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Bonding quality at the interface of solid propellant grains is crucial for the reliability and safety of solid rocket motors. Although bonding reliability is influenced by numerous factors, the lack of quantitative characterization of interface debonding mechanisms and the challenge of identifying key factors have made precise control of process variables difficult, resulting in unpredictable failure risks. This paper presents an improved fuzzy failure probability evaluation method that combines fuzzy fault tree analysis with expert knowledge, transforming process data into fuzzy failure probability to accurately assess debonding probabilities. The predictive model is constructed through a general regression neural network and optimized using the particle swarm optimization algorithm. Sensitivity analysis is conducted to identify key decision variables, including normal force, grain rotation speed, and adhesive weight, which are verified experimentally. Compared with classical models, the maximum error margin of the constructed reliability prediction model is only 0.02%, and it has high stability. The experimental results indicate that the main factors affecting debonding are processing roughness and coating uniformity. Controlling the key decision variable as the median resulted in a maximum increase of 200.7% in bonding strength. The feasibility of the improved method has been verified, confirming that identifying key decision variables has the ability to improve bonding reliability. The proposed method simplifies the evaluation of propellant interface bonding reliability under complex conditions by quantifying the relationship between process parameters and failure risk, enabling targeted management of key decision variables.
ABSTRACT
Bonding quality at the interface of solid propellant grains is crucial for the reliability and safety of solid rocket motors. Although bonding reliability is influenced by numerous factors, the lack of quantitative characterization of interface debonding mechanisms and the challenge of identifying key factors have made precise control of process variables difficult, resulting in unpredictable failure risks. This paper presents an improved fuzzy failure probability evaluation method that combines fuzzy fault tree analysis with expert knowledge, transforming process data into fuzzy failure probability to accurately assess debonding probabilities. The predictive model is constructed through a general regression neural network and optimized using the particle swarm optimization algorithm. Sensitivity analysis is conducted to identify key decision variables, including normal force, grain rotation speed, and adhesive weight, which are verified experimentally. Compared with classical models, the maximum error margin of the constructed reliability prediction model is only 0.02%, and it has high stability. The experimental results indicate that the main factors affecting debonding are processing roughness and coating uniformity. Controlling the key decision variable as the median resulted in a maximum increase of 200.7% in bonding strength. The feasibility of the improved method has been verified, confirming that identifying key decision variables has the ability to improve bonding reliability. The proposed method simplifies the evaluation of propellant interface bonding reliability under complex conditions by quantifying the relationship between process parameters and failure risk, enabling targeted management of key decision variables.
O 2025 China Ordnance Society. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC-ND license (<http://creativecommons.org/lice nses/by-nc-nd/4.0/).
Keywords:
Solid propellant Bonding reliability Prediction model FFTA PSO-GRNN
(ProQuest: ... denotes formulae omitted.)
1. Introduction
Solid propellants are widely used as power sources in rockets, missile weapons, and space launch systems [1,2]. The bonding reliability at the interface of the propellants directly affects the safety performance of the solid rocket motors [3,4]. To optimize performance, solid propellant grains are coated [5]. However, directly bonding the propellant to the coating layer can be problematic due to their low surface roughness, potentially resulting in unreliable adhesion and debonding [6]. During combustion, the gases can quickly rupture the bonding interface, potentially leading to motor explosions [7,8]. To address this issue, a surface roughening and bonding process has been adopted for propellant grains.
Surface roughening process is based on the mechanical interlocking theory, which is a method to increase bonding strength at the adhesive interface by enhancing surface roughness through material removal [9-11]. The processed surface becomes rough and uneven, with grooves that provide a larger contact area, facilitating the storage of adhesive [12]. This allows the adhesive to distribute across different planes, thereby improving bonding performance [13-15]. The processed workpieces are bonded rather than riveted or welded, with applications in aerospace, mechanical manufacturing, and construction industries [16-18]. Classical surface roughening is manually performed using files or coarse grinding wheels. Process reliability depends on operator experience and may result in abnormal conditions, potentially causing local mechanical interlock failure, debonding, or surface breakdown, rendering the product unusable. Hence, automated surface roughening is preferred for enhanced productivity and reduced costs. However, the quality of processing is influenced by various control variables. Some scholars have studied the material removal process and developed material removal models to improve the quality of surface roughening [19,20]. Regarding the process characteristics of surface roughening, the uniformity and degree of roughness are crucial indicators of treatment quality, necessitating monitoring of treatment quality based on machine vision.
As energy-containing materials, propellants are highly sensitive to mechanical impact and temperature fluctuations [21]. Parker et al. studied the ignition mechanism of HMX explosives under frictional impact and successfully captured the moment of ignition using high-speed photography [22]. Li et al. obtained the deformation and temperature of the propellant cutting process and conducted a safety analysis of the process [23]. These studies reveal that transient high temperatures or temperature accumulation due to friction, along with process parameters like normal force, are key factors in frictional heat generation. Parameter deviations may induce combustion or explosion hazards during manufacturing.
After surface roughening propellant grains undergo adhesive coating, bonding, and curing processes. Scholars have examined the effects of various bonding and curing conditions on bonding strength [24,25]. Hamilton et al. created an interlocking structure on the bonding surface through microstructure treatment and demonstrated, through tensile testing [14]. Yokozeki et al. studied the coupling effect of bonding strength on factors such as bonding layer thickness, type of adhesive and viscosity to optimize the bonding performance [26]. Li et al. experimentally studied the influence of curing temperature on the hardness and mechanical properties of the adhesive and proposed a predictive model for the time and adhesive hardness [27]. These findings highlight the importance of bonding and curing parameters for the quality and reliability of the final product. Furthermore, the preparation of raw materials, such as the propellant grain, is a critical step that directly affects the entire process and the materials involved [28].
