MEASURING BODY FOR VERIFYING GEOMETRICAL DEVIATIONS OF A 3-AXIS MACHINE TOOL, 3-AXIS MACHINE TOOL, AND METHOD FOR COMPENSATING GEOMETRICAL DEVIATIONS OF A 3-AXIS MACHINE TOOL

Abstract

The invention relates to a measurement body for checking geometric deviations in a 3-axis machine tool comprising a base plate, a first wall which protrudes perpendicularly from the base plate, a second wall which protrudes perpendicularly from the base plate and is arranged perpendicularly to the first wall. A first row of holes and a second row of holes are formed in the base plate. The first wall is a stepped triangle and comprises a step-shaped region having a plurality of steps, on an upper, exposed region. The second wall is a square wall and comprises a first row of wall holes on an upper, exposed region which extends in parallel with the base plate. The first row of holes is arranged in parallel with the row of step holes and the second row of holes is arranged in parallel with the first row of wall holes.

Claims

1. A measurement body for checking geometric deviations in a 3-axis machine tool (1), comprising: a base plate (8), a first wall (10) which is arranged on the base plate (8) and protrudes perpendicularly from the base plate (8), and a second wall (20) which is arranged on the base plate (8) and protrudes perpendicularly from the base plate (8) and is arranged perpendicularly to the first wall (10), wherein a first row of holes (101) and a second row of holes (102) are formed in the base plate (8), wherein the first wall (10) is a stepped triangle and comprises a step-shaped region (12) having a plurality of steps (13), on an upper, exposed region (11), wherein the second wall (20) is a square wall and comprises a first row of wall holes (22) on an upper, exposed region (21) which extends in parallel with the base plate (8), and wherein the first row of holes (101) is arranged in parallel with a row of step holes (14) and the second row of holes (102) is arranged in parallel with the first row of wall holes (22).

2. The measurement body according to claim 1, wherein the step-shaped region (12) comprises a first row of step holes (14), wherein in particular a hole (15) and a ground reference surface is formed in each step (13).

3. The measurement body according to claim 1, further comprising a third wall (30) which is arranged on the base plate (8) and protrudes perpendicularly from the base plate (8), wherein the third wall (30) is arranged perpendicularly to the second wall (20), and wherein the second wall (30) comprises a second row of wall holes (32) comprising holes (33) on an upper, exposed region (31).

4. The measurement body according to claim 3, wherein the first wall (10), the second wall (20) and the third wall (30) are arranged in a U-shape on the base plate.

5. The measurement body according to claim 3, further comprising a third row of holes (103) in the base plate (8) which extends in parallel with the second row of wall holes (32).

6. The measurement body according to claim 5, wherein the first row of holes (101), the second row of holes (102) and the third row of holes (103) each extend along an edge of the base plate (8), such that a hole of a row of holes is arranged at each corner of the base plate (8).

7. The measurement body according to claim 4, wherein the first wall (10), the second wall (20) and the third wall (30) are arranged on the base plate (8) at a spacing from a first edge (81), from a second edge (82) and from a third edge (83), wherein the spacing is greater than or equal to twice diameters of the holes of the first, second and third row of holes.

8. The measurement body according to claim 1, wherein in addition to the holes in the steps (13) ground surfaces are present, and/or in addition to the holes of the first and/or second and/or third row of holes (101, 102, 103) ground surfaces are formed.

9. The measurement body according to claim 1, further comprising a reinforcement element (7) which is arranged under the base plate (8) for mechanically reinforcing the base plate (8) and/or on the machine tool as a clamping aid.

10. A 3-axis machine tool, comprising a tool spindle (4), a measurement body (2) according to claim 1, a measuring device (5) which can be clamped in the tool spindle (4) and is configured to detect actual values of the measurement body (2) fixed in the 3-axis machine tool (1), and a control unit (9), configured for controlling the 3-axis machine tool (1), wherein the control unit (9) is further configured to perform a target/actual comparison based on geometric target values of dimensions of the measurement body (2) and the actual values of the measurement body (2) fixed in the 3-axis machine tool (1), determined for the 3-axis machine tool (1) by means of the measuring device (5), and, in the event of occurrence of deviations between the target values and the actual values, to perform a correction of geometric data of the 3-axis machine tool (1) in a control program of the control unit (9).

