A method for constructing a curing kinetics model of a thermosetting adhesive for precision instruments

Abstract

The application discloses a kind of precision instrument with thermosetting adhesive curing kinetics model construction method;First, differential scanning calorimetry (DSC) experiment is carried out, and corresponding heat flow density curve is obtained;Second, each heat flow density curve is carried out peak fitting, and multiple exothermic peak curve is obtained;Third, the exothermic quantity curve, degree of cure curve and curing rate curve of each exothermic peak are obtained;Fourth, the kinetic model parameters of each exothermic peak are obtained by using autocatalytic model fitting;Fifth, the percentage of the exothermic quantity corresponding to each exothermic peak in the total exothermic quantity of adhesive curing is calculated;Finally, the real-time curing rate of each exothermic peak is calculated according to the corresponding kinetic model, and the adhesive real-time curing rate is obtained by linear superposition after being multiplied by the corresponding percentage;The application can significantly improve the accuracy of adhesive curing process analysis results, provide reliable theoretical support for precision instrument with thermosetting adhesive curing forming process optimization, and improve the performance of precision instrument.

Description

Technical Field

[0001] This invention relates to the field of precision instrument technology, and specifically to a method for constructing a curing kinetic model of thermosetting adhesives for precision instruments. Background Technology

[0002] With the rapid development of modern science and technology, precision instruments are widely used in modern production, scientific research, and medical diagnosis, for measuring ambient temperature, carrier displacement, and physical diagnosis, among other applications. The research and development of precision instruments plays a vital role in improving production efficiency, promoting scientific progress, and enhancing human living standards. Precision instruments are mostly connected using adhesives, but the bonding process is often carried out in opaque environments, making it impossible to use light-curing adhesives. Furthermore, thermosetting adhesives offer advantages such as rapid curing at high temperatures, high strength, stability, and good adhesion, making them widely used in the connection of precision instruments.

[0003] In the manufacturing of precision instruments, thermosetting adhesives are widely used for bonding and fixing various components. However, during the curing process, residual stress inevitably arises due to temperature changes and chemical reactions, significantly impacting the performance of precision instruments. Furthermore, the complex curing process of thermosetting adhesives results in low accuracy of curing kinetic models constructed using traditional methods. This makes accurate prediction and control of the curing process difficult in precision instrument manufacturing, severely affecting the quality and performance of the instruments. To reduce residual stress after curing, in-depth research into the curing process of adhesives is necessary. This study begins with understanding the curing mechanism and establishing a kinetic model of the adhesive. This study analyzes the relationship between the degree of curing and process parameters (temperature, time, etc.) to provide a theoretical basis for optimizing the adhesive curing process and reducing residual stress. A high-precision kinetic model is fundamental to ensuring accurate results in the curing process analysis. However, traditional thermosetting adhesive curing kinetic models assume that the degree of curing corresponding to each exothermic peak is equal to the actual degree of curing of the adhesive in real time, leading to significant deviations between the model fitting results and actual experimental results. This has a substantial impact on subsequent curing process analysis and optimization. Therefore, it is urgent to improve the accuracy of the curing kinetic model to enhance the accuracy of adhesive curing process analysis, thereby achieving low-stress curing of adhesives and improving the performance and reliability of precision instruments. Summary of the Invention

[0004] To address the above problems, this invention discloses a method for constructing a curing kinetic model for thermosetting adhesives used in precision instruments. By dividing the heat flux density curve during the adhesive curing process into multiple simple exothermic peak curves, and analyzing and processing each exothermic peak curve, a corresponding kinetic model is established. Finally, by combining the percentage of heat released by each peak to the total heat released, the real-time theoretical curing rate of the adhesive under any conditions can be obtained.

[0005] The specific implementation steps of this invention are as follows:

[0006] Step 1: Conduct DSC experiments on uncured adhesive droplets at different heating rates to obtain the corresponding heat flux density curves;

[0007] Step 2: Use a Gaussian distribution model to perform peak fitting on the heat flux density curves of each group of experiments to obtain multiple exothermic peak curves;

[0008] Step 3: Perform integration and other processing on the heat flux density curve of each exothermic peak in sequence to obtain the heat release curve, degree of curing curve, and curing rate curve of each exothermic peak as a function of time.

