Prediction method for pull-out bearing capacity of friction welding of wooden pins induced by high-speed rotation

Abstract

The present invention discloses a method for predicting the pullout bearing capacity of high-speed rotation-induced friction welding of wood dowels. Using a multivariate nonlinear regression approach, the pullout bearing capacity of high-speed rotation-induced friction welding of wood dowels is #imgabs0#, expressed as the formula #imgabs1#. This method provides a precise calculation method for the use of wood dowel rotation welding technology to connect wood structural components in modern timber construction and solid wood furniture manufacturing. This method effectively addresses the long-standing lack of a theoretical basis for multi-factor prediction of weld joint pullout strength, further facilitating the wider application of this innovative technology in the processing and manufacture of timber structural products.

Description

Technical Field

[0001] The invention belongs to the field of modern wood structure construction and solid wood furniture manufacturing, and particularly relates to a method for predicting the pull-out bearing capacity of high-speed rotation-induced friction welding of wood pins in wood structures. Background Art

[0002] High-speed rotation-induced friction welding of wood dowels is a novel adhesive-free wood joining method. Using specialized welding equipment, a small-diameter dowel is inserted into a pre-drilled hole in the wood substrate. High-speed rotation causes friction between the dowel and the hole wall, increasing the temperature. This softens and causes polymeric materials (such as lignin and hemicellulose) at the interface to flow. Upon cooling, these materials form a hard compound, bonding the dowel to the wood substrate. The average pullout strength of these high-speed rotation-induced friction welded joints approaches that of PVAc glued joints, demonstrating significant potential for engineering applications. In the field of modern wood structure buildings and solid wood furniture, the connection between wooden components mainly adopts nail connection, bolt connection, mortise and tenon connection and adhesive connection. Compared with these connection methods, the new technology has some unique characteristics, including: (1) the new technology avoids the damage to the surface of the original wood structure products caused by traditional connection methods, and can retain the original natural color of the wood of the wood structure components; (2) it simplifies the connection method and construction process of mortise and tenon connection and adhesive connection. By using the same installation method and installation equipment as self-tapping screws, the welding of a product can be completed in 2s to 10s; (3) the strength of the welded joint is equivalent to that of PVAc adhesive, which can effectively replace the connection method of traditional adhesive; (4) the new technology truly realizes the sustainable use of materials and effectively achieves zero emission of harmful substances in the entire life cycle from component processing, installation, use, maintenance and recycling. Therefore, in summary, high-speed rotary induced wood pin friction welding technology, as an innovative connection method, can effectively reduce the excessive use of metal and petrochemical products in the field of modern wood structure buildings and solid wood furniture manufacturing, greatly improve construction efficiency and reduce production costs, and has great commercial promotion value.