11. The 3-axis machine tool according to claim 10, wherein the control unit (9) comprises a memory, in which the target values of the measurement body (2) are stored.

12. A method for checking and compensating geometric deviations in a 3-axis machine tool, comprising the steps of: clamping a measuring device (5) in a tool spindle (4) of the 3-axis machine tool, arranging a measurement body (2) according to claim 1 in a working space (3) of the 3-axis machine tool, approaching a plurality of positions of the measurement body (2) in order to acquire geometric actual data of the 3-axis machine tool by means of the measurement body (2), performing a target/actual comparison of the geometric actual data with the stored target data of the measurement body (2) in order to determine geometric deviations, and compensating the geometric deviations in a control unit (9) of the 3-axis machine tool.

Description

[0041] A preferred embodiment of the invention is described in the following, with reference to the accompanying drawings, in which:

[0042] FIG. 1 is a schematic, perspective view of a measurement body in a 3-axis machine tool according to a preferred embodiment of the invention,

[0043] FIG. 2 is a schematic, perspective view of the measurement body from FIG. 1, from a different perspective,

[0044] FIG. 3 is a schematic plan view of the measurement body from FIG. 2,

[0045] FIG. 4 is a schematic side view of the measurement body, which shows the determination, by way of example, of a pitch error of the X-axis,

[0046] FIG. 5 is a partial side view of the measurement body, which shows a determination, by way of example, of a roll error of the X-axis, and

[0047] FIG. 6 is a schematic illustration for determining a sheer error of the X-axis.

[0048] In the following, a 3-axis machine tool 1 and a measurement body 2 for checking geometric deviations of the 3-axis machine tool are described in detail with reference to FIGS. 1 to 6.

[0049] Furthermore, a method for checking and compensating geometric deviations of a 3-axis machine tool are described with reference to FIGS. 1 to 6.

[0050] As can be seen from FIGS. 1 to 5, the 3-axis machine tool 1 comprises a working space 3, a spindle 4 and a control unit 9.

[0051] As can be seen from FIG. 1, a measurement body 2 is arranged on a machine table 6 of the 3-axis machine tool 1.

[0052] The measurement body 2 is visible in detail from FIGS. 1, 2 and 3. The measurement body 2 is configured for checking geometric deviations of the 3-axis machine tool, wherein it is possible to determine all linear, rotational and perpendicularity errors, in total twenty-one errors, in a clamping of the measurement body. In particular, coordinates for positioning a tool of the 3-axis machine tool 1 can be determined very precisely by means of the measurement body 2.

[0053] The measurement body 2 comprises a planar base plate 8, which spans a base plane in an X-direction and a Y-direction. The measurement body 2 further comprises a first wall 10, a second wall 20 and a third wall 30. The first wall 10, the second wall 20 and the third wall 30 are arranged on the base plate 8 and protrude perpendicularly from the base plate 8 and form a U-shape.

[0054] As shown in FIG. 2, a Z-direction is perpendicular to the X-direction and perpendicular to the Y-direction.

[0055] As can be seen from FIG. 2, in this case the first wall 10 and the second wall 20 and the third wall 30 are arranged on the base surface of the base plate 8.

[0056] The base plate 8 is configured to be square and comprises a first edge 81, a second edge 82, a third edge 83 and a fourth edge 84.

[0057] The three walls 10, 20, 30 are, as can be seen in particular from FIGS. 1 and 2, configured differently in terms of geometry. In this case, the first wall 10 is a stepped triangle comprising an upper, exposed region 11 on which a step-shaped region 12 is formed. The step-shaped region 12 comprises a plurality of steps 13.

[0058] A hole 15 is formed in each step 13. The holes 15 form a row of step holes 14. In this embodiment, in this case the stepped triangle, configured as the first wall 10, comprises seven steps.

[0059] The second wall 20 is a rectangular wall, also having an upper, exposed region 21. A first row of wall holes 22 having a plurality of holes 23 is formed in the upper, exposed region 21.

[0060] The third wall 30 is also a rectangular wall and also has an upper, exposed region 31. A second row of wall holes 32 having a plurality of holes 33 is formed in the upper, exposed region 31.

[0061] As can be seen in particular from FIG. 2, a size of the second wall 20 is smaller than a size of the third wall 30.

