## 4 Discussion
Mechanical analysis of passive rail grinding is carried out, as shown in Figure 15. The \(F_{n}\) is the grinding pressure load and \(F_{t}\) is the grinding force that follows the rotating direction of the grinding wheel under the action of the deflection Angle (i.e., \(\theta\)). For a single abrasive particle, its grinding force \(F_{t}{}^{\prime}\) can be decomposed into \(F_{y}{}^{\prime}\) caused by grinding deformation and \(F_{x}{}^{\prime}\) caused by friction, as shown in Equation (2). \[F_{t}{}^{\prime}=F_{y}{}^{\prime}+F_{x}{}^{\prime} \tag{2}\]  
Figure 15: Mechanical analysis of passive rail grinding. The total grinding force is obtained by calculating the sum of grinding force of all abrasive per unit width, as shown in Equation (3) [26]. Figure 13:0  
In the formula, the grinding depth can be expressed as Equation (4) [26]. Figure 13:1  
Therefore, at low grinding load, the grinding depth generated by passive grinding is shallow and the grinding force is low, so the grinding wheel and rail wear less. However, when the grinding load is too high, the bond of grinding wheel will crack, and part of the abrasive will break owing to the excessive grinding force. It is also demonstrated by the presence of abrasive debris in the SEM image as shown in Figure 12e,f. This premature self-sharpening behavior is not conducive to continuous rail grinding and it causes the fluctuation of grinding force. In the meantime, the rail surface is worn. The abnormal wear area and residual stress on the rail surface are not beneficial to the extension of rail service life. The morphology and size of the debris produced by passive grinding under different pressure load can also explain the distinction of grinding process. It is not difficult to find that there is a lot of spherical melt debris under each grinding load. This is because passive grinding is often accompanied by a large number of sparks, and the main components of these sparks are spherical melt debris, as shown in Figure 1c. The number of spherical debris increases with the grinding load, which indicates that more grinding sparks are generated, thus reflecting that the higher grinding force will produce greater rail removal. Whereas the size of the debris is not just increasing with pressure load. In low pressure passive grinding, the cutting depth of the grinding wheel on the rail is shallow as a result of low grinding force, so that the rail is extruded by the abrasive without significant plastic deformation, resulting in large-size serrated lump debris. As the grinding force increases with pressure load, the cutting process returns to normal sliding, plowing and cutting accomplished by the abrasive [36], and the size of the debris decreases. After that, when the grinding load continues to increase, the size of the debris will increase again with the increase of grinding force. However, the large-size debris is not lumped when extruded, but continuous banging debris is. It shows that the change of grinding pressure load will influence the passive grinding process of rail by grinding wheel. Rail burn caused by grinding heat is one of the common problems in rail maintenance. Assuming that the grinding heat generated by passive grinding does not lose and is uniformly distributed within the grinding area, the maximum resulting heating value (\(\theta_{m}\)) rise can be expressed in terms of Equation (5) [26]. Figure 13:2  
The greater the grinding pressure, the more heat will be produced. In the grinding time of 30 s, the grinding temperature gradually increases with the increase of grinding time. There are two main reasons for the difference in grinding temperature between the grinding center and its vicinity, one is that the grinding debris goes away with the heat, and the other is that the self-sharpening of the grinding wheel also takes some of the heat away. The rapid relative motion causes a large number of spherical melt debris to emit along the grinding direction, forming a sparking bouquet that carries away heat.