Ultra-thin sapphire wafer processing is receiving increasing attention in the LED substrate industry. In the cascade clamping method, the motion state of the wafer determines the uniformity of material removal, while the motion state of the wafer is related to its friction coefficient in the biplane processing system, but there is little relevant literature discussing the relationship between the motion state of wafer and friction coefficient. In this study, an analytical model of the motion state of sapphire wafers in the layer-stacked clamping process based on the frictional moment is established, the effect of each friction coefficient on its motion is discussed, the base plate of different materials and different roughness are experimentally studied, the layer-stacked clamping fixture is prepared in this way, and finally the failure form of the limiting tab is analyzed experimentally. The theoretical analysis shows that the sapphire wafer is mainly driven by the polishing plate, while the base plate is mainly driven by the holder, and the rotation speed of the two is not the same; the material of the base plate of the layer-stacked clamping fixture is stainless steel, the material of the limiter is glass fiber plate, and the main form of failure of the limiter is to be cut by the edge of the sapphire wafer and damage the material structure.