Quantitative evaluation of rotational wood welding joint strength based on regression of data sets

Abstract

This study aimed to enhance rotational wood welding technology by developing a simplified prediction model for pull-out strength. The key findings can offer a robust evaluation framework to advance rotational wood welding and expand its applications in woodworking. For instance, (1) A comprehensive database of 689 previously published trials was curated to identify key factors: substrate diameter, effective welded length, and substrate density. (2) Comparative analysis of test outcomes and predictive models revealed consistent trends, suggesting that modeling techniques for self-tapping wood screws could be applied to rotational wood welding joints. (3) Univariate linear regression validated the primary factors, leading to a multivariate model for predicting withdrawal capacity. Theoretical predictions closely matched empirical data, highlighting the model’s industrial applicability.

Full Article

Quantitative Evaluation of Rotational Wood Welding Joint Strength Based on Regression of Data Sets

Yun Xu ,^a Xuejiao Wang ,^b,* Aleksandr G. Chernykh ,^c Roshchina I. Svetlana ,^d Pavel S. Koval ,^c Egor V. Danilov ,^c and Anatoly Y. Naichuk ^e

This study aimed to enhance rotational wood welding technology by developing a simplified prediction model for pull-out strength. The key findings can offer a robust evaluation framework to advance rotational wood welding and expand its applications in woodworking. For instance, (1) A comprehensive database of 689 previously published trials was curated to identify key factors: substrate diameter, effective welded length, and substrate density. (2) Comparative analysis of test outcomes and predictive models revealed consistent trends, suggesting that modeling techniques for self-tapping wood screws could be applied to rotational wood welding joints. (3) Univariate linear regression validated the primary factors, leading to a multivariate model for predicting withdrawal capacity. Theoretical predictions closely matched empirical data, highlighting the model’s industrial applicability.

DOI: 10.15376/biores.20.2.2933-2948

Keywords: Rotational wood welding; Performance Evaluation; Pull-out strength; Influential factor; Multivariate linear regression analysis

Contact information: a: School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, 450045, China; b: School of International Education, Zhengzhou Railway Vocational and Technical College, Zhengzhou, 451460, China; c: Faculty of Civil Engineering, Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg, 190005, Russia; d: Institute of Architecture Construction and Energy Engineering, Vladimir State University named after Alexander and Nikolay Stoletovs, 87 Gorky Street, Vladimir, 600000, Russia; e: Faculty of Civil Engineering, Brest State Technical University, Brest, 224023, Belarus;

* Corresponding author: wangxj151719@126.com

INTRODUCTION

Wood welding technologies, encompassing linear vibration and rotational wood welding, represent significant advancements within the wood industry (Ebner et al. 2014). These methods employ high-frequency vibrations and rapid rotational movements to generate frictional heat, triggering chemical and physical transformations. This process causes the wood at the interface to melt and soften. Upon solidification, the melted material forms a robust solid phase that securely bonds disparate wooden components.

The mechanical integrity of joints produced via rotational wood welding, particularly under tensile stress, has been the subject of extensive research (Zupcic et al. 2014). Reinforcement strategies for these joints have also been explored. Notably, Pizzi et al. (2004) found that the strength of welds created through this method can rival that of traditional PVAc adhesives. Furthermore, preheating the wood to temperatures around 100 °C before welding has been shown to enhance the tensile strength of the joints beyond that achieved with PVAc bonding. This emerging technology has the potential to revolutionize the industry by providing a viable substitute for petrochemical-based adhesives, potentially leading to significant cost savings in future wood product manufacturing.