The relationship between surface roughening, bonding and safety reliability is combed respectively, which not only helps to clarify the process objectives, but also provides a basis for the process variables involved. From the perspective of safety and reliability, failures often result from anomalies in process variables [29]. Therefore, monitoring these variables and taking preventive measures against potential malfunctions can help avoid safety and quality defects. It is essential to establish a model that can clearly describe the relationship between reliability and various factors. The safety and reliability of the manufacturing process are crucial for the processing and stable supply of solid propellants [30]. Current research in this area primarily focuses on individual process components, with few studies addressing the entire process. Some methods qualitatively describe system characteristics using graphics, tables or text, analyzing failure modes, influencing factors and risks without numeric quantification. For detailed assessments, quantitative descriptions of each process component are necessary, using methods like Event Tree Analysis (ETA) [31], Fault Tree Analysis (FTA) [32] and some other prediction algorithms [33]. FTA systematically analyzes root causes of failures and is widely used in failure prediction [32]. To solve the difficulty of obtaining accurate failure probabilities, researchers have combined Fuzzy Set Theory (FST) with expert experience, resulting in Fuzzy Fault Tree Analysis (FFTA), effectively handling uncertainties [28]. However, due to the limited and difficult-to-obtain sample data, combining machine learning methods for data enhancement provides a basis for early safety assessment and fault diagnosis [34]. This paper utilizes GRNN [35], introduced by Specht [36], which handles linear and nonlinear regression problems and is used for predictive modeling and control. The GRNN inherent advantages in bias reduction and smallsample adaptability, particularly effective for dynamic process data in propellant surface roughening and bonding process.
In the initial stages of model construction, the various factors involved in the process are typically considered, resulting in a wide range of factors, some of which may be redundant. Further optimization of the model is necessary to identify key decision variables and to evaluate their impact on reliability. However, there is no publicly available report on the safety reliability model for surface roughening and bonding processes of propellant grains. Therefore, the novelty of this paper mainly focuses on the following aspects:
(1) An improved fuzzy failure probability method is proposed to assess debonding risks.
(2) Key decision variables affecting the debonding of propellant grains are identified.
(3) A quantitative mapping relationship between process parameters and failure risk is established.
This work is organized as follows: Section 2 presents an improved FFTA integrated with expert knowledge to quantify debonding failure probability and develops a PSO-GRNN prediction model. Section 3 compares this model's performance with classical models, utilizing sensitivity analysis to identify key decision variables. Section 4 designed experiments to verify the improved method by evaluating the processing roughness and coating uniformity. And evaluate the impact of key decision variables on bonding reliability by comparing the binding strength at different levels. The paper concludes in Section 5.
2. Prediction model of surface roughening and bonding quality based on improved FFTA
2.1. FFTA for surface roughening and bonding process
The surface roughening and bonding process is a common method in the shaping of solid propellant grains. Fig. 1 illustrates the main process from solid propellant grain to coated grain. Upon analyzing the process, it can be divided into five consistent steps: grain preparation, surface roughening, coating, bonding, and curing. By breaking down each step, 17 key parameters were identified. The debonding of the interface is defined as the top event, which indicates that the failure of the processing will also cause a safety accident. The occurrence of the top event is generally determined by the logical connection of "OR" and "AND" between the basic events (BEs) [32].
Based on expert opinions in solid propellant manufacturing, "OR" is chosen to connect all events. A fault tree model based on the key parameters of the process is established, as shown in Fig. 2. The correspondence between the structures in the fault tree and the process steps and key parameters is shown in Table 1.
Due to the direct contact of the propellant with tools during the processes, there are inherent safety risks and characteristics of uncertainty and vagueness. Therefore, based on FST, the absolute membership relation of elements to sets in classical theory is fuzzified to describe the actual system. ид (x) represents the degree of membership of element x to the fuzzy set A, thus there exists a mapping relationship as shown in Eq. (1), where a higher ид (x) value indicates a higher degree of membership.
H. Lu, B. Zhang, W. Xu et al. ...HALA) :R>10,1) x A ид (1)
In the process, there is a lack of statistical data on safety accidents, making it difficult to determine the specific process steps responsible for safety accidents. Therefore, the experience of experts in this field is necessary to quantitatively assess the safety risks that may be triggered by different process steps. This paper uses the expert prediction method, usually the expert score between 5 and 9 points is more appropriate [37], and quantifies the expert predictions using FST. These experts come from the solid propellant charge field of Shanghai Space Propulsion Technology Research Institute and other organizations.
To align the experts' natural prediction language for the
possibility of safety accidents caused by process steps with the fuzzy environment, seven levels of fuzzy relations have been defined [38,39]: {Very Low (VL), Low (L), Fairly Low (FL), Moderate (M), Fairly High (FH), High (H), Very High (VH)}. Each linguistic variable is described by the corresponding fuzzy number, and then a series of operations are performed on the fuzzy numbers to obtain the fuzzy probabilities of the BEs. To simplify the calculations, this paper uses triangular and trapezoidal membership functions between 0 and 1 to quantitatively represent these natural language predictions, as shown in Fig. 3. Furthermore, to enhance the credibility of the expert predictions, the scores are weighted based on professional title, service time, educational level, and research correlations, with the specific weighting method shown in Fig. 4. For example, if an expert is a researcher with a doctoral degree, 30 years of work experience and is at the level of associate chief engineer, their weighted score is 0.2658 (0.215 x 0.303 + 0.375 x 0.231 + 0.151 x 0.381 + 0.259 x 0.281). The weights of expert predictions are then normalized, and the calculation method for the weight of any expert k is given by Eq.
