A study of the ability of the deformation of titanium sheet by hot single point incremental forming technology

 Abstract — Hot Single Point Incremental Forming (HOT SPIF) is a new technology of forming a metal sheet at high temperatures, especially for hard, high strength materials that are difficult to perform at normal temperatures such as Titanium and other materials. The paper presents the application of simulation method to determine the ability of the deformation of Titanium sheet through the angle of deformation αmax of the lateral profile of the model under the influence of tool diameter D (mm), step in the direction z of the tool VZ (mm), the velocity of the tool Vxy (mm/min), the temperature T(C). The content of this paper consists of the analyzing the influence of these 4 above parameters by building a finite element analyzing (FEA) model to determine the ability of deformation or the maximum lateral angle of forming and to compare the accuracy of FEM model to the one of Computer-aided design (CAD) model. The paper studies the influences of the 4 parameters to the ability to form of Titanium sheet by HOT SPIF.


INTRODUCTION
n small or single batch productions of forming metal sheet products, SPIF technology is selected in forming new products than other traditional methods of forming sheet by deformation because of its flexibility. In SPIF, the application of a circular end tool (spherical end pestle with no cutting edge) in a special SPIF machine or in a conventional CNC milling machine. Controlled by a digital program, the noncutting circular end tool moves in following a predefined trajectory to deform the workpiece sheet metal that is clamped on a special feature to format desired shape [1]. Especially in the manufacture of artificial joints and cranes for each personal patient in medicine, these products have to be made of Titanium for elimination of corrosion and deterioration. Although deformability of Titanium was performed by experimentation [2], simulation comparison of experimental results is necessary to verify the results and to build a simulation model for the product before manufacturing.

CAD model for simulation
The mechanical properties of commercial Titanium can be referred in [3]. The deformability of the method forming SPIF is determined by the maximum angle of deformation max. The largest shaping angle is the most important parameter, With the above selected parameters, the study applies the Full Design of Experiment (DOE) 2 levels, the numbers of the experimental model are: 2 4 = 16.

Building an analysis model in Abaqus
software Meshing and boundary conditions The element type of C3D6T are used to model with the initial selection of Titanium sheet that is selected as a deformation type with the size of 200x200x1mm and tool and feature are considered as analytical rigid. The Origin of coordinates is the sheet center [6]. Finite Element (FE) calculation considers 4 integration points in the thickness and is performed with ABAQUS/explicit. The meshing is shown in figure 3 The boundary conditions include a tool displacement, which is considered as a rigid body, and a clamping of all the external nodes. The value of the coefficient of friction is chosen equal to 0.1 according to stamping value found in the literature.
A typical explicit time step is presented in figure  2. The innovative part of this method concerns the way that the contact forces are taken into account. First, they are ignored when solving the equilibrium equation. Then, the error in the contact with the tool is computed geometrically. This depends only on the position 1 x and velocity 1 x of the nodes close to the tool at the end of the time step. Finally, the nodal acceleration 0 x at the beginning of the time step can be corrected in order to meet the required contact conditions at the end of the time step. The correction on the acceleration, multiplied by the nodal mass, is equivalent to the contact forces. In a first approach, elasto-plastic model is used. It includes a Von Mises yield criterion and an isotropic hardening law as presented in equations (2) and (3).
In order to simulate the process of deforming Titanium we have to follow strictly the following module steps in Abacus software: -Property module: to create the material and define its properties.
-Material properties: -Condition of contact (module interaction) -Boundary condition of base plate The base plate is fixed in space (limited to 6 degrees of freedom). Selecting Symmetry/ Antisymmetric/Encastre Boundary condition of sheet: 4 sides of the square sheet are fixed Symmetry/Antisymmetric/Encastre type The boundary condition of the tool: Tools allow to move in the direction x, y, z in the tool trajectory.

Analytical step (module Step)
Selected type step is Dynamic, Temp-disp, and Explicit to see the effects of temperature. The time period parameters are interested with the reason of the total running time of the tool is equal to the time of the last step that is not the time of the computer processes but the total time of the steps.     Table 3 4 COMPARISON OF SIMULATED AND EXPERIMENTAL RESULTS Table 3 displays the comparisons of experiment results and simulation results. The difference between Simulation and Experiment results is shown in the diagram in figure 7.

CONSIDERATION:
Simulation values with a 12mm tool diameter are greater than or equal to the experiment, simulation values with a diameter of 6mm are smaller than the experimental ones.
All deviations are less than 5%. This tolerance is acceptable for simulations close to experiment.

Regressive equation
The The Design-Expert software help to analyses the mutual influences of 2 in 4 parameters to the formability (angle α). Figure 8 illustrates the mutual influences of deformation angle  to 2 in 4 influenced parameters. Consideration the results: -The forming angle  is a positive correlation to the tool diameter.
-The forming angle  is a negative correlation between the feed rate Vxy and step depth Vz of the tool.
-The forming angle  is a positive correlation to the temperature T.
Analyses of the influence of input parameters Figure 9: Influence of 4 parameters: Step depth Vz, Feed rate Vxy, diameter D and temperature T to the formability angle 

CONCLUSIONS
The simulation and experimental results show that the diameter D of the tool and temperature T of the Titanium sheet are a positive correlation to the ability of deformation (angle ) in the meanwhile the Step depth Vz and the Feed rate Vxy of are negative to the angle. In reality, with the purpose of increasing the ability of deformation, we should use the bigger tool at high temperature but the diameter D of the tool cannot be increased freely because there is also the increase of force of forming and the SPIF technology could not perform the small radius of the product. The increase in the temperature T of the sheet is influenced by the mechanical properties of the tool and it must be limited. The decrease of feed rate and step depth will engender to the decrease of productivity of the process. In the future, it is possible to perform simulations before processing and will save the cost of testing, saving time and cost of machining. [5] Nguyen