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Accuracy of machine


The accuracy of the machine is often the primary criterion for the selection of a machine tool. Everyone would like to have the most accurate machine. However, the accuracy of the machine is often misunderstood, which sometimes may lead to confusion. The accuracy of the machine is a general concept and to make it more specific the following terms should be used: straightness of feed rates, perpendicularity of the axis, pitch error, backlash, perpendicularity of the spindle, resolution of positioning,  resolution of drives, resolution of the interpolator, positioning repeatability, rigidity.


Straightness of feed rates is a parameter indicating the maximum deviation of the tool path from the straight line on the specified distance of a given axis


Perpendicularity of the axis is a parameter indicating the maximum deviation of the track which is perpendicular to the axis of reference on the specified distance


Pitch error is a deviation of the displacement value of the ball screw nut from the theoretical displacement resulting from the nominal pitch


Backlash is the distance on which a given axis begins to move when changing the direction of movement


Perpendicularity of the spindle is a parameter specifying the error of the spindle perpendicularity in relation to the X-Y plane 


Resolution of positioning is the product of resolution of the pitch and drives (the smallest value by which a given axis may move due to the possibilities of the drive)


Resolution of the interpolator is the minimum displacement which can be imposed on the drives by the position set-point adjuster (interpolator) 


Positioning repeatability is the maximum deviation of the absolute position of the tool during multiple approaching to the selected point from different directions


Rigidity is a parameter specifying the value by which the machine will unbend when applying the setpoint force in the least favourable position of the axis


As you can see the total tool positioning error is the sum of all the errors mentioned. Of course, it may happen that individual errors in given circumstances will be neutralised, but you cannot count on that. Additionally, the matter is complicated by the phenomenon of thermal expansion. For steel it is about 0.01mm/m for each degree Celsius, therefore with the temperature jump from 10 to 30 degrees, the screw will expand by 0.2mm/m!


It is not that bad if steel is being machined, because it has a similar expandability as the feed screw, but if we want to treat aluminum, which has a thermal expansion of about three times higher than steel, some serious problems of tolerance preservation begin to appear, especially with long details.

Most of the mentioned factors affect the so-called static error that is measured at a given point when the machine is stopped. There is also a dynamic error which appears only during operation and is associated with the imperfection of the interpolator and drives. Servo drives work in the so-called closed loop of the position control (the position feedback). The controller in the servo drive is constantly trying to control the motor so that the position error (the difference between the setpoint and current position) was as small as possible. The servo drive cannot respond to the offset position immediately. For this it needs as much time as the period of the positioner is.


In most servo drives the position controller frequency is only 400 Hz. If the deviation increases immediately after measuring the position, the servo drive will not know about it for the next 2.5ms, and at a speed of 0.5m/s the machine will run 1.25mm at this time! This is the error which repeatedly exceeds the sum of all static errors of the geometry of the machine.


It should also be noted that the quality of setting the position, that is interpolation, is equally important. The interpolator is a part of the control system, which is responsible for providing to the servodrives the information on how fast each axis should move and what position should be reached. The most important task of the interpolator is the synchronization of the moves of each axes, that the shape plotted by the tool in the space was consistent with the program set by the operator. This is a very complex process which requires a very fast CPU to achieve a satisfactory resolution.