...
where, Wa; is the attribute weight of the expert, W(; is the category weight of the expert, Wg, is the prediction weight of the expert, i depends on the attribute definition of the expert, j is further subdivided based on the attribute, k corresponds to j and represents the characteristics of the expert attribute and category.
2.2. Improvement of FFP
2.2.1. Fuzzy failure probability
The fuzzy probabilities of BEs need to be adapted based on the weighting of expert categories. By using the weighted average of the prediction results, a comprehensive fuzzy probability can be derived. Due to the fuzzy numerical representations of expert fuzzy predictions containing both trapezoidal and triangular membership functions, directly averaging these fuzzy functions is not feasible. Therefore, the 4-cut set is used to obtain the result. According to the membership functions shown in Fig. 3, the 2-cut set for the corresponding fuzzy subsets can be calculated. Define the à-cut set in the fuzzy set as:
...
It represents the set of 72 elements with membership equal or greater than in the fuzzy subset. And are defined as the left cut set of the 2-cut set, fiv(7) and the right cut set of the i-cut set, frv(4).
Based on subsection 2.1, 20 experts were invited to score the safety and reliability BEs of surface roughening and bonding process, as shown in Fig. 5. Additionally, the prediction weights of the selected experts were calculated and normalized according to Fig. 4.
Summing each weighted à-cut set yields the expert-scored 2-cut set.
...
The membership function after expert scoring of a specific event, as shown in Fig. 6, where (x, Хэ, Хз, Хд) represents the four turning points of the membership function. However, the membership function alone cannot precisely express the probability of the event occurring. Therefore, defuzzification is necessary. In this paper, the fuzzy possibility space (FPS) is calculated using the Fuzzy Max-Min algorithm to obtain the maximum likelihood value of the fuzzy probability. This method involves computing the xaxis elements corresponding to the left and right intersection points of the processed membership function with the maximum (minimum) fuzzy set function, i.e., the fuzzy maximum value (FPSmax) and the fuzzy minimum value (FPSmin), and then taking the average of the corresponding FPS. The maximum fuzzy set function Eq. (5) and the minimum fuzzy set function Eq. (6) are as follows:
...
The intersection of the right cut set of Eq. (4) with Eq. (5) represents the fuzzy minimum value point, and the intersection of the left cut set of Eq. (4) with Eq. (6) represents the fuzzy maximum value point. The abscissa of these two points can be taken to obtain FPSmax and FPSmin. It can be represented by the four turning points of the membership function, denoted as Eqs. (7) and (8) respectively. Therefore, the FPS for each BE is given by Eq. (9). The calculation results are shown in Table 2.
...
Fuzzy failure probability (FFP) can be calculated by Eq. (10), and the calculation results are shown in Table 2.
...
where, к is the coefficient associated with the FPS, к = 2.301 x $/(1 = FPS) /FPS.
The probability of the top event can be represented by the minimal cut sets (MCS), which represent the minimal combination of BEs that can cause the top event to occur [28], and its calculation method is:
...
where, Pr is the probability of the top event occurring, a is the number of BEs, a = 17. P(X;) represents the probability of the BEs occurring, which can be calculated by Eq. (10). The calculation results for Pr are shown in Table 2.
2.2.2. FFP improvement based on the actual production process
In actual processes, the selection of each process parameter varies, and using a universal calculation method leads to discrepancies between the probability of the top event and the real situation. The FFP of different BEs should be improved based on actual processes and expert experience for each process parameter. The selection of process parameters usually falls within a certain range. According to the actual process and equipment capabilities, the range of process parameters is shown in Table 3. Suppose a process parameter г takes a value in the range of [r, ru], and the optimal parameter of the process is considered the median (TL + ru)/2. According to expert experience, the process parameters follow approximately a normal distribution, and the improvement function of FFP is also a normal distribution function, as shown in Fig. 7. To simplify the calculation, the mapping of any process parameters (r,,ry) to the standard normal distribution (-30,30) is carried out to obtain (r, , r,,) for subsequent calculations.
Within the process parameters, the median is assumed as the optimal parameter corresponding to the FFP of the parameters in Table 2, Other value selections have a noticeable impact on the safety and reliability of the manufacturing process. Therefore, the FFP of these values will be higher than the FFP at the median value. The function satisfies Eq. (12).
...
where f(r) represents the FFP improved, a represents the failure improvement factor, and г' is the value of the process parameter mapped to the standard normal distribution (-Зо, Зо). The improvement of FFP compensates for the differences of the BEs, and the FFP corresponding to any process parameters can be calculated.
2.3. PSO-GRNN prediction model
2.3.1. GRNN
The GRNN is a neural network model based on non-linear regression analysis, known for its strong mapping capability and fast learning speed when dealing with non-linear problems [40,41]. As shown in Fig. 8, GRNN consists of a four-layer network structure including the input, pattern, summation, and output.
In the model of GRNN, the predictive relationship between the BEs failure probability X(X1,X>, -,X17) input and the top event failure probability Y output is:
...
where, D; is a scalar function as shown in Eq. (14), and D; is the Euclidean distance between X and X;. (X;,Y;) represents the samples, п is the dimension of the training samples, and с is the smoothing factor.
