A new method for distortion calculations in additive manufacturing: Contact analysis between a workpiece and clamps

Abstract For the first time, contact theory is incorporated into the deformation calculation of additive manufacturing. Compared with the traditional boundary constraints of pure rigidity or elasticity, the model in this study considers the contact between a workpiece and clamps. The Coulomb friction law is utilized to solve the contact problems. A penalty function method is used to solve the Coulomb friction problems, and the tangential and normal behaviors of the contact parts are analyzed in detail. For both rigid and contact constraints, the deformation trend is consistent with the measured results; however, the deformation distribution of the contact constraints is closer to the real distribution. The maximum deformation that is obtained with the rigid constraints is only 60.6% of the actual measured value, compared to 90.4% with the contact constraints. The mean square error of multiple points between the results by rigid constraints and the measurement is 0.23, while it is 0.14 with contact constrains. Therefore, the incorporation of contact theory can improve the accuracy of deformation simulations for additive manufacturing. Relative motion analysis of the contact part between the workpiece and the clamp during electron beam freeform fabrication demonstrates that the dominant role of the transverse deformation of the substrate decreases with the increase in the number of deposition layers, and warping deformation gradually increases to become the main component of the contact force.