2.3 Formability of ISMF

When comparing the deformations of ISMF with other traditional forming process such as stamping, clawing, pulling, bending, and so on, researchers have shown that the forming limit diagram (FLD) of ISMF is raised much higher than the traditional forming limit diagrams calculated from the theory of plastic deformation as well as obtained from experiments through traditional testing methods. The forming limit diagrams of traditional deformations are V-shaped. But studies have shown that the formability in ISMF is larger and shaped almost like a straight line in the minor-major strain space. In order to obtain the FLDs of ISMF, they could be based on the ductile fracture criterion of Clift et al. as shown in Eq. (1). The points on FLDs are calculated based on the initial point of the minor-major strain point convergence at the equilibrium strain region; the following points are calculated according to the relationship between the minor-major strain ratios (Eq. (2)) and the equivalent strain function for the plane stress state (Eq. (3)):

$$\int\_{0}^{\overline{\epsilon}\_{f}} \overline{\sigma} d\overline{\epsilon} = \mathbb{C} \tag{1}$$

$$
\beta = \frac{e\_2}{e\_1} \tag{2}
$$

$$\overline{\varepsilon} = \frac{R\_m + \mathbf{1}}{\sqrt{2R\_m + \mathbf{1}}} \sqrt{\mathbf{1} + \frac{2R\_m}{R\_m + \mathbf{1}} \beta + \beta^2 \varepsilon\_1} \tag{3}$$

where ε<sup>f</sup> is the equivalent strain at the ductile fracture strain point, σ is the equivalent stress, ε is the equivalent strain, C is the constant of the material, β is the minor-major strain ratio, Rm is the anisotropic coefficient, and ε<sup>1</sup> and ε<sup>2</sup> are the minor and major strains, respectively. In addition, material tensile tests give a relationship between stress and strain, and they are often expressed through hardening equations as indicated in Swift's Eq. (4):

$$
\overline{\sigma} = K(\varepsilon\_0 + \overline{\varepsilon})^n \tag{4}
$$

where K is the plastic deformation coefficient of the curve and n is the hardening parameter of the curve. After substituting Eq. (4) into Eq. (1) and performing the integral calculation, we can solve the equivalent strain value at failure point of ISMF as a constant Eq. (5):

$$
\overline{e}\_f = \mathbf{C}\_1 \tag{5}
$$

To determine C<sup>1</sup> parameter, the values of the minor-major strain at the equilibrium biaxial strain position are used in combination with the fracture values on the traditional forming limit curve. After determining the value of C1, we can use this value to calculate the different points of the FLC during ISMF by giving the deformation ratio β changes in the permissible zone and replace in Eqs. (2), (3), and (5). Figure 7 depicts the forming limit curves in ISMF based on the forming limit curves of the traditional method (V-shaped) for various experimental forming tools [3].

#### 2.4 Applications of ISMF method

ISMF method can be considered a new rapid prototyping method without creating expensive molds, and the time to create parts from the idea of the final product is less than 24 hours. ISMS method can also be distinguished as a layered

topic to be further studied by the following reasons: Accuracy of deformed products are still limited; the heat generation by the contact and friction between the forming tool and the material sheet is significant; there are high surface roughness and low productivity. Some recent applications of ISMF process have been summarized by

Deformed shape in finite element simulation: (a) 45° wall angle, (b) 60° wall angle, and (c) 70° wall

Parameters Symbol Value Radius of forming tools rt 5–15 (mm) Metal sheet thickness to 0.5–3 (mm) Down step z 0.1–2 (mm) Tilt angle after deformation ψmax to 90(°) Deformation speed S 500–2000 (mm/min) Axial force FA 300–1000 (N) Horizontal bending force Fb 100–500 (N)

several researchers [11–16].

Basic parameters of ISMF.

Figure 6.

Mass Production Processes

angle [8].

Table 2.

102

collection of all tool positions. As illustrated in Figure 8 to create tool paths, products must be divided into several layers. Each forming layer has the outline of the tool path that is similar to the boundary of the slice of the formed part. Therefore, the tool paths are generated based on the deformed shape of the product (Figure 6). In order to obtain forming location data (CL data) for a complex surface, a threedimensional scanner could be used to create point clouds on the surface of the specimen. These points can be used to extrapolate the shape of the object. Typically, point clouds received by 3D scanners will not be directly usable. Because most applications use 3D polygon, NURBS surface models, or editable CAD models. The process of converting point clouds into 3D models into any of the listed formats is called model refactoring. So, refactoring and editing methods are often done through 3D CAD software such as CATIA, SOLIDWORK, Pro-E, and so on to create surface models from point clouds. After the CAD model is available, there are two methods that can be used to obtain forming location data during the simulation as

The first method is the basic programming through the use of MATLAB software which was implemented as follows: the initial CAD model is stored as standard triangular language (STL) files, which include a list of triangular shapes that describes the outer surface of the CAD object. These triangular surfaces are

described by a set of X, Y, and Z coordinates for three vertices and a normal vector. To find the internal intersection points of the triangle used for calculating the tool

well as creating ISMF tool path as shown in Figure 8.

