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Thursday, 15 September 2016


 Published Date

Jerzy Smardzewski, Adam Majewski, Karol Łabęda
Department of Furniture Design, Faculty of Wood Technology, Poznań University of Life Sciences, Poland

Few research papers deal with the important aspect of furniture design in the context of optimisation of hinge mounting techniques. The aim of the performed experiments was to determine stiffness of furniture door manufactured from laminated particleboards. The impact of spacings between concealed hinges as well as the diameter of screws mounting these hinges on stiffness and strength of doors was investigated. It was demonstrated on the basis of the obtained research results and their analyses that door stiffness increased together with the increase of distances between hinges. Employing the developed regression equations, it is possible to select spacings between hinges at an assumed deflection or, conversely, to determine a deflection at an assumed spacing of hinges.
Key words: stiffness, damage, particleboard, strength, FEM.

Usually, doors are mounted to furniture cabinets using concealed hinges screwed to particleboards by means of screws. Producers have a wide range of concealed-hinge constructions as well as many kinds of screws to choose from but their choice is generally restricted by their habits resulting from many years of practice. The appropriate selection of hardware and their correct fittings as well as their mounting exert a decisive effect on door strength and durability. In 1990s, studies were carried out on the load-carrying ability of screws depending on their type, depth of screwing in, fiberboard moisture content, density and strength [3, 7] as well as Taj et al. [13] determined the impact of the thread screw type and geometry on the load-carrying ability of screws mounted in wood. Atar et al. [1] investigated the effect of the process of wood impregnation on the load-carrying ability of screws mounted perpendicularly to wood grain, while Ozcifci [11] determined screw withdrawal strength depending on their type, the diameter of the pilot hole as well as the layer thickness in laminated veneer lumber. Gozdecki [8] presented results on the carrying capacity of screws in wood-polymer composites (WPC) depending on the length of wood particles. Mohamadzadeh et al. [10] determined experimentally the destruction process of single-shear joints consisting of WPC and screws. The effect of diameters of pilot holes on the withdrawal strength of screws mounted into plywood and OSBs was determined by Erdil et al. [5]. Similar experiments were conducted by Gates [6] who determined load carrying capacity of screws mounted in veneered particleboards and established the dependence between the above-mentioned withdrawal strength and the screw thread penetration depth and the pilot hole diameter. Tankut [14] determined the screw withdrawal strength in T-type joints subjected to tension and bending. Zhang et al. [16] determined the effect of screw diameter and length as well as the type and quality of the applied board on the value of the bending moment of an L-type joint. On the other hand, Vassiliou and Barboutis [15] determined the withdrawal strength of screws constituting part of eccentric joints. Screws with or without plastic sockets were mounted into particleboards or MDF. They referred the obtained screw withdrawal strengths to the density of the applied wood derived materials. Miljković et al. [9] determined the withdrawal strength of 4, 4.5, 5 mm diameter and 30 mm length screws mounted in particleboards and OSBs. Colakoglu [2] established physical and mechanical properties of particleboards, MDFs and modified wood frequently applied in furniture designing and, in addition, he also determined the carrying capacity of screws mounted in the above-mentioned materials. Some researchers [12] elaborated a mathematical model of a semi-rigid screw joint connecting elements of a furniture body manufactured from particleboards. The developed model was further verified numerically in order to determine stiffness and durability of the body using the finite element method (FEM). Employing this method, Zhou et al. [17] determined maximal deflections and strains for furniture doors at varying configuration of hinge distribution. On the basis of the results of these calculations, they came forward with a method of determination of the optimal number of hinges and distances between them, at the same time taking into account the elastic properties of the employed wood-derived materials. It also overlooked the work of screws and deformations developing in points of their fixation. Furthermore, door operational loads were also omitted assuming only slight mass loads which make practical assessment of the research results difficult. In addition, torsional deformations of the hinge construction mounted to the door and the side wall were not taken into consideration. Unpractical distances between hinges were applied which fail to refer to any multiplicity of 32 mm distance widely adopted in furniture practice. A Polish furniture manufacturer, one of the leaders on the European market of furniture for teenagers became interested in finding a solution to the above discussed issues. A conceptual form of a piece of furniture for storage was developed in the R&D Office of this company for which optimal techniques of hinge mounting were to be elaborated.

