阅读说明：本技术 一种凝胶注模陶瓷生坯热脱脂速率控制方法 (Method for controlling thermal degreasing rate of gel-casting ceramic green body ) 是由 黄金堤 李静 于 2021-02-04 设计创作，主要内容包括：一种凝胶注模陶瓷生坯热脱脂速率控制方法,通过对凝胶注模陶瓷生坯进行非等温热失重分析,并采用热分析动力学方法获得聚合物的热解动力学参数,而后构建陶瓷生坯热脱脂过程分阶段升温控制算法,以实现对陶瓷生坯热脱脂速率的精准预测及可控。本发明适用于陶瓷生坯中的凝胶聚合物存在多个热解峰的复杂情况,对整个热脱脂过程进行分阶段保温并进一步优化,计算周期小于一分钟,适用范围广。(A gel-casting ceramic green body thermal degreasing rate control method is characterized in that non-isothermal thermal loss analysis is carried out on a gel-casting ceramic green body, a thermal analysis dynamics method is adopted to obtain pyrolysis dynamics parameters of a polymer, and then a staged temperature rise control algorithm in the ceramic green body thermal degreasing process is constructed to realize accurate prediction and control of the ceramic green body thermal degreasing rate. The method is suitable for the complex condition that a plurality of pyrolysis peaks exist in the gel polymer in the ceramic green body, the whole thermal degreasing process is subjected to staged heat preservation and further optimized, the calculation period is less than one minute, and the application range is wide.)

1. A method for controlling the hot degreasing rate of a gel-casting ceramic green body is characterized by comprising the following specific steps:

(1) adopting a synchronous thermal analyzer to perform non-isothermal thermal loss analysis on the gel-casting ceramic green body under different atmospheres to obtain thermal loss data, performing multimodal deconvolution fitting treatment on the obtained thermal loss data, and then adopting a thermal analysis kinetic method to obtain pyrolysis kinetic parameters of a polymer so as to realize accurate prediction of pyrolysis behavior of the polymer in the thermal degreasing process of the ceramic green body;

(2) and constructing a staged heating control algorithm in the thermal degreasing process of the ceramic green body, thereby realizing the accurate control of the thermal degreasing rate of the ceramic green body.

2. The method of claim 1, wherein the ceramic green body is a composite of a polymer and a ceramic powder.

3. The method of claim 2, wherein the polymer has not less than 2 pyrolysis peaks.

4. The method of claim 1, wherein at least three different temperature-rise rates are used in the non-isothermal thermal gravimetric analysis to obtain the thermal gravimetric data of the gel-cast ceramic green body at different temperature-rise rates.

5. The method of claim 1, wherein the thermal analysis kinetics method comprises performing pyrolysis phase analysis on the entire thermal degreasing process by using a multi-step parallel reaction model, and calculating the activation energy E (α) based on a model-free method, the M-a lek method, and a single-step combined kinetics reaction mechanismThe model determines a mechanism function f (alpha) of each stage, the activation energy E (alpha) is combined with the activation energy model to calculate the activation energy change model coefficient, and then the pre-index factor k (alpha) is calculated through the mechanism function f (alpha) and the activation energy change model coefficient to obtain the reaction kinetic parameters of each stage, so that the prediction of the pyrolysis kinetic behavior of the polymer is realized.

6. The method as claimed in claim 1, wherein the staged temperature rise control algorithm for the ceramic green body thermal degreasing process develops and constructs a multistage temperature rise program for defining the reaction rate of the polymer by using a programming language according to the pyrolysis kinetic parameters obtained in step (1) and the characteristics of the polymer with multiple pyrolysis peaks, so as to realize accurate prediction and control of the pyrolysis behavior of the polymer.

7. The method as claimed in claim 6, wherein the step-by-step temperature-rise control algorithm for the thermal degreasing process of the ceramic green body is implemented by constructing a step-by-step temperature-rise program for limiting the reaction rate, with the goal of the shortest degreasing time.

8. The method of claim 7, wherein the step temperature programming is embodied as: the upper limit value of the starting constraint of d alpha/dt and the lower limit value of the ending constraint of the heat preservation process are given, and the shortest time and the longest time of the heat preservation are constrained to be realized in a mode of reducing the heat preservation steps.

9. The method of claim 1, wherein the atmosphere comprises an inert atmosphere or an air atmosphere.

Technical Field

The invention relates to the technical field of ceramic material colloidal forming, in particular to a method for controlling the thermal degreasing rate of a gel-casting ceramic green body.

Background

High temperature structural ceramics (e.g. Si)₃N₄SiAlON, etc.) has been attracting attention in advanced fields such as aerospace, military industry, etc. due to its excellent overall properties such as high hardness, corrosion resistance, and high chemical stability. At present, for a high-temperature structural ceramic material, in addition to improving the defect of essential brittleness, the improvement of the reliability and the realization of the low-cost preparation of a ceramic component with a complex shape are also one of the important directions of the future development, and the key technical problems restricting the further popularization and application of the high-temperature structural ceramic are also provided.

