How do 17 stepper motor for CNC machines measure so accurately?
First there is the feedback (measurement) mechanism. A device called an encoder reads the position of the axis in one of 2 ways. On most machines the encoder measures the rotary position of the ball screw that drives that axis. The downside of using a rotary encoder is that it can not take into account the backlash in the nut/screw combination. Machines that need to be more accurate use linear encoders on each axis to measure the absolute position of the axis.
The second part of CNC accuracy has to do with the mechanical guiding of each axis. Each axis needs to be stiff, perfectly linear, and perpendicular to the other axis. Modern recirculating ball slides have played a large role in guiding the axis accurately. Older, and larger machines are guided by ways - sliding flat surfaces lubricated with oil. These can be very accurate and carry huge loads, but they have the downside that they must be maintained by highly trained millwrights who know how to keep the sliding flat parts fitting perfectly.
The third piece of the accuracy puzzle is calibration or mapping. Each axis of the machine can be very carefully measured with special equipment. The measurements are then used by the controller in the machine to correct for any mechanical deviations.
Finally, if you want to really hold a tight tolerance, you keep the machine at a steady temperature and humidity. Some machines are run for hours just to get them up to operating temperature before any machining starts.
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