The aim of the performed experiments was to determine experimentally stiffness of furniture door manufactured from laminated particleboards. Furthermore, the authors also decided to establish the impact of spaces between cup hinges as well as diameters of screws fixing the cross-mounting plates of these hinges on door stiffness and strength. In addition, an attempt was also made to determine stresses in screw connections and laminated particleboards. It was also considered appropriate to establish analytical dependences which can facilitate the selection of optimal spacings between hinges.


Physical model
One kind of concealed hinges was selected characterised by a 52 mm drilling module (Fig. 1). Hinges were fixed to doors using Φ3.5 x 13 mm screws. Cross-mounting plates, depending on hinge construction, were fixed to body sides using EURO screws – Φ6 × 13 mm (Fig. 2a). Hinges were spaced at n·32 mm in accordance with widely-employed industrial practice in empirical trials n (9, 11) were applied. Figure 1a presents dimensions of individual elements as well as dimensions and spacings between holes for screws. All screws were screwed in with the assistance of commercial screwdrivers equipped in a clutch. The screwdriver was set to achieve a drive-in moment value of 1.342 Nm. In all, two sample variants differing with respect to distances between hinges were prepared for empirical tests. Each variant was made up of 10 samples. Fittings were mounted on to laminated 18 mm thick particleboards. The particleboard had an average: MOE of 2750 MPa (SD = 229.7 MPa), MOR of 28 MPa (SD = 1.9 MPa), density of 680 kg/m3 (SD = 14.2 kg/m3) and moisture content of 5.3% (SD = 0.2%). The value of applied load and sample measurements were dictated by EN 14074-2004 standard [4]. Door deflections were measured at points U1 and U2. The cycle was repeated 10 times for each sample. In the course of empirical trials, the principal quality evaluation criteria of the examined fittings comprised: damages caused by loads and values of U1 and U2 deflections.

Fig. 1. Construction of the hinge, side wall and door: a) mounting dimensions, b) method of loading and measurement of door deflection

Numerical analysis
The objective of the numerical calculations was to determine the effect of the hinge configuration on the dimensional behavior and the stress state of furniture doors. The prepared models included: five variants of hinge spacings n (6, 9, 11, 12, 13) and for each variant, two kinds of screws: Φ3.5 × 13 mm and Φ6 × 13 mm (Fig. 2). In all, ten models were prepared and in each of them, appropriate pairs of surfaces remaining in contact with each other were taken into consideration (Fig. 3). These comprised, respectively: the area of the hole for the hinge cup and the area of the hinge cup; areas for screw holes mounting hinges and areas of screws; areas of doors and areas of hinge cross mounting plates as well as the area of the side and areas of mounting plates. In order to obtain representation of the mounting forces of hinge screws, F1 force of 730 N resultant value (Fig. 3) was applied to the surface of holes for screws and to the surface of screws. This is the mean value of the screw withdrawal force by particleboards [2, 6, 15]. In the next step, a network model was developed made up of block four-, six- and eight-nodal isotropic finite elements (Fig. 4). Virtual modelling of the doors shape was carried out in a computer-integrated Autodesk® Inventor® Professional 2013 CAD/CAE application. The model was stored in a file in STP format and, as a solid, imported into the Autodesk® Algor® Professional 2013 system capable of carrying out calculations using the method of finite elements. Each of these models was supported and loaded in a way identical as in the models in laboratory samples. On the basis of the results of numerical calculations, the authors decided to determine stiffness of furniture doors manufactured from laminated particleboards and compare it with the results of empirical trials. Next, it was decided to ascertain the effect of spacings between concealed hinges and the diameter of screws fixing cross mounting plates of these hinges on door stiffness and strength. In addition, the authors also determined stresses in joints between screws and laminated particleboards. Last but not least, it was also considered appropriate to trace changes in the position of the door centre of rotation. For this purpose, (XY) coordinates of the rotation centre were calculated and presented in Figure 1b.

