Evaluation of the dynamic characteristics and damping of a vehicle’s suspension using the free-fall method

2.1. Design requirements and trolley design

To carry out free-fall tests in practice, it became necessary to develop a launch device that would ensure the immediate removal of resistance beneath the test wheel without causing lateral jolts or body misalignment. To this end, a special mobile trolley was designed and manufactured.

The main design requirements for the trolley were to ensure high rigidity under the weight of a quarter of a car, minimal rolling resistance of the wheels when the trolley is being pulled out, and geometric compatibility with the contact patch width of standard tyres. Based on geometric calculations, the optimum dimensions of the bogie were determined: height – 120 mm, track width – 375 mm, platform width – 300 mm, length – 275 mm. Structurally, the trolley comprises a rigid welded steel platform (deck) carrying the wheel, mounted on four low-friction rollers set in rolling bearings at the platform corners (Fig. 1(a), 1(c)); the platform height (120 mm) defines the drop distance, while the roller arrangement allows the loaded platform to be withdrawn horizontally from beneath the wheel with a single rapid pull. Because the rollers bear the full quarter-car load up to the point of release and offer minimal rolling resistance, withdrawal requires only a brief horizontal jerk rather than a lifting or tilting action, so the wheel is released essentially instantaneously and drops vertically without inducing lateral or angular (body-misalignment) disturbances – a requirement verified qualitatively during trial pulls prior to the recorded tests.

2.2. Strength analysis (FEA) and fabrication of a prototype

This load was adopted as a conservative design load rather than the actual in-service wheel load: the maximum measured static wheel load among the investigated vehicles is ≈ 222 kg (front axle of the standard ZAZ-1102, Table 1 mass value used in Section 5.2), so the 500 kg case corresponds to a safety margin of approximately 2.25 over the heaviest anticipated wheel load, ensuring adequate structural reserve for dynamic (impact) loading during free-fall release, occasional platform misalignment, and use with heavier test vehicles in future studies. St3 steel (${\sigma }_T=$ 235 MPa) was selected as the material. Analysis of the results (Fig. 1(b)) showed a maximum equivalent (von Mises) stress of ${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}=$ 20.2 MPa. Given the yield strength of St3 steel (${\sigma }_T=$ 235 MPa) and an allowable stress of $\sigma ={\sigma }_T/2=$ 117.5 MPa, the resulting factor of safety is $n={\sigma }_T/{\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ ≈ 11.6, confirming that the design satisfies the strength requirement; the total elastic deformation is only 0.211 mm. As this deformation is less than 0.2 percent of the drop height (12 cm), it was concluded that the trolley is absolutely rigid. On this basis, an experimental specimen was fabricated using metal rollers mounted on rolling bearings (Fig. 1(c)).

Fig. 1a) 3D model, b) FEA analysis of the stress-strain state of the trolley under a load of 500 kg, c) experimental specimen

a)

b)

c)

2.3. Vehicles under investigation

Two variants of the ZAZ-1102 were selected to assess the damping characteristics:

1. Standard ZAZ-1102 ‘Tavria’ (internal combustion engine): MeMZ-245 engine (1.1 l), 37.5 kW), kerb weight 745 kg, weight distribution: front axle – 444 kg (59.6 %), rear axle – 301 kg (40.4 %).

2. Modified ZAZ-11024 ‘Tavria EV’ (electric car): traction motor in the engine compartment, battery pack in the boot, kerb weight 709 kg with balanced weight distribution between the axles.

3.1. Experimental setup

The experimental setup comprised the test vehicle (ICE or EV variant), the free-fall trolley described in Section 2 as the wheel-release device, a Bosch BMI220 MEMS accelerometer, and a smartphone running the Accelerometer Meter app for data acquisition; the trolley itself constitutes only the release mechanism within this setup, not the setup as a whole.

The tests were carried out with the tyres inflated to the same pressure (2.0 atm). The test vehicle was raised using a hydraulic jack, and a 12 cm high trolley was placed under the wheel, after which the wheel rested entirely on the platform. A smartphone running Android was secured to the bodywork above the wheel axle.

A Bosch BMI220 MEMS accelerometer (range ±16 g, resolution 0.023 m/s²) built into a smartphone running Android was used with the Accelerometer Meter app (Graph mode, 100 Hz). Factory calibration was relied upon; no additional calibration was performed. The smartphone was rigidly mounted to the body above the wheel axle with its Z-axis aligned vertically; only the vertical channel was analysed. Peak amplitudes ($a_1$…$a_5$, $b_1$…$b_5$, Eq. (4)) were identified directly from the recorded raw trace without additional filtering. During a rapid horizontal jerk of the trolley, the wheel fell freely from a height of 12 cm, triggering transient damped vertical oscillations, which were recorded for analysis. Tests were performed for all eight wheel positions across the two vehicle variants (RF, LF, RR, LR for both the ICE and EV configurations), with each test repeated five times at every wheel position under identical conditions (tyre pressure 2.0 atm, drop height 12 cm); the $t_{damp}$ value reported in Table 1 for each position corresponds to the representative (median) run among the five repetitions, selected after discarding trials showing visible sensor clipping or trolley misalignment. Five repetitions per wheel position were adopted as a pragmatic balance between statistical reliability and the destructive/repetitive-loading nature of free-fall testing on the physical suspension components; the resulting standard deviations (Table 1) remained small relative to the front–rear differences reported in Section 5.1, supporting the statistical distinguishability of the axle-level trends despite the limited sample size. Recording was terminated once the oscillation amplitude fell below the accelerometer’s resolution threshold (0.023 m/s²), consistent with the criterion used to define $t_{damp}$. The damping time $t_{damp}$ (Table 1) was taken as the interval between the initial impact peak and the point where the oscillation amplitude fell below the accelerometer's resolution threshold (0.023 m/s²).

