**2. Powder-binder-jetting**

#### **2.1. Overview**

Additive manufacturing processes differ fundamentally from the conventional production process: The desired component, for example, a mold, is composed of layers. The production is directly related to the component data. In the case of the conventional manufacturing, the component data are at first realized as a model or tool, and this part is then further used for the actual production. The time required for an entire processing cycle is significantly reduced

This layer-based powder-binder-jetting technology produces porous material components by selective bonding of particle material. These characteristics (specifically strength) are disad‐ vantageous for the direct use, but parts manufactured in this manner can be used in the foundry process. A temperature-resistant material, such as sand, is used as particle material for this process. The binder is also selected in accordance to its properties and temperature resistance properties are adjusted. Due to the porosity of the parts, the resulting gas can escape during

The particular process associated with powder-binder-jetting which makes this process highly efficient is the use of particle material as a basis and the use of a limited amount of binder. In addition, the automation process can easily be expanded. It is possible to produce component sizes that are specific for foundry technology. Scalability during production allows production rates that are economical for small series. Here as well, a lot of potential can be seen, and

This chapter introduces the powder-binder-jetting method in detail and explains its suitability for the production of molds. Other additive manufacturing processes are briefly described and their different characteristics are shown. It is shown that powder-binder-jetting processes based on lot sizes and productivity are unique, and therefore hold a prominent position as an

The sand casting process plays an important role in the field of conventional casting technol‐ ogy. This sand casting process is carried out using three materials/binding systems, which can be directly transferred to AM production methods. The basic methodology of determining the characterizing parameters are explained further in the following sections. The data obtained for printed components using this method are compared with the data of conventionally

A subchapter deals with the application of 3D printed molds for metal casting in the area of cold-curing materials. Here, the problems arising out of de-coring are most crucial. The process of extracting the printed part from the mold is explained in detail using the examples of concrete casting. The results that are obtained in this area are presented in detail and discussed

Another section presents the use of the particle material, PMMA powder, as a basis for the investment casting process. Here, the investment casting process is explained and its embodi‐ ment as AM process is explained using 3D-printed forms. Within this context as well, the

casting, which eliminates casting defects by rising gas bubbles in the melt.

previously limited lot sizes increasingly move toward larger lot sizes (see [2]).

by applying additive manufacturing methods (see [1]).

54 New Trends in 3D Printing

industrial means of production within AM.

manufactured components and an assessment is carried out.

in the context of applications in structural engineering and architecture.

property requirement necessary for the 3D-printed parts is also elaborated.

This section provides an overview of the powder-binding-jetting technology. As in the case of several additive manufacturing processes, this process too comprises individual steps that are repeated continuously to form a three-dimensional component. **Figure 1** provides an over‐ view.

**Figure 1.** Schematic representation of the powder-binder-jetting-process: (a) lowering the build platform, (b) layering with particle material, and (c) printing process using binder.

The PBJ process steps are as follows: applying a layer of particle material (powder) on a build platform, bonding of the powder particles by a liquid, and lowering the build platform by the height of the desired layer thickness (see [3]).

The process begins with an empty build platform. It is usually set up within a build box. A seal prevents leakage of powder between the moving construction platform and the static walls of the build box. The recoater spreads the powder on the build platform (see [4]). The powder can either be placed in front of the recoater or is moved along with the recoater across the build platform.

At the start of the construction process, the space between the recoater blade and the build platform is sequentially built up with multiple layers of powder to eventually form an even layer of powder.

In the next step, the inkjet print head moves over the powder layer and doses binder onto the layer. The current height of the built component corresponds to a cross-section of the virtual component. The inside part of the cross-section is filled up by print data. Depending on the data processing process, the sliced images are eventually converted into a matrix, in this case in a bitmap structure (for data formats, see [5]).

The inkjet print head also represents a matrix-like arrangement and is guided across the entire built platform, depending on the size of the print head in a meandering motion or in one linear drive across the platform. In the simplest case, this matrix-like arrangement is a line of nozzles which correspond to the driving pattern as determined by the data matrix. During the drive, data change in rapid succession, thus forming the desired image.

The droplets are generated in the inkjet print head itself due to rapid pressure fluctuations and expelled through a micronozzle. Thus, a drop formed in the micronozzle is pressed out and leaves the nozzle as a free-flying independent droplet. Due to this process, certain restrictions are placed on the material range that can be applied (see [6, 7]).