Fig. 2. Screws used to mount hinges: a) EURO screw, b) conical screw

Fig. 3. Contact surfaces and hinge mounting forces

Fig. 4. Mesh model of the examined construction


Damage characterization
The most frequent sign of hinge damage was tearing off of one or two screws fixing cross mounting plates to the particleboard (Fig. 5). In the case of hinges with 9∙32 mm = 288 mm spacing, all ten samples suffered damage through pulling out of EURO screws, while in the case of hinges with 11∙32 mm = 352 mm spacing – all samples transmitted the assumed load. Usually, cross mounting plate screws of the upper hinge were torn off (Fig. 5a) and less frequently those of the bottom hinge (Fig. 5b). The above damages were caused by the occurrence of reaction forces HA, HB (Fig. 6) affecting individual screws with the following force:

n (6, 9, 11, 12, 13), 
L = 525 mm, 
L’ = L – 100 mm, 
F = 300 N. 

These forces caused failure of the particleboard by its delamination, primarily, as a result of pulling out of the screws fixing cross mounting plates of the upper hinge. 
Fig. 5. Typical damages: a) tearing off two screws from the side wall, b) tearing off one screw

Fig. 6. Distribution of internal forces in a hinge joint

Strength of doors
Taking into account varying values of spacings of hinges n∙32 mm, varying diameters of holes for screws d’ as well as varying thread diameters of the screws d and a constant number of thread coils p, stresses caused by the pulling out of the screw from the particleboard were determined from the following equation:

p = 6, 
d = 3.5, 6 mm, 
d’ = 2.5, 5 mm.

Values of normal stresses in the connection of the screw of the upper cross mounting plate with the particleboard were calculated for the above given equation (3) parameters. Next these results were compared with the values of numerical calculations and collated in Table 1. It is evident from this Table that the results of numerical calculations differ by 1.89 to 22.96% from the results of analytical calculations. In addition, these calculations exhibit a consistent regularity of decreasing values of stresses together with the increase of n number which is responsible for the distance between hinges. Bearing in mind significant similarities of the results of these calculations and also on the basis of the results of numerical calculations, it can be noticed the EURO Φ6 × 13 mm screws reduce stresses in the particleboard in comparison with stresses caused by conical screws Φ3.5 × 13 mm. For consecutive distances between hinges depending on number n (6, 9, 11, 12, 13), these differences amounted to 102%, 97%, 120%, 138% and 104%, respectively. Stresses caused by pulling out of screws from the particleboard decrease also together with the increase of the distance between hinges. For screws EURO Φ6 × 13 mm, their value declines from 6.56 to 2.62 MPa.

Table 1. Normal stresses in the connection of the screw and particleboard
nvariant of hinge spacing
Stress [MPa]
Numerical value
Analytical value
Conical Φ3.5 × 13
EURO Φ6 × 13
The effect of the distance of hinges on their strength is well illustrated by the stress coefficient S(d’):
Sn = i stress (6, 9, 11, 12, 13), Sn = 9 stress in the screw joint for n = 9 and d’ = 2.5, 5 mm. 

Figure 7 presents S(d’) = f(n) dependence. It is evident from this Figure that the above relationship is of power function nature which can be used to calculate allowable stresses in the screw/particleboard joint for the expected value ndeciding about the distance between hinges. It is also evident from here that for n > 9, the coefficient S(d’) < 1. This indicates increased strength of hinges together with the increase of the distance between them. 
Fig. 7. Dependence of the stress coefficient on the distance between hinges: S(2.5) = 8.8206 n-0.992R2 = 0.9023; S(5) = 11.027 n-1.122R2 = 0.9699

