The mathematical model of the ordinary machine tool control system is usually not an easy task to establish an appropriate mathematical description for the actual control system. In addition to choosing a suitable modeling method, it is also necessary to deal with problems such as model simplification. In order to accurately describe the mathematical relationship between the controlled quantity and the controlled quantity, various influencing factors and situations are generally involved, which often results in the relationship becoming very complicated. The more accurate the relationship between the controlled quantity and the controlled quantity is, the more complex the mathematical model is. An overly complex model is neither convenient for research nor conducive to the realization of the control system. In order to avoid this situation, it is generally necessary to make some reasonable assumptions and simplifications in order to properly idealize the system. An idealized physical system is usually called a physical model.

The height error of the headstock, grinding head, tailstock and other height errors of ordinary machine tools in the process of cnc machining will cause the tailstock, headstock and center line to shift in space to a certain extent. The surface of the workpiece will be a hyperboloid. The central connection of the headstock and tailstock of the ordinary machine tool needs to have the influence of the parallelism error of the axis of the grinding head in the horizontal plane on the dimensional accuracy of the workpiece. When the error occurs during the operation, the equipment The working shape ground by the grinder will be a cone. The movement of the grinding head of an ordinary machine tool will affect the machining accuracy relative to the verticality error of the machine tool rail during use. The final result of this error is that the axis of the spindle and the center line of the headstock and tailstock will be offset.

Even if the shape and size of the workpieces are different, but they are similar workpieces, it is easy to realize the parts of the group processing (GT) process. Complicated shape workpieces such as complex shape parts molds and aviation parts can be processed on ordinary machine tools with the help of automatic programming technology. Box and board parts use rotary table on ordinary machine tools to process box parts, such as spindle box, pump body, valve body, internal combustion engine cylinder, etc. If even the top surface is to be processed in one clamping, a pentahedral machining center can be used. Ordinary machine tools are suitable for processing box heads, cylinder heads, plane cams, etc. Ordinary machine tools are used to process large box and board parts, such as diesel locomotive cylinder blocks, machining center columns, bed bodies, and printed wall panel machines.