## 3 Experimental Determination of Coefficients \(K_{b}\) and \(K_{r}\)  
To experimentally determine the values of the coefficients \(K_{b}\) and \(K_{R}\), a series of experiments on cutting and scratching polished steel samples L3 (USA standard) HRC = 55...60, with a diamond pyramid with an angle of 136\({}^{\circ}\) at the top, a radius of 60 microns at the top, and a series of experiments on cutting and scratching samples with grains of an abrasive bar of green silicon carbide GC 150 N7 V220 with a height of 10 mm and an angle of 45\({}^{\circ}\) at the top, was carried out. To conduct these experiments, the diamond pyramid (1) was fixed in a metal disk (2) mounted on the faceplate of a circular grinding machine (3), Figure 2. To obtain drawings with different depths when cutting-scratching with a diamond pyramid, the axis of the part (4) was deflected by turning the table from its line of movement by 1-2 degrees. Cutting-scratching with a diamond pyramid was carried out at four speeds: 6, 10, 20 and 38 m\(\cdot\)s\({}^{-1}\). Cutting-scratching with abrasive bar grains was carried out at a bar speed of 35 m\(\cdot\)s\({}^{-1}\), a part speed of 40 m\(\cdot\)min\({}^{-1}\), \(S=1.0\) m\(\cdot\)min\({}^{-1}\), and a cross feed \(t=0.05\) mm\(\cdot\)min\({}^{-1}\). A 3% solution of Na\({}_{2}\) CO\({}_{3}\) was used as a cutting fluid. The median profile of a single mark was recorded on a profiler model 33319-13. The measurement of the areas \(S1\), \(S2\), and \(fcp\) was carried out with a planimeter of the Planix 5 model. The results of processing profilograms were calculated using the least squares method. Figure 3 shows an example of the dependence of the change in the extrusion coefficient on the speed and depth of cutting-scratching. As the figure data show, the extrusion coefficient decreases with the increasing depth of cutting-scratching and the speed of the wheel, while the influence of the speed of the wheel on the extrusion coefficient is significantly less than the influence of the depth of cutting-scratching. Mathematical processing of experimental data from 120 experiments established the following dependence of the extrusion coefficient on the depth and speed of cutting-scratching:  
\[K_{b}=1-0.34\cdot a_{cp}^{0.56}\cdot V^{0.06}r_{ka}=0.58,\,r_{kV}=0.22, \tag{23}\]  
where \(r_{ka}\) and \(r_{kV}\) are correlation coefficients of the coefficient \(K_{b}\) on the depth and speed of cutting-scratching. Figure 2: Scheme of cutting-scratching of a part with a diamond cone and an abrasive bar on a circular grinding machine. Analysis of Equation (23) shows that the exponent at the cutting-scratching speed is seven times less than the exponent at the cutting-scratching depth, Figure 3. Figure 4 shows the dependence of the coefficients \(K_{b}\) and \(K_{R}\) on the depth of cutting-scratching by the grains of the abrasive bar. The coefficient of extrusion, as well as cutting-scratching with a diamond pyramid, decreases with increasing depth of cutting-scratching. So, by increasing \(a_{cp}\) from 0.2 to 1 \(\upmu\)m, coefficient \(K_{b}\) decreases by 1.85 times. The coefficient of excess surface roughness increases with increasing cutting-scratching depth. So, by increasing \(a_{cp}\) from 0.2 to 1 \(\upmu\)m, coefficient \(K_{R}\) increases from 0.42 to 0.8. By processing the experimental data from 80 experiments, the following dependences of the extrusion coefficient and the coefficient of excess surface roughness on the depth of cutting-scratching were established:  
\[K_{b}=1-0.66\cdot a_{cp}^{0.38},\ r_{kb\cdot a}=0.44 \tag{24}\]  
\[K_{R}=0.8\cdot a_{cp}^{0.27},\ r_{kR\cdot a}=0.57 \tag{25}\]  
where \(r_{kb\cdot a}\) and \(r_{kR\cdot a}\) are correlation coefficients. During grinding in wheels GC 150 N7 V220, the surface roughness, depending on the mode, is within \(Ra_{0}=0.32\)-0.08 \(\upmu\)m, with an average value: \(Ra=0.16\)\(\upmu\)m. For the value of the depth of cutting-scratching, \(a_{cp}=1.0\)\(\upmu\)m. The coefficients can be assumed to be equal: \(K_{b}=35\); \(K_{R}=0.8\).