In recent years, with the rapid development of technology, various application fields have made higher demands on the performance, shape complexity, and dimensional accuracy of ceramic members. The traditional dry powder compression molding technology has the problems of large processing difficulty, high cost, easy introduction of micro cracks and other new defects in subsequent mechanical processing, and thus the application range of the ceramic member is limited. At present, the commonly used colloidal state forming technology, such as slip casting and injection molding, has the defects of high shrinkage of the blank in size during the preparation process, easy cracking, deformation, even collapse and the like during the drying and degreasing processes of the blank, and the reliability of the ceramic material is seriously reduced. The key way for solving the problems is to reduce the blank defects in the forming process as much as possible and reduce the processing cost of the green body and the sintered body while realizing the near-net-shape preparation of the ceramic component with the complex shape.

The emerging gel injection molding technology draws extensive attention in the field of ceramic material preparation due to a series of advantages of simple process, high green body strength, easiness in deep processing, small shrinkage and the like. The principle of the gel injection molding technology is to skillfully combine the powder molding technology with the organic chemical polymerization theory, form a three-dimensional high polymer network structure with higher strength and toughness based on the crosslinking reaction of an organic monomer and a crosslinking agent, tightly wrap and fix ceramic powder particles uniformly dispersed in slurry in situ by the network structure, finally obtain a ceramic green body with a specific shape, which contains the ceramic powder particles and organic matters and has a composite structure, and obtain high-temperature structural ceramic with excellent comprehensive performance through drying, degreasing and sintering.

However, in the preparation of ceramic components using the gel-casting technique, thermal degreasing is one of the important steps of the technique, and the process adequacy is crucial to the quality of the formed green body. The process has very strict requirements on polymer rate control, and if the design is not reasonable, the thermal stress or residual stress in the blank damages the ceramic component in a cracking, collapsing, deforming or other way; in addition to such macroscopic defects, any microscopic defects caused during thermal degreasing are further amplified during subsequent sintering, ultimately affecting the properties of the sintered body. To avoid such problems, long heating cycles are usually used or repeated attempts are made to maintain the temperature and time to remove the polymer and slow down the rate of precipitation of the pyrolysis product, but this reduces the production efficiency and increases the cost.

In summary, it remains a challenge to completely remove the polymer without introducing defects such as cracks, warping, etc. during the gel-casting thermal degreasing process. Therefore, the development of a rapid and efficient thermal degreasing process for removing polymer from green bodies is critical for gel-casting of low to defect free structural ceramic materials.

Disclosure of Invention

The invention aims to solve the technical problems that the existing thermal degreasing process is difficult to accurately predict the pyrolysis behavior of a polymer in a ceramic green body and cannot effectively control the thermal degreasing rate, and provides a thermal degreasing rate control method of a gel-casting ceramic green body, which can complete the optimization calculation of a multi-stage thermal degreasing heat preservation process in a short time (<1min) under the condition of limiting the pyrolysis rate of the polymer, so that a low-cost optimized degreasing scheme is quickly obtained to solve the problems in the background art.

The technical problem solved by the invention is realized by adopting the following technical scheme:

a method for controlling the hot degreasing rate of a gel-casting ceramic green body comprises the following specific steps:

(1) adopting a synchronous thermal analyzer to perform non-isothermal thermal loss analysis on the gel-casting ceramic green body under different atmospheres to obtain thermal loss data, performing multimodal deconvolution fitting treatment on the obtained thermal loss data, and then adopting a thermal analysis kinetic method (variable activation energy model, M & lta & gt lek method, B & lta & gt method, C & ltb & gt,Model) to obtain the pyrolysis kinetic parameters (activation energy, pre-exponential factor and mechanism function) of the polymer so as to realize accurate prediction of the pyrolysis behavior of the polymer in the thermal degreasing process of the ceramic green body;

(2) and constructing a staged heating control algorithm in the thermal degreasing process of the ceramic green body, thereby realizing the accurate control of the thermal degreasing rate of the ceramic green body.

In the present invention, in the step (1), the ceramic green body is a composite material formed by a polymer and a ceramic powder, the polymer is an organic macromolecule formed by polymerization of various gel systems, such as acrylamide and derivative systems thereof (such as acrylamide, 2-hydroxyethyl methacrylate, methacrylamide and the like monomers, and a corresponding cross-linking agent is N, N' -methylene bisacrylamide, poly (ethylene glycol) methyl ether methacrylate and the like), a non-aqueous gel system (trimethylolpropane triacrylate/hexanediol diacrylate) and the like.

In the invention, in the step (1), the ceramic green body is crushed, sieved by a sieve of 100-150 meshes, and fully dried to avoid influence of residual moisture or solvent on the thermal weight loss data of the polymer, and each test condition is repeated for at least 3 times to ensure the reliability of the thermal weight loss data, and the ceramic green body sample required in the whole implementation process only needs 1-2 g, so that the cost is low.

In the present invention, in the step (1), the atmosphere during the thermogravimetric analysis includes an inert atmosphere (e.g., high purity argon, nitrogen) and an air atmosphere.

