Method for generating numerical value of color response database of shear-sensitive liquid crystal coating

Abstract

The invention discloses a numerical generation method for a color response database of a shear-sensitive liquid crystal coating, which belongs to the field of experimental aerodynamics and comprises the following steps of: 1, establishing a stress response model of a shear-sensitive liquid crystal coating structure; 2, establishing an optical response model of the shear sensitive liquid crystal coating; 3, calibrating a color response model of the shear-sensitive liquid crystal coating; and 4, constructing a shear sensitive liquid crystal color response database. According to the method, the structural stress response model and the optical response model of the SSLC coating are established and calibrated, so that rapid numerical prediction and database construction of the color response of the coating are realized. Based on the database, reliable training and calibration data can be provided for an intelligent algorithm, so that the experimental data acquisition cost is reduced, the applicability and popularization value of an SSLC measurement technology are improved, and application of the SSLC measurement technology in the fields of boundary layer research, flow control and the like is promoted.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of experimental aerodynamics, and provides a method for generating color response data of a shear-sensitive liquid crystal coating, which is used for calibrating the color of the coating and realizing fine measurement of the wall friction field. BACKGROUND

[0002] In experimental aerodynamics research, the friction between the airflow and the solid wall is a crucial parameter. Through accurate measurement of the wall friction field, a large amount of key flow information can be obtained, which is of great significance to the development of boundary layer theory, boundary layer transition and control, vortex structure evolution analysis, flow control effect evaluation, computational fluid dynamics (CFD) software verification, and aircraft drag reduction design.

[0003] Shear-sensitive liquid crystal (SSLC) coating measurement technology is a method that can realize visualization and quantitative measurement of the wall friction field. This method usually coats SSLC on the wall to be measured. When the coating is subjected to shear force, the molecular orientation changes, and specific color responses are presented in different directions. Through processing of the color distribution and change law of the coating, the vector field of the surface friction can be obtained. However, the practical application of SSLC measurement technology still faces the bottleneck of complex calibration process. Early calibration methods are mostly based on Gaussian curve fitting or its extended form, which has strict requirements for light conditions and camera observation angles, limiting its popularization in wind tunnel experiments. In recent years, machine learning methods have been introduced into SSLC calibration research, which can alleviate the dependence on experimental conditions to a certain extent. However, this method often requires a large amount of experimental data for training, and the color response mechanism of SSLC coating is complex, making it difficult to use measurement data from different experimental scenarios, resulting in high data collection costs and insufficient adaptability.

[0004] Therefore, there is an urgent need for a SSLC coating color database generation method that can combine experimental scenarios, reduce data collection difficulty, and improve calibration versatility, to promote the application and development of this technology in experimental aerodynamics. SUMMARY

[0005] This invention aims to propose a numerical simulation-based method for generating a color database of shear-sensitive liquid crystal (SSLC) coatings, enabling efficient and accurate acquisition of the color response of SSLC coatings under wall friction. The method establishes and calibrates structural stress response and optical response models of the SSLC coating, achieving rapid numerical prediction of the coating's color response and database construction. Based on this database, reliable training and calibration data can be provided for intelligent algorithms, thereby reducing experimental data acquisition costs, enhancing the applicability and promotional value of SSLC measurement technology, and promoting its application in boundary layer research, flow control, and other fields.

[0006] This invention is implemented as follows:

[0007] A method for generating numerical values ​​for a color response database of a shear-sensitive liquid crystal coating, characterized in that the method comprises:

[0008] Step 1: Establish a stress response model for the shear-sensitive liquid crystal coating structure;

[0009] Step 2: Establish an optical response model for the shear-sensitive liquid crystal coating;

[0010] Step 3: Calibrate the color response model of the shear-sensitive liquid crystal coating;

[0011] Step 4: Construct a shear-sensitive liquid crystal color response database.

[0012] Furthermore, step 1 establishes a deformation model of the SSLC coating under shear stress using a dual-model framework, specifically as follows:

[0013] The first model treats the spiral structural unit of the SSLC coating as a micro-elastomer (the axial dimension of the spiral structure is about 450 nm), and assumes that within a small deformation range, the tilting effect of the spiral axis and the pitch compression effect dominate the structural response.

[0014] Based on this, axial and transverse stress-strain relationship models of helical structures can be constructed; an elastic deformation model of a helical structure unit: transverse deformation is mainly manifested as the tilting of the helical axis of the helical structure unit, and axial deformation is mainly manifested as the change of the axis spacing of the helical structure.