The pattern layer processes input data using Gaussian functions, where the с of the Gaussian function can adjust the response range. Generally, с is positively correlated with the prediction error, and when o approaches 0, overfitting is likely to occur. By adjusting o, the network's generalization ability and learning effectiveness can be improved, thus enhancing the model's predictive accuracy and stability.
The process system studied in this paper is characterized by difficulties in obtaining process parameters, a small amount of data, many process parameters, strong coupling, and a high degree of nonlinearity. Therefore, applying the GRNN algorithm to construct a safety risk prediction model presents certain advantages.
2.3.2. PSO-GRNN
While using the FFTA method to compute the failure probability of events, this paper generates a large number of statistical data samples to train the model. This approach somewhat replaces the traditional real data-oriented prediction pattern but also presents a challenge to the accuracy of the GRNN algorithm. In order to overcome these limitations of GRNN, and help it escape local optima to improve regression accuracy, the PSO algorithm is introduced to dynamically adjust the smoothing factor for different test samples. The model construction process proposed in this paper is shown in Fig. 9.
Research has shown that PSO is effective in handling the challenges posed by high-dimensional and large-scale training data [34,42]. Classical GRNN is prone to getting trapped in local optima during the training process, which negatively impacts the model's generalization ability and predictive accuracy. However, With the global search ability of PSO, it can effectively optimize the weights and biases of GRNN, minimizing regression errors and improving the overall performance of the model, thereby providing important supplementation to GRNN. Additionally, the PSO algorithm can compensate for the limitations of GRNN when dealing with highly fluctuating data. When faced with significant data fluctuations, the PSO algorithm can dynamically optimize and adjust the smoothing factor, achieving smooth processing of prediction results [43].
2.3.3. Prediction data
Data for model prediction will be obtained through stratified sampling of process parameters within the range. Stratified sampling ensures a uniform distribution of samples and effectively preserves the original characteristics of the data. However, the selection of the number of strata needs to consider the accuracy of the inspection equipment in the actual process to ensure data availability. As shown in Fig. 10, the number of strata m;, corresponds to each BE process parameter. Based on the process parameter ranges in Table 3, the stratification is determined by the operational capabilities of the equipment and the sampling accuracy of the sensors. For instance, given the force sensor's accuracy of 40.5 № the data interval for the normal force is set to 0.5 N, resulting in a number of strata m; = 160. Random sampling of the stratified parameters is performed using Latin Hypercube Sampling (LHS), and the sampled data constitutes a set of process parameters for each BE. The corresponding Fuzzy Failure Probability (FFP) was derived through the improvement method described in subsection 2.2. Subsequently, the probability of the top event Pr for each set of BEs was calculated using Eq. (11), thereby generating a dataset of process parameters for each BE group. To meet the requirements for model training and validation, a total of 25000 data are generated.
3. Numerical analysis of model prediction
3.1. Model training and comparison
In subsection 2.3.3, 25000 sets of data are generated via the LHS method. To facilitate method comparison, reproducibility verification, and reduce computational complexity in model training, the 25000 sets are evenly partitioned into 10 subsets. One subset (2500 sets) is selected for algorithmic comparison. Within this subset, 2000 sets are allocated as the training set and 500 sets as the test set. From the perspective of data partitioning, utilizing 80% of the data for model training enhances model performance and generalization capability, while reserving 20% for testing ensures the evaluation of predictive accuracy and generalization ability. This configuration aligns with established practices in machine learning and demonstrates methodological rationality. The GRNN algorithm is introduced to explore the influence of different parameter values on the variation of top event. The 2500 sets of virtual working cases constructed in subsection 2.3.3 are used for training and validation of the GRNN model, in addition, the PSO algorithm is selected to optimize the smoothing factor of GRNN.
To demonstrate the superior predictive performance and strong forecasting capabilities of the PSO-GRNN algorithm for predicting the occurrence probability of the top event, comparisons were made with the ordinary GRNN algorithm and the PSO-BPNN algorithm. The fitting results of the three methods were plotted, with the calculated values as the x-axis and the predicted values as the yaxis, as depicted in Fig. 11. The results illustrate that the PSO-GRNN algorithm exhibits the best fit, with a coefficient of determination of 0.99989, surpassing the 0.99708 of the PSO-BPNN algorithm and the 0.98155 of the ordinary GRNN algorithm, and closer to 1. This indicates the PSO-GRNN algorithm's superior accuracy in predicting the occurrence probability of the top event in the surface roughening and bonding process of solid propellants.
Each of the three algorithms was tested 10 times to obtain the coefficient of determination for the predicted results, as shown in Fig. 12. The coefficient of determination for the PSO-GRNN algorithm is consistently high, with minimal fluctuations. Although the coefficient of determination for the PSO-BPNN algorithm also demonstrates stability, it generally remains lower than that of the PSO-GRNN algorithm. The ordinary GRNN algorithm does not show significant improvement. Table 4 shows the optimized smoothing factors for the PSO-GRNN algorithm in the 10 tests conducted.
The dynamic updating of the smoothing factor is closely linked to changes in data. In the 10 tests, although some fluctuations are observed in the smoothing factor, it generally remains at a low level, reflecting the dynamic nature of the PSO algorithm in searching for optimal solution. It is noteworthy that the smoothing factor never approaches zero in these 10 tests, effectively avoiding the risk of overfitting. The varying results of the smoothing factors in Table 4 are mainly attributed to the random partitioning of the training data, leading to differences in the datasets used for each optimization, which in turn affects the optimization results. Additionally, the size of the smoothing factor is directly proportional to the prediction error, with smaller values indicating higher accuracy and stability in the prediction results.