The upper limit for the viscosity is currently approximately 30 mPa s. The surface tension should be substantially below that of water, so less than 50 mN/m. The printable material can include solvents, aqueous solutions, oils, or monomers. The media should not expel particles larger than approximately 1 μm so that no blockages are formed in the microjets.

The final step in the construction process is the lowering of the build platform. After lowering, the resultant space is again filled with the help of the recoater. The layer thickness corresponds to the vertical distance the build platform moved while lowering. An alternative process is the continuous 3D printer. According to this method, the printing is performed on an inclined plane and the powder-bed movement takes place via a conveyor belt at an angle to the plane (see [8]).

#### **2.2. Distinction from other processes**

The MultiJet modeling process works similar to the PBJ process. The focus of the method is also an inkjet print head that works on matrix basis. Contrary to the method described above, powder is not used, but the desired shape is composed by the medium expelled from the print head. Here, the medium is cured in layers with the help of a UV source. Overhangs can be achieved by using a support medium that is applied over a second print head. Curing is done using UV technology (see [9]).

Under the vector-based methods, the fused deposition modeling is the only method that is not based on energy beam technology and is thus similar to the PBJ process. As opposed to the two procedures mentioned above, this method does not involve free-flying droplets. The model is constructed using an extruded filament (see [9]).

In the beam-based method, there is no additional mass involved during construction process, reflecting the total mass of the finished model. Existing volume is modified. During stereolithography, resin is cured by a laser beam [10]. When laser sintering process is applied, a powder is used as a base which is similar to the PBJ process and a high-energy beam is used to fuse the powder; Currently, the most widely used methods are the ones making plastic or metal parts. Materials such as ceramics, concrete, or biological materials are the subject of research on an industrial scale but not yet main stream (for ceramic see [11]). **Table 1** provides information on the different distinction possibilities.


**Table 1.** Characteristics and categorizations of various AM methods.

#### **2.3. Scalability**

The inkjet print head also represents a matrix-like arrangement and is guided across the entire built platform, depending on the size of the print head in a meandering motion or in one linear drive across the platform. In the simplest case, this matrix-like arrangement is a line of nozzles which correspond to the driving pattern as determined by the data matrix. During the drive,

The droplets are generated in the inkjet print head itself due to rapid pressure fluctuations and expelled through a micronozzle. Thus, a drop formed in the micronozzle is pressed out and leaves the nozzle as a free-flying independent droplet. Due to this process, certain restrictions

The upper limit for the viscosity is currently approximately 30 mPa s. The surface tension should be substantially below that of water, so less than 50 mN/m. The printable material can include solvents, aqueous solutions, oils, or monomers. The media should not expel particles

The final step in the construction process is the lowering of the build platform. After lowering, the resultant space is again filled with the help of the recoater. The layer thickness corresponds to the vertical distance the build platform moved while lowering. An alternative process is the continuous 3D printer. According to this method, the printing is performed on an inclined plane and the powder-bed movement takes place via a conveyor belt at an angle to the plane

The MultiJet modeling process works similar to the PBJ process. The focus of the method is also an inkjet print head that works on matrix basis. Contrary to the method described above, powder is not used, but the desired shape is composed by the medium expelled from the print head. Here, the medium is cured in layers with the help of a UV source. Overhangs can be achieved by using a support medium that is applied over a second print head. Curing is done

Under the vector-based methods, the fused deposition modeling is the only method that is not based on energy beam technology and is thus similar to the PBJ process. As opposed to the two procedures mentioned above, this method does not involve free-flying droplets. The

In the beam-based method, there is no additional mass involved during construction process, reflecting the total mass of the finished model. Existing volume is modified. During stereolithography, resin is cured by a laser beam [10]. When laser sintering process is applied, a powder is used as a base which is similar to the PBJ process and a high-energy beam is used to fuse the powder; Currently, the most widely used methods are the ones making plastic or metal parts. Materials such as ceramics, concrete, or biological materials are the subject of research on an industrial scale but not yet main stream (for ceramic see [11]). **Table 1** provides

larger than approximately 1 μm so that no blockages are formed in the microjets.

data change in rapid succession, thus forming the desired image.

are placed on the material range that can be applied (see [6, 7]).

(see [8]).

56 New Trends in 3D Printing

**2.2. Distinction from other processes**

using UV technology (see [9]).

model is constructed using an extruded filament (see [9]).

information on the different distinction possibilities.