[0009] Step 4: Use an autocatalytic model to fit and obtain the kinetic model parameters for each exothermic peak: pre-exponential factor, activation energy, and reaction order;

[0010] Step 5: Calculate the percentage of the total heat released by each exothermic peak relative to the total heat released during adhesive curing;

[0011] Step 6: Calculate the real-time curing rate of each exothermic peak according to the corresponding kinetic model, multiply it by the corresponding percentage, and then linearly superimpose the results to obtain the real-time curing rate of the adhesive.

[0012] Furthermore, step one specifically includes:

[0013] The study investigated the effects of uncured adhesive droplets on N different heating rates β. i In the DSC experiment (i = 1, 2, ... N), the time t, the corresponding temperature T, and the heat flux density q data during the heating process of the adhesive were recorded, and the corresponding heat flux density curves q(t) and q(T) as a function of time and temperature were plotted.

[0014] Furthermore, step two specifically involves:

[0015] (1) Analyze the slope of the q(t) curve and find the points where the slope changes significantly. Each point will correspond to an exothermic peak.

[0016] (2) The Gaussian distribution model was used to perform peak fitting on the q(t) curve of each group of experiments to obtain multiple exothermic peak curves;

[0017] (3) Record each exothermic peak curve in the order in which its peak points appear as: peak 1, peak 2, peak 3, ..., peak j, ..., peak M.

[0018] Furthermore, step three specifically involves:

[0019] (1) For a heating rate of β i In the experiment, the heat flux density corresponding to peak 1 is shown by the time curve q. i,1 Integrating (t) over time yields the curve H of its heat release versus time. i,1 (t) and total heat release ΔH i,1 ;

[0020] (2) H i,1 (t) divided by the total heat released ΔH i,1 The curve α of its curing degree as a function of time was obtained. i,1 (t);

[0021] (3) α i,1 (t) Differentiating time yields the curve of its curing rate versus time.

[0022] (4) Process the exothermic peak (peak 1, peak 2, peak 3, ..., peak j, ..., peak M) curves of each group of experiments according to the steps (1) to (3) above to obtain the corresponding exothermic heat curve with respect to time, the curing degree curve with respect to time and the curing rate curve with respect to time.

[0023] Furthermore, step four specifically includes:

[0024] (1) Plot the heat flux density of peak 1 as a function of temperature for each group of experiments. i,1 (T), taking the extreme value yields the peak temperature of peak 1 at each heating rate.

[0025] (2) Solve for the activation energy in the kinetic model parameters using the Kissinger equation.

[0026]

[0027] Where, β i The heating rate for each group of experiments; The heating rate is represented by β. i The peak temperature at that time, which is taken as the Kelvin temperature; E a R is the activation energy; R is the molar gas constant, which is equal to 8.314 J·mol⁻¹. -1 ·K -1 C is a constant to be solved.

[0028] draw about The curve is obtained and a linear fit is performed, with its slope being... Furthermore, the activation energy E of peak 1 can be obtained. a1 ;

[0029] (3) Solve the pre-exponential factor and reaction order in the kinetic model parameters using the autocatalysis model.

[0030]

[0031] Where α represents the degree of curing; denoted as curing rate; A as pre-exponential factor; T as temperature; and m and n as reaction order.

[0032] Combining the previously solved activation energy E a1 Curing rate Curing degree α i,1 and the heating rate is β i Temperature T of peak 1 i,1 Using equation (2), the heating rate β is fitted. i The curing rate curve of peak 1 versus temperature yielded the corresponding parameters: pre-exponential factor A. i,1 and reaction order m i,1 and n i,1 The value;

[0033] (4) Take the average value of each parameter of peak 1 obtained at each heating rate, and use the solution formula to record them as A1, m1 and n1 respectively, which are used as the pre-exponential factor and reaction order in the kinetic model parameters of peak 1.

[0034]

[0035]

[0036]

[0037] The dynamic model of peak 1 can be expressed as follows:

[0038]

[0039] Where α1 represents the degree of curing of peak 1. The curing rate of peak 1 is given.

[0040] (5) Similarly, the curves of other exothermic peaks (peak 2, peak 3, ..., peak j, ..., peak M) are processed according to the steps (1) to (4) above to obtain the corresponding kinetic models.