To further validate the performance of the model, the smallest smoothing factor from the 10 tests was selected as an example, and the predicted results obtained using the three algorithms were compared with the calculated results, as shown in Fig. 13. The prediction errors for different methods were also computed and . o. . compared, as depicted in Fig. 14, The analysis revealed that the PSO-GRNN algorithm produced the smallest proportion of errors.
In addition, the model can be evaluated using metrics such as Mean Absolute Error (MAE), Sum of Squared Errors (SSE), and Root Mean Square Error (RMSE). The experimental results demonstrate that the PSO-GRNN algorithm outperforms the other algorithms. Specifically, in terms of MAE and RMSE, it is only one-thousandth the size of the other two algorithms, and in terms of SSE, it is only one-hundredth the size of the other two algorithms, as shown in Fig. 15.
As shown in Fig. 15, the comparative results indicate that the performance of the PSO-GRNN algorithm surpasses that of the PSO-BPNN algorithm and the ordinary GRNN algorithm. This illustrates that the predictive model constructed by the PSO-GRNN algorithm can be effectively used to assess the safety and reliability of the surface roughening and bonding process for solid propellants.
3.2. Sensitivity analysis
Based on the research conducted above, 17 BEs were found to have an impact on the occurrence of the top event. However, in practical processes, it is common to select a few major influencing factors to monitor safety and reliability. Therefore, sensitivity analysis is employed to reduce the dimensionality of the highdimensional input samples while retaining the original data information, in order to identify several major BEs that have the greatest impact on data variability [44]. In this paper, Principal Component Analysis (PCA) is utilized. It transforms potentially correlated multidimensional input variables into a set of linearly uncorrelated variables through orthogonal transformations, concentrating most of the information in a few principal components with larger variances. This method has advantages in handling nonlinear interaction models [45]. The sensitivity of each BE can be determined by the obtained generalized first-order sensitivity index in Eq. (15) and the generalized total-order sensitivity index in Eq. (16).
...
where, à, is the k-th eigenvalue, à; represents the eigenvalue, SI; stands for the first-order sensitivity index, and o; is accounts for all items in the variance decomposition of the input variable principal component. GSI; is used to measure the individual input variable's impact on the model output, and GTSI; combines the total effect of individual input variables and their interactions on the model output. The specific computation method can be found in Ref. [44].
By performing PCA on the data samples, the global sensitivity of the BEs can be derived, as shown in Fig. 16. Six BEs exhibit high sensitivity and are identified as the most key decision variables influencing the process: normal force (X4) > processing time (X7) > processing temperature (Xg) > curing temperature (X15) > grain rotation speed (Xs) > adhesive weight (Хо).
Based on the sensitivity analysis, the key decision variables identified are as follows: normal force (X4), processing time (X7), grain rotation speed (Xs), and processing temperature (Хз) are control parameters in the surface roughening process. The adhesive weight (Ха) is the control parameter in the bonding process, and the curing temperature (X15) is the control parameter in the curing process. In the actual processing environment, since the equipment operates in a constant-temperature environment, the processing temperature is usually consistent. Once the type of adhesive is determined, the curing temperature is also fixed, and the processing time is constrained by the production cycle, which is also set as a fixed parameter. Therefore, the only controllable key decision variables are the normal force, rotation speed, and adhesive weight, while the remaining decision variables are set to the median value of the parameter ranges listed in Table 3.
Due to their high sensitivity, these decision variables play a crucial role in affecting the probability of the top event in the actual process. To simplify the assessment method, these six variables are considered the main focus for observation, instead of using a complex prediction model.
4. Experiment results and discussions
4.1. Experimental setting
To verify the feasibility of improving the FFP method by controlling three levels of each key decision variable. Since the normal force and grain rotation speed are the key decision variables for the surface roughing, the adhesive weight corresponds to the bonding process. The experiment is conducted in two parts.
The first part is the surface roughening experiment, utilizing a 5-DOF device, as shown in Fig. 17. The chuck holds the propellant grain and rotates it, while a pneumatic constant force device with a sandpaper tool fixed at the end applies controlled feed to bring the sandpaper tool in contact with the surface of the propellant grain. The constant force parameters are adjusted to achieve surface roughening process on the propellant grain. A laser confocal microscope (KathMatic KC-X1000) is used to obtain the surface depth information after process and to extract the contour lines for evaluating the effect of different normal forces and rotation speed. The workpieces involved in the surface roughening experiment are HTPB-based (HTPB-AP-Al) solid propellant grains. The tool is sandpaper made of brown corundum, with dimensions of 100 mm x 100 mm and a grit size of 60#. The experimental parameters for each decision variable in the surface roughening process are shown in Table 5.
The second part is the bonding experiment, which includes coating, bonding, and curing. To avoid the impact of surface quality on the coating effect, all process parameters are controlled at the median value of the parameter ranges given in Table 3 during surface roughening. After process, the propellant grains are transferred to the coating equipment, which is a screw precision coating machine, to apply adhesive in varying amounts. Upon completion of the adhesive coating, machine vision equipment (Camera: HIKROBOT MV-CE200-10UM, Lens: HIKROBOT MVLKF2528M-12 MP) captures the adhesive coating effects. In the bonding experiment, the adhesive used is epoxy resin AB adhesive (MJZM - 465), and the experimental parameters for each decision variable in the bonding process are shown in Table 5 [46].