5.1. Analysis of experimental data

A series of drops yielded vertical acceleration diagrams (Fig. 2). The experimental oscillogram is obtained from a large dataset of acceleration measurements recorded by a smartphone equipped with a Bosch BMI220 MEMS accelerometer using the Accelerometer Meter app. The data is imported into Excel and a graph showing the relationship between acceleration and time is plotted.

The period and frequency of the damped oscillations, as well as the amplitudes of successive cycles, are determined from the plotted oscillogram. To ensure the reliability of the results, the parameters are determined over at least three periods; in this study, five complete oscillation cycles were used.

Based on the determined amplitudes, the mean logarithmic decay rate is calculated, followed by the viscous resistance coefficient, the natural frequency and the stiffness of the elastic system; a mathematical model of the damped oscillations is then formulated and verified against the experimental data.

The damping times are given in Table 1.

The analysis shows that, in the standard internal combustion engine (ICE) car, with the front-rear difference (0.6-0.8 s) substantially exceeding the within-position standard deviation 0.06-0.11 s, confirming that the observed axle-level trend is not attributable to measurement scatter. In the EV version, the relocation of the battery pack to the boot provides a more balanced axle weight distribution, which is hypothesized to contribute to the observed convergence of front and rear damping times (1.30…1.36 s front vs. 1.21…1.24 s rear).

5.2. Analytical calculation and diagnosis

For the right-hand front wheel of the base vehicle ($m=$ 222 kg), the following values were obtained from the graph (Fig. 2(a)): $\mathrm{\Delta }t=$ 1.39 s, $T_1=$ 0.278 s, $k_1=$ 22.601 rad/s, $\delta =$ 1.868, $n=$ 6.72 s⁻¹, $k=$ 23.579 rad/s, $\alpha =$ 2984 N·s/m.

The analytical equation for damping is as follows:

Fig. 2Typical experimental diagrams showing the damping of vertical accelerations for the front wheel of a) the standard ZAZ-1102 and b) the modified ZAZ-11024 EV

a)

b)

The analytical curve (Fig. 3) quantitatively reproduces the key features of the experimental record (Fig. 2(a)): the initial peak acceleration matches within < 2 % (–8.94 m/s² modeled vs. –8.8 m/s² measured), the damped period matches exactly ($T_1=$ 0.278 s, $k_1=$ 22.601 rad/s), and the signal settles within 0.4-0.5 s. The observed front-rear damping-time equalisation in the EV variant (Section 5.1) is consistent with the redistribution of unsprung/sprung mass ratio reported for battery-relocated EV conversions [3], [5]. However, because inter-vehicle differences in component wear or damping state cannot be fully eliminated outside bench calibration, mass redistribution is interpreted as a plausible primary factor rather than an exclusive causal proof. Plots are displayed separately to maintain visual clarity against high-frequency sensor noise. Point-by-point RMSE was precluded by the app’s graphical export format and is designated for future continuous digitized acquisition.

Fig. 3Theoretical curve showing the damping of suspension oscillations, calculated and visualised

During testing of the electric vehicle, the rear-right suspension underwent 5 oscillations versus 3 for the rear-left before amplitude decay below the sensor resolution threshold, indicating markedly slower damping on the right side. As the raw amplitude traces for these two positions were not retained for full parameter identification ($c_f$, Eq. (9)), this difference is reported qualitatively, based on $t_{damp}$ and oscillation count (Table 1), as evidence of a shock-absorber deficiency on the rear-right side rather than as a precisely quantified percentage reduction in $\alpha$.

The observed front-rear damping-time equalisation in the EV variant (Section 5.1) is consistent with the redistribution of unsprung/sprung mass ratio reported for battery-relocated EV conversions [3], [5], where a more balanced axle load reduces the disparity in dynamic wheel-load transfer and hence in effective damping response between axles. The method’s sensitivity to the 5-vs-3 oscillation-count asymmetry (Section 5.2) aligns with free-vibration diagnostic approaches reported in [19], [20], while extending them by requiring no stationary test rig – a practical advantage for field diagnostics, at the cost of lower measurement repeatability control (single trolley release vs. rig-controlled excitation) and reliance on smartphone-grade rather than laboratory-grade accelerometry, which limits the attainable precision of derived parameters $\left(n,k_1,\alpha \right)$ relative to bench-based methods [19].