An improved fourier eight-sensor (F8S) method for separating straightness, yawing and rolling errors of a linear slide

This paper proposes an improved Fourier eight-sensor (F8S) measurement method for separating the straightness, yawing and rolling motion errors as well as determining the profile of a linear slide. The previous F8S method [1] used the constant parameters C2 and C4 to estimate the profile function f1(θ) in different angle ranges and f 2(θ) is also computed with the same fused sensor data. By constant parameters, the profile estimation and error separation are implemented via iterative method which is a time-consuming procedure and can not maintain the acceptable accuracy. Here, the improved F8S method applies the matrix technique instead of the iterative method to estimate the profile functions by three distinct sets of C2 and C4 parameters and different fused sensor data according to the linear slide motion within different angle ranges. Furthermore various errors can be separated through simple equations based on the calculated profile functions. In the second part of this paper the uncertainty induced by the sensor reading error is analyzed in both frequency and spatial domains, and the uncertainty for the profile function can also be obtained. The simulation results confirm that the improved F8S method provides better performance and effectiveness, and is more feasible than the previous F8S method [1].