In the present invention, the specific process of step (1) is as follows:

firstly, connecting a test instrument to ensure the normal operation of the test instrument, and then clicking a synchronous thermal analyzer to start;

performing non-isothermal thermal loss analysis on the gel-casting ceramic green body by a synchronous thermal analyzer to obtain thermal loss data;

multimodal deconvolution fitting processing is carried out on the thermal weight loss data obtained in the step two);

fourthly, the data processed in the third step of deconvolution fitting are processed by adopting a thermal analysis kinetic method to obtain the pyrolysis kinetic parameters of the polymer, the thermal analysis kinetic method comprises the steps of adopting a multi-order parallel reaction model (M-PRM) to carry out pyrolysis stage analysis on the whole thermal degreasing process, calculating the activation energy E (alpha) based on a model-free method (Friedman differential method), and calculating the activation energy E (alpha) based on an Ma lek method and a method capable of describing a single-step combined kinetic reaction mechanismDetermining a mechanism function f (alpha) by a model, calculating a variable activation energy model coefficient by combining activation energy E (alpha) with a variable activation energy model, and calculating a pre-pointing factor k (alpha) by the mechanism function f (alpha) and the variable activation energy model coefficient to realize polymerizationPredicting the physical pyrolysis kinetic behavior;

fifthly, carrying out kinetic parameter verification on the prediction of the pyrolysis kinetic behavior of the polymer obtained in the step (iv), and outputting a prediction result;

and sixthly, finishing.

In the second step), at least three different heating rates (such as 2.5 ℃/min, 5 ℃/min, 10 ℃/min as a group or 5 ℃/min, 10 ℃/min, 15 ℃/min as a group) are adopted in the implementation process of the thermal weight loss analysis, so as to obtain a thermogravimetric difference DTG curve and a reaction rate d alpha/dT curve of the gel-casting ceramic green body at different heating rates.

In the step (c), performing multimodal deconvolution fitting on the obtained three or more groups of reaction rate d alpha/dT curves by adopting a Gaussian function to obtain a plurality of Gaussian distribution function parameters; and (3) adopting a Levenberg-Marquardt algorithm for multimodal deconvolution fitting, taking a Gaussian distribution function formula (1) as a fitting peak function, and performing multimodal fitting on a plurality of overlapped peaks in the d alpha/dT curve to finally obtain a plurality of groups of Gaussian distribution function parameters matched with one or more pyrolysis peaks:

in the formula (1), A is a peak area, pi is a circumference constant, w is a half-peak width, y₀And x_cIs a real constant.

In the step (iv), the multiple-order parallel reaction model (M-PRM) is an effective multiple-peak fitting model, which is a weighted sum of several independent reactions according to the whole pyrolysis process, and performs kinetic analysis on each sub-stage, respectively, to determine the corresponding kinetic parameters of each sub-stage, assuming that each sub-peak represents the independent reaction of a single assumed substance in the process, and the weighting factor is the ratio of the mass loss to the total mass loss of each stage, the mathematical expression of the differential form of the kinetic equation of the pyrolysis sub-stage i is:

in the formula (2), α_iThe conversion of the i component of the polymer in the green body, T is the temperature, T is the time, k (. alpha.)_i) Is a pre-exponential factor of the reaction sub-stage i, E (. alpha.)_i) For the activation energy of sub-stage i, R is the ideal gas constant, β is the rate of temperature rise, f (α)_i) As a function of the reaction mechanism of the reaction sub-stage i;

weighting factor r for reaction sub-phase i_iThe following formula is adopted for calculation:

the conversion α and activation energy E of the entire stage are then described as:

in the formulae (3) and (4), N is the number of the reaction sub-stages, and m_i0、m_ifRespectively the initial and final masses, m, of the corresponding reactants in the reaction sub-stage i₀、m_fRespectively the initial and final mass of the polymer, m_TIs the mass of the polymer at a temperature value T.

In the step (c), the model-free method (Friedman differential method) is a logarithmic form equal conversion rate method based on a rate equation and is used for solving the kinetic parameter E (alpha) of each pyrolysis sub-stage_i) The formula involved is:

the specific process is as follows: based on the Gaussian distribution function of each sub-stage calculated in the step (c), under the condition of equal conversion rate, drawing ln (beta d alpha)_iRegression line of/dT) to 1/TBy the slope of the line to obtain a corresponding α_iActivation energy E (. alpha.) of_i)。

In the step (iv), the variable activation energy model is used for describing the dependency between the activation energy and the conversion rate, and a polynomial shown in formula (7) is adopted to obtain the model parameter (p) through regression fitting_i,5、p_i,6、p_i,7And p_i,8)：

E(α_i)＝p_i,5+p_i,6α_i+p_i,7α_i ²+p_i,8α_i ³ (7)

In the formula (7), p_i,5、p_i,6、p_i,7And p_i,8Model parameters are obtained for polynomial regression fitting.

In the above step (a), the Ma lek method is used to determine the function f (alpha) of the reaction mechanism_i) And G (. alpha.) (a)_i) An effective method of (a), where the M-lek method is considered to be f (a)_i) Function and y (alpha)_i) The function is proportional and by plotting the experimental curve and the theoretical curve, if the experimental data coincide with the theoretical curve or most of the values fall on the curve, it is assumed that it corresponds to f (α) of the theoretical curve_i) And G (. alpha.) (a)_i) The specific process is as follows: will be alpha_i，T，(dα_iDt) (i ═ 1,2, … N) and α_i＝0.5，T_0.5，(dα_i/dt)_0.5Substituting into equation (8) by (T/T)_0.5)²(dα_i/dt)/(dα_i/dt)_0.5For alpha_iPlotting, the experimental curve can be drawn:

in the formula (8), y (. alpha.) is_i) To define a function, T_0.5And (d α)_i/dt)_0.5The temperature and the reaction rate at a conversion of 0.5, respectively.