Numerous studies have explored the factors affecting the tensile strength of wood welded joints in civil engineering. Key variables include wood moisture content, rotational speed, grain orientation, dowel and predrilled hole dimensions, and additives such as ethylene-glycol (Costa Viana et al. 2023; Zhu et al. 2023; Zhong et al. 2024). Kanazawa et al. (2005) highlighted the importance of the diameter difference between the dowel and the predrilled hole, finding that minimal differences maximize welding strength. Belleville et al. (2013) identified wood species and rotational speed as crucial for peak temperature at the contact interface, influencing welding strength. Ebner et al. (2014) noted that tensile strength varies with the operational mode of automated wood welding machinery. Zupcic et al. (2014) found a significant correlation between wood species, welding direction, and welding strength. A welding depth of 30 mm for dowels loaded by tensile force was recommended by Zupcic et al. (2024). Leban et al. (2008) showed that increased rotational speed and insertion rate could reduce welding strength due to material expulsion from the interface. Recent research by Zhu et al. (2017) revealed that weld depth and CuCl₂ pretreatment of dowels enhance joint withdrawal capacity. Dowels immersed in CuCl₂ for 30 minutes showed superior tensile strength, especially at a 30 mm weld depth. Biological pretreatment of dowels significantly increased pull-out force after 4 weeks, but not after 2 weeks. Grooved dowels increased pull-out force by 26.9%, compared to 21.1% for smooth dowels (Zupcic et al. 2023b). Despite extensive research over the past two decades, identifying the primary factors influencing rotational wood welding strength remains challenging, hindering technological advancement and broader application of this technique.

The calculation model of glued-in-rod has been validated to predict the withdrawal strength of welded joints, with rotational speed, a critical variable, expressed through a trigonometric function based on Zhu et al. (2017). However, Belleville et al. (2013) identified species and rotational speed as the sole parameters influencing peak temperature and tensile strength at the welded line. Notably, 39% of studies focused on the 1500 to 2000 rpm range, where the maximal pull-out force was also observed (Xu et al. 2022). Thus, it can be inferred that for the withdrawal strength of welded joints, rotational speed may be a fixed variable. Failure to achieve a specific rotational speed could hinder the high densification of bonded interfaces, suggesting that the validated model may not comprehensively describe the physical process of rotational wood welding (Xu et al. 2022). Xu and Wang (2024) investigated the elastic deformation of rotational wood-dowel welding joints using the variational method. The findings indicated that the elastic solution method could accurately estimate the ultimate pull-out bearing capacity and deformation characteristics of the welding joints. This study represents a significant attempt to elucidate the physical process of rotational wood welding from the perspective of elastic deformation. It is noteworthy that the fabrication processes of rotational wood welding and self-tapping wood screws have some similar aspects. Compared to the glued-in-rod calculation model, the strength calculation model for self-tapping wood screws may better predict the tensile strength of welding joints from both physical and theoretical perspectives.

Wood friction welding, utilizing high-speed rotation, presents a promising avenue for producing eco-friendly and cost-effective wooden products without relying on adhesives. Recent studies have delved into the analysis of axially-loaded dowel-welded wood joints, providing a wealth of experimental data to elucidate the interplay between various factors and the tensile strength of the welding joints. To date, only a couple of predictive models, proposed by Zhu et al. (2017) and Ganne-Chedeville et al. (2005), respectively, have been put forward to estimate the optimal withdrawal capacity of these joints. However, the limited sample sizes in these studies have precluded the development of a robust assessment framework. This study aimed to compile a comprehensive database of pull-out test results from existing literature and develop a multivariate predictive model to accurately assess the tensile strength of welding joints. The research was expected to significantly advance this emerging technology, facilitating its application in timber structure construction and furniture manufacturing. However, a potential limitation is the presence of systematic differences across datasets, which may introduce variability and affect the accuracy of the analysis. Despite this, the approach offers the potential for a robust fit with minimal error. The primary objective is to evaluate the feasibility of achieving a robust data fit across multiple studies, aiming to establish a foundational relationship for global research applications. For clarity, a flow chart detailing the proposed solution is presented in Fig. 1.