[0015] Lateral elastic deformation is

[0016]

[0017] Axial elastic deformation is

[0018]

[0019] In the formula: τ is the wall friction force, ε ⊥ and ε ||E represents the transverse and axial elastic strains of the SSLC-coated spiral structural unit, respectively. ⊥ and E || These are the transverse and axial elastic moduli, respectively;

[0020] The second model relies on Frank's elasticity theory, establishing an expression for the free energy density of a continuous medium. It integrates torsional, twisting, and bending elastic terms, and uses finite element simulation to model deformations such as helical axis tilting and pitch changes induced by shear stress. Frank's elasticity theory is a classic method for describing the elastic deformation of cholesteric liquid crystal structures, encompassing three deformation modes: twisting, twisting, and bending, and considering the natural helical twisting characteristics. This is expressed as...

[0021]

[0022] In the formula: n is the vector describing the average orientation of liquid crystal molecules, which is the normalized vector (||n||=1); K is the spatial gradient operator, used to describe the spatial variation of the vector field; 11 K 22 K 33 q0 = 2π / P0 is the elastic constant for twisting, bending, and rotation, respectively, describing the liquid crystal's resistance to the corresponding deformations; q0 = 2π / P0 is the natural twist wave vector, determined by the pitch P0 of the cholesteric liquid crystal's helical structure; F d This is the elastic free energy density per unit volume; this expression is used to describe the energy change of the macroscopic arrangement of liquid crystal molecules, rather than the deformation of the internal structure of a single molecule. Its core function is to quantify the energy cost required when the molecular arrangement of liquid crystal deviates from its natural helical structure under external conditions, thereby revealing its mechanical response and stability.

[0023] Furthermore, step 2 specifically includes:

[0024] Based on the stress response model of the SSLC coating structure, a model describing the optical response of the cholesteric liquid crystal is established. This model, based on the Bragg reflection condition and liquid crystal birefringence theory, considers the effects of pitch variation, molecular orientation distribution, and light incident angle on the reflection wavelength and intensity, and can predict the color change of the coating under different frictional forces. The output of the SSLC coating optical model is the reflection spectrum distribution and RGB colors under the corresponding frictional conditions. The central reflection wavelength of the cholesteric liquid crystal satisfies the Bragg condition.

[0025] λ=nPcosθ (9)

[0026] In the formula: λ is the center wavelength of the reflected light; n is the effective refractive index of the liquid crystal; P is the pitch of the cholesteric liquid crystal; θ is the angle between the incident light and the helical axis; under the action of external shear stress, the structure of the SSLC coating is deformed, the pitch P and the orientation angle θ change, thereby causing changes in the reflection spectrum and color;

[0027] To achieve the conversion from optical response to visible color, a three-color mapping model is further introduced; assuming the reflectance spectral distribution is I(λ), the three primary color components can be expressed as:

[0028]

[0029] In the formula: S r (λ),S g (λ),S b (λ) represents the red, green, and blue sensitivity functions of the human visual system or camera sensor, respectively; R, G, and B are the corresponding three-channel color values; based on this, a mapping relationship between the friction vector and the RGB colors of the SSLC coating can be established, providing a theoretical basis for subsequent database generation.

[0030] Furthermore, step 2 is a basic model describing the optical properties of cholesteric liquid crystals. The actual optical response model is more complex and can usually be solved using numerical methods.

[0031] Furthermore, step 3 specifically includes:

[0032] 3.1: Calibration of the optical response model of the SSLC coating under conditions of no shear stress;

[0033] First, the optical response model of the SSLC coating was calibrated under conditions without shear stress to ensure its effectiveness and reliability. The color of the SSLC coating was collected for calibration of the numerical simulation model. During calibration, the SSLC coating parameters that needed attention included: pitch P0, effective refractive index n, birefringence Δn, chiral torsional strength (a parameter related to the doping ratio or helical wave vector), coating thickness d, and coating viscosity μ. By comparing the experimentally measured spectral data with the model simulation results, the above parameters were corrected to ensure the effectiveness and feasibility of the optical model under the basic conditions, laying the foundation for subsequent simulations and database generation under shear stress conditions.