[0041]

[0042] Where A j Eaj m j and n j These represent the pre-exponential factor, activation energy, and reaction order in the peak j kinetic model parameters, respectively; α j The degree of curing of peak j Let be the curing rate of peak j.

[0043] Furthermore, step five specifically includes:

[0044] (1) The total heat release ΔH of peak j in each group of experiments i,j Take the average value, denoted as ΔH j It can be obtained from the following formula.

[0045]

[0046] (2) The average value of the total heat release of each exothermic peak, ΔH j By performing linear addition, the total heat release ΔH during the adhesive curing process is obtained;

[0047]

[0048] (3) The average value ΔH of the total heat released corresponding to each heat release peak j The ratio of this peak to the total heat released during adhesive curing, ΔH, is taken as the percentage of the curing process and denoted as k. j .

[0049]

[0050]

[0051] Furthermore, step six specifically includes:

[0052] (1) The real-time curing rate of each exothermic peak of the adhesive under any curing conditions can be solved by the corresponding kinetic model.

[0053] (2) The real-time curing rate of each exothermic peak Multiply by the percentage k of the peak in the curing process. j The real-time curing rate of the adhesive under these conditions is obtained by linear addition;

[0054]

[0055] The beneficial effects of this invention are as follows: This invention achieves the construction of a mathematical model for the curing kinetics of thermosetting adhesives through six steps, enabling accurate prediction and control of the curing process of thermosetting adhesives, and improving the precision and quality of precision instrument manufacturing. Specifically, the invention first conducts differential scanning calorimetry (DSC) experiments on uncured adhesive droplets at multiple different heating rates to obtain the corresponding heat flux density curves; second, it uses a Gaussian distribution model to fit the peaks of each heat flux density curve, obtaining multiple exothermic peak curves; third, it sequentially integrates the heat flux density curve of each exothermic peak with respect to time to obtain the heat release curve, degree of cure curve, and curing rate curve for each exothermic peak; fourth, it uses an autocatalytic model to fit and obtain the kinetic model parameters for each exothermic peak: pre-exponential factor, activation energy, and reaction order. Fifth, calculate the percentage of heat released by each exothermic peak relative to the total heat released during adhesive curing. Finally, obtain the real-time curing rate of each exothermic peak based on the corresponding kinetic model, multiply it by the percentage, and then linearly superimpose it to obtain the real-time curing rate of the adhesive curing process. This method addresses the problem of low model accuracy caused by the assumption that the degree of curing corresponding to each exothermic peak is equal to the degree of curing of the adhesive in real time in traditional curing kinetic model solving methods. This invention considers the difference in the real-time degree of curing corresponding to each exothermic peak and innovatively proposes a method to obtain the real-time curing rate of the adhesive by linearly superimposing the real-time curing rates of each peak by the corresponding percentage. This can significantly improve the accuracy of the adhesive curing process analysis results, provide reliable theoretical support for the optimization of the curing and molding process of thermosetting adhesives for precision instruments, and improve the performance of precision instruments.

[0056] Meanwhile, this method has high practicality and operability, and can be widely applied to various types of thermosetting adhesives. This method constructs a mathematical model based on experimental data, including using time and heat flux density as independent variables and heat release as dependent variables, and temperature and curing time as independent variables and degree of curing as dependent variables. The mathematical model can be continuously adjusted and optimized by comparing experimental data and the prediction results of the mathematical model. More importantly, the method of this invention enables the verification and optimization of the constructed mathematical model. Specifically, it can be verified using experimental data under known conditions, and the difference between the actual results and the predicted results can be compared. If the difference is large, the mathematical model needs to be adjusted and optimized. Through repeated verification and optimization, a kinetic model that can accurately predict and control the curing process of thermosetting adhesives can finally be obtained. Attached Figure Description

[0057] Figure 1 The heat flux density curves are shown at different heating rates.

[0058] Figure 2 The peak division results of the heat flux density curve at a heating rate of 4K / min are shown.

[0059] Figure 3The peak division results of the heat flux density curve at a heating rate of 6 K / min are shown.