[0003] High-speed rotation-induced wood pin friction welding technology, as a method of connecting wood structural components, mainly includes two forms: (1) the wood pin directly penetrates two wood substrates; (2) the wood pin penetrates one wood substrate and only reaches a certain depth in the other wood substrate without penetrating. Since wood is mainly composed of cellulose, hemicellulose and lignin, lignin can soften under high temperature conditions and produce a similar effect to thermoplastic adhesives, which makes it possible to induce high-speed rotation to induce wood pin friction to heat up and soften lignin. Through high-speed rotation induction technology, friction heat can be generated between the welding interfaces of the above two connection methods, thereby causing thermoplastic substances such as lignin to soften and melt. After the interface layer coats the fibers, it cools and solidifies to form a welding node with a certain strength. The performance of timber joints depends primarily on the pullout resistance of the connectors. Therefore, since the introduction of wood rotational welding and vibration welding technologies in 1997, experts and scholars at home and abroad have focused on the factors affecting the pullout resistance of wood dowels in rotational friction welding, hoping to further improve the pullout resistance of welded joints. These factors include welding temperature, weld interface pretreatment, dowel rotation speed, insertion rate, dowel species, dowel diameter, weld depth, drilling direction, the difference in equilibrium moisture content between the wood substrate and the dowel, and the difference in pre-drilled hole diameter between the dowel and the wood substrate. Among these factors, rotation speed, wood species, effective weld depth, and dowel diameter are key factors affecting weld joint performance. Although domestic and foreign scholars have conducted extensive experimental and theoretical research on high-speed rotation-induced wood pin friction welding technology over the years, most of the published research results have only studied the mechanism of action of a single influencing factor on the strength of welded joints. To date, there is still a lack of a formula for predicting the pull-out bearing capacity of welded nodes based on the comprehensive action mechanism of multiple factors. This directly restricts the further promotion and application of this new technology in the fields of modern wooden structure construction and solid wood furniture industry. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for predicting the pull-out bearing capacity of high-speed rotation-induced wood pin friction welding. The calculation formula of the present invention can provide an accurate calculation method for the use of wood pin rotation welding technology to connect wood structure components in the fields of modern wood structure construction and solid wood furniture manufacturing. It solves the important problem that this technology has long lacked a theoretical basis for multi-factor prediction of the pull-out strength calculation of welded nodes, and makes it easier to apply this innovative technology more widely to the processing and production of wood structure products.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for predicting the pull-out bearing capacity of friction welding of high-speed rotation-induced wooden pins is proposed, which adopts a multivariate nonlinear regression method. The pull-out bearing capacity of friction welding of high-speed rotation-induced wooden pins is F ax，90 , which is expressed as formula (1),

[0007] F ax，90 =f(n)·d A ·L eff B ·ρ C (1)

[0008] in:

[0009] F ax，90 – The pull-out bearing capacity of the joint where the welding direction is perpendicular to the wood grain direction of the wood substrate, N;

[0010] f(n) – nonlinear function related to the rotation speed;

[0011] n – rotation speed, rpm;

[0012] d – diameter of pre-drilled hole in wooden substrate, mm;

[0013] L eff –Effective welding depth, mm;

[0014] ρ – air-dry density of the wood substrate, kg / m 3 ;

[0015] A, B, C – coefficients to be determined.

[0016] The above-mentioned method for predicting the pull-out bearing capacity of friction welding of wooden pins induced by high-speed rotation is based on the experimental data collected from different references (Table 1). The multivariate nonlinear regression method is used to determine the unknown coefficients A, B, C, and D in formula (1): A = -1.103, B = 0.187, and C = 1.805; the nonlinear function related to the rotation speed,

[0017] The above-mentioned high-speed rotation-induced wood pin friction welding pull-out bearing capacity prediction method, formula (3) can well fit the rotation speed, pre-drilled hole diameter d, effective welding depth L eff The four influencing factors of the wood substrate, the air-dry density of the tree species used, and the pull-out bearing capacity F of the welded joint are ax，90 The nonlinear relationship between:

[0018] F ax，90 =f(n)·d -1.103 ·L eff 0.187 ·ρ 1.805 (3)

[0019] in: Where n – rotation speed, rpm;

[0020] The above-mentioned method for predicting the pull-out bearing capacity of friction welding of high-speed rotation-induced wooden pins, the diameter d of the pre-drilled hole of the wooden substrate is 7.67mm-9.5mm, and the effective welding depth L eff The thickness of the wood substrate is 15mm to 40mm, and the air-dry density of the wood species used is 450 to 710 kg / m 3 The welding direction should be at an angle of 0° or 90° to the wood grain of the wood substrate.

[0021] By adopting the above technical solution, the present invention has the following advantages:

[0022] This invention accurately predicts the pullout strength of welded joints, whether welding perpendicular to the wood grain or parallel to the grain. This new formula provides a precise method for calculating the pullout strength of wood structural components connected using wooden dowels in modern timber construction and solid wood furniture manufacturing. This effectively addresses the long-standing lack of a theoretical basis for multi-factor prediction of welded joint pullout strength, further facilitating the widespread application of this innovative technology in the processing and manufacture of timber structural products. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a schematic diagram of the welding process of the wooden dowel and the wooden base material of the present invention.