[0034] After completing the calibration under normal light illumination, the light direction can be adjusted from the normal direction to the tilt direction to verify the correctness of the optical response model established under tilted light illumination.

[0035] 3.2: Calibration of the optical response model of SSLC coating under shear stress;

[0036] After calibrating the optical model under no shear stress conditions, the optical response model is further calibrated under shear stress conditions to achieve comprehensive verification of the SSLC coating color numerical model. Since the deformation of the SSLC coating spiral structure is independent of external factors such as the illumination direction (including two degrees of freedom), the observation direction (including two degrees of freedom), and the wall bending direction, the stress response model of the SSLC coating spiral structure is calibrated under normal illumination and planar wall conditions. When the error of the SSLC coating optical response model is negligible, calibrating the SSLC coating color response model under specific experimental conditions can indirectly complete the calibration of the SSLC coating spiral structure stress response model.

[0037] Furthermore, in the experimental setup, the camera or spectrometer observes from multiple uniformly distributed circumferential directions and can adjust the downward viewing angle; during the experiment, a point on the symmetry line of the platform surface is selected as a calibration point, and the direction of frictional force along the symmetry line is determined based on the flow symmetry.

[0038] The calibration steps are as follows: First, the friction force at the calibration point on the plate is measured using a friction sensor; second, the multi-directional spectral response characteristics of the SSLC coating under the action of the friction force are measured using a camera or spectrometer; then, the spectral characteristics under different viewing directions are obtained by adjusting the top angle; the friction force is adjusted by changing the airflow speed, and the above measurements are repeated to obtain the multi-directional optical response characteristics of the SSLC coating under different friction forces.

[0039] The experimental data were fitted to reduce optical measurement errors. Based on the denoised data, the structural stress response model and its parameters in the SSLC coating color response model were adjusted to ensure that the numerical simulation results were highly consistent with the experimental measurement results, thereby completing the calibration of the SSLC coating structural deformation model and its parameters.

[0040] Furthermore, step 4 specifically includes:

[0041] After calibrating the SSLC coating color response model, numerical simulations can be performed based on this model to generate a color database of the SSLC coating under frictional force, thereby obtaining the color of the SSLC coating as a function of the magnitude τ and direction φ of the frictional force. τ The angle of view α of the direction of light illumination C and circumferential angle φ C The downward angle α of the observation direction C and circumferential angle φ C The variation characteristics of the parameters are denoted as Color(τ,φ). τ ,α L ,φ L ,α C ,φ C );

[0042] For curved walls, in order to eliminate the influence of changes in the wall normal direction, the direction of light illumination and the direction of camera observation are both defined relative to the local normal of the wall, which can reduce the dimensionality and complexity of the data.

[0043] In wind tunnel experiments, due to the limitations of the observation window, the color of the SSLC coating can only be observed from specific directions. Therefore, it is only necessary to generate a color database of the SSLC coating in these specific observation directions for research. The specific method is as follows: First, according to the specific experimental scenario, set the light illumination direction and several observation directions (selected flexibly according to the specific scenario); then, based on the SSLC coating color response model, generate the colors displayed by the SSLC coating in these selected observation directions under the action of frictional forces of different magnitudes and directions.

[0044] Furthermore, based on a sufficiently large and representative database, the intelligent algorithm can establish a precise mapping relationship between the color of the SSLC coating and the friction vector through efficient training on the data. Using this mapping model, the wall friction field can be quickly and accurately inverted solely based on the color distribution of the SSLC coating without the need for complex experimental calibration. This significantly improves measurement efficiency, reduces experimental complexity, and promotes the application and widespread adoption of SSLC coating technology in high-precision aerodynamic measurements. In addition, based on the established numerical model, the color response characteristics of the SSLC coating can be studied through numerical simulation. In particular, research on the mechanism of the effect of the mechanical-optical coupling on the color response of the SSLC coating not only helps to deepen the understanding of its physical nature but also provides theoretical support and guidance for the optimized design and application of this technology.