[0062] The holes 23 of the second wall 20 lie in a straight line. The holes 33 of the third wall 30 also lie in a straight line. In this case, the holes of the second and third wall are arranged such that the straight lines formed by the holes 23 and 33 intersect at right angles.

[0063] As can be seen in particular from FIG. 2, the first wall 10 is arranged at right angles with respect to the second wall 20. The second wall 20 is also arranged at right angles with respect to the third wall 30. As a result, the first wall 10 and the second wall 20 are in parallel with one another.

[0064] Furthermore, the first, second and third walls 10, 20 and 30 are arranged at a spacing from the respective edges 81, 82, 83 of the base plate 8, along their long sides. Only an end region of the third wall 30 extends as far as the fourth edge 84 (see FIG. 2).

[0065] For the purpose of weight reduction, the base plate 8 has a larger central opening and a plurality of longitudinal openings (without reference numerals).

[0066] A reinforcement element 7 is arranged on the underside of the base plate 8, which element comprises a first slat 71 and a second slat 72. The two slats 71, 72 are arranged in a cross shape and reinforce the base plate 8 and thus the measurement body 2. The reinforcement element 7 furthermore makes it possible for the measurement body 2 to be clamped in a simple manner on the machine table 6. This in particular prevents undesired stresses being introduced into the base plate or the three walls 10, 20, 30 by the clamping process, which stresses could lead to falsification of the measurement result.

[0067] Furthermore, the measurement body 2 comprises a first row of holes 101, a second row of holes 102 and a third row of holes 103 in the base plate, on the upper side. The first row of holes 101 comprises a plurality of holes 101a, which are arranged on a first straight line 111. The first straight line 111 extends in parallel with the first edge 81. The second row of holes 102 comprises a plurality of holes 102a, which are arranged on a second straight line 112. In this case, the second row of holes 102 is in parallel with the second edge 82. The third row of holes 103 comprises a plurality of holes 103a, which are arranged on a third straight line 113. The third row of holes 103 is in parallel with the third edge 83 (cf. FIG. 3). For improved clarity, in FIG. 3 not all the holes of the first, second and third row of holes are provided with a reference numeral.

[0068] As is furthermore visible from FIG. 3, the first row of holes 101 is in parallel with the row of step holes 14. The second row of holes 102 is in parallel with the first row of wall holes 22 of the second wall 20. The third row of holes 103 is in parallel with the second row of wall holes 32.

[0069] The number of holes of the first, second and third row of holes is preferably the same as is the geometric size, in particular the hole spacing.

[0070] It is noted that strip-shaped, ground reference surfaces (not shown in FIG. 3) can be provided for example in parallel beside the three rows of holes.

[0071] Furthermore, the first, second and third row of holes 101, 102, 103 are provided such that a hole is provided in each corner of the base plate 8.

[0072] Further preferably, a thickness of the base plate 8 is also the same as the wall thicknesses of the walls 10, 20, 30.

[0073] The measurement body 2 is arranged on the machine table 6 of the 3-axis machine tool 1. Furthermore, a 3D measuring sensor, by means of which a determination of actual coordinates of the 3-axis machine tool by the measurement body 2 is performed, is arranged in the spindle 4.

[0074] The 3-axis machine tool 1 further comprises the control unit 9, which is configured for controlling the 3-axis machine tool. The control unit 9 is further configured, based on a target/actual comparison of the geometric dimensions of the measurement body 2, to perform a correction of the geometric data of the 3-axis machine tool 1.

[0075] The 3-axis machine tool comprises, as already explained above, three linear axes, specifically a first axis in the X-direction, a second axis in the Y-direction, and a third axis in the Z-direction.

[0076] Overall, the three linear axes result in twenty-one deviations, wherein three thereof are perpendicularity deviations of the linear axes relative to one another. Thus, a total of twenty-one error parameters result for the 3-axis machine tool.

[0077] Thus, by means of the method according to the invention, checking and correction of all straightness deviations, rotation deviations and perpendicularity deviations of the 3-axis machine tool can be performed.