Fig. 1. Flowchart of the solution scheme

EXPERIMENTAL

Theoretical Approach

Figure 2 schematically depicts the axially-loaded dowel-welded wood joint, comprising: (a) a wood dowel rotationally welded into a substrate with a predrilled hole; (b) the fusion of the bonding interface during welding; (c) the pull-out test setup. The figure annotates various parameters as follows: L denotes the total length of the wood dowel, L_eff signifies the effective welded length, L_out represents the remaining length of the dowel, α is the angle between the insertion direction and the grain orientation of the substrate, D is the initial diameter of the dowel, d is the diameter of the predrilled hole in the substrate, P stands for the welding force, and F is the pull-out force. Previous research (Pizzi et al. 2004; Ganne-Chedeville et al. 2005) has demonstrated that rotational wood welding shares similar characteristics and material alterations with linear welding. According to Cornuault and Carpentier (2020), the rotational wood welding process can be distilled into three distinct phases, taking into account the contact-boundary conditions between the dowel and the substrate: (i) initial boundary contact, where the wood samples’ moisture content is the predominant factor influencing joint withdrawal capacity; (ii) boundary collapse, characterized by friction-induced heat that catalyzes the release of lignin and the creation of welded spots; (iii) boundary fusion, during which the molten material flows and solidifies to form a durable adhesive bond upon cooling.

Fig. 2. Schematic representation of the axially-loaded dowel-welded wood joint: (a) Wood dowel rotation welded in the substrate with a predrilled hole; (b) Welding fusion of bonding interface; (c) Pull-out test

Figure 2 elucidates the parallels between the fabrication processes of dowel-welded wood joints and the operational mechanics of self-tapping wood screws. In contemporary timber construction, self-tapping screws serve as pivotal load-bearing elements, both directly and indirectly, thereby optimizing the efficacy of fasteners and joints while concurrently curtailing expenses. The withdrawal capacity of these screws within timber is known to be contingent upon a spectrum of factors, including moisture content, ambient temperature, wood density, screw tip geometry, orientation relative to the wood grain, pre-drilling practices, and the insertion depth of partially threaded screws. Table 1 compiles a comprehensive array of parameters gleaned from prevailing standards and scholarly research that inform predictive models for self-tapping wood screws. Equation 1, as delineated in Table 1, is the foundational formula endorsed by a majority of research papers and normative documents. The equation considers the effective threaded length of the screw (L_eff), the wood density (ρ), and the screw diameter (d) as the principal variables influencing the model. It is noteworthy that there is a marked disparity in the coefficients (A, B, C, and D) across different codes and studies. Moreover, it is the withdrawal capacity of screws aligned perpendicular to the wood grain that is typically referenced as the standard measure. The calculation is as follows,

(1)

where is the withdrawal capacity of self-tapping screw perpendicular to the grain of substrate (N), d is the screw diameter (mm), L_eff is the effective threaded length of the self-tapping screw (mm), is the substrate density (kg/m³), and A, B, C, and D are undetermined coefficients.

Table 1. Overview: Parameters of Current Codes and Research for F_ax,90

The research conducted by Pizzi et al. (2004) revealed that within a certain rotational speed range, the angle of welding direction relative to the grain orientation of the substrate, as well as the surface texture of the dowels (whether rough or smooth), did not significantly affect the welding outcome. Building on this insight, this paper posited that the predictive methodology employed for self-tapping wood screws can be equally applicable to welding joints. This assumption was grounded in the adoption of the foundational equation, Eq. 1, as a model. Consequently, the primary factors influencing welding joints have been identified as distinct from those affecting self-tapping wood screws, specifically highlighting wood density, the difference in diameter between the wood dowel and the predrilled hole, and the effective welded length. In contrast, Yin et al. (2022) highlighted that the welding speed and the moisture content of the wood substantially influenced the interfacial force and the temperature at the welding interface. In an effort to streamline the computation of the withdrawal capacity for welding joints, this paper proposes four working hypotheses, analogous to the modeling strategy for self-tapping wood screws:

• The welding parameters, such as rotational speed and holding pressure duration, have been optimized.

• The high-speed rotation ensures a uniform welded layer along the bonding interfaces.

• The difference in grain orientation between the dowel and the substrate has been disregarded.

• The size effect of the substrate has been ignored.

• The impact of wood moisture content has been neglected.

Experimental Database

In this study, a comprehensive database was compiled from 659 trials documented in previous research, as referenced in Table 2, to analyze rotational wood welding joints.

