**3. Analyzing Machining Forces Underlying SU–SC**

This section describes the machining forces underlying the bimetallic specimens denoted as SU–SC. Figure 4 shows the machining forces (thrust, feed, and cutting forces) in the time domain. The plots in Figure 4a,d,g,j show the expected machining forces of the constituent materials (S15CK + SUS304), neglecting the joint area. The plots in Figure 4b,e,h,k show the machining forces manifested in the joint area while machining from the S15CK direction to the SUS304 direction. The plots in Figure 4c,f,i,l show the machining forces manifested in the joint area while machining from the SUS304 direction to the S15CK direction. As seen in Figure 4, if a low feed (0.1 mm/rev) and low cutting speed (25 m/min) are used and machining is done from the hard material (SUS304) direction to the soft material (S15CK) direction, then the machining forces can be reduced. When a high feed is preferred, then the choice is to machine from the opposite direction—from the soft material (S15CK) direction to the hard material (SUS304) direction. For a high cutting speed (50 m/min), this argument is still valid for both low and high feeds, but a low feed is perhaps a better option.

**Figure 4.** Machining forces underlying SU–SC.

To be more specific, the uncertainty in the cutting forces was studied by constructing the possibility distributions [25,26] (probability-distribution-neutral representation of uncertainty) for the cutting forces, as shown in Figure 4. Appendix B shows the mathematical settings for inducing a possibility distribution from a set of numerical data. The results are shown in Figure 5. In the plots in Figure 5, the phrase "DoB" means the degree of belief (or membership value, see Appendix B), which is a value in the interval [0, 1]. The possibility distributions also support the abovementioned conclusions regarding the relationships between cutting conditions and cutting forces. In particular, the possibility distributions show that the use of a low feed and low cutting speed and the cutting direction hard-to-soft is a better option for reducing the cutting force and its uncertainty.

**Figure 5.** Uncertainties in the machining forces underlying SU–SC.

#### **4. Analyzing Machining Forces Underlying Al–Ti**

This section describes the machining forces underlying the bimetallic specimens denoted as Al–Ti. It is worth mentioning that this is a uniform combination similar to SU–SC because the tensile strength, hardness, and percent elongation of CP titanium are greater than those of aluminum (A1070), as listed in Table 1. As such, it will help validate the conclusion made in the previous section.

Figure 6 shows the machining forces (thrust, feed, and cutting forces) in the time domain for the dissimilar metallic specimens denoted as Al–Ti for the cutting conditions listed in Table 1. The plots in Figure 6a,d,g,j show the expected machining forces of the constituent materials (Al + Ti), neglecting the joint area. The plots in Figure 6b,e,h,k show the machining forces manifested in the joint area while machining from the Al direction to the Ti direction. The plots in Figure 6c,f,i,l show the machining forces manifested in the joint area while machining from the Ti direction to the Al direction. As seen in Figure 6, if a low feed (0.1 mm/rev) and low cutting speed (25 m/min) are used and the machining is done from the soft material (Al) direction to the hard material (Ti) direction, then the machining forces can be reduced. The same conclusion regarding the feed is valid for a high cutting speed. This is somewhat an opposing conclusion compared to that of the previous case. The reason for this somewhat dissimilar result is perhaps the hardness of the materials. Here, Al is too soft compared to the other material. This means that when a very soft metal is used in a dissimilar metallic object, it is better to start the machining operation from the soft material side using a low feed and low cutting speed.

**Figure 6.** Machining forces underlying Al–Ti.

To be more specific, the uncertainty in the cutting forces shown in Figure 6 was further studied by constructing possibility distributions similar to the previous case. The results are shown in Figure 7. The possibility distributions also support the abovementioned conclusions regarding the relationships between cutting conditions and cutting forces. In particular, the possibility distribution shows that the use of a low feed and low cutting speed and employing the cutting direction soft-to-hard is the right approach for reducing the cutting force and its uncertainty.

**Figure 7.** Uncertainties in the machining forces underlying Al–Ti.

#### − **5. Analyzing Machining Forces Underlying Al–CI**

This section describes the machining forces underlying the bimetallic specimens denoted as Al–CI. It is worth mentioning that this is a uniform combination similar to the previous two cases, because the tensile strength, hardness, and percent elongation of cast iron are greater than those of aluminum (A5052), as listed in Table 1 (note that the hardness equal to 79.2 HRB is about 142 HV.) Compared to the previous case, the Al alloy used here is much harder. As such, it will help validate the conclusions made in the previous two sections.