[0078] For this purpose, the measurement body 2 must first be measured by means of a coordinate measuring machine (not shown), in order to generate target values. Said target values are then supplied to the control unit 9 of the 3-axis machine tool 1 and stored in a memory. In this case, in order to measure the measurement body 2, a coordinate system is spanned such that an X-Y plane is in parallel with the base plate 8. Thus, on the basis of Z-positions, X-positions and Y-positions, determined multiple times, of different reference elements of the measurement body 2, the geometry of the measurement body 2, which is preferably produced from Invar, is determined. At the same time, a zero point of the coordinate system of the measurement body 2 is also specified. For example, the ground step surfaces or the ground reference surfaces serve as reference elements for the Z-positions. The holes of the rows of holes 101, 102, 103 and the holes 15 in the steps 13 and the holes 23, 33 in the exposed regions 11, 21 serve as reference elements for the X-positions and Y-positions.

[0079] In order to now detect the geometric deviations of the 3-axis machine tool, the measurement body 2 is introduced, on the machine table 6, into the working space 3 of the 3-axis machine tool. In this case, the measurement body 2 can be clamped or fastened on a machine table in another manner. In this case, the X-Y-Z coordinate system of the measurement body should in principle be oriented in parallel with the X-Y-Z coordinate system of the 3-axis machine tool. The measurement of the measurement body 2 in the 3-axis machine tool 1 is then performed by means of the 3D measuring device 5, e.g. in a 3D measuring sensor. Typically, modern 3-axis machine tools comprise a 3D measuring sensor of this kind, for example for detecting component positions and component geometries.

[0080] Thus, before the measurement the coordinate system of the 3-axis machine tool is oriented identically to the coordinate system of the coordinate measuring machine in which the measurement body 2 was previously measured.

[0081] After the measurement body 2 is fixed in the working space 3 of the 3-axis machine tool, the control unit 9 can preferably allow a fully automatically executed NC program to be executed, in order to measure the measurement body 2 by means of the 3D measuring sensor 5 and thereby to determine the actual values of the 3-axis machine tool 1.

[0082] Preferably, during the measurement of the measurement body 2 in the working space of the 3-axis machine tool 1, the temperature of the working space 3 of the 3-axis machine tool 1 is also detected and stored. Should this temperature of the working space differ from a reference temperature, e.g. 20 C., a coefficient of thermal expansion of the workpieces to be machined on the 3-axis machine tool must be taken into account during the workpiece machining. Here, a corresponding correction of the actual values of the 3-axis machine tool must then be performed.

[0083] After completion of the measurement of the measurement body 2 in the 3-axis machine tool 1, and optionally a thermal adjustment of the actual values, the actual values of the 3-axis machine tool are determined and can be compared with the target values of the measurement body. Thus, the geometric deviations of the 3-axis machine tool in the form of position deviations, straightness deviations and perpendicularity deviations can be calculated, and thus checked and corrected, by the comparison of the target and actual values. In this case, FIG. 3 shows, by way of example, in a plan view of the measurement body 2, straightness deviations G, a perpendicularity deviation R (angle ), and position deviations P.

[0084] For example, first a position deviation of the X-axis can be determined, in that the differences of actual positions and target positions in the X-direction of the measured reference elements on the base plate 8 along the X-axis are evaluated. Since the zero point of the measurement body 2 and the position of the reference elements relative to the zero point are known, the determined differences can be associated with X-axis positions of the 3-axis machine tool. Thus, a table of X-axis positions of the 3-axis machine tool and positions deviations in the X-direction at these X-axis positions results. In this case, these position deviations can be stored and used directly, in the control unit 9, as correction data or an error compensation of the 3-axis machine tool.

[0085] Alternatively, the deviations could also be pre-processed mathematically. The deviations can for example also be approximated with different mathematical functions. Precisely in the case of small measurement bodies 2 having few reference elements, for example an approximation of the differences with a straight line (line of best fit) is conceivable. In this case, only a scaling error is corrected.

[0086] Since the measurement body 2 covers only a part of the working space 3 of the 3-axis machine tool, the detected actual values are preferably extrapolated by means of a corresponding mathematical function. As a result, deviations for the entire working space 3 of the 3-axis machine tool 1 are obtained.

[0087] Straightness deviations G of the X-axis are determined in the same way. In this case, the position deviations P in the Y-direction or Z-direction are associated with the X-axis positions. In this case, the differences between actual position and target positions in the Y-direction result from the determined centers of the holes of the three rows of holes 101, 102, 103 and the reference holes on the first, second and third walls 10, 20, 30. The differences between actual positions and target positions in the Z-direction result e.g. from the reference surfaces on the base plate 8 and the ground surfaces of the steps 13. In this case, too, a mathematical pre-processing or approximation is possible.