[0045] The advantages of this invention compared to the prior art are as follows:

[0046] This invention establishes a numerical simulation model of the color response of SSLC coatings. By calibrating the fundamental issue of the helical structure deformation of SSLC coatings under shear stress, it effectively avoids interference from external factors such as light direction and observation direction, significantly reducing calibration difficulty and improving model versatility. Based on the calibrated SSLC coating color response model, a color response database of SSLC coatings under the action of frictional force vector is generated in combination with the optical path conditions required by specific experimental scenarios, overcoming the technical bottleneck of the high difficulty and cost of obtaining SSLC coating color databases through experiments. This method can effectively reduce the calibration difficulty of SSLC coating measurement technology and promote the widespread application of this measurement technology in aerodynamic experiments. Attached Figure Description

[0047] Figure 1 Methods for constructing color response models for SSLC coatings;

[0048] Figure 2 This is a schematic diagram of the elastic response model of an SSLC-coated spiral structure under shear stress.

[0049] Figure 3 Schematic diagram of the SSLC coating color response model calibration device (normal light illumination);

[0050] Figure 4 A method for generating numerical values ​​for the SSLC coating color response database;

[0051] Figure 5 A schematic diagram illustrating the mapping relationship between SSLC coating color and friction for machine learning algorithms;

[0052] Figure 6 An example of the wall tangential jet friction field calculated by a machine learning algorithm. Detailed Implementation

[0053] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the following examples provide a more detailed description of the invention. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. Figure 1 As shown, this invention establishes a numerical simulation model of the color response characteristics of SSLC coating under friction.

[0054] Step 1: Establish a stress response model for the shear-sensitive liquid crystal coating structure.

[0055] The SSLC coating is composed of cholesteric liquid crystal (chiral nematic liquid crystal), whose molecules are periodically arranged along the helical axis to form a helical structure. Chirality determines the direction of helical rotation (left-handed or right-handed), while the pitch (P), as a key parameter, characterizes the axial distance required for the molecule to complete a 360° helical rotation. Its scale matches the wavelength of visible light, equivalent to one optical lattice period, thus exhibiting active optical properties. Under shear stress, the cholesteric liquid crystal mainly undergoes physical changes in molecular orientation and topology, without chemical bond breakage or recombination. This patent establishes a deformation model of the SSLC coating under shear stress using a dual-model framework.

[0056] The first model treats the helical structural unit of the SSLC coating as a micro-elastic body (the axial dimension of the helical structure is approximately 450 nm), and assumes that within a small deformation range, the tilting effect of the helical axis and the pitch compression effect dominate the structural response. Based on this, axial and transverse stress-strain relationship models of the helical structure can be constructed. Figure 2 A schematic diagram of an elastic deformation model for a helical structural unit is given. Lateral deformation is mainly manifested as the tilting of the helical axis of the helical structural unit, while axial deformation is mainly manifested as a change in the wheelbase of the helical structure.

[0057] Lateral elastic deformation is

[0058]

[0059] Axial elastic deformation is

[0060]

[0061] In equations (1) and (2), τ is the wall friction force, and ε ⊥ and ε || E represents the transverse and axial elastic strains of the SSLC-coated spiral structural unit, respectively. ⊥ and E || These are the transverse and axial elastic moduli, respectively.

[0062] The second model relies on Frank's elasticity theory, establishing an expression for the free energy density of a continuous medium. It integrates torsional, twisting, and bending elastic terms, and uses finite element simulation to model deformations such as helical axis tilting and pitch changes induced by shear stress. Frank's elasticity theory is a classic method for describing the elastic deformation of cholesteric liquid crystal structures, encompassing three deformation modes: twisting, twisting, and bending, and considering the natural helical twisting characteristics. Specifically, it is expressed as follows:

[0063]

[0064] In the formula: n is the vector describing the average orientation of liquid crystal molecules, which is the normalized vector (||n||2=1); K is the spatial gradient operator, used to describe the spatial variation of the vector field; 11 K 22 K 33 q0 = 2π / P0 is the elastic constant for twisting, bending, and rotation, respectively, describing the liquid crystal's resistance to the corresponding deformations; q0 = 2π / P0 is the natural twist wave vector, determined by the pitch P0 of the cholesteric liquid crystal's helical structure; F d This represents the elastic free energy density per unit volume. This expression describes the energy change in the macroscopic arrangement of liquid crystal molecules, rather than the deformation of the internal structure of a single molecule. Its core function is to quantify the energy cost required for the molecular arrangement of liquid crystals to deviate from their natural helical structure under external conditions (mechanical stress, electric field, etc.), thereby revealing their mechanical response and stability.

[0065] The first model requires less computation but has lower accuracy, while the second model is more accurate but requires more computation.

[0066] Step 2: Establish an optical response model for shear-sensitive liquid crystal coatings.