In the step (iv) above, the step (iv),the model is a three-parameter transfer function for describing solid state reaction mechanism dynamics, and the mathematical expression of the model is as follows:

in the formula (9), n_i、m_iAnd p_iReaction series, power law and diffusion mechanism exponential factors (usually non-integers);

the specific process is as follows: f (alpha)_i)、G(α_i) F (0.5) and G (0.5) into equation (10) by f (α)_i)·G(α_i) G (0.5) · f (0.5) vs. alpha_iPlotting, theoretical curves can be drawn:

in the formula (10), G (. alpha.)_i) Is f (alpha)_i) An integral form of the mechanism function is calculated based on a generalized reduced gradient algorithm to obtain a curve which can meet the condition that the curve of the experimental data is coincident with the theoretical curve or most of values fall on the curveModel parameter (m)_i、n_iAnd p_i)。

In the step (c), the pre-exponential factor is calculated to obtain the mechanism function f (alpha)_i) And activation energy E (. alpha.)_i) Then, taking the formula (2) as an evaluation function, based on a generalized reduced gradient algorithm, taking the formula (11) as an objective function, and calculating to obtain a pre-exponential factor k (alpha)_i)：

k(α_i)＝exp(p_i,1+p_i,2α_i+p_i,3α_i ²+p_i,4α_i ³) (11)

In the above-mentioned step (v), the pre-exponential factor k (alpha)_i) And (3) carrying out kinetic parameter verification, wherein the specific implementation process is as follows: temperature rise for calculation based on kinetics of divisionJudging whether the thermal weight loss experimental data obtained by the heating conditions outside the preparation degree is superposed with the calculation result of the kinetic theory; if substantial coincidence is possible, the calculated kinetic parameters are feasible.

In the invention, in the step (2), a staged heating control algorithm for the ceramic green body thermal degreasing process constructs a multistage heating program for limiting the polymer reaction rate by adopting a programming language according to the pyrolysis kinetic parameters obtained in the step (1) and the characteristic that the polymer has multiple pyrolysis peaks, so as to realize accurate prediction and controllability of the polymer pyrolysis behavior; the basic principle of the gel thermal degreasing process staged temperature rise control algorithm is as follows: aiming at the shortest degreasing time, the method is realized by constructing a segmented temperature rise program for limiting the reaction rate (d alpha/dt), but in the thermal degreasing linear temperature rise process, when the reaction rate (d alpha/dt) value corresponding to the temperature is higher than the agreed allowable d alpha/dt upper limit value (d alpha/dt)_uThen the linear temperature rise process enters the heat preservation step; in the heat preservation step, the temperature is kept constant, and the minimum heat preservation time value used is t_dThe maximum heat preservation time value is t_uI.e. t_d≤t_n≤t_uWhen the holding time is t_nThe corresponding reaction rate (d alpha/dt) value is lower than the lower limit value (d alpha/dt) of the allowed d alpha/dt of the contract_dWhen the temperature is higher than the preset temperature, the temperature is kept for a long time; if the value of the subsequent temperature rising process (d alpha/dt) is higher than the set upper limit value (d alpha/dt) of the reaction rate (d alpha/dt)_uIf so, repeating the heat preservation step; repeating the steps until the reaction rate (d alpha/dt) is kept lower than the stipulated upper limit value (d alpha/dt) all the time during the whole thermal degreasing process_u(ii) a Setting an upper limit t of the heat preservation time_uAnd lower limit value t of holding time_dFor subsequent condition judgment and selection; while continuously adjusting the lower limit allowed by the contract (d α/dt)_dAnd repeating the heating-heat preservation-heating calculation steps to obtain the shortest degreasing time and obtain the heating curve control strategies with different heat preservation sections.

In the step (2), the multi-stage temperature raising program passes through a given initial d alpha/dt upper limit value (d alpha/dt)_uAnd lower d α/dt limit value (d α/dt) for the termination of the incubation process_dAnd the minimum time t of heat preservation is restrained_dWhen the longest isTime t_uIn a manner that the number of heat-insulating steps is reduced.

Has the advantages that: the method is suitable for ceramic green bodies prepared by adopting various gel systems, and can realize effective description and accurate prediction of multiple pyrolysis stages of the ceramic green bodies by adopting the thermal analysis dynamics method and only calculating non-isothermal thermal weight loss data according to the characteristic that multiple pyrolysis peaks exist in polymerization formed by the gel systems; meanwhile, a multi-stage heat preservation strategy is implemented on the premise of ensuring elimination of a pyrolysis rate peak of the polymer by limiting the pyrolysis reaction rate of the polymer and restricting the heat preservation time, so that the thermal degreasing process is optimized; furthermore, in the whole algorithm implementation process, the time consumed by calculation is less than 1 minute; and because of eliminating the peak of the pyrolysis rate of the polymer, the release rate of pyrolysis gas products in the ceramic green body in the thermal degreasing process is effectively controlled, and the generation of internal stress of the green body can be reduced, so that the formation of defects is reduced, and the reliability of the gel-casting ceramic material is effectively improved; the application range is wide, and the method can be popularized to the optimized design of the thermal degreasing process scheme of other gel casting materials; furthermore, the method is suitable for the design and research and development of the novel intelligent thermal degreasing furnace, and has important theoretical significance and industrial application value.

