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