[0067] Based on the stress response model of the SSLC coating structure, a model describing the optical response of the cholesteric liquid crystal is established. This model, based on the Bragg reflection condition and liquid crystal birefringence theory, considers the effects of pitch variation, molecular orientation distribution, and light incident angle on the reflection wavelength and intensity, and can predict the color change of the coating under different frictional forces. The output of the SSLC coating optical model is the reflection spectrum distribution and RGB colors under the corresponding frictional conditions. The central reflection wavelength of the cholesteric liquid crystal satisfies the Bragg condition.

[0068] λ=nPcosθ (4)

[0069] In the formula: λ is the center wavelength of the reflected light; n is the effective refractive index of the liquid crystal; P is the pitch of the cholesteric liquid crystal; θ is the angle between the incident light and the helical axis. Under external shear stress, the structure of the SSLC coating deforms, and the pitch P and orientation angle θ change, thereby causing changes in the reflection spectrum and color.

[0070] To achieve the conversion from optical response to visible color, this invention further introduces a three-color mapping model. Let the reflectance spectral distribution be I(λ), then the three primary color components can be expressed as:

[0071]

[0072] In the formula: S r (λ),S g (λ),S b (λ) represents the red, green, and blue sensitivity functions of the human visual system or camera sensor, respectively; R, G, and B are the corresponding three-channel color values. Based on this, a mapping relationship between the friction vector and the RGB colors of the SSLC coating can be established, providing a theoretical basis for subsequent database generation.

[0073] The above is only a basic model describing the optical properties of cholesteric liquid crystals. Actual models are much more complex and usually require numerical methods (such as custom-written programs or finite element-based software like COMSOL Multiphysics) for solving. Currently, numerical simulation techniques for the optical properties of cholesteric liquid crystals are relatively mature, and published literature shows that the spectral distributions obtained from numerical simulations are in excellent agreement with experimental measurements.

[0074] Step 3: Calibrate the color response model of the shear-sensitive liquid crystal coating.

[0075] (1) Calibration of the optical response model of SSLC coating under the condition of no shear stress

[0076] Currently, mathematical modeling and numerical simulation techniques for the optical properties of cholesteric liquid crystals are relatively mature, and the accuracy of related numerical simulation methods has been rigorously verified through numerous studies. Nevertheless, it is still necessary to calibrate key parameters to reduce optical model deviations caused by improper parameter settings.

[0077] Since the optical response model of the SSLC coating is the same under both shear stress and non-shear stress conditions, this patent first calibrates the optical response model of the SSLC coating under non-shear stress conditions to verify the effectiveness and reliability of the established optical model, thus reducing calibration difficulty. For planar walls, the following approach is adopted... Figure 3 The experimental setup shown collects the color of the SSLC coating for calibration (airflow off). During calibration, the SSLC coating parameters that need attention include: pitch P0, effective refractive index n, birefringence Δn, chiral torsional strength (a parameter related to the doping ratio or helical wave vector), coating thickness d, and viscosity μ. The experimentally measured spectral data are compared with the numerical simulation results to confirm the correctness of these parameter settings (if inconsistent, the model and parameters are improved), ensuring the effectiveness and feasibility of the established optical response model under the basic conditions, laying the foundation for subsequent simulations under shear stress conditions and database generation.

[0078] After completing the calibration under normal light illumination, the light direction is adjusted from the normal direction to the tilt direction. Typical tilt angles relative to the wall normal can be 75°, 60°, 45°, and 30°. The calibration process is repeated, and the correctness of the optical model under tilted light illumination is verified by comparing the simulation results and the colors captured by the camera.

[0079] (2) Calibration of the optical response model of SSLC coating under shear stress

[0080] After calibrating the optical model under no-shear stress conditions, the optical response model is further calibrated under shear stress conditions to achieve comprehensive verification of the numerical color model of the SSLC coating. Since the stress-deformation of the SSLC coating spiral structure is independent of external factors such as the illumination direction (including two degrees of freedom), the observation direction (including two degrees of freedom), and the wall bending direction, this invention calibrates the stress response model of the SSLC coating spiral structure under normal illumination and planar wall conditions for ease of calibration. When the error of the SSLC coating optical property model is negligible, calibrating the SSLC coating color response model under specific experimental conditions can indirectly complete the calibration of the stress response model of the SSLC coating spiral structure.

