Study On Static Characteristics And Vortex Torque Of Spherical Air Bearings For Three-axis Test-bed

Externally pressurized spherical air bearings can offer a nearly torque-free environment, perhaps as close as possible to that of space, and for this reason it is the key component of the ground-based three-axis test-bed for simulation of spacecraft dynamics and control. The static characteristic of spherical air bearings and the vortex torque affect the performance of the test-bed directly. In this dissertation, externally pressurized spherical air bearings with inherent compensation possessing good dynamic characteristics are studied by means of theoretical analysis and experimental validation.. The static characteristics as well as the impact of manufacturing and installation errors on vortex torque are investigated, which can provide guidance for the design, manufacturing and installation of spherical air bearings. The main contents of this dissertation consist of the following parts.First, the calculation method of three-dimensional model for spherical air bearings is given. Since the air film thickness is usually far smaller than the size of the other two directions, the hexahedral unit and pyramid unit fitting for large aspect ratio are mainly used when performing grid division, and the structured as well as unstructured grids are combined, which greatly reduces the number of grids and improve the computational efficiency. An finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations, and the modified SIMPLE algorithm suitable for the compressible gas is applied to solve the discretized governing equations. The pressure field and velocity field inside of the gas film of spherical air bearings are obtained.Secondly, the solution is proposed for the static characteristic of externally pressurized spherical air bearings with inherent compensation. The pressure distribution, velocity distribution, bearing capacity, static stiffness and mass flow characteristic of spherical air bearings are studied. By comparing with the results of the finite element method based on the classic two-dimensional Reynolds equation, the validity of the three-dimensional finite volume method proposed in this dissertation is verified. The impact of manufacturing error on the static characteristic of spherical air bearings is analyzed, studies show that the negative dimension error and the prolate spheroid-type error should be avoided when machining the ball head, whereas the positive dimension error and the oblate spheroid-type error are acceptable to some extent. Similarly, the negative dimension error and the prolate spheroid-type error should be avoided when machining the ball socket, whereas the positive dimension error and the oblate spheroid-type error are acceptable to some extent. In view of the shortcoming of the smaller static stiffness of traditional externally pressurized spherical air bearings with inherent compensation, a new style of spherical bearing structure called over-filled externally pressurized spherical gas bearings is developed. Studies show that the new-style over-filled spherical gas bearing has the advantage of larger bearing capacity, higher static stiffness and smaller air consumption.Thirdly, the impact of the manufacturing error of the spherical air bearing on the vortex torque is studied. The calculation method of vortex torque is given, the computing accuracies of different forms of grid division are compared, and the impacts of the air intake diameter and location errors, the ball head roundness error as well as the ball socket installation error on the vortex torque are analyzed. Studies show that, under the current processing conditions, the difficulty of air intake machining is possible to overcome, however, in order to achieve the desired vortex torque, the manufacturing precision of the ball head and the installation precision of the ball socket are hard to ensured. The investigation in this dissertation will provide some theoretical guideline for the tolerance choice in the design and manufacturing of spherical air bearings, and puts forward some requirements for the installation precision of the ball socket.Fourthly, a method of vortex torque compensation is put forward to reduce the vortex torque of spherical air bearings. For the vortex torque caused by air intake processing errors and ball socket installation errors, the compensation is realized by independent air supply of the air intake. For the vortex torque arising from the ball head roundness error, the compensation is realized by adjusting the center of mass of the test-bed. The compensation effect is proved good, and the vortex torque significantly descends after compensation. The impacts of gas medium and the operating point on vortex torque are studied, results show that the usage of nitrogen can reduce the vortex torque slightly at the expense of much higher cost, therefore, air is chosen as the gas medium for air bearings. It also points out that, to reduce the vortex torque caused by manufacturing errors, the operating point with lower air supply pressure and smaller center film thickness is preferred.Last, the test-bed for bearing capacity characteristic and vortex torque is established. The bearing capacity, and the vortex torque caused by ball socket installation error, as well as the vortex torque compensation provided by independent air supply of externally pressurized spherical air bearings are studied. The experimental results of bearing capacity characteristics coincide with the theoretical results, indicating that the proposed calculation method of bearing capacity characteristics is correct. A low-cost composite ball socket is designed and manufactured, which is applied in the vortex torque test-bed successfully. In the experiment for the vortex torque caused by the ball socket installation error, the existence of the manufacturing error of the spherical air bearing leads to the greater vortex torque measured experimentally compared with the theoretical values, but the overall trends are basically the same. In the experiment for the vortex torque compensation provided by independent air supply, a new set of socket components is designed and manufactured, and the method is proposed to use independent air supply mode to compensate the vortex torque caused by the ball socket installation error. Experimental results show that the compensation effect is distinct, the vortex torque after compensation is only 7.92 per cent of the original value.