[0060] Figure 4 The heat flux density curve of peak 3 at a heating rate of 4K / min;

[0061] Figure 5 The heat release curve of peak 3 at a heating rate of 4K / min;

[0062] Figure 6 The curing degree curve of peak 3 at a heating rate of 4K / min;

[0063] Figure 7 The curing rate curve of peak 3 at a heating rate of 4K / min;

[0064] Figure 8 The heat flux density versus temperature curves for peak 3 at each heating rate are shown.

[0065] Figure 9 for about The fitted curve;

[0066] Figure 10 Peak 3 is the autocatalytic model fitting curve at a heating rate of 2K / min.

[0067] Figure 11 Peak 3 is the autocatalytic model fitting curve at a heating rate of 8K / min.

[0068] Figure 12 The theoretical curing rate curves for each exothermic peak at a heating rate of 4K / min;

[0069] Figure 13 The curve shows the theoretical curing rate at a heating rate of 4K / min. Detailed Implementation Plan

[0070] To better understand the purpose, technical solution, and advantages of this invention, the invention will be further described in detail below with reference to the accompanying drawings and experimental data.

[0071] A method for constructing a curing kinetic model of a thermosetting adhesive for precision instruments is mainly achieved through the following steps;

[0072] Step 1: Conduct DSC experiments on uncured adhesive droplets at multiple heating rates. The specific implementation methods in this step include the following:

[0073] DSC experiments were conducted on uncured adhesive droplets at different heating rates: 2 K / min, 4 K / min, 6 K / min, and 8 K / min, within a temperature range of 20℃ to 250℃. The time, corresponding temperature, and heat flux density data during the adhesive heating process were recorded, and the corresponding heat flux density versus time curves were plotted. Figure 1 As shown.

[0074] Step 2: Use a Gaussian distribution model to perform peak fitting on the heat flux density versus time curves for each experimental group. The specific implementation methods in this step include the following:

[0075] (1) Based on the fact that each point on the heat flux density curve where the slope changes corresponds to an exothermic peak, observe that there are five obvious slope changes on the heat flux density curve, and determine that it is formed by the superposition of five exothermic peaks.

[0076] (2) A Gaussian distribution model was used to perform peak fitting on the heat flux density curves of each group of experiments, dividing the heat flux density curves into five exothermic peak curves. Taking the DSC experiments with heating rates of 4K / min and 6K / min as examples, the peak fitting results are as follows: Figure 2 , Figure 3 As shown;

[0077] (3) According to the order of the peak values ​​of the heat release peaks, the five heat release peaks are respectively named peak 1, peak 2, peak 3, peak 4 and peak 5.

[0078] Step 3: Perform integration and other processing on the heat flux density versus time curve for each exothermic peak sequentially. Specific implementation methods include the following:

[0079] (1) Taking peak 3 at a heating rate of 4K / min as an example, its Figure 4 Integrating the heat flux density shown on the time curve q(t) yields the following result: Figure 5 The heat release curve H(t) shown is given by time, and the total heat release is 236.443 J / g.

[0080] (2) Divide the heat release curve H(t) of peak 3 at a heating rate of 4K / min by its total heat release of 236.443J / g to obtain the curing degree curve α(t) as a function of time, as follows: Figure 6 As shown;

[0081] (3) Differentiate the curing degree of peak 3 with respect to time α(t) at a heating rate of 4K / min to obtain the curing rate with respect to time curve. like Figure 7 As shown;

[0082] (4) Process the exothermic peaks (peak 1, peak 2, peak 3, peak 4, peak 5) curves under each heating rate (2K / min, 4K / min, 6K / min, 8K / min) experiment according to the above steps (1) to (3) to obtain the corresponding exothermic curve, curing degree curve and curing rate curve.

[0083] Step 4: Obtain the kinetic model parameters for each exothermic peak using an autocatalytic model. The specific implementation methods for this step include the following:

[0084] (1) Taking peak 3 as an example, plot the q of peak 3 under each group of heating rates (2K / min, 4K / min, 6K / min, 8K / min) in the experiment. i,3 (T) curve, determine the corresponding peak temperature. The corresponding values ​​are 361.93642K, 371.42865K, 378.78562K, and 383.56718K, respectively. Figure 8 As shown;

[0085] (2) Solve for the activation energy in the kinetic model parameters using the Kissinger equation.