[0081] This patent adopts Figure 3The experimental setup shown allows for observation from six uniformly distributed circumferential directions using a camera or spectrometer, with an adjustable top-down viewing angle. During the experiment, a point on the symmetry line of the platform surface is selected as a calibration point, and the direction of the frictional force is determined to be along the symmetry line based on symmetry. The calibration steps are as follows: First, the magnitude of the frictional force at the calibration point on the plate is measured using a MEMS friction sensor; second, the multi-directional spectral response characteristics of the SSLC coating under this frictional force are measured using a camera or spectrometer; subsequently, the spectral characteristics under different viewing directions are obtained by adjusting the top-down viewing angle. By changing the airflow speed to adjust the magnitude of the frictional force and repeating the above measurements, the multi-directional optical response characteristics of the SSLC coating under different frictional forces are obtained. The experimental data is fitted to reduce optical measurement errors. Then, based on the denoised data, the structural stress response model and its parameters in the SSLC coating color response model are adjusted to ensure a high degree of consistency between the numerical simulation results and the experimental measurement results, thus completing the calibration of the SSLC coating structural deformation model and its parameters.

[0082] Step 4: Construct a shear-sensitive liquid crystal color response database.

[0083] After calibrating the SSLC coating color response model, numerical simulations can be performed based on this model to generate a color database of the SSLC coating under frictional force, thereby obtaining the color of the SSLC coating as a function of the magnitude τ and direction φ of the frictional force. τ The angle of view α of the direction of light illumination C and circumferential angle φ C The downward angle α of the observation direction C and circumferential angle φ C The changing characteristics are denoted as Color(τ,φ). τ ,α L ,φ L ,α C ,φ C To eliminate the influence of changes in the wall normal direction, both the illumination direction and the observation direction are defined relative to the wall normal.

[0084] In wind tunnel experiments, due to the limitations of the observation window, the color of the SSLC coating can only be observed from specific directions. Therefore, it is only necessary to generate a color database of the SSLC coating in these specific observation directions for research purposes. Figure 4 The specific method is illustrated as follows: First, based on the specific experimental scenario, set the direction of light illumination and several observation directions (select flexibly according to the specific scenario). Assume the direction of light illumination is α. L ,φ L Several observation directions were selected as α Ci ,φ CiThen, based on the numerical model of the SSLC coating color response, the colors displayed by the SSLC coating under frictional forces of different magnitudes and directions are generated in these selected observation directions. Compared to obtaining color information through experimental measurements, generating a color database based on the calibrated SSLC coating color response model can significantly reduce the difficulty of data acquisition, improve measurement efficiency, and effectively reduce measurement costs.

[0085] This invention presents a numerical method for generating color response samples of SSLC coatings. By generating a sufficiently large and representative database, it provides reliable training data support for intelligent algorithms such as machine learning. Based on this database, intelligent algorithms can learn and establish the mapping relationship between the color displayed by the SSLC coating and the friction force vector in different observation directions, such as... Figure 5 As shown. Based on this mapping relationship, the frictional force field of the wall surface can be quickly and accurately inverted simply by relying on the color distribution of the SSLC coating in different observation directions, without the need for complex experimental calibration. Figure 6 An example of the wall tangential jet friction field calculated by a machine learning algorithm trained on a color response database is presented. This demonstrates that the sample generation method proposed in this invention can significantly improve the efficiency and practicality of wall friction vector field measurement, and provides strong support for the widespread application of SSLC coating technology in high-precision aerodynamic measurements.

[0086] Furthermore, based on the established model, the color response characteristics of the SSLC coating can be studied through numerical simulation. For example, the effects of factors such as friction, illumination direction, observation direction, coating thickness, and viscosity, and their coupling effects on the coating color, can be analyzed to reveal the underlying laws. In particular, studying the mechanism of the mechanical-optical coupling effect on the color response of the SSLC coating not only helps to deepen the understanding of its physical nature but also provides theoretical support and guidance for the optimized design and application promotion of this technology.

[0087] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for generating numerical values ​​for a color response database of a shear-sensitive liquid crystal coating, characterized in that, The method is as follows: Step 1: Establish a stress response model for the shear-sensitive liquid crystal coating structure; Step 2: Establish an optical response model for the shear-sensitive liquid crystal coating; Step 3: Calibrate the color response model of the shear-sensitive liquid crystal coating; Step 4: Construct a shear-sensitive liquid crystal color response database.

