Development of die-less single-tool multi-point plate forming technology for 3D curved shape

Abstract

To avoid degradation of material properties, high equipment investment, low efficiency, and potential safety issues caused by conventional technologies like line heating, multi-point plate forming, and explosive forming, a new die-less single-tool multi-point plate forming (DS-MPF) technology is proposed. In DS-MPF, a moving bar is used as a single forming tool and combined with horizontal and vertical motions relative to the plate. To reduce forming force component from the membrane stress, simple support boundary condition is preferred to avoid the plate edge being bent, trimmed, or thinning after being formed. However, this boundary may easily cause instability of the forming process and worse geometric accuracy of a formed part if an unsuitable toolpath is employed. In this paper, the forming mechanism and toolpath design principle are clarified to develop this new technology. Numerical and experimental forming case from an 8-mm SS400 steel plate into a spherical surface with a radius of curvature of 1000 mm was performed to validate the new technology and its design principle. The strain analysis of results shows DS-MPF tends to be a local forming method. The formed plate normally has local positive bending strain at the tool-contacted area and limited negative bending strain at the tool-uncontacted area between adjacent strokes. Forming a 3D curved shape with high geometric accuracy in DS-MPF can be achieved with appropriate control of the local bending strain produced in each stroke, stroke position, and forming sequence.

Appendix. Toolpath compensation for spring back

Due to the elastic strain component ε_elastic, spring back of plate after each stroke will lead to some deviation from the target. Modifying the toolpath to compensate for this deviation is needed. All strokes in this toolpath are kept at the same position X and Y. Only Z coordinates are adjusted. Since the behavior is nonlinear, compensation is carried out by iteration in several steps. The result of each iteration step, by analysis or physical testing, is used to find out the stroke Z of the next step, until the resulting surface converges to the target surface within the allowable tolerances. The strokes Z of the last iteration is to be used in forming. Fig. 24 shows a cross section of four surfaces used in compensation calculations: (A) plate surface after spring back, (B) the surface of the target, (C) surface used to calculate Z coordinates of the toolpath in the last iteration cycle n, and (D) surface to be used to calculate Z coordinates of the toolpath in the next iteration cycle n+1. Z coordinate of each point on surface D is calculated as given by Eq. (12). The logic behind this equation is that if a toolpath calculated using surface C produces surface A, then a toolpath calculated using surface D, as corrected by Eq. 12, should produce surface B.

$$ {\mathrm{Z}}_{\mathrm{tool}\ \mathrm{n}+1}={\mathrm{Z}}_{\mathrm{tool}\ \mathrm{n}}+\left({\mathrm{Z}}_{\mathrm{target}}\hbox{--} {\mathrm{Z}}_{\mathrm{result}\ \mathrm{n}}\ \right) $$

(12)

Fig. 24

A-1 Compensation logic of Z-displacement along the cross -section