# Effect of Feed Rate on the Force and Energy in the Cutting Process Using Planar Technical Blades
## 3 Results and Discussion  
The results of the performed tests of the cutting force \(F\) of the chosen blade relative to cutting speed \(v_{f}\) are shown in Figure 6. Figure 6a shows the averaged curves of cutting force \(F\) for each cutting speed \(v_{f}\) in time \(t\). Figure 6b shows all measured values of cutting forces \(F\) relative to cutting speeds. Mean values, trend line, and area under the cutting force, represented by the impulse \(I\) of the force \(F\) curve, are also shown. The impulse \(I\) is calculated from the following formula:  
\[I=F\times t,\,\text{N}\cdot\text{s}; \tag{1}\]  
where \(I\) is impulse, \(F\) is force, and \(t\) is time. Collected data enabled us to calculate work \(W\) and power \(P\) for each cutting speed \(v_{f}\) from the average force values. Results are presented in the chart in Figure 7. Work \(W\) is calculated from the following formula:  
\[W=F\times s,\,\text{J}; \tag{2}\]  
where \(W\) is work, \(F\) is force, and \(s\) is distance. Power \(P\) is calculated from the following formula:  
\[P=W/t,\,\text{W}; \tag{3}\]  
where \(P\) is power, \(W\) is work, and \(t\) is time. Collected data were also used to determine the unit energy intensity index \(e_{j}\)[26] of the cutting process, calculated as follows:  
\[e_{j}=W/A,J/\text{m}^{2}; \tag{4}\]  
where \(W\) is work and \(A\) is cross-sectional area of the sample. Figure 8 shows the graph of \(e_{j}\) relative to cutting speed \(v_{f}\). Figure 6: Experimental results of cutting force \(F\) relative to cutting speed: (**a**) averaged cutting force curves for each cutting speed; (**b**) measured values of cutting force, mean values, and the impulse \(I\) of force \(F\). The obtained measurement data show changes in the cutting force \(F\) depending on the cutting speed used. A tendency for the force to increase with increasing cutting speed was observed. The maximum force recorded was 3.99 N for a cutting speed of 340 mm/s. The lowest cutting force occurred when testing at the lowest cutting speed considered, namely 70 mm/s, and was 2.37 N, which is 59% of the maximum value. The average highest recorded cutting force occurred at 310 mm/s and was equal to 3.44 N, and the lowest average force occurred at 70 mm/s and was equal to 2.6 N, which is 75% of the maximum force averaged for each cutting speed test. Despite the fact that the recorded maximum force and averaged maximum force did not occur at the highest cutting speed tested, from the collected data shown in Figure 6b, the trend clearly shows that the cutting force \(F\) increases along with cutting speed. Therefore, it can be concluded that it will be desirable from the point of view of extending tool life to  
Figure 8: Graph for unit energy intensity of the cutting process \(e_{j}\) relative to cutting speed \(v_{j}\). Figure 7: Chart for work \(W\) and power \(P\) relative to \(v_{j}\) cutting speed. reduce the cutting speed in the process. This is because lower forces have been associated in the literature with slower cutting edge wear. In industrial conditions, however, the use of a slower cutting speed leads to an increase in the unit time of the operation, which is also not advantageous from an economic point of view. It is therefore necessary to seek an optimum, controlling the cutting speed in such a way as to minimize the process time and forces occurring during cutting. The increased forces \(F\) in the cutting tests were due to the material properties of the polyurethane. Properties such as tensile strength, elastomer density, and shore hardness characterize the decohesion process of this material. In this case, the material properties directly influenced the increase in cutting force \(F\) with increasing \(v_{f}\) cutting speed. Based on the observed data, it is possible to observe characteristic points, such as a sudden decrease in force \(F\) at 380 mm/s, a decrease in the energy intensity of the cutting process \(e_{f}\) at 340 mm/s, and a decrease in work \(W\) and power \(P\) at a blade feed rate of 340 mm/s.