Abstract
In this paper, the working principle of the grating measurement system is combined with the Fourier analysis method of Moiré fringe to establish the mathematical model of the grating signal Lissajous figure to know the quality of the grating signal intuitively. The Mathematica numerical analysis software is used to obtain the graphics of the model, and the correctness of the relationship between the parameters of the grating measurement system and the Lissajous figure equation of the grating signal is verified. The influence of the grating pair angle α on the output voltage signal and Lissajous figure of the grating measurement system is studied. The results show that the intensity of the two-phase output electrical signal decreases gradually with the increase of the deviation of the angle α of the grating pair, but the equal-amplitude of the two-phase output electrical signal does not change; Meanwhile, the shape of the grating signal Lissajous figure gradually changes from the ideal circle to the non-ideal ellipse, until a straight line with a strip slope of 135° is formed.
Highlights
In the mechanical precision machining and testing, in order to achieve the expected effect of the design of the manufactured product, it is necessary to configure the measurement and detection device for real-time measurement and control of the product processing in the entire processing control system
It is concluded that the phase difference of two-phase output electrical signal can be changed by adjusting the grating pair angle α, so that the grating signal Lissajous figure is close to the circle and has the largest shape, so as to obtain highquality grating signal
By studying the mathematical model of grating signal Lissajous figure and the output voltage signal and the Lissajous figure corresponding to the different grating pair angle α, the following conclusions are drawn: (1) The mathematical model of the grating signal Lissajous figure is established, which provides a theoretical basis for obtaining the grating signal Lissajous figure
Summary
In the mechanical precision machining and testing, in order to achieve the expected effect of the design of the manufactured product, it is necessary to configure the measurement and detection device for real-time measurement and control of the product processing in the entire processing control system. The standard signal output by the grating sensor measurement system is fourphase or two-phase sine wave or square wave with a phase difference of 90° in turn, and the measurement accuracy of the system is closely related to the quality of waveform. In the published literature and practical applications, the grating signal Lissajous figure is the most intuitive way to express the improvement of signal quality before and after correction, compensation and filtering, its acquisition method is to simulate two-phase sine or cosine signals assuming phase difference or to connect oscilloscope measurements with hardware circuits [7,8,9], without using the mathematical relationship in theory, the acquisition of the grating signal Lissajous figure has been fully studied from the point of view of the working principle of the grating measuring system. It is concluded that the phase difference of two-phase output electrical signal can be changed by adjusting the grating pair angle α, so that the grating signal Lissajous figure is close to the circle and has the largest shape, so as to obtain highquality grating signal
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