ORIGINAL ARTICLE Thickness improvement in single point incremental forming deduced by sequential limit analysis M. J. Mirnia & B. Mollaei Dariani & H. Vanhove & J. R. Duflou Received: 13 March 2013 /Accepted: 15 October 2013 /Published online: 10 November 2013 # Springer-Verlag London 2013 Abstract Multistage forming is one of the most practical solutions to avoid severe thinning in single point incremental forming (SPIF). A successful implementation of multistage SPIF is strongly dependent on an appropriate deformation path. In this paper, firstly, a simplified modeling technique is proposed using sequential limit analysis. It is shown that sequential limit analysis can predict the thickness distribution faster than an equivalent model in a commercial finite element modeling code like Abaqus can. The reliability of the model is assessed by comparing experimental and simulated results for single-stage and multistage SPIF cones. This model is utilized to study the effect of various deformation paths on the thick- ness distribution. As a result, a new multistage strategy is designed and implemented to form a 70° wall angle cone in three stages. The thickness distribution of the cone is im- proved significantly compared to cones formed by a single- stage and a conventional three-stage strategy. Besides this improvement, the new multistage SPIF can be carried out in much less time. Keywords Multistage SPIF . Sequential limit analysis . Second-order cone programming . Thickness distribution 1 Introduction Single point incremental forming (SPIF) is a promising pro- cess for customized and low-volume production of sheet metal parts. SPIF distinguishes itself from other sheet metal processes by applying consecutive local deformations tracing a predefined path on a metal sheet. In this process, a simple stylus tool with hemispherical head forms a metal sheet, which is clamped firmly on a backing plate, along a path generated according to a desired shape. This means that no dedicated, part-dependent tools are required. Figure 1 depicts a typical SPIF setup. In this figure, a truncated cone with wall angle β is formed by a tool with the radius of r T . This process can be carried out on either conventional machines like a CNC mill- ing machine or an industrial robot or on dedicated multi-axis SPIF platforms. SPIF, however, suffers from a limited geometrical accuracy and excessive thinning of the material, preventing a wide application in the metal working industry [1, 2]. This paper focuses on the latter problem. Kim and Yang [3] used a two- stage SPIF strategy to achieve a uniform thickness distribution and to improve the formability for both an ellipsoidal and a clover-shaped part. They used intermediate shapes based on an assumption that shear is the main deformation mechanism. The proposed two-stage forming strategy improved the thick- ness distribution uniformity by increasing the minimum thick- ness in both mentioned parts. Young and Jeswiet [4] studied the thinning in a cone with a 70° wall angle. They found that it is possible to avoid the excessive thinning in a specific area by using an appropriate two-stage forming strategy in which the preform is a cone with the same diameter and height as the final part, but with a wall angle of 55°. By the proposed strategy, no improvement of the minimum thickness in the two-stage SPIF was observed compared to the single-stage SPIF. Cerro et al. [5] showed that the forming strategy in SPIF is of crucial importance and should be selected by an appro- priate model of the process. The authors formed a 75° wall angle square-based pyramid of AA1050-O with the thickness of 1.5 mm in one, three, and seven stages. The part could be successfully completed by the seven-stage SPIF strategy M. J. Mirnia : B. Mollaei Dariani (*) Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran e-mail: dariani@aut.ac.ir H. Vanhove : J. R. Duflou Department of Mechanical Engineering, KU Leuven, Leuven, Belgium Int J Adv Manuf Technol (2014) 70:2029–2041 DOI 10.1007/s00170-013-5447-2