Among all processes, the powder-binder-jetting process is considered the most scalable. This has an impact on possible component sizes and system performance. Different categories of scalability are discussed and evaluated as below.

In the PBJ process, the build size is defined by the distances covered by the linear axes. In principle, these axes can be extended as required. Merely the axle supporting structure needs to be adjusted according to the increased point of deflection. Limitations are generally not posed by the device, but by the strength of the product produced relative to its weight. This ratio largely determines the handling of the parts and is therefore size restricted.

The performance of a system is often quantified on the basis of the time taken to print one layer.

During the PBJ process, the pixels of a layer are printed by individual parallel controllable nozzles. Here, the number of the nozzles is proportional to the print performance. When measures are taken to parallelize the coating process, the number of nozzles is often nearly proportional to the time per layer. The performance of the printing system can thus be easily scaled by increasing the number of nozzles.

Within PBJ process, there is another option to improve the performance: Several spatially successively arranged coating and printing units are able to generate quasiparallel layers. The applicable layer time is then the layer time of such a "layer unit" divided by the number of the active "layer units" [12].

For procedures having a vector control, such scales cannot be realized. In laser-based methods, the radiation field cannot be expanded indefinitely. This is mainly due to the flat field lens required for a focused exposure. Similarly, it is not possible to use arbitrarily many laser sources simultaneously since the beam path would rapidly become complicated, particularly due to the necessary deviation.

In the case of FDM, axis scaling is possible as which the PBJ processes. However, due to the mass inertia of the print-head discharge, speeds are limited. A parallelization of several printhead discharges is possible albeit only with considerable effort.

The parallelization described by several "layer units" is not possible in the laser sintering process and the SLA process. Both methods use contour procedures that require a complete "visibility" of the current layer. A parallelization would require at least the simultaneous formation of a new layer and the laser exposure of an old layer. The FDM method combines the shaping and layer formation. In this case, this principle can also not be used.

The PBJ method thus provides unique opportunities to improve performance. A summary of these bearings can be found in **Table 2**. Thus, applying this technology as a production process within established production procedures seems to be realizable.


**Table 2.** Assessment of the scalability of different processes.

#### **2.4. Basic modeling**

The mechanical properties of the PBJ processes are, apart from the cohesion of the binder and the adhesion of the binder to the particles, essentially determined by two variables: the grain size and the relative amount of binder. During the model forming process, the particles are thought to be stronger than the bond.

**Figure 2.** Schematic representation of the model particles/bond: (a) illustration of a particle cluster under tension, (b) illustration of two particles under tension, and (c) highly simplified model for calculating the volume of the bond.

A model of the bond can be represented as in the following simplified diagram: Between two particles that are considered as ideal for the spherical model, there exists an external nearly cylindrical binder bridge (see **Figure 2**). This bridge is formed by capillary action shortly after application of the binder by the print head and the respective strengthening mechanism freezes this condition. This form of connection is similar to the sintering process. Basic deviations, necessary for the basic understanding of the conditions, can be obtained by simple consider‐ ations.

In the case of FDM, axis scaling is possible as which the PBJ processes. However, due to the mass inertia of the print-head discharge, speeds are limited. A parallelization of several print-

The parallelization described by several "layer units" is not possible in the laser sintering process and the SLA process. Both methods use contour procedures that require a complete "visibility" of the current layer. A parallelization would require at least the simultaneous formation of a new layer and the laser exposure of an old layer. The FDM method combines

The PBJ method thus provides unique opportunities to improve performance. A summary of these bearings can be found in **Table 2**. Thus, applying this technology as a production process

The mechanical properties of the PBJ processes are, apart from the cohesion of the binder and the adhesion of the binder to the particles, essentially determined by two variables: the grain size and the relative amount of binder. During the model forming process, the particles are

**Figure 2.** Schematic representation of the model particles/bond: (a) illustration of a particle cluster under tension, (b) illustration of two particles under tension, and (c) highly simplified model for calculating the volume of the bond.

the shaping and layer formation. In this case, this principle can also not be used.

**Process Size Layer speed** *Z***-speed** PBJ ++ ++ ++ FDM ++ 0 - SLS - + + SLA 0 + -

head discharges is possible albeit only with considerable effort.

within established production procedures seems to be realizable.

**Table 2.** Assessment of the scalability of different processes.

thought to be stronger than the bond.

