## 3 Results and Discussion
As the piston mass increases, the initial and subsequent amplitudes and period of oscillation \(\dot{\varphi}\) decrease, and the line around which the oscillation process occurs is defined by the zero magnitude value \(\dot{\varphi}\). The greater the magnitude of the force moment resulting from the piston gravity (or piston mass) directed opposite to the \(a\) engine torque, the smaller the maximum magnitudes of the oscillations \(\varphi\) and \(\dot{\varphi}\), and the smaller the repeatability of their oscillations. It follows from Formula (27) that the power of the mixing and whipping force is \(P\)-\(\dot{\varphi}^{3}\sin^{3}\varphi\). Then, in turn, the limit value of the excitation source shaft rotation angle based on Equation (25) or (26) is as follows: \(\varphi_{l}\)-\(\arcsin\bigl{[}1/\bigl{(}J_{m}\omega_{0}^{2}\bigr{)}\bigr{]}\). At \(\dot{\varphi}\to\dot{\varphi}_{l}=0\) (\(\dot{\varphi}_{l}\)--engine shaft rotational speed limit value) limit, the magnitude value is \(P_{l}\)-\(\frac{1}{m^{3}}\dot{\varphi}_{l}^{3}\), taking into account \(\omega_{0}^{2}\)-\(m\). The limit values of the rotation angle corresponding to the power value \(P=P_{l}\) coincide with the values of this angle in the dependencies \(\varphi=\varphi(t)\) in Figure 6. Dependency graphs \(P=P(\dot{\varphi})\) and \(P=P(\dot{\varphi})\) in Figures 8 and 9 show that the larger the mass of the piston, the smaller the maximum power values of the mixing and whipping forces \(P\). The decrease in the maximum value of \(P\) with increasing mass \(m\) is accompanied by a shift in the corresponding magnitudes of the values \(\varphi\) and \(\dot{\varphi}\) to the beginning of the abscissa. The graphs in Figure 9 show that, when approaching the end of the oscillating damping process, the technological process of whipping intensifies, which is demonstrated by a sharp increase in the force of mixing and whipping and its power and at some of their values and a sharp drop in their values. At \(\dot{\varphi}\to 0\), \(P\to 0\) (Figure 9). The rightmost limits of the graphs \(P=P(\varphi)\) and \(P=P(\dot{\varphi})\) are limited by the maximum values of \(\varphi\) and \(\dot{\varphi}\). The leftmost limits of the graphs \(P=P(\varphi)\) and \(P=P(\dot{\varphi})\) are defined by the minimum values of \(\varphi\) and \(\dot{\varphi}\). Figure 7: Dependence \(\dot{\varphi}=\dot{\varphi}(t)\) for different values of \(m\). The device parameters, including the crank length, influence the kinematic oscillation parameters of the engine shaft motion (Figures 10 and 11). After a lapse of time, the rotation angle of the driven engine shaft oscillates around the values to which it tends to oscillate, with an amplitude and period of oscillation smaller the longer the length of the driving member, as it is known that the limiting value of the rotation angle \(\varphi\): \(\varphi_{l}\)-\(\arcsin\left(k_{2}/\omega_{0}^{2}\right)\), while \(\omega_{0}^{2}\)-\(r\). From Formula (27), we obtain \(P\)\(\sim\)\(r^{3}\varphi^{3}\sin^{3}\varphi\). From this dependence, the first thing to note is the proportionality \(P\)\(\sim\)\(r^{3}\). Despite this dependence, based on the graphical relationships in Figures 12 and 13, the predominant relationship is \(P\)-\(\sin^{3}\varphi\varphi^{3}\), i.e., the value \(\sin^{3}\varphi\) is proportional to the minus \(n\)-th degree of \(r\), the value \(\varphi^{3}\) is proportional to the minus \(m\)-th degree of \(r\), and the total should be \(n+m>3\). Figure 8: Dependence \(P=P(\varphi)\) for different values of \(m\). Figure 9: Dependence \(P=P(\hat{\varphi})\) for different values of \(m\). Figure 11: Dependence \(\dot{\varphi}=\dot{\varphi}(t)\) for different values of \(r\). Figure 10: Dependence \(\varphi=\varphi(t)\) for different values of \(r\). On the other hand, the limit values of the excitation source shaft angle \(\varphi_{l}\)-arcsin\((k_{2}/r)\) for different values of \(r\), to which the value of \(\varphi\) at the end of the oscillating damping process will tend, are the same in Figures 10 and 12.