[0024] Figure 2 Schematic diagram of low speed welding process.

[0025] Figure 3 Schematic diagram of medium speed welding process.

[0026] Figure 4 Schematic diagram of high speed welding process.

[0027] Figure 5 It is a force diagram of the pull-out test after the wooden pin is welded to the wooden base material of the present invention.

[0028] Figure 6 yes Figure 5 AA cross-section of the middle wooden dowel and the welded layer.

[0029] Among them, 1 is the wooden dowel, 2 is the pre-drilled hole, D is the wooden substrate, 3 is the welding layer, 4 is the carbonized layer, and E is the smoke formed during the rotation process. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solutions and experiments of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the embodiments. It should be understood that the specific examples described herein are only used to explain the present invention and are not intended to limit the present invention.

[0031] The present invention Figure 1 This is a diagram of a wooden dowel being inserted into a pre-drilled hole in a wood substrate through high-speed rotation. The high-speed rotation friction between the wooden dowel and the pre-drilled hole in the wood substrate increases the temperature, causing the hemicellulose and lignin in the wooden dowel and the wood substrate to decompose, producing a molten substance with an adhesive effect, which forms a glue after cooling. Figure 5 The welding layer connects the wooden dowel and the wooden substrate together. Figures 2-4 As shown, under high rotation speed, the hemicellulose and lignin in the wooden dowel and the wooden substrate are completely decomposed, and the molten material with adhesive effect, that is, the welding layer is optimal. Therefore, in the process of rotary induced welding of the wooden dowel and the wooden substrate, high-speed rotation can achieve good welding effect.

[0032] A method for predicting the pull-out bearing capacity of friction welding of high-speed rotation-induced wooden pins is proposed, which adopts a multivariate nonlinear regression method. The pull-out bearing capacity of friction welding of high-speed rotation-induced wooden pins is F ax，90 , its general expression is formula (1),

[0033] F ax，90 =f(n)·d A ·L eff B ·ρ C (1)

[0034] in:

[0035] F ax，90 – The pull-out bearing capacity of the joint where the welding direction is perpendicular to the wood grain direction of the wood substrate, N;

[0036] f(n) – nonlinear function related to the rotation speed;

[0037] n – rotation speed, rpm;

[0038] d – diameter of pre-drilled hole in wooden substrate, mm;

[0039] L eff –Effective welding depth, mm;

[0040] ρ – air-dry density of the wood substrate, kg / m 3 ;

[0041] A, B, C – coefficients to be determined.

[0042] Based on the research results and practical experience at home and abroad, the inventors set the rotation speed n, the pre-drilled hole diameter d of the wood substrate, and the effective welding depth L eff The air-dry density ρ of the wood substrate is used as the main influencing factor for evaluating the pull-out bearing capacity of the wood pin rotary friction welding node. It should be pointed out that the rotation speed plays a decisive role in the formation of the welding node, and its influence degree can be divided into three stages: (1) low speed level: 0≤n<1000rpm. At this stage, the speed cannot provide enough lignin softening energy, and it is difficult to effectively form the welding interface; (2) medium speed level: 1000rpm≤n≤2500rpm. When the speed reaches this stage, a higher friction temperature will be generated, thereby softening the lignin at the welding interface to form a welding bonding layer. However, different combinations of influencing factors will result in different required speeds; (3) high speed level: 2500rpm≤n≤6500rpm. At this stage, due to the ultra-high speed, the generated lignin will be further squeezed and penetrated into the wood base, thereby dispersing the lignin content. At the same time, the carbonization phenomenon caused by the high speed also destroys the original welding bonding layer, and the welding interface cannot be effectively formed.