Rapid Prototyping for Sheet Metal Products DOI: http://dx.doi.org/10.5772/intechopen.88435

Figure 8.

Figure 9.

105

Intersection point recognition.

Tool path generation ISMF simulation and experiment.

Figure 7. Forming limiting curves of ISMF compared to traditional FLC methods [3].

technology process because the products are deformed according to the continuous layers of the tool path. Because the processing time for a product is large, this method could not be applied to mass production. However, the low initial cost makes it suitable for small series of products or rapid prototyping. The cost for a product of the ISMF method is difficult to identify and is often higher than the initial prediction. Products must be created in a CAD system, and tool paths are generated in a CAM system. It will consume about 2–5 hours of continuous work by a technician for a product with complex shapes. The setup and operation times on a CNC machine will also take about 3 hours. Therefore, this method should not be used to manufacture simple products.

In the medical industry, this method can be used to make replacement parts of the human body. Specific examples are shown in Figure 1a and b, where researchers have applied ISMF to create details such as teeth support plates and fragments of the skull with light titanium material. Recently, this method has been tested and applied in the automotive industry to make some new models of heatsink, headlamp, automotive cover, and some other products (Figure 1c and e). Currently, this processing method is still a hot topic in research for many different products and different materials.

#### 2.5 Tool path generation

The tool path generation of ISMF method is similar to the tool path generation for finishing the surface with CNC machines by the cutting method, where the metal sheets are clamped on a dedicated jig. Along the depth of product will be divided into a number of required forming layers. At each forming layer, from the top to the bottom of the product, the sheet metal will be deformed step by step along with the shape profile of each layer. Every time a forming layer is completed, the elevation Z is shifted a certain distance. The forming process will be finished when all the forming layers are completed. Obviously, the deformed shape and accuracy of the products are dependent on the position of the forming tool and the

## Rapid Prototyping for Sheet Metal Products DOI: http://dx.doi.org/10.5772/intechopen.88435

collection of all tool positions. As illustrated in Figure 8 to create tool paths, products must be divided into several layers. Each forming layer has the outline of the tool path that is similar to the boundary of the slice of the formed part. Therefore, the tool paths are generated based on the deformed shape of the product (Figure 6). In order to obtain forming location data (CL data) for a complex surface, a threedimensional scanner could be used to create point clouds on the surface of the specimen. These points can be used to extrapolate the shape of the object. Typically, point clouds received by 3D scanners will not be directly usable. Because most applications use 3D polygon, NURBS surface models, or editable CAD models. The process of converting point clouds into 3D models into any of the listed formats is called model refactoring. So, refactoring and editing methods are often done through 3D CAD software such as CATIA, SOLIDWORK, Pro-E, and so on to create surface models from point clouds. After the CAD model is available, there are two methods that can be used to obtain forming location data during the simulation as well as creating ISMF tool path as shown in Figure 8.

The first method is the basic programming through the use of MATLAB software which was implemented as follows: the initial CAD model is stored as standard triangular language (STL) files, which include a list of triangular shapes that describes the outer surface of the CAD object. These triangular surfaces are described by a set of X, Y, and Z coordinates for three vertices and a normal vector. To find the internal intersection points of the triangle used for calculating the tool

Figure 8.

technology process because the products are deformed according to the continuous layers of the tool path. Because the processing time for a product is large, this method could not be applied to mass production. However, the low initial cost makes it suitable for small series of products or rapid prototyping. The cost for a product of the ISMF method is difficult to identify and is often higher than the initial prediction. Products must be created in a CAD system, and tool paths are generated in a CAM system. It will consume about 2–5 hours of continuous work by a technician for a product with complex shapes. The setup and operation times on a CNC machine will also take about 3 hours. Therefore, this method should not be

Forming limiting curves of ISMF compared to traditional FLC methods [3].