Table 2. Overview: Parameters and Pull-out Test Results

Notes: Group A-1 from the work (Zhu et al. 2017), and Group A-2/3 from the work (Zhang et al. 2017); Group B from the work (Zupcic et al. 2014); Group C from the work (Ebner et al. 2014); Group D from the work (Belleville et al. 2013); Group E from (Ganne-Chedeville et al. 2005).

The standard practice in the field involves inserting a wood dowel into a substrate via a pre-drilled hole, utilizing either a high-speed manual or a benchtop drilling machine. This is followed by a pull-out test performed with a universal testing machine. To ensure the reliability of the data, 20 sets were meticulously selected as representative samples from the 659 trials, corroborated by established online databases (Green et al. 1999; Meier 2007; European Wood 2011; MatWeb 2011). Table 2 summarizes the parameters and outcomes of the pull-out tests, detailing dowel diameters ranging from 8 to 12 mm, predrilled hole diameters from 7.67 to 9 mm, effective welded lengths between 15 to 40 mm, the orientation angle relative to the substrate grain (perpendicular or parallel), the densities of both dowel and substrate, and the peak pull-out forces observed (F_max).

The types of wood dowels utilized in the trials included:

• ø 10 mm/60 mm, ø 10.04 mm/120 mm, and ø10 mm/80 mm dowel of European beech (Fagus sylvatica);

• ø 10 mm/100 mm and ø 12 mm/100 mm dowel of Chinese birch (Betula);

• ø 9.68 mm/82 mm dowel of yellow birch (Betula alleghaniensis);

• ø 9.68 mm/82 mm dowel of sugar maple (Acer saccharum);

The following types of substrates were used:

• 50 mm×50 mm×20 mm substrate of European beech (Fagus sylvatica);

• 30 mm×30 mm×200 mm substrate of European beech (Fagus sylvatica);

• 30 mm×30 mm×200 mm substrate of European oak (Quercus petraea);

• 30 mm×30 mm×200 mm and 60 mm×60 mm × 40 mm substrate of European spruce (Picea abies);

• 40 mm×50 mm×500 mm and 60 mm×60 mm × 40 mm substrate of Eastern larch (Larix laricina);

• 30 mm×30 mm×400 mm substrate of sugar maple (Acer saccharum);

• 30 mm×30 mm×400 mm substrate of yellow birch (Betula alleghaniensis);

RESULTS AND DISCUSSION

Comparison Between the Measured and Calculated Values

This paper integrated equations from prevailing standards and recent studies, as outlined in Table 1, to predict the withdrawal capacity of rotational wood welding joints, utilizing the empirical data from Table 2. The juxtaposition of measured versus predicted values, depicted in Fig. 3, reveals a significant discrepancy, suggesting that the current equations may not precisely forecast the experimental outcomes (indicated by the red line).

Nonetheless, the envelope diagram (highlighted in green) demonstrates that Eq. 1, which is based on the foundational formula from existing codes and research, can approximate the trend of the pull-out test results from Table 2. This observation suggests that the basic structure of Eq. 1, commonly used for self-tapping screws, might be extendable to wood dowels. The four working hypotheses presented in the section above appeared to hold merit. Moreover, it is recommended that wood density, the relative diameter difference between the dowel and the predrilled hole, and the effective welded length should be regarded as the principal factors in the modeling of welding joints.

Fig. 3. Comparison between the calculated values obtained from the prediction models (refer to Table 1) and the measured values provided in Table 2

