## 3 Results
### Comparison of the Simulation Results Obtained for the Two Models and the Experimental Test Results
This is not in conformity with the widely known thesis (promoted in  
Figure 8: Minimum values of the phase shift angle vs. relative damping coefficient \(\vartheta_{1}\) (Thetal’) for the rear suspension of the Opel Agila car: (**a**) \(\Phi_{\text{min}}\) (Fimmin) values for the contact force between the tyre and the vibration plate; (**b**) \(\Phi_{\text{mmin}}\) (Fimmin) values for the force measured in the test stand. Figure 7: Minimum values of the phase shift angle vs. relative damping coefficient \(\vartheta_{1}\) (Thetal’) for the rear suspension of the Opel Astra Van car: (**a**) \(\Phi_{\text{min}}\) (Fimmin) values for the contact force between the tyre and the vibration plate; (**b**) \(\Phi_{\text{mmin}}\) (Fimmin) values for the force measured in the test stand. theoretical publications, e.g., [40; 41]) that friction (or, more precisely, dry friction) has no impact on the phase shift angle between the input and response of a system under analysis. The quantitative differences between the results of simulations where the linear model was used and the results of experiments are big (although smallest for low relative suspension damping coefficients) in spite of qualitative similarities in the dependences of the minimum phase angle on the relative suspension damping. This indicates the necessity to limit the application of linear models to qualitative analyses only. What should additionally be recalled here are the general criteria for the assessment of the technical condition of a shock absorber, proposed in publications [16; 17] (see also [28]). The acceptable minimum values of the phase shift angle should be higher than 0.52360 rad (30 deg). The suspension systems with \"strong\" shock absorbers are characterised by the values of this angle exceeding 1.04720 rad (60 deg). In consideration of the results presented in Figures 7 and 8, the minimum value of this angle, i.e., 0.52360 rad (30 deg), corresponds to the relative suspension damping \(\vartheta_{1}\) (Theta1) in the interval 0.1-0.15 (for the assessment based on the contact force between the tyre and the vibration plate). In publication [16] (see also [28]), the very good shock absorbers' condition is described by the minimum phase shift angle values exceeding 1.5708 rad (90 deg). As an additional problem, we should also mention the significant differences between the values obtained by analysing the contact force \(\mathrm{F_{dz}}\) between the tyre and the vibration plate (the angle \(\Phi_{\mathrm{min}}\) = Fimin) and the force \(\mathrm{F_{md}}\) measured (the angle \(\Phi_{\mathrm{mmin}}\) = Fimmin) clearly visible in Figures 7 and 8. This indicates that the correction made to take into account the value of the force of inertia of the vibration plate is very important in both qualitative and quantitative terms. The values determined without the correction are lower, although this is not justified by the condition of the vehicle under examination, defined by the relative suspension damping \(\vartheta_{1}\). This confirms the reasonableness of correcting the force measured in the diagnostic test stand to take into account the force of inertia of the vibration plate, as postulated in publications [16; 17; 27]. For the non-linear model, relative error (simulation versus real car) is on level 0.4-11.0% (Figure 7), but for very small \(\Delta\vartheta\), it reaches values up to 44%. Similar values for Figures 8 and 9 are up to 30%. For the linear model, the relative error reaches 11.8-38% (Figure 8a) and 36-57% (Figure 8b). A similar situation is for Figure 9, an inverted version (prepared for diagnostic purposes) of Figure 8. So, we can say that the non-linear model shows better properties of real cars than linear ones. Based on the results presented, we can also state that the method presented is very sensitive to suspension friction forces.