## 4 Vibration-Based Road Friction Monitoring
### Low Frequency Vibrations  
Following the reasoning defended by slip slope approaches, the main hypothesis behind low frequency-based contributions is that the tyre longitudinal \(C_{\lambda}\) or lateral slip stiffness \(C_{a}\) depends on the road friction potential. Due to the controversy associated with this assertion, experimental research works on the dependence of the longitudinal stiffness on the road condition are summarised in the following [127; 128; 129]. Figure 21: Classification followed on the discussion of vibration-based road friction monitoring approaches. In [PERSON] et al. [127] tyre force versus slip graphs were presented that showed different longitudinal and lateral slip slope curves for different icy road surfaces. The icy road surfaces presented also distinct maximum road friction coefficients. The experimental data were gathered using a drum tyre tester at 5.55 m/s (20 km/h) and for temperatures ranging from \(-1\)\({}^{\circ}\)C to \(-7.5\)\({}^{\circ}\)C. Temperature influenced significantly the maximum road friction, especially at temperatures close to 0 \({}^{\circ}\)C where ice melts. The experiments showed that the road friction potential was maximum at \(-7.5\)\({}^{\circ}\)C and reduced significantly at \(-5\)\({}^{\circ}\)C, \(-3\)\({}^{\circ}\)C and \(-1\)\({}^{\circ}\)C. The longitudinal slip stiffness \(C_{\lambda}\) seemed to remain invariant at different temperatures, however the lateral slip stiffness coefficient \(C_{\alpha}\) changed. The more close the temperature was to 0 \({}^{\circ}\)C, the lower the lateral slip stiffness \(C_{\alpha}\). In [PERSON] et al. [128] field trials were conducted on four different road surfaces: dry concrete at T \(\approx\) 0 \({}^{\circ}\)C, wet ice, and wet snow at T \(\approx\) 0 \({}^{\circ}\)C, dry packed snow at T \(\approx\) -7 \({}^{\circ}\)C and dry rough ice (formed by snowflakes bonding with ice) at T \(\approx\) -7 \({}^{\circ}\)C. The vehicle speed ranged between 0 and 22.2 m/s (80 km/h). The experimental results showed that the longitudinal slip stiffness coefficients \(C_{\lambda}\) varied on dry rough ice, wet ice and dry concrete. Wet ice presented the lowest \(C_{\lambda}\) and largest discrepancy with respect to dry rough ice and dry concrete. In [PERSON] and [PERSON] [129], a number of field trials were conducted at different tyre temperature, inflation pressure, normal load, tread depth and road surface wetness. A passenger car was used for this purpose. The authors estimated the longitudinal stiffness \(C_{\lambda}\) for all cases and reported high consistency, 2.5%, between the estimations. The reported changes in longitudinal stiffness are summarised in Table 4. As observed, the longitudinal slip stiffness is less influenced by the road wetness. Moreover, variations in the tyre tread or the normal load have a drastic influence on \(\Delta C_{\lambda}\). Such results correlate with the conclusions presented in [PERSON] [6] and [PERSON] et al. [7], where it was remarked that the slip slope presents significant variations depending on the tyre wear or tyre pressure. Nevertheless, in spite of these difficulties, a number of recently published papers have focused on estimating the coefficient of friction assuming a correlation between the tyre frequency responses, slip slope, and road friction potential [4; 5; 50; 51; 130]. It can be understood that there is a lack of standardised experiments that monitor all the parameters that may influence the tyre performance (tyre temperature, inflation pressure, tread depth, presence of third bodies etc.). [PERSON] et al. [51] presented a method for detecting the coefficient of friction by monitoring the tyre rotational vibration. By using a simple tyre rotational model, the authors derived a transfer function relating the road disturbances \(\Delta T_{d}\) and the wheel speed responses \(\Delta\omega\).