# In Situ Experimental Study of the Friction of Sea Ice and Steel on Sea Ice
## 3 Results  
### Friction Regimes  
Three types of friction regimes were obtained in these tests. The first type represents steady sliding (Figure 4a), which occurs in most conditions. The first peak load was the force needed to overcome static friction to initiate sliding. Subsequently, the slider kept a stable sliding state once it initiated to move, and the force dropped to balance the kinetic friction. The fluctuations of the regime was caused by the small bumps on the track surface, and the load oscillations in the steady sliding had no obvious frequency (Figure 4b). \(\mu_{\mathrm{k}}\) was calculated as the ratio of the pulling force \(F_{\mathrm{f}}\) to the normal load \(F_{\mathrm{n}}\)  
\[\mu_{\mathrm{k}}=\frac{F_{\mathrm{f}}}{F_{\mathrm{n}}}, \tag{1}\]  
where \(F_{\mathrm{f}}\) was taken as the mean value of the stationary portion of the regime. The final \(\mu_{\mathrm{k}}\) under a given set of conditions was the average value from repeated tests.  
Figure 5a shows the second type of regime, which was related to stick-slip behavior. Stick-slip motion was observed in steel-ice friction at a velocity of 0.02 m\(\cdot\)s\({}^{-1}\). Compared with steady sliding, the motion of stick-slip was different. The slider adhered to the track instantaneously and moved once the pulling force exceeded a certain threshold. Thus, the regime of stick-slip motion had a saw-tooth shape, and Fourier analysis indicated that load oscillations in the stick-slip motion had a frequency of 30.10 Hz (Figure 5b). The \(\mu_{\mathrm{k}}\) of stick-slip motion was calculated in the same manner as in the steady-slide case [(37; 23)].  
The third type of motion was a regime with repeated U-shapes (Figure 6a). The regime was observed only on ice-ice contact at velocities less than 0.10 m\(\cdot\)s\({}^{-1}\). The ice block adhered to the ice track temporarily until it was pulled to slide again. Once the slip was initiated, the pulling cable sagged, and the slider moved because of inertia and then was stopped by friction. Hence, movement in the U-shape regime was a kind of enhanced stick-slip. However, because a stationary portion of friction force failed to be determined from this type of regime, the \(\mu_{\mathrm{k}}\) of ice-ice friction at velocities less than 0.10 m\(\cdot\)s\({}^{-1}\) was not considered in the analysis that followed. Fourier analysis showed that the load oscillations had frequencies between 0.28 and 0.96 Hz. Besides, ice-ice friction regimes showed large  
Figure 3: Sliding configurations for ice-ice friction tests: (**a**) Top-Top, Bottom-Top, Lateral\(\perp\)-Top, and Lateral/ -Top; (**b**) Bottom-Bottom, Lateral\(\perp\)-Bottom, and Lateral/ -Bottom; (**c**) Lateral\(\perp\)-Lateral // and Lateral/ -Lateral//; (**d**) Lateral\(\perp\)-Lateral\(\perp\).  
fluctuations when sliding velocities were higher than 1.00 m\(\cdot\)s\({}^{-1}\), making \(\mu_{\mathrm{k}}\) difficult to determine. Hence, \(\mu_{\mathrm{k}}\) at velocities greater than 1.00 m\(\cdot\)s\({}^{-1}\) was not analyzed.  
Figure 4: (**a**) Steady-sliding friction for SS-Top at a velocity of 0.19 m\(\cdot\)s\({}^{-1}\) and a normal stress of 3.10 kPa. The mean friction force of the stationary portion used in calculation was 20.9 N (red line) and the standard deviation was 5.4 N; (**b**) Frequency of load oscillations in steady sliding.  
Figure 5: (**a**) Stick-slip friction regime on SS-Top at a velocity of 0.02 m\(\cdot\)s\({}^{-1}\) and a normal stress of 4.56 kPa. The mean value of the portion used in the calculation was 10.4 N (red line), and the standard deviation was 3.6 N; (**b**) Frequency of load oscillations in stick-slip motion.