Influence of Wood Moisture Content on the Withdrawal Capacity of Welding Joints

The interactions between parameters that are crucial in wood dowel welding through high-speed rotation have been evaluated by Ganne-Chedeville et al. (2005). Among these, the interplay between rotation rate and dowel moisture content emerged as the most significant, with a descending order of importance. Rotary friction welding of heat-treated Scotch pine is feasible, and the joint strength exceeds that of glued and hammered joints (Zhang et al. 2024). Li et al. (2023) found that the dry bonding strength and the wet bonding strength (after immersion in cold, hot, and boiling water) of pretreated dowels were higher than those without pretreatment and significantly superior to traditional polyvinyl acetate (PVAc) adhesive bonding. Biwôlé et al. (2023) investigated the cold water resistance of welded joints in Iroko wood (Milicia excelsa C. C. Berg) and identified water-insensitive oligomers as key to their water resistance. Thermal modification can enhance the dimensional stability of wood by reducing its hygroscopicity, but it can also cause cracks, affecting welding strength. Adjusting welding parameters can prevent cracks but may reduce pull-out strength by more than 25%. Citric acid treatment of wood and dowels significantly reduces pull-out strength, questioning its use in wood welding (Župčić et al. 2023a). For the commercial wood dowels, an equilibrium moisture content of 12% has been widely accepted in scientific and industrial contexts. Therefore, once the most determinant factor from previous studies was controlled, the most impactful factors were identified as the welding depth, wood species, the dowel/hole diameter difference.

Influence of Diameters on the Withdrawal Capacity of Welding Joints

The study of Pizzi et al. (2004) demonstrated that the relative diameter difference between the wood dowel and the predrilled hole was the primary factor impacting on the withdrawal capacity of welding joints. While the relative diameter difference was considered a major factor, other influential parameters could also enhance joint strength (Kanazawa et al. 2005). In line with existing literature, the findings of Pizzi et al. (2004) indicated that a dowel diameter of 10 mm and a predrilled hole diameter of 8 mm yielded optimal results. Another study (Rodriguez et al. 2010) suggested that a dowel/hole diameter ratio of 5/4 (i.e., 1.25) was the optimal ratio, with no significant differences observed for higher ratios under the same conditions. Table 2 shows that the range of dowel/predrilled hole diameter ratios falls between 1.11 and 1.41. It is worth noting that a ratio of 1.26 has been accepted by 79% of the test groups, supporting the findings of work (Rodriguez et al. 2010). While the diameter ratio is important for evaluating the withdrawal capacity of welded joints, previous studies have not established a uniform reference. Given the complex interactions among different factors, it is hard to believe that a ratio of 1.26 will be the optimal value under all conditions. Considering future standardization in design and manufacture, if the dowel diameter remains constant and the diameter ratio is restricted within limited ranges, the predrilled hole diameter will have a greater impact on welding strength than the wood dowel.

The research by Pizzi et al. (2004) highlighted the significance of the relative diameter difference between the wood dowel and the predrilled hole as a key determinant of the withdrawal capacity of welding joints. Although this diameter difference is a crucial factor, Kanazawa et al. (2005) identified additional parameters that could further enhance joint strength. Consistent with these findings, a dowel diameter of 10 mm and a predrilled hole diameter of 8 mm were found to be optimal. Rodriguez et al. (2010) proposed an ideal dowel/hole diameter ratio of 5/4 (1.25), with negligible variance observed for higher ratios under identical conditions. According to Table 2, the observed range of dowel to predrilled hole diameter ratios spans from 1.11 to 1.41, with a ratio of 1.26 being prevalent in 79% of the test groups, corroborating the conclusions of Rodriguez et al. (2010). While the diameter ratio is a critical metric for assessing the withdrawal capacity of welded joints, there is no consensus on a standard reference value across previous studies. The intricate interplay of various factors suggested that a ratio of 1.26 might not universally represent the optimal value. In anticipation of future standardization in design and manufacturing, maintaining a constant dowel diameter and limiting the diameter ratio within a specific range implies that the predrilled hole diameter can exert a more pronounced influence on the welding strength than the dowel itself.