[0043] The pull-out failure mechanism of friction-welded joints induced by high-speed rotation is similar to that of glued-rebar joints in wood structures. By referring to the calculation method of glued-rebar joints in wood structures perpendicular to the wood grain direction, the mathematical relationship between the above four influencing factors and the pull-out bearing capacity of the joint is extracted as formula (1), which involves four unknown coefficients, namely A, B, C and a nonlinear function f(n) related to the rotation speed.

[0044] In order to avoid the interference of other influencing factors on the pull-out bearing capacity of welded joints, the following four assumptions need to be defined for the general form of the above bearing capacity prediction formula: (1) The welding parameters (including the external pressure and pressing time of the welding equipment) have reached the optimal level during the entire welding process; (2) A uniform and stable weld layer can be formed on the bonding interface after welding; (3) The angle formed by the welding direction and the wood substrate is simplified to two directions: parallel and perpendicular to the wood grain, and the influence of other welding directions on the joint performance is ignored; (4) The size effect of the wood base on the pull-out performance of the welded joint is ignored.

[0045] The above-mentioned high-speed rotation-induced wood pin friction welding pull-out bearing capacity prediction method, the inventors of the present invention summarized 1338 experimental research results at home and abroad, and divided them into 23 groups of representative data results according to different influencing factors, of which 20 groups were perpendicular to the wood grain direction of the wood substrate, and 3 groups were parallel to the wood grain direction of the wood substrate, including the wood substrate pre-drilled hole diameter d (7.67mm ~ 9.5mm), the effective welding depth L eff(15mm~40mm), welding direction and wood grain angle of wood substrate (0° and 90°) and different tree species including (Chinese birch, Northeast larch, European beech, North American yellow birch, North American sugar maple, European larch, European oak).

[0046] In order to find the size of the three unknown coefficients A, B, and C in formula (1) and determine the complete expression of f(n), the following three steps are required: First, logarithmize both ends of the equal sign of formula (1), and the nonlinear expression based on multiple parameters can be expressed as formula (2); Use SPSS and Excel to bring the 20 sets of data collected (Table 1) into formula (2) to complete the nonlinear regression analysis calculation, and the size of the three unknown coefficients A, B, and C and the complete expression of f(n) can be determined; From the results of the multivariate nonlinear regression analysis calculation, it can be seen that when A=-1.103, B=0.187, C=1.805, and Coefficient of determination R 2 =0.969. In statistics, when performing regression analysis on variables and using the least squares method to estimate parameters, R 2 R is the ratio of the regression sum of squares to the total deviation sum of squares, indicating the proportion of the total deviation sum of squares that can be explained by the regression sum of squares. The larger the ratio, the better, the more accurate the model, and the more significant the regression effect. 2 It is between 0 and 1. The closer it is to 1, the better the regression fitting effect. It is generally believed that the model fitting goodness of more than 0.8 is relatively high. Therefore, formula (3) can fit the data listed in Table 1 very well.

[0047]

[0048] The above-mentioned high-speed rotation-induced wood pin friction welding pull-out bearing capacity prediction method, formula (3) can well fit the rotation speed, pre-drilled hole diameter d, effective welding depth L eff The three influencing factors of the wood substrate, the air-dry density of the tree species, and the pull-out bearing capacity of the welded joint F ax，90 The nonlinear relationship between:

[0049]

[0050] in:

[0051] Where n – rotation speed, rpm;

[0052] To further verify the effectiveness of formula (3) for prediction results, the 20 sets of collected data were substituted into formula 3. The error between the predicted and experimental values ​​of the pull-out bearing capacity of welded joints with the welding direction perpendicular to the wood grain was obtained (Table 2). The minimum deviation was 0.97%, the maximum was 15.02%, and the average error was 6.25%, indicating good prediction results. At the same time, the data results of another three sets of welding directions parallel to the wood grain were used as test targets. The error between the predicted and experimental values ​​(Table 3) was the minimum deviation of 0.39%, the maximum was 10.29%, and the average error was 6.4%, indicating good prediction results. From the verification results of formula (3), it can be seen that the mathematical model established based on the 23 sets of representative test data and the nonlinear regression analysis method can well predict the pull-out bearing capacity of welded joints, whether in the direction perpendicular to the wood grain or in the direction along the wood grain. The new calculation formula can provide an accurate calculation method for the use of wooden pin rotary welding technology to connect wooden structural components in modern wooden structure construction and solid wood furniture manufacturing. It effectively solves the important problem that this technology has long lacked a theoretical basis for multi-factor prediction of the pull-out strength calculation of welded nodes, and makes it easier to apply this innovative technology more widely in the processing and production of wooden structure products.