2. The method for generating a color response database of a shear-sensitive liquid crystal coating according to claim 1, characterized in that, Step 1, which establishes a deformation model of the SSLC coating under shear stress using a dual-model framework, specifically involves: The first model treats the spiral structural unit of the SSLC coating as a micro-elastic body and assumes that within a small deformation range, the tilting effect of the spiral shaft and the pitch compression effect dominate the structural response. Based on this, axial and transverse stress-strain relationship models of helical structures can be constructed; an elastic deformation model of a helical structure unit: transverse deformation is mainly manifested as the tilting of the helical axis of the helical structure unit, and axial deformation is mainly manifested as the change of the axis spacing of the helical structure. Lateral elastic deformation is Axial elastic deformation is In the formula: τ is the wall friction force, ε ⊥ and ε || E represents the transverse and axial elastic strains of the SSLC-coated spiral structural unit, respectively. ⊥ and E || These are the transverse and axial elastic moduli, respectively; The second model relies on Frank's elasticity theory, establishing an expression for the free energy density of a continuous medium. It integrates torsional, twisting, and bending elastic terms, and uses finite element simulation to model the deformation caused by shear stress-induced helical axis tilting and pitch variation. Frank's elasticity theory is a classic method for describing the elastic deformation of cholesteric liquid crystal structures, encompassing three deformation modes: twisting, twisting, and bending, and considering the natural helical twisting characteristics. This is expressed as... In the formula: n is the vector describing the average orientation of liquid crystal molecules, which is the normalized vector (||n||=1); K is the spatial gradient operator, used to describe the spatial variation of the vector field; 11 K 22 K 33 q0 = 2π / P0 is the elastic constant for twisting, bending, and rotation, respectively, describing the liquid crystal's resistance to the corresponding deformations; q0 = 2π / P0 is the natural twist wave vector, determined by the pitch P0 of the cholesteric liquid crystal's helical structure; F d This is the elastic free energy density per unit volume; this expression is used to describe the energy change of the macroscopic arrangement of liquid crystal molecules, rather than the deformation of the internal structure of a single molecule. Its core function is to quantify the energy cost required when the molecular arrangement of liquid crystal deviates from its natural helical structure under external conditions, thereby revealing its mechanical response and stability.

3. The method for generating a color response database of a shear-sensitive liquid crystal coating according to claim 1, characterized in that, Step 2 specifically refers to: Based on the stress response model of the SSLC coating structure, a model describing the optical response of cholesteric liquid crystal is established. This model is based on the Bragg reflection condition and the theory of liquid crystal birefringence, and considers the effects of pitch change, molecular orientation distribution and light incident angle on reflection wavelength and reflection intensity. It can predict the color change of the coating under different friction forces. The output of the SSLC coating optical model is the reflection spectrum distribution and RGB colors under the corresponding friction conditions; the central reflection wavelength of the cholesteric liquid crystal satisfies the Bragg condition. λ=nPcosθ (4) In the formula: λ is the center wavelength of the reflected light; n is the effective refractive index of the liquid crystal; P is the pitch of the cholesteric liquid crystal; θ is the angle between the incident light and the helical axis; under the action of external shear stress, the structure of the SSLC coating is deformed, the pitch P and the orientation angle θ change, thereby causing changes in the reflection spectrum and color; To achieve the conversion from optical response to visible color, a three-color mapping model is further introduced; assuming the reflectance spectral distribution is I(λ), the three primary color components can be expressed as: In the formula: S r (λ),S g (λ),S b (λ) represents the red, green, and blue sensitivity functions of the human visual system or camera sensor, respectively; R, G, and B are the corresponding three-channel color values; based on this, a mapping relationship between the friction vector and the RGB colors of the SSLC coating can be established, providing a theoretical basis for subsequent database generation.

4. The method for generating a color response database of a shear-sensitive liquid crystal coating according to claim 1, characterized in that, Step 2 is a basic model describing the optical properties of cholesteric liquid crystals. The actual optical response model is more complex and can usually be solved using numerical methods.