Additionally, in order to assess the effect of key decision variables on the interfacial bonding performance, six sets of single lap shear joint (SLJ) tests were designed to demonstrate the effect of controllable key decision variables on reliability. Before bonding composite joints using epoxy resin AB adhesive, the propellant (adhesion workpiece 1) undergoes surface roughening process to obtain samples under three different normal force. For detailed procedures, refer to the first part of the experiment. Meanwhile, the coating layer (adhesion workpiece 2) is prepared by cleaning its surface. The bonding surface is cleaned with ethanol, gently rinsed with distilled water, and then dried with a hot air source for 3 min to ensure it is completely dry during bonding. To assess the effect of surface quality on bonding performance, the adhesive weight is controlled at a median value, and three sets of SL] samples with different surface qualities are obtained. To evaluate the effect of adhesive weight on bonding performance, the normal force/rotation speed is maintained at a median level, leading to three sets of SL] samples with different adhesive weight. Among them, two sets have the same configuration, so only five sets are the processed specimens, and a blank control set needs to be set. Since the adhesive weight parameter corresponds to the entire bonding surface while the SLJ sample requires only localized bonding, a scaling method is applied to the adhesive weight in the SL]. The scaling calculation method is shown in Ед. (17).
where, X9 sy is the adhesive weight in the SL), Sa is the bonded joint area, S is the total original bonded surface area of the propellant, and Xg is the original adhesive weight.
After bonding the propellant and coating layer, curing is performed according to Table 5. Each sample is kept in a airtight container and maintained at a temperature of 22 °C and humidity of 45%. Using a self-developed bonding strength testing device equipped with a 5 kN pulling sensor and a linear moving module with a speed of 5 mm/min, SL] tests are conducted 12 h after curing, as illustrated in Fig. 18.
4.2. Results and discussions
4.2.1. Processing roughness
Since the propellant grain is a rotational body, sampling near any meridian can effectively represent the surface process outcome, The visual images of the processed surface and the positions of four sampled areas are shown in Figs. 19(a)-19(d), representing the blank control and the processing effects of 20 N, 60 N, and 100 N, respectively. The intensity plots for the four corresponding sampled areas are depicted in Figs. 19(e)-19(h), while the surface depth distributions for the four sampled areas are shown in Figs. 19(i)-19(1).
When the normal force parameter reaches the median value Within the range, the resulting surface processing effect is optimal. As shown in Fig. 19(c), the processing scuffs exhibit uniform concentric circles. At this point, the intensity plot of the sampled area (Fig. 19(g)) displays a uniform distribution of light and dark regions in the processed area. The surface depth distribution (Fig. 19(k)) shows a consistent processing depth with a certain amount of higher regions due to localized burr protrusions, which do not affect the overall uniformity of the processing. Excessive normal force increases surface roughness but may lead to excessive material removal. As shown in Fig. 19(d), the processing area hardly shows any concentric circles or scuffs. The intensity plot of the sampled area (Fig. 19(h)) reveals an uneven processing effect, with darker regions making up a larger portion and clustering together, failing to form a uniform processing contour. Further examination of the surface depth distribution (Fig. 19(1)) shows significant material removal with the accumulation of numerous burrs on the surface, which further suppresses the roughness of the surface. This can result in insufficient adhesive at the bonding interface, thereby reducing the reliability. Conversely, if the normal force is too small, effective roughening cannot be achieved. As shown in Fig. 19(b), although there are concentric circle scuffs in the processing area, a significant portion remains unprocessed. In this case, the intensity plot of the sampled area (Fig. 19(f)) shows an uneven processing effect with bright areas being predominant and clustered together, which is precisely the opposite of the excessive normal force scenario. Further analysis of the surface depth distribution (Fig. 19(j)) indicates that the material removal depth is minimal, thus failing to effectively increase roughness. When adhesive is applied to such a surface, the lack of sufficient grooves to store the adhesive can lead to adhesive overflow, reducing the contact area for mechanical interlocking at the bonding interface and potentially causing detachment issues.
To further illustrate the impact of normal force on process the surfaces shown in Figs. 19(j)-19(1) to obtain their surface contours, as depicted in Fig. 20. The blank control is also subjected to contour extraction, and its contour lines are shown in Fig. 20(a). Figs. 20 (b)-20(d) correspond to Figs. 19(j)-19(1) respectively. In Fig. 20, the lines from top to bottom represent sampling lines 1, 2, and 3. The trends of contours and roughness are used to evaluate the quality of surface roughening and thereby assess the impact of normal force on reliability.
From the perspective of contour trends, it is evident that Fig. 20 (с), corresponding to a normal force of 60 №, shows the most uniform processing effect across the three sampling profiles, with stable grooves throughout the sampling length. The areas with greater height, as seen in Fig. 19(k), are due to material accumulation and burrs, but they do not affect the formation of micro mechanical interlocking structures during subsequent bonding processes. As shown in Fig. 20(d), which corresponds to a normal force of 100 N, demonstrates enhanced processing depth due to the greater normal force, with continuous regions of significant local depth. This would cause excessive adhesive retention, thereby reducing the contact with the bonded surface and consequently lowering the bond strength. As shown in Fig. 20(b), corresponding to a normal force of 20 N, shows less pronounced processing effects due to the smaller force, with some areas remaining inadequately processed and shallow depth. This would prevent adhesive from entering the grooves and result in adhesive overflow, making it difficult to form a mechanical interlocking structure, thus reducing bond strength.
