This function consists of two parts: k is attenuation coefficient of shifting amplitude which determines the change degree in the next shifting cycle and m represents the t shifting cycle. By this function, the shifting amplitude in every shifting cycle can be obtained clearly and the rhythm of attenuation can be adjusted easily. According to the characteristics of the sin function, in a shifting cycle, when the shifting position is O, it is the shifting start position, and then the shifting amplitude is equivalent to the limit position value of the shifting. Another characteristic of the function is that the shifting position is less distributed near the O position during a shifting cycle, and more at the limit position, It can be seen from Figure 1 that the area of the roll contacted by the edge of the strip is more severely worn, and the number of shifting position distributed in the extreme position causes a severe wear area of the work roll. When k