Finite element analysis of dovetail joint made with the use of CNC technology

SEBERA, V. SIMEK, M.: Finite element analysis of dovetail joint made with the use of CNC technology. Acta univ. agric. et silvic. Mendel. Brun., 2010, LVIII, No. 5, pp. 321–328 The objective of the paper is the parametrization and the fi nite element analysis of mechanical proper ties of a through dovetail joint made with the use of a specifi c procedure by a 3-axis CNC machine. This corner joint was used for the simulation of the bending load of the joint in the angle plane – by compression, i.e. by pressing the joint together. The deformation fi elds, the stress distribution, the stiff ness and the bending moment of the joints were evaluated. The fi nite element system ANSYS was used to create two parametric numerical models of the joint. The fi rst one represents an ideal ly stiff joint – both joint parts have been glued together. The second model includes the contact between the joined parts. This numerical model was used to monitor the response of the joint stiff ness to the change of the static friction coeffi cient. The results of both models were compared both with each other and with similar analyses conducted within the research into ready-to-assemble furniture joints. The results can be employed in the designing of more complex furniture products with higher demands concerning stiff ness characteristics, such as furniture for sitting. However, this assumption depends on the correction of the created parametric models by experimental testing. furniture, dovetail joint, numerical simulation, mechanical properties, CNC technology The through dovetail joint is a classical furniture joint with outstanding strength properties. The joint consists of tails and pins, see fi g. 1. The specifi c construction of the joint, which ensures its self-locking character and consequently considerable strength, requires a demanding technology. This joint is usual ly made manually (individual production) or by special machines and devices (batch production). The technology of current 3-axis CNC machines makes the manufacture of dovetail joints fast and accurate. However, it also bears some specifi cs. One of them is the inability of the technology to make sharp inner edges of the milled profi le from angle 0° to 180° because of the rotating movement of the cutting tools. This limitation can be removed by boring a hole in place of the demanded edge which results in what is called “the Mickey Mouse ears”, see fi g. 2c. CNC manufacturing technologies have a big potential in the fi elds of furniture production and wood processing, for example in competition with cheap labour. A new manufacturing technology of CNC machines and new composite materials are pre requi sites for successful usage of this joint in the current environment of wood and furniture industry (Susnjara, 2006). Testing of furniture joints has been dealt with many times, both by means of experiments and numerical simulations. Mihailescu (2003) analysed various forms of parametric models of joints using the fi nite element method (FEM). He simulated loading of a glued joint on the tenon and the mortise made from beech and oak wood by a bending moment in the angle plane in tension. The result of his research was the analysis of the infl uence of in di vidual joint parameters on the deformation and stress. Smardzewski and Prekrad (2002) examined the stress distribution in ready-to-assemble furniture corner joints using experimental testing and numerical simulation. The authors tested three types of ready-to-assemble joinery in combination with beech pins and particleboard by bending in the angle plane in compression. The results show 322 V. Sebera, M. Simek that besides mechanical connectors the pins play an important role in the joint as they support its strength. The numerical simulation of the examined joints clarifi ed how specifi c connecting elements transmit stress in the joint. Joscak (1999) used experimental testing to explore mechanical properties of several typical furniture corner joints used for joining composite wood materials. By loading selected joints he found the maxi mum values of the bending moment and stiff ness. Furthermore, Cernok, Joscak and Lang (2004) analysed the stress distribution, the stiff ness and the deformation of a glued beech pin joint using the fi nite element method. Zhang and Eckelman (1993) tested the resistance to the bending moment of single-dowel and multi-dowel (glued) furniture corner joints in particleboard. These authors studied the dependence of load capacity in various dimensional modifi cations of specimens, pins and pin distribution in the joined material. Similarly, Veselovský (1996) and Simek et al. (2010) dealt with the capacity of corner joints within the research into the methods of testing and designing joints. MATERIAL AND METHODS Before the manufacture itself a parametric joint is analysed using numerical simulation of me chani cal loading, which makes the subsequent geometry and material optimization possible. Thus we obtain the fi rst strength characteristics of the joint and the distribution of stress which allows us to propose modifi cations. The manufactured joints are analysed by experimental mechanical testing. The objective factors for evaluation will be the strength (capacity), the stiff ness (the ratio of deformation to the bending moment), and the defl ection of the joint when loaded by bending (with this type of load furniture joints achieve the lowest values of capacity). The aim of the paper is the parametrization of a numerical model and a fi nite element analysis of mechanical properties of dovetail joints manufactured from 12 mm thick birch plywood boards. Two parametric numerical models were created, both loaded by a bending moment. These are intended to serve as tools for designing furniture with the joints in question. The models were solved in the form of a structural analysis; in the fi rst model, both parts (tail and pin) were designed as a glued joint with all degrees of freedom constrained; in the second model a contact was defi ned between both parts (see below). Both models are supposed to be compared with, or corrected by, experimental testing. The contact analysis of the dovetail joint includes another derived material characteristic – the static friction coeffi cient μ, as follows from this equation: