameter analysis method for fiber-optic gyroscope, characterized in that, The method for analyzing the non-metallic material parameters of fiber optic gyroscopes based on numerical models includes the following steps: Step 1: Construct a finite element analysis model with the same dimensions as the actual fiber optic gyroscope fiber optic ring structure used in production; Step 2: Establish the thermoviscoelastic constitutive equation of the non-metallic material of the fiber optic gyroscope ring based on the finite element analysis model and test the relevant non-metallic material parameters; Step 3: Based on the actual service environment temperature, set a temperature load consistent with the service environment, assign non-metallic material property parameters to the fiber optic gyroscope fiber ring, write and call the non-metallic material thermoviscoelastic constitutive equation subroutine, and perform simulation analysis on the fiber ring creep characteristics in the finite element simulation model. Step 4: Post-process and analyze the finite element simulation results, screen out the names of the non-metallic materials that are most critical to fiber ring creep, and summarize their influence laws. Step 2 also includes the following steps: Step 21: Based on the actual service environment of the fiber optic gyroscope, derive the thermoviscoelastic constitutive equation of the non-metallic material of the fiber optic ring considering temperature and time factors. Step 22: Test the relaxation modulus of the non-metallic material of the fiber optic ring at different temperatures, obtain the master curve at the reference temperature point, and fit it into a multi-order Prony series. Step 23: Combine the non-metallic materials of the fiber optic gyroscope fiber ring structure and test their Poisson's ratio and coefficient of thermal expansion. In step 21, the thermoviscoelastic constitutive equation for nonmetallic materials is: ； In the formula, Represents the stress tensor. Represents the stress deviatoric tensor; Represents the Kronecker symbol, and hour, ; hour, ; Represents the stress sphere tensor. Represents Poisson's ratio. Indicates relaxation modulus. Represents the strain deviator tensor. Represents the strain sphere tensor. Indicates the coefficient of thermal expansion. It is the temperature difference between the real-time ambient temperature and the reference temperature. Indicates time, Represents the time integral variable, Indicates the conversion time. It can be written as: ； In the formula, express Time-temperature equivalence factor at temperature, For temperature Zero time below; In step 22, the master curve at the reference temperature point is obtained and fitted into a multi-order Prony series as follows: ； In the formula, At reference temperature Modulus at time, For the constant term in the Prony series, and For the first Each Maxwell model corresponds to a relaxation modulus and relaxation time. Let be the order of the Prony series.

2. The method for analyzing non-metallic material parameters of fiber optic gyroscopes based on numerical models according to claim 1, characterized in that, In step 1, the finite element analysis model applies constraints to the inner coating, outer coating, wrapping adhesive, and bonding adhesive structure of the fiber optic ring and performs mesh generation, with a minimum mesh size of 0.02 mm.

3. The method for analyzing non-metallic material parameters of fiber optic gyroscopes based on numerical models according to claim 1, characterized in that, In step 3, the temperature load conditions of the finite element model are set to be consistent with the actual service conditions of the fiber optic gyroscope fiber optic ring. The fiber optic gyroscope is assigned non-metallic material property parameters to the fiber optic ring. A user subroutine is written for the viscoelastic constitutive equation of the non-metallic material of the fiber optic ring. The subroutine is then called through finite element software to simulate and analyze the creep characteristics of the fiber optic ring under temperature load conditions.

4. The method for analyzing non-metallic material parameters of fiber optic gyroscopes based on numerical models according to claim 1, characterized in that, In step 4, based on the creep of the fiber core position in the high-temperature isothermal section of the fiber ring in the temperature cycle of the fiber ring digital simulation model, multiple sets of modeling simulations are carried out by changing the modulus parameters of different non-metallic materials to screen out the names of non-metallic materials that have the most critical impact on creep.

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