From the perspective of surface roughness, the impact of normal force on the quality of surface roughening can be quantitatively described. The surface roughness (Ra) and root mean square roughness (Ry) of each sampling line in Fig. 20 are provided in Table 6, and the two evaluation indexes are represented in Egs. (18) and (19). In terms of surface roughness data, when the normal force is 60 N, the mean R, is 19.31 pm, showing the most significant processing effect. These values represent an improvement of at least 50.56% compared to a normal force of 100 N, and an improvement of at least 131.16% compared to a normal force of 20 N. When the normal force is 100 №, the mean R, is 10.66 um, although the roughness increases, the intensification of removal depth weakens the depth variation, preventing further enhancement of roughness. In contrast, when the normal force is 20 N, the mean Ra is only 6.71 um, significantly lower than the other two groups, indicating that the surface roughening effect is not significant, But compared to the blank control, even if the normal force is small and the processing is insufficient, Ra can still be effectively improved, at least by 367.19%. In terms of root mean square roughness, which reflects the degree of surface microcosmic irregularities and provides a statistical analysis of height variations, all three processed contours show an increase in Ry. When the normal force is 60 N, the Ry values for each sampling line, as well as the mean, are notably higher than those of the blank control, 20 N and 100 ? groups, with mean R, values increased by 1309.72%, 134.68%, and 58.22% respectively.
...
where, n is the number of sampling points, h; is the height of the deviation for each sampling points.
Additionally, the influence of different grain rotation speed parameters of the propellant grains on surface quality is similar to that of the normal force. This is because, under the same processing time conditions, the rotation speed translates to the number of processes on the propellant. The greater the number of rotations, the more times the process is applied, resulting in greater depth, similar to the effect of higher normal force. Conversely, fewer rotations lead to fewer processes, causing local unprocessed areas or uneven process, which corresponds to the effect of lower normal force. The optimal surface processing effect is achieved when the rotation speed parameter reaches a median value within the range. It also indirectly indicates that the rotation speed, as a key decision variable in the process, likewise plays a decisive role in reliability.
The results show that normal force and grain rotation speed, as key decision variables in the surface roughing process, have a significant impact on bonding performance. Analysis of surface roughness and contour line trends shows that variations in these variables directly influence the roughness of the interfacial microstructure, which in turn determines the risk of bonding failure. Notably, when the normal force and grain rotation speed are set to their median values, their synergistic effect maximizes surface roughness, promoting the formation of mechanical interlocking structures. This phenomenon reveals the optimization effect of the median process parameters on the quality of processing from a microscopic perspective. The surface morphology under median conditions avoids under-processing caused by low parameters and over-processing caused by high parameters. The experimental results also validate the feasibility of the improved fuzzy failure probability evaluation method.
4.2.2. Coating uniformity
Firstly, before the experiment, surface roughening process experiments were conducted on propellant grains using normal force of 60 N and rotation speed of 900 rpm to ensure uniform roughness. Three sets of propellant grains were prepared for the bonding experiments. In these experiments, the three sets of grains were processed using a screw precision coating machine, controlling the adhesive volume at 12 mL, 14 mL, and 16 mL respectively. After completing the adhesive coating and curing, the adhesive effect was captured using machine vision technology, as shown in Figs. 21(а)-21(с). Through threshold segmentation and binarization image processing techniques, the visual appearances under different coating conditions were obtained, as illustrated in Figs. 21(d)-21(f).
To ensure accuracy, error compensation was applied to the processed images, with particular improvement of the black areas on the outer ring caused by occlusion. Fig. 21(a) shows the result for 12 mL adhesive, with Fig. 21(d) indicating a white area proportion of 71.71% after error compensation, suggesting uneven adhesive distribution. Compared to Fig. 21(b), the adhesive is slightly insufficient, potentially leading to uncovered areas on the surface. Fig. 21(b) displays the surface with a 14 mL adhesive, which is considered the optimal value. The image processing result is shown in Fig. 21(e), where the proportion of white areas after error compensation is as high as 98.08%, indicating uniform coating and a smooth surface without significant gaps or irregularities. Fig. 21(c) corresponds to a 16 mL adhesive, where Fig. 21(f) shows possible defects from over coating after threshold segmentation and binarization. After error compensation, the white area proportion is only 59.01%, suggesting that excessive adhesive caused uneven accumulation and increased black area proportions, resulting in poor visual effect.
The results show that the adhesive weight, as a key decision variable in the bonding process, directly affects the uniformity of the adhesive layer and the risk of bonding failure. Under consistent surface roughening conditions, the median value of adhesive weight demonstrates optimal uniformity in the adhesive layer coverage. This median parameter ensures sufficient wetting of the solid propellant surface while effectively avoiding localized accumulation defects caused by insufficient or excessive adhesive, thereby reducing the tendency for debonding. This result further validates the engineering applicability of the improved evaluation method.
4.2.3. Bonding strength
The summarized results of the SL] tests are presented in Table 7 and Fig. 22. SL] tests involves two factors: surface roughening quality and adhesive weight, each evaluated at three levels (high "+1", medium "0", low "-1"). The optimal parameters correspond to the median values of the parameter ranges. For the grain corresponding to each level of surface roughness quality, obtained from subsection 4.2.1, "+1" represents over-processing (normal force of 100 N, resulting in excessive material removal, Fig. 19(d)); "О" is the most suitable surface roughness (normal force of 60 N, at Which point the surface roughness is maximum, as shown in Fig. 19(c)); "-1" represents under-processing (due to insufficient material removal caused by a normal force of 20 N, as shown in Fig. 19(b)). The adhesive effect corresponding to each level of adhesive weight should be consistent with subsection 4.2.2, and "+1" represents the overflow situation (Fig. 21(c) shows that the adhesive application amount is 16 mL); "0" is the optimal amount of adhesive to be applied, with no defects of overflow or insufficient adhesive, corresponding to Fig. 21(b) with a adhesive amount of 14 mL; "-1" represents the situation of insufficient glue corresponds to Fig. 21(a), where the amount of adhesive applied is 12 mL. The control group (SLJ-6) is set without the surface roughening, the amount of adhesive weight is an appropriate value but through the classic manual coating.
