## 1 Introduction  
As an effective method to eliminate rail defects such as ripples and rolling contact fatigue cracks [1, 2] and to reprofile the rail head that affects the safety of train-running [3], rail grinding has become a routine maintenance operation for the railway network [4]. The rail grinding can be divided into corrective operation and preventative operation [5, 6]. The operational difference between them is that the cutting depth of preventative operation is shallower than corrective operation [7]. Thus, the preventative operation can more effectively prolong the rail service life and reduce the operating costs [8], because only the rail surface is polished periodically before rail defects appear in order to nip the disease in the bud [9]. The customary way of rail grinding is to use the end face of the grinding wheel to grinding wheel to grind the rail. The grinding wheels are driven by the motor to actively rotate with the grinding train on the rail [10]. The maintenance speed of this grinding method is in the range from 3 to 20 km/h with grinding train speed [11]. However, in preventive grinding, since only a small amount of metal is required to be removed from the rail surface, this rail maintenance strategy with slow train speed and high grinding volume shows low maintenance efficiency. It is not conducive to the application of rail preventive maintenance. Recently, the scale of High-Speed Railway has become larger and larger in the world, and the spacing interval of departure time is shorter and shorter [12]. As a result, the \"skylight time\" of maintenance operation is ever-shortening; therefore, the rail grinding speed and efficiency is critical [13]. How to grind the longest possible railway line in the shortest possible time has become the focus of rail preventive grinding. The rail high-speedgrinding technique, involving \"non-driven\" grinding wheels that remove a very shallow depth of cut, has been introduced in the preventative operation for High-Speed Railway by VOSSLOH company [14]. In this case, the grinding train speed can reach a range from 60 to 80 km/h, and it is also beneficial for noise control [15]. This high-speed grinding for railroad maintenance is not the traditional \"HSG\" with high linear speed of grinding wheels but means that the grinding train can run at high speed on the rail. Thus, rail grinding can be completed quickly. The emergence of rail high-speed grinding is of great significance. Not only can it significantly improve the grinding efficiency because of the high working speed, but it can also extend the service life of the rails because of the lower grinding volume of passive grinding compared to the frequently-used active grinding. These can help reduce railway operations and maintenance costs and contribute to the development of preventative grinding in railroads. Because of \"non-driven\"' grinding wheels, the rail high-speed grinding is also known as \"passive grinding\". The passive grinding process is significantly different from the active grinding way. The grinding wheels are rotated freely without driven power, and the axial direction is set at an angle with the rail surface [16]. Under the motion and pressure of the grinding train, the grinding wheels roll forward along the rail surface; hence, the grinding process of grinding wheels on rail surface is realized [17]. In this way, the grinding train can run at high speed while grinding the rail. This new rail grinding process has just been applied. However, there are still many problems worth studying. Many research works reported that grinding parameters have a great effect on grinding efficiency, surface roughness, consumption of grinding wheel, and so on. [PERSON] et al. [18] investigated the influence of rail grinding process parameters on rail surface. This study verified the correlation between rail grinding process parameters and grinding results. The effects of grinding parameters on the processing results were described qualitatively. For active grinding wheels, [PERSON] et al.