Warping Analysis in Laminated Object Manufacturing Process

This study presents an analysis of warping that occurs in the laminated object manufacturing process. Based on the study of thermal-mechanical behavior of the adhesive and its effect on the laminated materials, the cause of warping, the relationship between temperature and adhesive viscosity, and the adhesive connecting intensity is investigated. A heat transfer mathematical model and finite difference solution algorithm was developed to calculate the intralaminar thermal force induced by the material addition in the processing of laminated object manufacturing. The results of the model prediction were compared to available experimental data. Simulation of intralaminar thermal force and case studies show that the processing parameters, such as roller temperature, speed, and contact pressure, the mechanical properties of laminated material and adhesive will all contribute to the formability and warping of the laminated prototype. An optimal combination of the processing parameters may reduce the undesired warping effect. @DOI: 10.1115/1.1403447# Dimensional accuracy and optimal processing have always been the research topics in the development of rapid prototyping techniques @1‐3#. In laminated object manufacturing ~LOM!, the process is often interrupted by warping and delamination of the prototyping part, especially when fabricating a large-sized object @4,5#. In some cases, the effect of warping is severe enough to lead to the failure of the prototypes @6#. Recent research has been reported on studying the effect of the processing parameters on the thermal-mechanical behavior of LOM processing. For example, Pak and Nisnevich @7# investigated the influence of rolling, the roller temperature, and speed to the strength of laminated bonding. Sonmez and Hahn @8# developed a 2-dimensional finite element model to study the relationship of heat transfer and pressing stress during a heating and pressing working cycle and presented the temperature distribution and pressing stress in the vicinity of the roller contact region. Flach, Klosterman and Chartoff @9# and Flach et al. @10# used finite difference modeling to analyze the thermal behavior of the LOM process and simulated the iterative process of the layer addition. Their finite differential model was also used to investigate the effect of the process parameters, including the temperatures of the roller, the base plate and chamber environment, the speed of the roller, and the laser cutting time in the LOM process. All the previous studies reported that the poor adhesion, which results from low temperature and insufficient pressure, would cause the delamination. But no quantitative predictions were given in their presentations. In addition, the research addressing the warping of the LOM prototypes, its cause and relationship to the LOM processing parameters, and to material addition has not been established. This paper presents a study of the warping analysis for the LOM process. Section 2 describes the mechanism of warping based on the study of the thermal-mechanical behavior of adhesive and its effect on laminated materials. The relationship between temperature and adhesive viscosity is investigated and the connecting intensity of the adhesive is defined. A onedimensional heat transfer mathematical model is established in Section 3 to predict the intra-laminar thermal force induced by the addition of the material in the LOM process. A finite difference approach is used to develop the solution algorithm. Results of the prediction and comparisons to the experimental data are all presented in this section. Section 4 presents two case studies which simulate the intra-laminar thermal forces and explain the mechanism of laminate warping. Finally, Section 5 summarizes the results of the study and presents some discussion and conclusions.