[0086]

[0087] Where, β i The heating rate for each group of experiments; The heating rate is represented by β. i The peak temperature at that time, which is taken as the Kelvin temperature; E a R is the activation energy; R is the molar gas constant, which is equal to 8.314 (J·mol⁻¹). -1 ·K -1 C is a constant to be solved for;

[0088] draw right The curve, such as Figure 9 As shown, a linear fit was performed, and its slope was... The activation energy E of peak 3 is -8087.50616. a3 ;

[0089] E a3 =-8.314×-8087.50616=67239.52621(J / mol) (2)

[0090] (3) Solve the pre-exponential factor and reaction order in the kinetic model parameters using the autocatalysis model.

[0091]

[0092] Where α represents the degree of curing; denoted as curing rate; A is the pre-exponential factor; T represents the curing temperature; m and n are the reaction orders.

[0093] Combining the previously solved activation energy E a3 Curing rate Curing degree α i,3 and the heating rate is β i Peak temperature T i,3 Using equation (3), the heating rate β is fitted. i The curing rate curve of peak 3 versus temperature yielded the corresponding parameters: pre-exponential factor A. i,3 and reaction order m i,3 and n i,3 .

[0094] Based on the fitting results, the pre-exponential factor A in the model parameters of the four experimental peaks was determined. i,3 The reaction orders are 3.27958E7, 3.47792E7, 3.62933E7, and 3.56926E7, respectively; the reaction order m is... i,3 The values ​​are 0.57847, 0.57561, 0.59927, 0.59593, and the reaction order n, respectively. i,3 The values ​​are 1.03807, 1.03979, 1.01882, and 1.02173, respectively. Some of the fitted curves are shown below. Figure 10 and Figure 11 As shown;

[0095] (4) Take the average values ​​of each parameter in the peak 3 model for each experimental group, and denot them as A3, m3, and n3, respectively. These values ​​are used as the pre-exponential factor and reaction order in the peak 3 model parameters.

[0096]

[0097]

[0098]

[0099] Therefore, the dynamic model of peak 3 is:

[0100]

[0101] in, α is the curing rate of peak 3; α3 is the degree of curing of peak 3;

[0102] (5) Process the curves of each exothermic peak (peak 1, peak 2, peak 3, peak 4, peak 5) according to the steps (1) to (4) above to obtain the model parameters of each exothermic peak, where the pre-exponential factor A j(j=1, 2, 3, 4, 5) are 8.96200E5, 3.02341E7, 3.48902E7, 7.99798E7, and 1.38927E15 respectively; activation energy The values ​​are 51994.78991, 63214.59785, 67239.52621, 67566.37924, and 132633.60141, respectively; the reaction order m. j (j=1, 2, 3, 4, 5) are 0.4669, 0.61213, 0.58732, 0.73192, and 0.28348 respectively; reaction order n j The values ​​for (j = 1, 2, 3, 4, 5) are 1.12169, 1.00747, 1.0296, 0.90956, and 1.4396, respectively. Therefore, a kinetic model for each exothermic peak can be established.

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] Step 5: Calculate the percentage of heat released by each exothermic peak relative to the total heat released during adhesive curing. The specific implementation methods for this step include the following:

[0109] (1) The total heat release ΔH of peak j in each group of experiments i,j Take the average value, denoted as ΔH j (j = 1, 2, 3, 4, 5), Their values ​​were 24.76815 J / g, 85.60549 J / g, 232.03568 J / g, 126.24477 J / g, and 36.23604 J / g, respectively.

[0110] (2) The average values ​​of the total heat release of each heat release peak are linearly added together to obtain the total heat release ΔH of the adhesive curing process, which is 504.89014 J / g;

[0111] ΔH=24.76815+85.60549+232.03568+126.24477+36.23604=504.89014J / g(14)

[0112] (3) The average value of the total heat released by each heat release peak, ΔH jThe ratio of this peak to the total heat release ΔH during adhesive curing is denoted as k, representing the percentage of the peak during the entire curing process. j (j = 1, 2, 3, 4, 5), with values ​​of 0.049, 0.16966, 0.45939, 0.24985, and 0.0721.

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] Step Six: Calculate the real-time theoretical curing rate of each exothermic peak according to the corresponding kinetic model, multiply it by the corresponding percentage, and then linearly sum the results to obtain the total real-time theoretical curing rate of the adhesive.

[0119] (1) Taking the 4K / min heating rate experiment as an example, the real-time curing rate of each exothermic peak of the adhesive during curing can be solved by the corresponding kinetic model. like Figure 12 As shown;

[0120] (2) The real-time theoretical solidification rate of each exothermic peak Multiply by the percentage k of the peak in the entire curing process. j The curing rates of the adhesives were obtained by linearly adding the results and compared with the curing rate curves obtained experimentally. Figure 13 As shown.

[0121]

[0122] This invention relates to a method for constructing a curing kinetic model for thermosetting adhesives used in precision instruments, which is mainly achieved through six steps. First, differential scanning calorimetry (DSC) experiments are conducted on uncured adhesive droplets at multiple heating rates to obtain corresponding heat flux density curves. Second, a Gaussian distribution model is used to fit each heat flux density curve to obtain multiple exothermic peak curves. Third, the heat flux density curve of each exothermic peak is integrated over time to obtain the heat release curve, degree of cure curve, and curing rate curve for each exothermic peak. Fourth, a self-catalytic model is used to fit and obtain the kinetic model parameters for each exothermic peak: pre-exponential factor, activation energy, and reaction order. Fifth, the percentage of heat release corresponding to each exothermic peak relative to the total heat release during adhesive curing is calculated. Finally, the real-time curing rate of each exothermic peak is obtained based on the corresponding kinetic model, multiplied by the percentage, and linearly superimposed to obtain the real-time curing rate of the adhesive curing process. To address the low accuracy issues caused by traditional methods for solving curing kinetic models that assume the degree of curing corresponding to each exothermic peak is equal to the degree of curing of the adhesive in real time, this invention considers the differences in the real-time degree of curing corresponding to each exothermic peak. It innovatively proposes a method to obtain the real-time curing rate of the adhesive by linearly superimposing the real-time curing rates of each peak by their respective percentages. This significantly improves the accuracy of the adhesive curing process analysis results, providing reliable theoretical support for optimizing the curing and molding process of thermosetting adhesives for precision instruments, and enhancing the performance of precision instruments. Furthermore, this method has high practicality and operability, and can be widely applied to various types of thermosetting adhesives. Mathematical models are constructed based on experimental data, including those with time and heat flux density as independent variables and heat release as dependent variables, and those with temperature and curing time as independent variables and degree of curing as dependent variables. The mathematical model can be continuously adjusted and optimized by comparing experimental data with the prediction results of the mathematical model. More importantly, the method of this invention enables the verification and optimization of the constructed mathematical model. Specifically, it can be verified using experimental data under known conditions, and the difference between the actual results and the predicted results can be compared. If the difference is large, the mathematical model needs to be adjusted and optimized. Through repeated verification and optimization, a kinetic model that can accurately predict and control the curing process of thermosetting adhesives is finally obtained.

[0123] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for constructing a curing kinetic model of a thermosetting adhesive for precision instruments, characterized in that, The method includes the following steps: Step 1: Conduct DSC experiments on uncured adhesive droplets at different heating rates to obtain the corresponding heat flux density curves; Step 2: Use a Gaussian distribution model to perform peak fitting on the heat flux density curves of each group of experiments to obtain multiple exothermic peak curves; Step 3: Integrate the heat flux density curve of each exothermic peak with respect to time to obtain the heat release curve, degree of curing curve, and curing rate curve of each exothermic peak with respect to time. Step 4: Use an autocatalytic model to fit and obtain the kinetic model parameters for each exothermic peak: pre-exponential factor, activation energy, and reaction order; Step 5: Calculate the percentage of the total heat released by each exothermic peak relative to the total heat released during adhesive curing; Step 6: Calculate the real-time curing rate of each exothermic peak according to the corresponding kinetic model, multiply it by the corresponding percentage, and then linearly superimpose the results to obtain the real-time curing rate of the adhesive.

2. The method for constructing a curing kinetic model for thermosetting adhesives for precision instruments according to claim 1, characterized in that, Step one includes the following: (1) Conduct experiments on uncured adhesive droplets at N different heating rates DSC experiments with i=1,2,…,N; (2) Record the time during the heating process of the adhesive. and the corresponding temperature and heat flux density data; (3) Plot the corresponding heat flux density as a function of time. and the curve of heat flux density with respect to temperature .