Figure 8 shows the machining forces (thrust, feed, and cutting forces) in the time domain for the dissimilar metallic specimens denoted as Al–CI for the cutting conditions listed in Table 1. The plots in Figure 8a,d,g,j show the expected machining forces of the constituent materials (Al + CI), neglecting the joint area. The plots in Figure 8b,e,h,k show the machining forces manifested in the joint area while machining from the Al direction to the CI direction. The plots in Figure 8c,f,i,l show the machining forces manifested in the joint area while machining from the CI direction to the Al direction. As seen in Figure 8, if a low feed (0.1 mm/rev) and low cutting speed (25 m/min) are used, both machining directions provide similar cutting forces. For the high cutting speed, the machining direction soft-to-hard provides a better result only for the low feed. To be more specific, the uncertainty in the cutting forces shown in Figure 8 was further studied by constructing the possibility distributions similar to the previous two cases. The results are shown in Figure 9. The possibility distributions also support the abovementioned conclusions regarding the relationships between cutting conditions and cutting forces. In particular, the possibility distributions show that the use of a low feed and low cutting speed and using the cutting direction soft-to-hard is the best procedure for reducing the cutting force and its uncertainty.

**Figure 8.** Machining forces underlying Al–CI.

**Figure 9.** *Cont.*

**Figure 9.** Uncertainties in the machining forces underlying Al–CI.

#### **6. Discussions**

Manufacturers who support sustainable product development (including design, manufacturing, and assembly) can benefit from the outcomes of this study because parts/products made of dissimilar materials (or multi-material objects) are better than their mono-material counterparts in terms of sustainability (cost, weight, and CO2 footprint). Particularly, this kind of study will help them by supplying the knowledge of material wastages and energy conceptions during the manufacturing processes. Regarding the material wastage calculation, the methodology described in [2] can be used. As far as the energy consumption is concerned, the machining force signals shown in Figures 4–9 can be used. For example, the machining power (*PM*) (kW) can be estimated using the cutting and feed force signals, which is a useful piece of information for determining the energy efficiency of a manufacturing process [2]. The machining power, denoted as *PM*, has two components, namely, Cutting power (*Pc*) and Feed power (*Pf*) components. As such, the following formulation holds:

$$P\_M(i) = P\_\varepsilon(i) + P\_f(i) = \frac{1}{60 \times 10^3} \left[ F\_{\rm S\mathcal{C}}(i)v\_\varepsilon + \frac{F\_{\rm SF}(i)fN}{10^3} \right] \tag{1}$$

Figure 10 shows, for example, the *PM* of the bimetallic specimen called SU–SC for the cutting conditions *vc* = 25 m/min and *f* = 0.2 mm/rev. As seen in Figure 10, *PM* varies in the range of [0.2, 0.45] kW. The variability in the cutting power for the four possibilities are illustrated in Figure 10a–d that correspond to the segments S15CK, SUS304, S15CK to SUS304, and SUS304 to S15CK, respectively. When the cutting tool passes the joint area, a gradual decrease/increase in the cutting power is observed, which is similar to that of the machining forces. This means that when the force sensors are not available, a power measurement instrument can be used to monitor the machining behavior of a bimetallic object.

**Figure 10.** *Cont.*

**Figure 10.** Machining power of the SU–SC bimetallic specimen (*vc* = 25 m/min, *f* = 0.2 mm/rev).

#### **7. Concluding Remarks**

This study reports the cutting/feed/thrust forces exhibited by three sets of bimetallic specimens. It was found that an entirely different machining force behavior arises due to the presence of two different materials, as well as the joint area.

The results shown in Figures 4–9 lead to the following conclusions:

Referring to the results in Figures 4 and 5, while machining steel-based bimetallic objects, keeping a low feed and high cutting speed is the better option, and the machining operation can be performed in both hard-to-soft and soft-to-hard material directions, but machining in the soft-to-hard material direction is the better option.

It is not recommended to create a bimetallic object using very soft material. Otherwise, it creates a machining problem (e.g., the case shown in Figures 6 and 7).

If an aluminum-based bimetallic part is preferred, then it is better to use a relatively harder alloy (e.g., compare the results shown in Figures 6 and 7 with those of shown in Figures 8 and 9). For the aluminum-based bimetallic objects, it is better to machine at a low cutting speed and low feed when the hard-to-soft material direction is needed.

Nevertheless, the research on machining is mostly concerned with the machining of objects made of mono-material and special alloys, whereas the research on machining objects made of multiple materials is in its infancy. The outcomes of this study can be used as a reference while enriching the machining technology of multi-material parts.

**Funding:** This work was funded by Kitami Institute of Technology.

**Acknowledgments:** The author gratefully acknowledges two of his former graduate students, Shin Matsui and Dongyuan Wu, and Masaaki Kimura at the University of Hyogo for their valuable inputs during the course of this study.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Appendix A Pictures of the Bimetallic Specimens Taken after Machining**

This Appendix shows the pictures of the three types of specimens after conducting the turning experiments. The respective cutting conditions and directions are shown.

**Figure A1.** The SU–SC specimens.

**Figure A2.** The Al–Ti specimens.

**Figure A3.** The Al–CI specimens.