Drawings

FIG. 1 is a schematic diagram of the process for predicting the pyrolysis behavior of the gel polymer in the present invention.

FIG. 2 is a schematic diagram of a segmented temperature rise constraint strategy according to the present invention.

FIG. 3 is a schematic diagram illustrating a multi-stage temperature-raising program calculation process according to the present invention.

FIG. 4 is a graphical representation of TG and DTG curves of a green article from an argon atmosphere thermal degreasing process at different ramp rates in accordance with the present invention.

FIG. 5 is a diagram illustrating the prediction result of the polymer pyrolysis behavior in the thermal degreasing process of the ceramic green body under the argon atmosphere in the present invention.

FIG. 6 is a schematic diagram of TG and DTG curves of a green body in an air atmosphere thermal degreasing process under different temperature-rising rates in the invention.

FIG. 7 is a diagram illustrating the prediction result of the polymer pyrolysis behavior in the thermal degreasing process of the ceramic green body in the air atmosphere according to the present invention.

Detailed Description

In order to make the technical means, creation features, achievement objects and effects of the invention easy to understand, the following description is combined with the specific figure and Si₃N₄、Al₂O₃And AlN powder as raw material, adopting low-toxicity water-based N, N-dimethylacrylamide/N, N' -methylene bisacrylamide (DMAA/MBAM) gel system, and adopting the thermal degreasing process of gel injection molding preparation SiAlON ceramic green body as an example to further illustrate the invention.

Example 1

Adopting a synchronous thermal analyzer to perform non-isothermal thermal loss analysis on the ceramic green body under an inert gas atmosphere (high-purity argon), and obtaining thermal loss data with the heating rates of 2.5 ℃/min, 5 ℃/min, 15 ℃/min and 20 ℃/min, as shown in figure 4;

according to the thermal weight loss data obtained by a synchronous thermal analyzer, the whole thermal degreasing process is divided into three pyrolysis stages, the pyrolysis kinetic parameters and the mechanism function of the SiAlON ceramic green body DMAA/MBAM polymer in the thermal degreasing process are obtained, the activation energy functions of the three sub-stages 1,2 and 3 are obtained through calculation, and the change relational expression of the activation energy along with the conversion rate is respectively E (alpha) ═ 139.862-110.481 alpha +156.161 alpha²-88.714α³kJ/mol、E(α)＝160.791+152.496α-236.906α²+163.724α³kJ/mol and E (alpha) 72.132+452.830 alpha-669.039 alpha²+507.015α³kJ/mol；

The kinetic mechanism function of the three partial phases 1,2 and 3 is respectively f (alpha) ═ 1-alpha^0.668α^3.049(-ln(1-α))^-3.874、f(α)＝(1-α)^0.700α^3.177(-ln(1-α))^-3.962And f (α) ═ 1- α)^1.049α^-0.161(-ln(1-α))^0.518；

According to the obtained kinetic parameters, the pyrolysis behavior of the DMAA/MBAM polymer in the SiAlON ceramic green body in the inert atmosphere thermal degreasing process is predicted, as shown in FIG. 5, the prediction result has high goodness of fit with experimental data, and the maximum error is less than 9%;

as shown in fig. 2 and 3, calculateThe incubation period and time required for the thermal degreasing process are targeted to control the maximum pyrolysis rate of the DMAA/MBAM polymer to 30% at linear temperature rise (1 ℃/min, start temperature 25 ℃, end temperature 600 ℃), i.e., to set the upper limit of d α/dt to 0.3 x (d α/dt)_maxAnd d α/dt lower limit of 0.06 (d α/dt)_maxSetting the upper limit of the heat preservation time to 480min and the lower limit of the heat preservation time to 30min, calculating to obtain an inert atmosphere optimized degreasing process scheme through a staged temperature rise control algorithm in the ceramic green body thermal degreasing process, wherein the calculation results are shown in table 1:

TABLE 1

Example 2

Adopting a synchronous thermal analyzer to perform non-isothermal thermal loss analysis on the ceramic green body in an air atmosphere to obtain thermal loss data with the heating rates of 5 ℃/min, 8 ℃/min, 10 ℃/min and 15 ℃/min, as shown in figure 6;

according to the flow shown in fig. 1, according to the thermal weight loss data obtained by a synchronous thermal analyzer, the whole thermal degreasing process is divided into five pyrolysis stages, the pyrolysis kinetic parameters and mechanism functions of DMAA/MBAM polymer in SiAlON ceramic green bodies in the thermal degreasing process are obtained, the activation energy functions of the five sub-stages 1,2, 3, 4 and 5 are obtained through calculation, and the change relational expressions of the activation energy along with the conversion rate are respectively E (alpha) ═ 115.027+11.950 alpha-39.241 alpha²+10.624α³kJ/mol、E(α)＝139.595-66.162α+75.702α²-38.041α³kJ/mol、E(α)＝190.854+135.755α-214.801α²+116.093α³kJ/mol、E(α)＝64.068+280.086α-380.270α²+264.724α³kJ/mol and E (alpha) 188.257-77.086 alpha +74.129 alpha²-48.669α³kJ/mol, kinetic mechanism functions of sub-stages 1,2, 3 and 5 are all f (α) ═ 1- α)^0.711α^2.970(-ln(1-α))^-3.761The mechanism function of the sub-stage 4 is f (α) ═ 1- α^1.050α^-0.025(-ln(1-α))^0.134；