3. The method for constructing a curing kinetic model for thermosetting adhesives for precision instruments according to claim 1, characterized in that, Step two includes the following: (1) To Analyze the slope of the curve to find the points where the slope changes significantly, and each point will correspond to an exothermic peak. (2) A Gaussian distribution model was used for each group of experiments. The curves were subjected to peak fitting to obtain multiple exothermic peak curves; (3) Each exothermic peak curve is recorded in the order in which its peak points appear: peak 1, peak 2, peak 3, ..., peak 4. j ,…,peak .

4. The method for constructing a curing kinetic model for thermosetting adhesives for precision instruments according to claim 3, characterized in that, Step three includes the following: (1) For a heating rate of The heat flux density corresponding to peak 1 in the experiment is shown in the time curve. Integrating over time yields the curve of its heat release as a function of time. and total heat release ; (2) Divide by total heat release The curing degree as a function of time was obtained. ; (3) Differential processing of time yields a curve of curing rate versus time. ; (4) Following the steps (1) to (3) above, analyze each exothermic peak in each experimental group, peak 1, peak 2, peak 3, ..., peak 4. j ,…,peak The curves are processed to obtain the corresponding curves of heat release as a function of time, degree of curing as a function of time, and curing rate as a function of time.

5. The method for constructing a curing kinetic model for thermosetting adhesives for precision instruments according to claim 3, characterized in that, Step four includes the following: (1) Plot the heat flux density of peak 1 versus temperature for each group of experiments. The peak temperature of peak 1 at each heating rate is obtained by taking the extreme value. ; (2) Solve for the activation energy in the kinetic model parameters using the Kissinger equation. （1） in, The heating rate for each group of experiments; Indicates the heating rate as The peak temperature at that time, which is taken as the Kelvin temperature; Activation energy; Here is the molar gas constant, and its value is equal to... ; Let be the constant to be solved; draw about The curve is obtained and a linear fit is performed, with its slope being... Furthermore, the activation energy of peak 1 can be obtained. ; (3) Solve the pre-exponential factor and reaction order in the kinetic model parameters using the autocatalysis model. （2） in, This refers to the degree of curing. Curing rate; Pre-exponential factors; Indicates temperature; The reaction order is [number]. Combining the previously solved activation energies Curing rate , curing degree and the heating rate is Temperature of peak 1 Using equation (2) to fit the heating rate is The curing rate curve of peak 1 versus temperature yielded the corresponding parameters: pre-exponential factor. and reaction order The value; (4) Take the average value of each parameter of peak 1 obtained at each heating rate, and denot them respectively using the solution formula. And used as the pre-exponential factor and reaction order in the kinetic model parameters of peak 1. （3） （4） （5） The dynamic model of peak 1 can be expressed as follows: （6） in, The degree of curing of peak 1 The curing rate of peak 1; (5) Similarly, follow the steps (1) to (4) above for other exothermic peaks, peak 2, peak 3, ..., peak 4. j ,…,peak The curves are processed to obtain the corresponding dynamic model. （7） in j=2,3,…,M ; Peaks j Pre-exponential factor, activation energy, and reaction order in the kinetic model parameters; For Peak j degree of curing For Peak j The curing rate.

6. The method for constructing a curing kinetic model for thermosetting adhesives for precision instruments according to claim 3, characterized in that, Step five includes the following: (1) For each experimental group, the lower peak j Total heat release Take the average value, and denote it as ; （8） (2) Average the total heat release corresponding to each heat release peak Linear addition yields the total heat released during the adhesive curing process, denoted as . ; （9） (3) Average the total heat released by each heat release peak Total heat released during adhesive curing The ratio is taken as the percentage of the peak in the curing process, and is denoted as . ; （10） （11）。 7. The method for constructing a curing kinetic model for thermosetting adhesives for precision instruments according to claim 1, characterized in that, Step six includes the following: (1) The real-time curing rate of each exothermic peak of the adhesive under any curing conditions can be solved by the corresponding kinetic model. ; (2) The real-time curing rate of each exothermic peak Multiply by the percentage of the peak in the curing process. The real-time curing rate of the adhesive under these conditions is obtained by linear addition. （12）。

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