## 3 Results
### Comparison of the Simulation Results Obtained for the Two Models and the Experimental Test Results  
Figure 7 is a juxtaposition of the minimum values of the phase shift angle, obtained as a result of simulation calculations where the linear and non-linear models were used, and results of experimental tests carried out on a prototype diagnostic test stand. The independent variable is the relative suspension damping coefficient \(\vartheta_{1}\) ('Theta1'). It should be remembered that the force Fts\({}_{1}\) of sliding friction in the suspension system is not taken into account in this coefficient. Figure 7a shows the minimum values (\(\Phi_{\min}=\text{Finn}\)) of the phase shift angle for the contact force between the tyre and the vibration plate, and Figure 7b  
Figure 5: Phase angle vs. frequency curves for various levels of relative suspension damping \(\vartheta_{1}\) (’Theta1’ in the drawing) in the rear suspension system of the Opel Astra Van car (the dots indicate the minimum values): (**a**) values of \(\Phi\)(f) (’F1’ in the drawing) for the response understood as the force between the tyre and the vibration plate; (**b**) values of \(\Phi_{\min}\)(f) (’F1’ in the drawing) for the response understood as the force measured in the test stand. Figure 6: Simulation results obtained for the non-linear ‘quarter-car’ model and results of measurements carried out on the prototype test stand TUZ-1/E for the rear suspension system of the Opel Astra Van car where the relative damping coefficient was \(\vartheta_{1}=0.242\): (**a**) curves representing the phase angle as a function of the frequency of the contact force between the tyre and the vibration plate (without the disturbing impact of the inertia of the plate); (**b**) curves representing the phase angle as a function of the frequency of the force measured in the test stand (and including the disturbing impact of the inertia of the vibration plate). shows the minimum values (\(\Phi_{\text{mmin}}\) = Fimmin) of this angle for the force measured in the test stand (and including the disturbing impact of the inertia of the vibration plate). Both of these illustrations apply to the rear suspension of the Opel Astra Van car. Figure 8a,b present analogous quantities for the rear suspension of the Opel Agila car. The results of calculations where the linear and non-linear models were used and the results of experiments have a similar qualitative nature. With growing relative suspension damping \(\vartheta_{1}\), the minimum values of the phase angle \(\Phi_{\text{min}}\) (Fimmin) and \(\Phi_{\text{mmin}}\) (Fimmin) are increasing almost linearly, too. In quantitative terms, however, they differ considerably from each other. The monotonicity observed, and the noticeable sensitivity to changes in the condition of shock absorbers (measured by the slope of the \(\Phi_{\text{min}}(\vartheta_{1})\) and \(\Phi_{\text{mmin}}(\vartheta_{1})\) characteristic curves) is a crucial and desired feature in diagnostics. The simulation results obtained for the linear and non-linear models significantly differ from each other in quantitative terms in the case of the Opel Astra Van car (Figure 7) and are close to each other for the Opel Agila car (Figure 8). When the data of the 'quarter-car' models of the two cars are compared with each other (Tables 1 and 2 vs. Tables 3 and 4), significant similarity can be seen. However, a considerable difference is observed as regards the sliding friction force, whose amplitude for the Opel Astra Van suspension system is twice as big as that for the Opel Agila car (see Tables 2 and 4: \(\text{Ats}_{1}\) is equal to 40 N and 20 N, respectively). It should be pointed out here that the equivalent damping adopted in the linear model stems from the assumption of equality of the value of the energy dissipated in the shock absorber in a single cycle. However, the sliding friction is not taken into account in such an assumption. As can be seen, increased friction raises the minimum value of the phase shift angle.