According to the obtained kinetic parameters, the pyrolysis behavior of the DMAA/MBAM polymer in the air atmosphere thermal degreasing process of the SiAlON ceramic green body is predicted, as shown in figure 7, the prediction result has high goodness of fit with experimental data, and the maximum error is less than 6%;

as shown in FIGS. 2 and 3, the incubation period and the incubation time required for the thermal degreasing process were calculated to control the maximum pyrolysis rate (d α/dt) of the polymer_maxThe upper limit of d α/dt (d α/dt) was set to 30% at linear temperature rise (1 ℃/min, start temperature 25 ℃, end temperature 600 ℃), i.e., 0.3X (d α/dt)_maxAnd d α/dt lower limit of 0.06 (d α/dt)_maxSetting the upper limit value of the heat preservation time to 480min and the lower limit value of the heat preservation time to 30min, calculating to obtain an air atmosphere optimized degreasing process scheme through a staged temperature rise control algorithm in the ceramic green body thermal degreasing process, wherein the calculation results are shown in table 2:

TABLE 2

In examples 1 and 2 above, the specific procedure for predicting the pyrolysis behavior of DMAA/MBAM polymers during thermal degreasing of SiAlON ceramic green bodies in different atmospheres is as follows:

firstly, connecting a test instrument to ensure the normal operation of the test instrument, and then clicking a synchronous thermal analyzer to start (101);

performing non-isothermal thermal loss analysis (102) on the gel-casting ceramic green body by a synchronous thermal analyzer to obtain thermal loss data;

carrying out multimodal deconvolution fitting processing (103) on the thermal weight loss data obtained in the step 102);

fourthly, for the data which are processed by the deconvolution fitting in the step 103), a thermal analysis kinetic method (104) is adopted to obtain the pyrolysis kinetic parameters of the polymer, the thermal analysis kinetic method (104) comprises the steps of adopting a multi-order parallel reaction model (M-PRM) to carry out pyrolysis stage analysis on the whole thermal degreasing process, and calculating the activation energy E (alpha) based on a model-free method (Friedman differential method)_i) (105), based on the M-lek method and can describe a single step combined kinetic reactionOf mechanismsModel determination of the mechanistic function f (α)_i) (107) activation energy E (. alpha.) of_i) The variable activation energy model coefficients are calculated (106) in combination with the variable activation energy model, and then the mechanism function f (alpha) is passed_i) (107) calculating a pre-exponential factor k (alpha) with the variable activation energy model coefficient (106)_i) (108) realizing prediction of the pyrolysis kinetic behavior of the polymer;

fifthly, carrying out kinetic parameter verification on the prediction of the pyrolysis kinetic behavior of the polymer obtained in the step (109), and outputting a prediction result;

and ending (110).

In the second step), at least three different heating rates (such as 2.5 ℃/min, 5 ℃/min, 10 ℃/min as a group or 5 ℃/min, 10 ℃/min, 15 ℃/min as a group) are adopted in the implementation process of the thermal weight loss analysis, so as to obtain a thermogravimetric difference DTG curve and a reaction rate d alpha/dT curve of the gel-casting ceramic green body at different heating rates.

In the step (c), performing multimodal deconvolution fitting on the obtained three or more groups of reaction rate d alpha/dT curves by adopting a Gaussian function to obtain a plurality of Gaussian distribution function parameters; and (3) adopting a Levenberg-Marquardt algorithm for multimodal deconvolution fitting, taking a Gaussian distribution function formula (1) as a fitting peak function, and performing multimodal fitting on a plurality of overlapped peaks in the d alpha/dT curve to finally obtain a plurality of groups of Gaussian distribution function parameters matched with one or more pyrolysis peaks:

in the formula (1), A is a peak area, pi is a circumference constant, w is a half-peak width, y₀And x_cIs a real constant.

In the step (iv), the multiple-order parallel reaction model (M-PRM) is an effective multiple-peak fitting model, which is a weighted sum of several independent reactions according to the whole pyrolysis process, and performs kinetic analysis on each sub-stage, respectively, to determine the corresponding kinetic parameters of each sub-stage, assuming that each sub-peak represents the independent reaction of a single assumed substance in the process, and the weighting factor is the ratio of the mass loss to the total mass loss of each stage, the mathematical expression of the differential form of the kinetic equation of the pyrolysis sub-stage i is:

in the formula (2), α_iIs the conversion of the i component of the polymer in the green body, T is the temperature, k (. alpha.)_i) Is a pre-exponential factor of the reaction sub-stage i, E (. alpha.)_i) For the activation energy of sub-stage i, R is the ideal gas constant, β is the rate of temperature rise, f (α)_i) As a function of the reaction mechanism of the reaction sub-stage i;

weighting factor r for reaction sub-phase i_iThe following formula is adopted for calculation:

the conversion α and activation energy E of the entire stage are then described as:

in the formulae (3) and (4), N is the number of the reaction sub-stages, and m_i0、m_ifRespectively the initial and final masses, m, of the corresponding reactants in the reaction sub-stage i₀、m_fRespectively the initial and final mass of the polymer, m_TIs the mass of the polymer at a temperature value T.