In the medical industry, this method can be used to make replacement parts of

heatsink, headlamp, automotive cover, and some other products (Figure 1c and e). Currently, this processing method is still a hot topic in research for many different

The tool path generation of ISMF method is similar to the tool path generation for finishing the surface with CNC machines by the cutting method, where the metal sheets are clamped on a dedicated jig. Along the depth of product will be divided into a number of required forming layers. At each forming layer, from the top to the bottom of the product, the sheet metal will be deformed step by step along with the shape profile of each layer. Every time a forming layer is completed, the elevation Z is shifted a certain distance. The forming process will be finished when all the forming layers are completed. Obviously, the deformed shape and accuracy of the products are dependent on the position of the forming tool and the

the human body. Specific examples are shown in Figure 1a and b, where researchers have applied ISMF to create details such as teeth support plates and fragments of the skull with light titanium material. Recently, this method has been tested and applied in the automotive industry to make some new models of

used to manufacture simple products.

products and different materials.

2.5 Tool path generation

104

Figure 7.

Mass Production Processes

Tool path generation ISMF simulation and experiment.

Figure 9. Intersection point recognition.

Figure 10. Calculation of tool location points (CL data).

position at each Z layer, the points are projected in the radial direction from the center axis and calculate their intersection with the created surface. Those intersection points must be checked to see whether they are inside or outside of corresponding triangular elements as illustrated in Figure 9. After finding the points in the inner domain of the triangle, it is possible to calculate the position points of the tool according to Eq. (6) and Figure 10.

$$\begin{aligned} c &= m + Rn\_v \\ t &= c - Rn \\ |CE| &= |CG| = |Rn\_v n| \\ e &= c - |CE|n \\ |ET| &= |E - T| \\ h &= e - |ET|n\_v \\ |ST| &= \frac{(|ET|)^2}{|HT|} \\ cl &= m + |ST|n\_{\text{xoy}} \end{aligned} \tag{6}$$

The second method used to calculate tool position points is to immediately utilize the advantage of CAM software, where CAD models are stored in IGES file format and exported to CAM environment such as CIMATRON, DELCAM, MASTERCAM, etc. to conduct the simulation according to different types of tools. Usually, the selected tool path type will be a Z-level spiral-type and top-down

Numerical simulations for ISMF are still one of the challenges that need to be solved due to the loss of time in the simulation process, and the contact between the tool and the forming surface is always replaced. Therefore, the meshed surfaces in

programmed and imported into the input files of CAE software such as ABAQUS, DEFORM, LS-DYNA, and so on. This software can provide a simulation of elastic and plastic deformation of the sheet metal forming process. Characteristics such as stress distribution, deformation, ductile fracture, etc. can be easily inspected through the simulation process. The results of the simulation process can then be used to obtain the optimal shape as well as the material properties required for the final product. Before simulating the process of forming deformation, mechanical properties of 3D models, geometric profiles of products, and contact surfaces must be built. Elastoplastic model is often selected to simulate through material properties such as elastic modulus, Poisson's coefficient, and density of materials. The flow stress curve equations of materials and anisotropic models must be applied to

Meshed elements used in finite element simulation of ISMF are often shell element models with more than five integral points according to the thickness of the shell. Using the integral points in the thickness direction of the shell element could be replaced by the solid element and described the effects of the tension and compression area on the simulation results. Most shell elements consider the normal stress to be zero in the direction of the thickness, but because the shear stress in that direction may be not zero, then the stress state is not plane stress. Some shell elements consider the normal stress in the thick direction, and they are called thick shell elements. Figure 12 shows the finite element model for the ISMF simulation process, in which forming tools and supported molds are designed and calibrated with 3D software, the blank is modeled with shell elements (S4R), and tools and

the simulation should not be too complicated, and the tool paths must be

method as shown in Figure 11.

Rapid Prototyping for Sheet Metal Products DOI: http://dx.doi.org/10.5772/intechopen.88435

3. Numerical simulation in ISMF method

describe the plastic flow rule of materials.

3.1 Select simulation elements

Figure 12.

107

Finite element model for simulation.

where c, m, t, e, h, and cl are vectors corresponding to peak points of C, M,T, E, H, and CL; R is the radius of forming tool; nn is a unit normal vector; nv is the vector along the unit axis; and nxoy is a projection of the nn vector on the (XoY) bottom plane.

Figure 11. Tool path generated from CAM software.

### Rapid Prototyping for Sheet Metal Products DOI: http://dx.doi.org/10.5772/intechopen.88435

The second method used to calculate tool position points is to immediately utilize the advantage of CAM software, where CAD models are stored in IGES file format and exported to CAM environment such as CIMATRON, DELCAM, MASTERCAM, etc. to conduct the simulation according to different types of tools. Usually, the selected tool path type will be a Z-level spiral-type and top-down method as shown in Figure 11.
