Determination of the pressure field in the gasstatic support of a high-speed spindle assembly of a metal-cutting machine

Accuracy, speed and durability of spindle assemblies allow to achieve high performance during grinding of products. The use of spindle assemblies on rolling bearings is characterised by a relatively low peripheral cutting speed, which forces to resort to strong pressing of the wheel. This leads to distortion of the geometry of the product and to a decrease in the quality of the ground surface. The use of hydrostatic and hydrodynamic bearings in the designs of high-speed spindle assemblies leads to a limitation of the spindle rotation frequency due to friction losses. Spindles on electromagnetic supports have not yet found wide application due to the complexity and high cost of spindles and electronic control systems. The introduction of gas-lubricated bearings into the design of spindle assemblies allows to increase the rigidity and mass of the spindle by increasing the diameter of the working journals while simultaneously increasing the peripheral speed of the tool. Increasing the peripheral speed allows grinding with high feeds, which leads to increased productivity, improved grinding quality and reduced sensitivity to imbalance of the mandrel and circle, since their mass is noticeably less than the mass of the spindle. However, it is necessary to note the significant mathematical complexity of describing the dynamics of the flow of gas lubricant in the gap of a gas-static support by using classical methods of engineering flow theory. Therefore, the article proposes to describe the flow of gas lubricant in the gap of the support by solving the boundary value problem for the Navier-Stokes equations. As a result of numerical solution of the obtained equations in conservative form, the dependences of dimensionless pressure on relative load and stiffness coefficient were obtained. The analysis of experimental and theoretical obtained characteristics of the spindle assembly was performed and it was shown that the developed method allows to determine the operational characteristics of the spindle assembly with gas-permeable key flow limiters with sufficient accuracy for practical application