Based on analyzing the problem of the screen with circular, linear, and elliptical trajectory, the spatial Lissajous trajectory has been put forward. The article analyzes the dynamic theory of the spatial Lissajous trajectory screen, and the virtual simulation with discrete-element method is applied to study the solid migration rules. A discrete-element model is developed based on the JKR contact model which takes into considerations viscous forces of contacting particles. Two important factors, migration velocity and filter ratio, are selected to describe the working performance of the vibrating screen. The research results show that the spatial Lissajous vibrating screen has approximate solid migration velocity like the linear vibrating screen, but the filter rate of spatial Lissajous trajectory is the highest. Therefore, the spatial Lissajous trajectory vibrating screen can reduce the phenomenon of screening blockage, and the advantage will be more evident in the case of high drilling fluid viscosity, high mesh number, and serious screen blockage.
A statically designed derrick of deep oil well drilling rig may have poor dynamic characteristics, which can cause earlier structure failure of the drilling rig and harsh working condition. One such designed derrick is found to vibrate severely in operation while the rotation speed of rotary table is about 120 r/min with the working frequency of 2.0 Hz. To solve this problem, an experimental modal test of the derrick is conducted and the modal frequencies and vibration shapes are obtained. Through comparison of modal frequencies with that of exciting devices, it is found that the severe vibration of the drilling rig is caused by the resonance of second modal frequency (1.96 Hz) and the working frequency of rotary table. Based on principles of sensitivity analysis and structural dynamics modification method, the frequency sensitivities of all nodes on the derrick are calculated and compared, and then seven nodes with high-frequency sensitivity are selected on which corresponding mass are added to vary the modal frequency. Result shows that the second modal frequency of the derrick is reduced to 1.42 Hz and is out of the normal working frequency range of rotary table, which demonstrates that the dynamic characteristics of the derrick is improved and severe vibration can be avoided.
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