Influence of Species on the Withdrawal Capacity of Welding Joints

In comparison to linear vibrational welding, studies by Kanazawa et al. (2005) and Gfeller et al. (2003) have shown that rotational wood welding could induce the formation of furanic compounds at elevated temperatures. Notably, the concentration of these compounds was found to be lower on the wood dowel than on the substrate. Further research by Zupcic (2010) revealed that the density of the wood, even within the same species but at varying densities, could significantly bolster the strength of the welded joints. This suggested a direct, positive relationship between the tensile strength of the weld and the density of the substrate, especially when using denser wood species. To corroborate the influence of wood density, three test cases from Table 2 are graphically represented in Fig. 4, where the density ratio between the dowel and the substrate is the variable of interest. For a constant dowel density, an increase in substrate density leads to stronger welds, as shown in Fig. 4(a) and 4(b). Conversely, maintaining a consistent substrate density while increasing the dowel density also enhances the joint strength, as indicated in Fig. 4(c). Although dowels can be fashioned from various wood types, beech wood has been recommended by Zupcic et al. (2014) as the optimal material, with the grain orientation of the dowel being a negligible factor. Therefore, it can be deduced that when beech wood is employed for the dowel, the substrate density emerges as a more pivotal factor influencing the welding strength.

Fig. 4. The influence of the density ratio on the withdrawal strength of welded joints. (a) The influence of density ratio (substrate/wood dowel) on the withdrawal strength of joints or the wood dowel of European beech with group B-7/8/9. (b) The influence of density ratio (substrate/wood dowel) on the withdrawal strength of joints for the wood dowel of Chinese birch with group A-2/3. (c) The influence of density ratio (wood dowel/substrate) on the withdrawal strength of joints for the substrate of European beech with group A-3&B-12.

Pearson Correlation Analysis

To evaluate the impact of key factors such as predrilled hole diameter, welded length, and substrate density on the tensile strength of wood welding, Table 3 showcases the Pearson correlation analysis used to investigate the relationship between the withdrawal capacity of welded joints and various influencing factors. The analysis indicated that the effective welded length of the dowel correlated with a coefficient of -0.64, suggesting a notable inverse relationship with withdrawal capacity. Additionally, the dowel diameter had a correlation coefficient of -0.32, and the diameter of the predrilled hole in the substrate had a coefficient of -0.52, both indicating negative correlations with withdrawal capacity. While the effective welded length of the dowel showed a stronger correlation with withdrawal capacity than the other factors, the diameter of the predrilled hole was identified as having a more significant impact on the welding strength, particularly when the dowel diameter and diameter ratio were held constant. Conversely, the substrate density exhibited a positive correlation with withdrawal capacity, marked by a coefficient of 0.68. It is crucial to recognize that a univariate linear regression model is insufficient to capture the withdrawal capacity of welded joints based solely on these factors. As such, a multivariate linear regression model is recommended to more accurately reflect the complex interplay among these variables.

Table 3. Pearson Correlation Analysis

Notes: Pearson correlation analysis conducted to examine the relationship between the withdrawal capacity of the welded joints and other factors. A is denoted as the dowel diameter. B is denoted as the effective welded length of dowel. C is denoted as the substrate density. D is denoted as the diameter of the predrilled hole in substrate. E is denoted as the Withdrawal capacity of welding joints perpendicular to the grain of the substrate.

Multivariate Linear Regression Analysis

The histogram of the dependent variable log10 (F_ax,90) in Fig. 5(a) suggested that the standardized residuals of the regression adhere to a normal distribution, with a mean close to zero (μ=-2.29E-15) and a standard deviation near one (σ=0.866). Figure 5(b) shows the data points dispersed around the diagonal line within the first quadrant, reinforcing the normal distribution assumption for the residuals.

Figure 5(c) depicts the residuals forming a consistent “horizontal band” around the zero line, lacking any apparent pattern or variability in relation to the predicted values, thus indicating homoscedasticity.

Table 4 presents Variance Inflation Factor (VIF) values below 10 for each independent variable, signifying no substantial multicollinearity. After verifying the linear regression assumptions, it is evident that the collected data met the criteria for normality, linearity, homoscedasticity, and the absence of multicollinearity, making it suitable for multiple linear regression modeling.