**2.4. Basic modeling**

58 New Trends in 3D Printing

If the binder bridge is small in relation to the radius of the sphere (*h* = const), then considering the above assumptions, a model of a cylinder minus two cones describes

$$W\_{\rm FI} = 2 \cdot \frac{2}{3} \Big/ 3 \cdot a^2 \cdot \pi \cdot h \tag{1}$$

the volume of the bond or the printed quantity of liquid. If the model is modified to determine the influence of the volume, it can be assumed that a constant distance of the particles exists. Only the radius of the cylinder varies. Thus, the relation holds true:

$$V\_{Fl} \sim a^2. \tag{2}$$

The contact area *A* and the maximum mechanical tension *σ*Max are accessible via simple equations

$$A = a^2 \cdot \pi \,\text{and}\,\sigma\_{\text{Max}} \sim A. \tag{3}$$

The relationship of the printed amount to the mechanical stress at break is thus linear:

$$
\sigma\_{\text{Max}} \sim V\_{\text{Fl}}.\tag{4}
$$

The strength is thus linearly dependent on the volume of the printed material. The printed volume corresponds to the organic or inorganic binder content minus the evaporated solvent content.

Considering the influence of the particle size, the model must be mentally expanded to form a particle cluster. As a minimal model, a cubic packing may be used and a voxel as observa‐ tional volume. A voxel is defined by the smallest possible volume that can be produced with a PBJ system. The dimensions of a voxel are made up of layer thickness and the resolution of the inkjet print head together in two directions. For the number of binding areas per voxel *N* holds true:

$$N = \mathbf{6} \cdot N\_p = \mathbf{6} \cdot \left(\frac{I\_\nu}{D\_p}\right)^5 \tag{5}$$

with the number of particles per voxel *N*p, the dimension *l*p, a cubic voxel, and the grain diameter *D*p of the considered perfect monomodal particle size distribution.

For the volume of a single bond *V*B and the total binder volume per voxel *V*v, the following equation applies:

$$V\_V = V\_B \cdot N = V\_B \cdot 6 \cdot \left(\frac{I\_\nu}{D\_p}\right)^3. \tag{6}$$

As with the approximation of the print volume, in this case only one-half, it is again assumed to form a binding as shown below:

$$W\_{\mathfrak{g}} = \frac{2}{\mathfrak{J}} \oint \cdot d^2 \cdot \boldsymbol{\pi} \cdot \boldsymbol{h} \,. \tag{7}$$

For calculating the bond area, relevant for the maximum mechanical stress at break, the following equation applies:

$$A = a^2 \cdot \pi \cdot \left(\frac{I\_{\nu}}{D\_{\rho}}\right)^2\tag{8}$$

and by applying the above relationship for *V*B , we obtain

$$A = \frac{3 \cdot V\_B}{2 \cdot h} \cdot \left(\frac{l\_\nu}{D\_\rho}\right)^2 = \frac{3}{2 \cdot 6 \cdot h} \cdot V\_\nu \cdot \left(\frac{D\_\rho}{l\_\nu}\right)^3 \cdot \left(\frac{l\_\nu}{D\_\rho}\right)^2 = \frac{V\_\nu}{4 \cdot l\_\nu \cdot h} \cdot D\_{\nu}.\tag{9}$$

The relationship between *σ*Max and the particle diameter *D*p is therefore, at *V*V, *l*V, and *h* = const, almost linear:

$$
\sigma\_{\text{Max}} \sim D\_p. \tag{10}
$$

The particle diameter is directly proportional to the breaking stress value in the same way as the amount of liquid. This implies that the use of finer particles leads to a reduction of strength. Similarly, when particle size is reduced (improving the surface properties), the amount of liquid printed needs to be adjusted. In the given model assumptions, the density is not affected by changes in the particle diameter.

**Figure 3.** Diagram of the pore-channel diameter at different particle diameters: (a) diameter of an average particle clus‐ ter with inscribed minimum passage diameter and (b) particle cluster with half a particle diameter for comparison.

The dimension of the size of the pores is changed by changing the particle diameter (see **Figure 3**). In this example, the diameter of the respective largest circular diameter *D*Por is inversely proportionate to the particle diameter. This can be roughly described as

$$D\_{p\_W} \sim \frac{1}{D\_p}.\tag{11}$$

According to this relationship, the resistance of a gas flowing through such channels greatly increases because the volume flow is proportional to the diameter to the fourth power. A change in the particle diameter (for example to influence surface finish) has a strong influence on the behavior of the gas penetration in the printed model.
