Rotating bodies; the Kerr metric

Spacetime around a general rigidly rotating body is discussed, and the Kerr solution explored in detail. First we obtain generic properties of stationary, axisymmetric metrics. The stationary limit surface and ergoregion is defined. Then the Kerr metric is presented (without derivation) and discussed. Horizons and limit surfaces are obtained, and the overall structure of the Kerr black hole deduced. The mass and angular momentum is extracted. Equations for particle orbits are obtained, and their properties discussed.

Theoretical Modeling and Machining Experiments of Cylindrical Microstructure Assisted by Single Point Diamond Turning

Micro structure requires nanometer-scale surface roughness and micro- or even sub-micron form error accuracy in different applications. Two kinds of modeling theories and methods of micro-feature of rotating body and non-rotating body are studied, and the corresponding tool turning trajectory planning method is put forward. In order to process the designed micro-feature structure successfully and avoid the interference and overcutting between tool and workpiece caused by improper selection of tool parameters, the cutting parameters are analyzed and two error theories are proposed. Then a precision driven turning trajectory planning method is proposed, which can optimize the turning parameters according to the setting error and then optimize the trajectory. The experiments are carried out to verify the proposed theory. The surface roughness and surface accuracy of the features were measured by Talysurf PGI 1240 and KEYENCE vhx900 respectively. The surface roughness and surface accuracy of the cylindrical sine wave groove micro feature surface are 0.1714µm and 1.32µm respectively. The surface roughness and surface accuracy of the cylindrical sinusoidal mesh micro feature surface are 0.1625µm and 1.8µm respectively. The results meet expectations and verify the reliability of the error theory and the trajectory optimization theory.