Building on the analysis of the primary factors and their influence on welding strength, the prediction model incorporated the predrilled hole diameter, welded length, and substrate density. To derive a multivariate linear relationship, a logarithmic transformation was applied to both sides of Eq. 1, yielding Eq. 2. Subsequent multivariate linear regression analysis, based on test results perpendicular to the grain of the substrate (referenced in Table 2), formulated the prediction model for the withdrawal capacity of rotational wood welding joints as Eq. 3.

Table 4. Check of Multicollinearity

The model coefficient of determination, R², is notably high at 0.966, signifying its robust predictive accuracy for the variations observed in the dataset.

(2)

(3)

To ascertain the precision of Eq. 3, the data from Table 2 was bifurcated into two categories: (i) the first type, encompassing 17 groups derived from pull-out tests executed perpendicular to the substrate’s grain, and (ii) the second type, consisting of 3 groups from tests conducted parallel to the grain (Note: these were not included in the original model data). Figure 6 juxtaposes the empirical values from Table 2 with those calculated via Eq. 3. The figure revealed that for the first type, deviations range from a minimum of 0.61% to a maximum of 14.44%, with an average deviation of 5.55%. For the second type, the deviations spanned from a minimum of 0.28% to a maximum of 14.36%, averaging at 5.50%. Prior studies (Pizzi et al. 2004; Zupcic et al. 2014) have established that the welding strength is not significantly affected by the angle between the welding direction and the grain orientation. Thus, the proposed model is adept at predicting the withdrawal capacity for joints welded both perpendicular and parallel to the grain. It must be noted, however, that this study was not without its limitations. While the primary factors were considered, the new prediction model did not account for the relationship between welding strength and other potential factors, due to a lack of extensive research. Nonetheless, the proposed model (with R²=0.966) demonstrated sufficient accuracy to enhance product optimization within the timber structure and furniture industries. For further validation of Eq. 3, additional data from pull-out tests conducted parallel to the grain is necessary.

Fig. 6. Comparison between the measured values presented in Table 2 and the calculated values derived using the prediction model defined by Eq. 3.

CONCLUSIONS

1. A robust database comprising 689 trials was curated from existing literature to facilitate data analysis and modeling for pull-out tests. Through examination of the experimental data, pivotal factors were pinpointed: substrate diameter, effective welded length, and substrate density. These elements formed the cornerstone for predicting the withdrawal capacity of rotational wood welding joints.
2. A comparative analysis of the test outcomes detailed in Table 2 against the calculated values derived from various predictive approaches (as outlined in Table 1) revealed congruent trends across all models, barring SNIP 64.13330.2011. Given the analogous manufacturing processes and mechanical behaviors of both joint types, it was posited that the modeling techniques employed for self-tapping wood screws might be transferable to rotational wood welding joints.
3. The study utilized univariate linear regression analysis to validate the three primary factors integral to the prediction model. Leveraging the modeling strategies associated with self-tapping wood screws and the insights from linear regression analysis, a multivariate model, expressed as Eq. 3, was introduced for forecasting the withdrawal capacity of rotational wood welding joints. The theoretical predictions of the proposed model aligned closely with empirical measurements, underscoring its robust correlation and potential applicability in industry settings.

ACKNOWLEDGMENTS

The authors thank Professor Chernykh A.G. of Saint Petersburg State University of Architecture and Civil Engineering, Professor Naichuk A.Y. of Brest State Technical University, and Professor Svetlana R.I. of Vladimir State University named after Alexander and Nikolay Stoletovs for their contribution in the critical discussion of the manuscript. The authors gratefully acknowledge the financial support from the Research Project of Colleges and Universities in Henan Province (grant no. 23A560007), Henan Provincial Natural Science Foundation (grant no. 242300420037), Training Program for Young Backbone Teachers of Undergraduate Colleges and Universities in Henan Province (grant no. 2023GGJS075), Research Project of Science and Technology Plan of Henan Province Housing and Urban-Rural Construction (grant no. K-2336), National Foreign Expert Individual Projects (grant no. S20240101).

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Article submitted: January 6, 2025; Peer review completed: February 14, 2025; Revised version received and accepted: February 17, 2025; Published: February 27, 2025.

DOI: 10.15376/biores.20.2.2933-2948