Simultaneous Measurement Method and Error Analysis of Six Degrees of Freedom Motion Errors of a Rotary Axis Based on Polyhedral Prism

A novel method is proposed for measuring the six degrees-of-freedom (DOF) geometric motion errors of a rotary axis based on a polyhedral prism. An error-sensitive unit which consists of a polyhedral prism and a planar reflector, is designed to carry out measurement of all six DOF errors, including the angular positioning error, the tilt motion error around the Y axis, the tilt motion error around the X axis, the radial motion error along the X and Y axes, and the axial motion error along the Z axis. The mathematical error model, including the six DOF geometric motion errors of the rotary axis, the installation errors between the polyhedral prism and the rotary axis, the manufacturing errors of the polyhedral prism, and the position errors of the sensors, are established. The effectiveness of the proposed method and the compensation model was simulated and experimentally verified.

Fourier-domain modeling of gravity effects caused by a vertical polyhedral prism, with application to a water reservoir storage process

We have developed a new Fourier-domain algorithm for the modeling of gravity effects caused by a vertical polyhedral prism. Simplified and more compact Fourier-domain expressions are derived for the vertical gravity anomaly on a 2D plane either above, in the middle of, or below the vertical polyhedral prism. A new Fourier-domain algorithm, which combines a low-order Gauss fast Fourier transform (FFT) algorithm and a low-order nonuniform FFT algorithm, to permit polar sampling near the zero wave vector, is introduced. To validate the numerical efficiency of the new algorithm, we carry out a series of synthetic tests. Numerical results show that the new algorithm is superior in numerical accuracy and efficiency compared to a pure Gauss-FFT algorithm, and both Fourier methods run much faster than traditional space-domain analytical solutions. We then apply the Fourier forward algorithms to the prediction of vertical component of gravity at many survey points, as a function of the water level of a reservoir located in Xianlin, Hangzhou, China. The reservoir geometry is approximated by a single vertical polyhedral prism. Water storage corresponds to increased heights of the polyhedral prism. Detailed maps of vertical gravity value changes corresponding to a water level rise of 5 and 10 m, with spatial resolution [Formula: see text], on the local topography covering a study area of approximately [Formula: see text] around the water reservoir, are calculated using the new algorithm. Then, the gravity values are classified according to the accuracy of the gravimeter, providing a reference of optimal site selection for a proposed cold-atom gravimetry survey to be carried out in the near future.