The results show that the shear strength of the sample improved after surface roughening process. The SLJ-1, which combines optimal surface roughness quality and uniform adhesive application, exhibited the highest shear strength, reaching 1.113 MPa, a 200.7% increase compared to the control set. Other sets also showed significant improvements in shear strength. The SL]-2 set with optimal surface roughness and excessive adhesive amount showed a similar effect to SLJ-1, increasing shear strength by 151.3%. Analysis of the curve's trend indicates that at the initial stage of tension, the excessive adhesive weight prevented the occurrence of locally unbonded areas. However, as the tension intensified, the local unevenness of adhesive led to the failure of the mechanical interlocking structure, resulting in a stable plateau period for shear strength. The SLJ-3 set with optimal surface roughness quality and insufficient adhesive weight showed an increase in shear strength by 127.9% due to local incomplete adhesion, with a rapid decline in strength after reaching a peak due to debonding.
In contrast, the increased shear strength for sets with overprocessing and under-processing surfaces at uniform adhesive application was smaller, at 85.4% and 35.8%, respectively. The relatively high shear strength in the SLJ-4 group is attributed to the appropriate adhesive weight and over-processing surface, which enhanced bonding uniformity and allowed for a peak shear strength. However, due to the absence of a mechanical interlocking structure, the bond failed at medium tensile forces, resulting in extensive debonding and a rapid decline in shear strength. In the SLJ-5 set with under-processing surfaces, some regions completely lacked roughening process and have the lowest roughness. Only certain areas exhibited higher bond strength, but as the tensile force increased, the interface was quickly peeled off.
The results show that the quality of surface roughening process and the uniformity of adhesive layer have a synergistic enhancement effect on the interfacial bonding strength. From a microscopic mechanism analysis, surface roughening significantly improves shear strength by increasing the interface contact area and forming a mechanical interlocking structure, while a moderate adhesive weight ensures uniform coverage of the adhesive layer, thereby reducing interface defects caused by local stress concentration. It is particularly noteworthy that when the three key decision variables of normal force, grain rotation speed, and adhesive weight are all taken as the median, their coupling effect can achieve the peak shear strength, which is 200.7% higher than classical processes. This phenomenon validates the effectiveness of the improved fuzzy failure probability evaluation method. Further indicating that precise control of the key decision variables mentioned above is sufficient to achieve synchronous improvement in adhesive strength and reliability.
5. Conclusions
This paper establishes a reliability prediction model using an improved FFTA integrated with a PSO-GRNN, elucidating the mechanism of key decision variables in the process of surface roughening and bonding of solid propellants, as well as their quantitative impact on product reliability. An improved FFP evaluation method is proposed to quantify the relationship between process parameters and bonding failure probabilities. The GRNN model optimizes the network smoothing factor via PSO algorithm, achieving a nonlinear mapping of process parameter bonding failure probabilities with a prediction accuracy of 0.99989 and a determination coefficient stabilized at 0.99952 + 0.00037, which surpasses classical prediction models.
Through sensitivity analysis, such as normal force, grain rotation speed, and adhesive weight are further identified as key decision variables. Experiments assessed the influence of these variables on processing roughness, coating uniformity, and bonding reliability across different levels, confirming the feasibility of the proposed improved FFP evaluation method. It is proved that a significant improvement of bonding strength can be achieved by controlling these key decision variables. When variables are at their median values, their synergistic effect improves roughness by at least 50.56% and coating uniformity reaches 98.08%, resulting in a bonding strength increase of 200.7% compared to classical methods.
This paper simplifies the complex multidimensional parameter optimization problem into the management of key variable, enhancing interface strength and reliability while avoiding the complexity of comprehensive process adjustments. This approach provides a quantifiable pathway for enhancing the reliability of solid propellant manufacturing processes and offers a framework that extends from model-driven insights to experimental validation and variable simplification. Future research will expand the material compositions and geometric configurations, integrating mechanistic models of energetic materials to further refine model parameters and enhance the model's generalization capability. By expanding the expert pool to strengthen decision-making robustness, and by investigating the impact of adhesive compatibility on debonding failure probability, this aims to deepen the understanding of interfacial failure mechanisms.
CRediT authorship contribution statement
Han Lu: Writing - review & editing, Writing - original draft, Validation, Methodology, Data curation, Conceptualization. Bin Zhang: Visualization, Validation, Methodology, Data curation. Wei Xu: Supervision, Project administration, Funding acquisition, Conceptualization. Zhigang Xu: Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Xinlin Bai: Writing - review & editing, Resources, Project administration, Conceptualization. Zheng Hu: Visualization, Validation, Investigation.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was supported in part by the Equipment Development Pre-research Project funded by Equipment Development Department, PRC under Grant No. 50923010501, and in part by the Fundamental Research Program of Shenyang Institute of Automation (SIA), Chinese Academy of Sciencess under Grant No. 355060201.
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