Bearing the above in mind, the value of the allowable stress treated as the stress criterion for the remaining joints was determined, at the same time taking into consideration the fact that the laboratory experiments with hinges fixed to sides at the distance of 352 mm (n = 11) using EURO Φ6 x 13 mm screws failed to exhibit any damage. According to Table 1, in the case of numerical calculations, the value of this stress amounts to 3.58 MPa. Further, it can be noticed that fixing of hinge cross-mounting plates using screws of Φ3.5 mm diameter can result in destruction of these connections. It is evident from Table 1, that stresses in the joint of this screw with a particleboard, depending on n, can reach values from 5.32 to 13.25 MPa. Therefore, even the smallest of them exceed allowable stresses by 49%. On the other hand, stresses in the EURO screw joint for hinges mounted at the distance of 12∙32 mm and 13∙32 mm are favourable. Their values constitute, respectively, 80% and 73% of the value of allowable stresses. This clearly indicates that the recommendable solution is to place hinges at the distance of minimum 11∙32 mm employing screws of minimum diameter of Φ6 mm.
Figure 8 presents distribution of normal stresses depending on distances between hinges n (6, 13). It is apparent that small distances between hinges (n = 6) do not only result in the increase of stresses in the screw joint but additionally also lead to a distinct increase of the area on which stresses of 1 to 83 MPa value occur.
Fig. 8. Distribution of normal stresses depending on hinge distance [MPa]: a) n = 6, b) n = 13

Stiffness of doors

Figure 9 presents the results of numerical calculations in the form of door deformation loaded with operational forces in accordance with the standard [4]. It is clear from this Figure, that the side undergoes torsion and the door – rotation. The resultant dislocation amounts to 8.48 mm. Figure 10 illustrates also the form of torsional deformation of the hinge. It is evident from this Figure that the value of experimentally measured U1 and U2 deflections was significantly influenced by the torsional deflection of arms of cup hinges. This means that the position of the rotation centre of the door also depends on the distance between hinges. Figure 11 shows the dependence of coordinate displacement of the rotation centre of the door (X, Y) on the distance between hinges. It is apparent that as a result of loading, the rotation centre of the door moves horizontally right and vertically downwards because its X coordinate increases positively, while coordinate Y – negatively. Moreover, it should be emphasised that in the case of screws with Φ6 mm diameter, the increase in the n number causes a gradual positive increase of the X coordinate and, at the same time, a negative increase of the Y coordinate. In the case of screws with Φ3.5 mm diameter, the increase in the n number causes a decrease in the value of the X coordinate accompanied by changes in negative values of the Y coordinate. These relationships were described by polynomials of the second and third degree. Taking this into consideration and monitoring the form of deformation presented in Figure 9, it can be concluded that the distribution of reaction forces presented in Figure 6 is of theoretic nature and, in real life, the top reaction HA will have a greater value than the bottom reaction HA. This, in turn, is the cause of more frequent failure of top screws than screws fixing bottom cross mounting plates.

Fig. 9. Resultant displacement of the side wall and door [mm]

Fig. 10. Hinge resultant displacement

Fig. 11. Dependence of the displacement of door rotation centre on the distance between hinges:
Xd’=2.5 = -0.6577 n2 + 11.447 n - 17.12, R2 = 0.9803
Xd’=5 = 0.0566 n2 - 0.1427 n + 27.622, R2 = 0.7538
Yd’=2.5 = -0.2479 n3 + 6.9482 n2 + 62.529 n - 173.04, R2 = 0.742
Yd’=5 = -0.7396 n2 + 11.577 n - 50.176, R2 = 0.7339

Figure 12 collates downward deflections of doors determined empirically in the lab and numerically. Whisker present minimal and maximal values. It can be noticed from this Figure that both deflections U1 as well as U2 measured in the laboratory confirmed the displacement of the door downwards. Such trends were also indicated by the results of numerical calculations shown in Figure 11 and discussed above. Moreover, it is evident from Figure 12 that values of numerical calculations for determined U1 differed only slightly from the results of experimental measurements. For n = 9, deflection U1 determined numerically was by 32.1% lower in comparison with the mean result of laboratory measurements. This corroborates satisfactory quality of the numerical model correctly fitted to the real model.
Fig. 12. Door deflection
The impact of hinge spacings on the U1 door deflection is well illustrated by the deflection coefficient K(d’):
U1n = i door deflection for n (6, 9, 11, 12, 13), 
U1n = 9 door deflection for n = 9 and d’ = 2.5, 5 mm. 

Figure 13 illustrates K(d’) = f(n) dependence. It is evident from this Figure that the given relationship has the nature of a power function which can be used to calculate allowable door deflection for the expected n value affecting distances between hinges. At the same time, it is also clear that for > 9, the coefficient K(d’) < 1. This indicates smaller door deflections and increase of hinge stiffness together with the increase of distances between them.

