A Method for Correction of Dynamic Errors When Measuring Flat Surfaces

This paper presents a new method for correction of dynamic errors occurring when measuring flat surfaces in the presence of mechanical effects. Mechanical effects cause inertial forces and moments that affect the moving components of measuring instruments, thereby causing dynamic errors. The study proposes a mathematical model, on the basis of which algorithms for correction of dynamic errors can be developed. The basic concept of the model is based on determining the optimal estimate in the current coordinate point on the basis of the theoretical model of the measured surface and the information from the measurement that contains errors caused by internal and external factors. Based on this model, an algorithm for real-time data processing has been developed. The algorithm works in "predictor-corrector" mode at each step of which the best estimate is obtained. The estimate is based on minimizing the variance of a random component in which the main values are formed from the accumulated statistical data of the error of the model and the measurement error. This paper presents the results of experimental studies, carried out with simulations of mechanical effects in four modes. The results confirm the high efficiency of the algorithm for high-accuracy measurement of flat surfaces in the presence of mechanical effects.