5. The method for generating a color response database of a shear-sensitive liquid crystal coating according to claim 1, characterized in that, Step 3 specifically includes: 3.1: Calibration of the optical response model of the SSLC coating under conditions of no shear stress; First, the optical response model of the SSLC coating is calibrated under conditions free from shear stress to ensure the effectiveness and reliability of the model. The color of the SSLC coating was collected for calibration of the numerical simulation model; During calibration, the SSLC coating parameters that need to be considered include: pitch P0, effective refractive index n, birefringence Δn, chiral torsional strength, coating thickness d, and coating viscosity μ. By comparing the experimentally measured spectral data with the model simulation results, the above parameters are corrected to ensure the effectiveness and feasibility of the optical model under the basic conditions, laying the foundation for subsequent simulation and database generation under shear stress conditions. After completing the calibration under normal light illumination, the light direction can be adjusted from the normal direction to the tilt direction to verify the correctness of the optical response model established under tilted light illumination. 3.2: Calibration of the optical response model of SSLC coating under shear stress; After calibrating the optical model under no shear stress conditions, the optical response model is further calibrated under shear stress conditions to achieve comprehensive verification of the numerical color model of the SSLC coating. Since the deformation of the SSLC coating spiral structure is independent of external factors such as the direction of illumination (including two degrees of freedom), the direction of observation (including two degrees of freedom), and the direction of wall bending, the stress response model of the SSLC coating spiral structure is calibrated under normal illumination and planar wall conditions. When the error of the SSLC coating optical response model is negligible, calibrating the SSLC coating color response model under specific experimental conditions can indirectly complete the calibration of the stress response model of the SSLC coating spiral structure.

6. The method for generating a color response database of a shear-sensitive liquid crystal coating according to claim 5, characterized in that, In the experimental setup used, the camera or spectrometer observes from multiple uniformly distributed circumferential directions and can adjust the top-down angle; during the experiment, a point on the symmetry line of the platform surface is selected as a calibration point, and the direction of frictional force along the symmetry line is determined based on the flow symmetry. The calibration steps are as follows: First, the magnitude of the friction force at the calibration point is measured using a sensor; second, the multi-directional spectral response characteristics of the SSLC coating under the action of the friction force are measured using a camera or spectrometer; then, the spectral characteristics under different viewing directions are obtained by adjusting the top angle; the magnitude of the friction force is adjusted by changing the airflow speed, and the above measurements are repeated to obtain the multi-directional optical response characteristics of the SSLC coating under different friction forces. The experimental data were processed to reduce measurement errors. Based on the denoised data, the structural stress response model and its parameters in the SSLC coating color response model were adjusted to ensure that the numerical simulation results were highly consistent with the experimental measurement results, thereby completing the calibration of the SSLC coating structural deformation model and its parameters.

7. The method for generating numerical values ​​for a color response database of a shear-sensitive liquid crystal coating according to claim 1, characterized in that, Step 4 specifically includes: After calibrating the SSLC coating color response model, numerical simulations can be performed based on this model to generate a color database of the SSLC coating under frictional force, thereby obtaining the color of the SSLC coating as a function of the magnitude τ and direction φ of the frictional force. τ The angle of view α of the direction of light illumination C and circumferential angle φ C The downward angle α of the observation direction C and circumferential angle φ C The variation characteristics of the parameters are denoted as Color(τ,φ). τ ,α L ,φ L ,α C ,φ C ); For curved walls, the direction of light illumination and the direction of camera observation are both defined relative to the local normal of the wall, which can reduce the dimensionality and complexity of the data. In wind tunnel experiments, it is only necessary to generate a color database of the SSLC coating in these specific observation directions for research. The specific method is as follows: First, according to the specific experimental scenario, set the light irradiation direction and several observation directions; then, according to the SSLC coating color response model, generate the colors displayed by the SSLC coating in these selected observation directions under the action of friction of different magnitudes and directions.

8. The method for generating a color response database of a shear-sensitive liquid crystal coating according to claim 7, characterized in that, Based on a sufficiently large and representative database, intelligent algorithms can establish a precise mapping relationship between the color of SSLC coating and the friction vector through efficient training on the data. With the help of this mapping model, the wall friction force field can be quickly and accurately inverted based solely on the color distribution of the SSLC coating without the need for complex experimental calibration. This significantly improves measurement efficiency, reduces experimental complexity, and promotes the application and popularization of SSLC coating technology in high-precision aerodynamic measurements. Furthermore, based on the established numerical model, the color response characteristics of the SSLC coating can be studied through numerical simulation, providing theoretical support and guidance for the optimization and application of this technology.

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