Positioning accuracy

The positioning accuracy describes a property of moving mechanical systems, mainly in machine tools and positioning systems . It is a measure of how precisely a desired position can be approached or reached, and thus for the manufacturing accuracy that can be achieved with the machine.

A method for checking the positioning accuracy or for assessing the controller settings of a CNC machine tool is the circularity test .

The position uncertainty is a parameter for the positioning accuracy . This indicates how large the deviation of the actual position from the target position is in the direction of movement. The total permissible deviation of a movement axis is known as the position tolerance.

To determine the position uncertainty target positions are each of positive ( ) and negative ( started up) direction, and so the actual positions and measured. ${\displaystyle \uparrow }$ ${\displaystyle \downarrow }$ ${\displaystyle {\overline {x}}_{i}\uparrow }$ ${\displaystyle {\overline {x}}_{i}\downarrow }$

The positional uncertainty of a movement axis is made up of three parts: ${\displaystyle P}$

${\displaystyle P=max({\overline {\overline {x}}}_{i}+{\tfrac {1}{2}}(U_{i}+P_{si}))-min({\overline {\overline {x}}}_{i}-{\tfrac {1}{2}}(U_{i}+P_{si}))}$

With

• the systematic deviation at location x _i from the target value: ${\displaystyle {\overline {\overline {x}}}_{i}}$

${\displaystyle {\overline {\overline {x}}}_{i}={\frac {{\overline {x}}_{i}\uparrow +{\overline {x}}_{i}\downarrow }{2}}}$

• the reversal range at location x _i , which indicates the difference in position by approaching from positive and negative directions: ${\displaystyle U}$

${\displaystyle U_{i}=\left|{\overline {x}}_{i}\uparrow -{\overline {x}}_{i}\downarrow \right|}$

• the position spread at location x _i , which is a measure of the random deviations : ${\displaystyle P_{s}}$

${\displaystyle P_{si}=6\cdot s_{i}=6\cdot {\frac {s_{i}\uparrow +s_{i}\downarrow }{2}}}$

• the standard deviation ${\displaystyle s}$

• the position deviation ( systematic total deviation ): ${\displaystyle P_{a}}$

${\displaystyle P_{a}=\left|{\overline {\overline {x}}}_{i,max}-{\overline {\overline {x}}}_{i,min}\right|}$.

literature

• Manfred Weck , Christian Brecher : Machine tools Vol. 5: Metrological investigation and assessment . Issue 7. Springer, 2006, ISBN 3-540-32951-X .