In the step (c), the model-free method (Friedman differential method) is a logarithmic constant conversion rate method based on a rate equation and is used for solving the kinetic parameter E (alpha) of each pyrolysis stage_i) The formula involved is:

the specific process is as follows: based on the Gaussian distribution function of each sub-stage calculated in the step (c), under the condition of equal conversion rate, drawing ln (beta d alpha)_iA regression line of/dT) to 1/T, and a corresponding alpha is obtained by the slope of the line_iActivation energy E (. alpha.) of_i)。

In the step (iv), the variable activation energy model is used for describing the dependency between the activation energy and the conversion rate, and a polynomial shown in formula (7) is adopted to obtain the model parameter (p) through regression fitting_i,5、p_i,6、p_i,7And p_i,8)：

E(α_i)＝p_i,5+p_i,6α_i+p_i,7α_i ²+p_i,8α_i ³ (7)

In the formula (7), p_i,5、p_i,6、p_i,7And p_i,8Model parameters are obtained for polynomial regression fitting.

In the above step (a), the Ma lek method is used to determine the function f (alpha) of the reaction mechanism_i) And G (. alpha.) (a)_i) An effective method of (a), where the M-lek method is considered to be f (a)_i) Function and y (alpha)_i) The function is proportional and by plotting the experimental curve and the theoretical curve, if the experimental data coincide with the theoretical curve or most of the values fall on the curve, it is assumed that it corresponds to f (α) of the theoretical curve_i) And G (. alpha.) (a)_i) The specific process is as follows: will be alpha_i，T，(dα_iDt) (i ═ 1,2, … N) and α_i＝0.5，T_0.5，(dα_i/dt)_0.5Substituting into equation (8) by (T/T)_0.5)²(dα_i/dt)/(dα_i/dt)_0.5For alpha_iPlotting, the experimental curve can be drawn:

in the formula (8), y (. alpha.) is_i) To define a function, T_0.5And (d α)_i/dt)_0.5The temperature and the reaction rate at a conversion of 0.5, respectively.

In the step (iv) above, the step (iv),the model is a three-parameter transfer function for describing solid state reaction mechanism dynamics, and the mathematical expression of the model is as follows:

in the formula (9), n_i、m_iAnd p_iReaction series, power law and diffusion mechanism exponential factors (usually non-integers);

the specific process is as follows: f (alpha)_i)、G(α_i) F (0.5) and G (0.5) into equation (10) by f (α)_i)·G(α_i) G (0.5) · f (0.5) vs. alpha_iPlotting, theoretical curves can be drawn:

in the formula (10), G (. alpha.)_i) Is f (alpha)_i) An integral form of the mechanism function is calculated based on a generalized reduced gradient algorithm to obtain a curve which can meet the condition that the curve of the experimental data is coincident with the theoretical curve or most of values fall on the curveModel parameter (m)_i、n_iAnd p_i)。

In the step (c), the pre-exponential factor is calculated to obtain the mechanism function f (alpha)_i) And activation energy E (. alpha.)_i) Then, taking the formula (2) as an evaluation function, based on a generalized reduced gradient algorithm, taking the formula (11) as an objective function, and calculating to obtain a pre-exponential factor k (alpha)_i)：

k(α_i)＝exp(p_i,1+p_i,2α_i+p_i,3α_i ²+p_i,4α_i ³) (11)

In the above-mentioned step (v), the pre-exponential factor k (alpha)_i) And (3) carrying out kinetic parameter verification, wherein the specific implementation process is as follows: judging whether the thermal weight loss experimental data obtained according to the heating conditions except the heating degree for the kinetic calculation is coincident with the kinetic theoretical calculation result; if substantial coincidence is possible, the calculated kinetic parameters are feasible.

According to the staged heating control algorithm in the thermal degreasing process of the ceramic green body, a multistage heating program for limiting the reaction rate of the polymer is developed and constructed by adopting a programming language according to the obtained pyrolysis kinetic parameters and the characteristic that the polymer has multiple pyrolysis peaks, so that the pyrolysis behavior of the polymer is accurately predicted and controlled; the basic principle of the gel thermal degreasing process staged temperature rise control algorithm is as follows: aiming at the shortest degreasing time, the method is realized by constructing a segmented temperature rise program for limiting the reaction rate (d alpha/dt), as shown in figure 2, when the reaction rate (d alpha/dt) value corresponding to the temperature is higher than the agreed allowable d alpha/dt upper limit value (d alpha/dt) in the thermal degreasing linear temperature rise process_uThen the linear temperature rise process enters the heat preservation step; in the heat preservation step, the temperature is kept constant, and the minimum heat preservation time value used is t_dThe maximum heat preservation time value is t_uI.e. t_d≤t_n≤t_uWhen the holding time is t_nThe corresponding reaction rate (d alpha/dt) value is lower than the lower limit value (d alpha/dt) of the allowed d alpha/dt of the contract_dWhen the temperature is higher than the preset temperature, the temperature is kept for a long time; if the value of the subsequent temperature rising process (d alpha/dt) is higher than the set upper limit value (d alpha/dt) of the reaction rate (d alpha/dt)_uIf so, repeating the heat preservation step; repeating the steps until the reaction rate (d alpha/dt) is kept lower than the stipulated upper limit value (d alpha/dt) all the time during the whole thermal degreasing process_u(ii) a Setting an upper limit value and a lower limit value of the heat preservation time for subsequent condition judgment and selection; while continuously adjusting the lower limit allowed by the contract (d α/dt)_dRepeating the above steps of heating, keeping warm and heatingAnd the temperature calculation step obtains the shortest degreasing time and obtains temperature rise curve control strategies of different heat preservation section numbers.