Fig. 13. Dependence of door deflection on distances between hinges:
K(5) = 101.35 n-2.197, R2 = 0.9890
K(2.5) = 75.195 n-2.036, R2 = 0.9859
Bearing the above in mind, the value of allowable deflection UD = 1 mm was determined arbitrarily as a criterion of stiffness evaluation of the remaining joints. The adopted value should fulfil functional requirements and aesthetic expectations. In addition, the fact was also taken into account that in the course of laboratory experiments, no damages were recorded when hinges were fixed to sides at the distance of 352 mm (n = 11) and when the applied screws were those of EURO Φ6 × 13 mm. Employing equation K(5) = 101.35 n-2.197, for d’ = 5 mm (refers to the screw EURO Φ6 × 13 mm), U1n = 9 = 3.33 mm and UD = 1 mm, the calculated value n = 14.15. Therefore, it can be assumed that n = 15. For d’ = 2.5 mm (refers to the conical screw Φ3.5 × 13 mm), U1n = 9 = 3.58 mm andUD = 1 mm, using equation K(2.5) = 75.195 n-2.036, the calculated value n = 15.61. Therefore it can be assumed that n = 16. The achieved solution shows that it is possible to employ analytical solutions to distribute hinges optimally using for this purpose Φ3.5 mm and Φ6 mm screws widely used in practice. Figure 14 shows the animations of performed numerical analysis.

Fig. 14. Animations of performed numerical analysis
Download Video "Figure 14.MPG"


In their general approach, the results of numerical calculations presented in this study corroborate the results presented in paper [17] because the authors demonstrated an identical regularity between the dependence between the distances of hinges and door deflection. However, the size of the calculated deflections varies. Using mass loads of doors manufactured from MDF, Zhou et al. [17] obtained deflections ranging from 0.0093 mm to 0.0172 mm for two hinges placed at different distances. However, it is usually accepted in furniture design that door deflections which do not exceed 0.05 mm exert no influence on the improvement of their proportions or aesthetics. Therefore, in this study, for door operational loads, maximal deflections range from 1.12 mm to 7.23 mm, which are values possible to accept in industrial practice. Similar remarks can be made with respect to the distribution of stresses. In paper [17], reduced stresses according to Mises were determined and their values fluctuated from 0.33 to 0.14 MPa together with the increase of distances between hinges as well as the number of hinges. Those stresses were concentrated around hinges but their values did not pose a serious threat to the strength of doors or to connectors fixing hinges to doors. In this experiment, detailed representation of the hinge construction, cross-mounting plate as well as holes in doors and body sides made it possible to determine critical stresses for the construction and, on this basis, to select more precisely distances between hinges and diameters of screws used to screw in cross-mounting plates. On the basis of the obtained research results and their analysis the following remarks and conclusions were put forward: door stiffness increases together with the increase of the distance between hinges, changes in the position of the centre of door rotation affects values of reaction forces in hinges, in comparison with Φ3.5 mm diameter screws, screws with Φ6 mm diameter increase twofold the strength of connection of the cross-mounting plate with the particleboard, durable and rigid door suspension can be guaranteed using hinge spacing of n >= 11, results of numerical calculations of door deflections are sufficiently consistent with the results of empirical studies. Therefore, such calculations can be considered sufficiently reliable to be used for hinge distribution optimization, employing the developed regression equations K(d’) = f(n), it is possible to select hinge spacings assuming a required deflection or conversely to determine a deflection assuming a given hinge spacing.

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Accepted for print: 24.11.2014

Jerzy Smardzewski
Department of Furniture Design, Faculty of Wood Technology, Poznań University of Life Sciences, Poland
Wojska Polskiego 38/42, 60-637 Poznań, Poland 
Phone: +48 61 848 7475 
Adam Majewski
Department of Furniture Design, Faculty of Wood Technology, Poznań University of Life Sciences, Poland
Wojska Polskiego 38/42, 60-637 Poznań, Poland 
Phone: +48 61 848 7475 
Karol Łabęda
Department of Furniture Design, Faculty of Wood Technology, Poznań University of Life Sciences, Poland
Wojska Polskiego 38/42, 60-637 Poznań, Poland 
Phone: +48 61 848 7475 

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