[0053] Table 1 Experimental data collected based on different references

[0054]

[0055] Table 1 - Notes

[0056]

[0057]

[0058] Table 2 Comparison of test values ​​and calculated values ​​when welding perpendicular to the wood grain of the wood substrate

[0059] Grouping Test value (N) Calculated value (N) error(%) A-1 2290 2634 15.02％ A-2 2966 2780 6.27％ B-1 2712 2677 1.29％ B-2 1856 1828 1.51％ B-3 3602 3236 10.16％ C-1 4990 5210 4.41％ C-2 2240 2409 7.54％ C-3 5540 5486 0.97％ D-1 4215 4155 1.42％ D-2 3251 3622 11.41％ D-3 3673 4160 13.26％ D-4 4275 3997 6.50％ D-5 3191 3484 9.18％ E-1 3324 3442 3.55％ E-2 3251 3307 1.72％ E-3 3215 2883 10.33％ F-1 1491 1427 4.29％ F-2 1530 1657 8.30％ F-3 1277 1409 10.34％ G-1 2320 2261 2.54％ A-1 2290 2634 15.02％ A-2 2966 2780 6.27％ Average error 6.25％

[0060] Table 3 Comparison of test values ​​and calculated values ​​for welding parallel to the wood grain of the wood substrate

[0061] Grouping Test value (N) Calculated value (N) error(%) C-4 5190 5210 0.39％ C-5 2220 2409 8.51％ G-2 2050 2261 10.29％ Average error 6.4％

[0062] The technical solutions disclosed in the technical solutions of the present invention are not limited to those disclosed in the above-mentioned embodiments, but also include technical solutions composed of any combination of the above-mentioned technical features. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for predicting the pull-out bearing capacity of high-speed rotation-induced friction welding of wooden pins, characterized by: Using the multivariate nonlinear regression method, the pull-out bearing capacity of the high-speed rotation-induced wooden pin friction welding is F ax,90 , which is expressed as formula (1), F ax,90 =f(n)·d A ·L eff B ·ρ C (1) in: F ax,90 – The pull-out bearing capacity of the joint where the welding direction is perpendicular to the wood grain direction of the wood substrate, N; f(n) – nonlinear function related to the rotation speed; n – rotation speed, rpm; d – diameter of pre-drilled hole in wooden substrate, mm; L eff –Effective welding depth, mm; ρ – air-dry density of the wood substrate, kg / m 3 ; Among them, A=-1.103, B=0.187, C=1.805; The diameter of the pre-drilled hole in the wood substrate is 7.67mm to 9.5mm, and the effective welding depth is L eff The thickness of the wood substrate is 15mm to 40mm, and the air-dry density of the wood species used is 450 to 710 kg / m 3 , the welding direction is at an angle of 0° or 90° to the wood grain of the wood substrate; The multivariate nonlinear regression method is used to determine the unknown parameters in formula (1). The three coefficients A, B, and C are substituted into formula (1) to obtain formula (3). Formula (3) fits the rotation speed, pre-drilled hole diameter d, and effective welding depth L. eff And the four influencing factors of wood density ρ and the pull-out bearing capacity F of the welded joint ax,90 The nonlinear relationship between: F ax,90 =f(n)·d ；1.103 ·L eff 0.187 (3) ·r 1.805 in: Where n is the rotation speed, rpm.

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