The multi-step temperature program passes a given initial d alpha/dt upper limit value (d alpha/dt)_uAnd lower d α/dt limit value (d α/dt) for the termination of the incubation process_dAnd the minimum time t of heat preservation is restrained_dMaximum time t_uThe method is realized in a mode of reducing the number of heat preservation steps, and a specific calculation flow is shown in figure 3:

step 301), in an initial state, the time T is 0min, and the temperature T is 25 ℃; setting the upper d alpha/dt limit (d alpha/dt)_uLower d α/dt limit (d α/dt)_dMinimum time t of heat preservation_dThe maximum time t of heat preservation_uThe time step dT and the temperature step dT, and the heat preservation step of the current heating system is 0 step;

step 302), inputting dynamic parameters of weighting factors r related to each sub-stage in a multi-stage parallel reaction model (M-PRM)_iThe mechanism function f (alpha) included in each sub-stage_i) N in (1)_i、m_i、p_iActivation energy E (. alpha.)_i) P of (a)_i,5，p_i,6，p_i,7，p_i,8And a pre-finger factor k (alpha)_i) P in (1)_i,1，p_i,2，p_i,3，p_i,4；

Step 303), updating time and temperature once per cycle iteration, and adding a time step dT and a temperature step dT to the time and temperature values;

step 304), kinetic calculation, which adopts a multi-order parallel reaction model (M-PRM), and calculates the pyrolysis rate d alpha of each sub-stage through a formula (12)_i/dt：

In formula (12), ln [ k (. alpha.)_i)]＝p_i,1+p_i,2α_i+p_i,3α_i ²+p_i,4α_i ³，E(α_i)＝p_i，5+p_i，6α_i+p_i，7α_i ²+p_i，8α_i ³。

The reaction rate (d α/dt) and the conversion rate α are calculated using equations (13) and (14), wherein the integration function in equation (14) is calculated using a piecewise variable step trapezoidal integration:

in the formulae (13) and (14), n_cTo simulate the total amount of the substance, n_tIs the number of temperature stages, c_iAs a substance weighting factor, Δ t_jIs the time of the jth temperature period;

step 305), judging a time value, and if the time value reaches a preset termination value in the current calculation process, entering step 306) to execute if the time value is met, or entering step 312) to execute;

step 306) for printing out the heat preservation system used by the current calculation by means of text output, display screen output and the like, and then entering step 307);

and 307) updating the number of heat preservation sections and the shortest heat preservation time. Comparing currently stored shortest heat preservation time and shortest heat preservation section number data in the program, and if the shortest heat preservation time and the shortest heat preservation section number data are smaller than the current value, replacing the current value to be a heat preservation system used in the calculation;

step 308) for determining the lower limit value (d α/dt) of the response rate dynamically updated by the current calculation step_dWhether or not the upper limit value of d α/dt (d α/dt) is not less than_uIf yes, entering step 309) to execute, otherwise, entering step 311) to execute;

step 309) printing out the heat preservation system used for the shortest heat preservation time under different heat preservation section number conditions in all the calculation steps by text output, display screen output and the like, and then entering step 310) to finish, wherein the output data can be used for compiling the temperature rise system of the thermal degreasing furnace;

step 310) ends;

step 311), updating the lower limit of the reaction rate d α/dt (d α/dt)_d；

Step 312) for determining whether the d α/dt value of the current calculation step is higher than the upper limit value (d α/dt)_uIf yes, go to step 313), otherwise return to step 303);

step 313), adding 1 to the current heat preservation step number, and then entering step 314);

step 314) for updating the time t_nAdding dt time elements to the value, keeping the temperature value unchanged, and then entering step 315);

step 315), performing kinetic calculation by adopting a multi-order parallel reaction model (M-PRM), and then entering step 316);

step 316), determine if the current d α/dt value is less than the reaction rate lower limit (d α/dt)_dIf yes, go to step 317), otherwise go to step 319);

step 317), judging the current t_nWhether the value is more than or equal to the lower limit t of the heat preservation time_dIf yes, go to step 318), otherwise go to step 314);

step 318), recording the heat preservation temperature and time of the current calculation step for outputting subsequent results; and then returns to step 303);

step 319) judging whether the current heat preservation time is higher than the upper limit t of the heat preservation time_uIf yes, go to step 318), otherwise go to step 314).