[0088] When the correction data for the position deviation and straightness deviation of the X-axis have been calculated, all the measurement data of the actual positions of the reference elements are adjusted, for the further evaluation, on the basis of the correction data for the position deviation of the X-axis, the straightness deviation of the X-axis in the Y-direction, and the straightness deviation of the X-axis in the Z-direction. It is preferably assumed at this point that the adjusted actual position no longer has any errors in the X-direction. As a result, in the further evaluation the errors in the X-direction can be disregarded.

[0089] In a next step, a perpendicularity error R between the X-axis and the Y-axis can be calculated. For this purpose, two lines of best fit are calculated. The first line of best fit results from the X-axis position of the reference elements on the base plate 8 along the X-direction and the position deviations thereof in the Y-direction. The second line of best fit results from the Y-axis positions of the reference elements on the base plate 8 along the Y-direction and the position deviations thereof in the X-direction. Subsequently, an angle a between the two lines of best fit is calculated (cf. FIG. 3). In this case, the determined deviation can be used directly as a correction value for error compensation in the control unit 9.

[0090] Subsequently, the actual positions of all the reference elements in the measurement data are adjusted according to their Y-position, on the basis of the perpendicularity error, such that the measurement data no longer contain any X-Y perpendicularity errors.

[0091] Subsequently, the position deviations and the straightness deviations of the Y-axis are calculated in the same way as in the case of the X-axis. For this purpose, the differences in the actual and target position of the reference positions on the base plate 8 along the Y-axis are evaluated (cf. FIG. 3). Together with the zero point, a table with Y-axis positions of the 3-axis machine tool and the positions deviations in the X, Y and Z-directions at these Y-axis positions results. As in the case of the X-axis, the data can be further processed or used directly as correction data for error compensation of the 3-axis machine tool, in the control unit 9. Here, too, the correction data should be extrapolated with a corresponding mathematical function in order to define the entire working space 3.

[0092] Subsequently, all the actual positions of the reference elements are adjusted, for the further evaluation, on the basis of the correction data for the position deviation and the two straightness deviations of the Y-axis. It is preferably assumed at this point that the adjusted actual position no longer has any errors in the Y-direction. As a result, in the further evaluation the errors in the Y-direction can be disregarded. FIGS. 4, 5 and 6 show, by way of example, the determination of pitch error in the X-axis (FIG. 4) and the determination of a roll error of the X-axis (FIG. 5), as well as the determination of a sheer error of the X-axis (FIG. 6).

[0093] In order to be able to determine a sheer error of the X-axis (FIG. 6), geometric features must be present in the X-direction, the X-position of which can be detected using the measuring sensor. In order that the error can be determined independently of other errors, the Y- and Z-positions of the features must be identical. In order to be able to measure the influence of the X-sheer error, furthermore a measurement must be made at a different Y-position from the case of the first X-feature series. Furthermore, the Y-spacing d from the first X-feature series must be known (cf. FIG. 6).

[0094] In a next step, the pitch error of the X-axis is calculated. For determining the pitch error of the X-axis (FIG. 4), geometric features must be present in the X-direction, the X-position of which can be detected using the measuring sensor. In order that the error can be determined independently of other errors, the Y- and Z-position of the features must be identical. In order to be able to measure the influence of the X-pitch error, furthermore a measurement must be made at a different Z-position from the case of the first X-feature series. Furthermore, the Z-spacing d from the first X-feature series must be known.

[0095] For determining a roll error of the X-axis (FIG. 5), geometric features must be present in the X-direction, the Y-position of which can be detected using the measuring sensor. In order that the error can be determined independently of other errors, the Y- and Z-positions of the features must be identical. In order to be able to measure the influence of the X-roll error, furthermore a measurement must be made at a different Z-position from the first X-feature series. Furthermore, the Z-spacing d from the first X-feature series must be known (cf. FIG. 5).

[0096] A determination of the roll error and the sheer error of the Y-axis takes place according to the measurement described in FIG. 4 and FIG. 5.

[0097] In a next step, the perpendicularities between the X-axis and the Z-axis are calculated. For this purpose, two lines of best fit are calculated. The first line of best fit results from the X-axis positions of the reference elements on the base plate 8 along the X-direction and the position deviations thereof in the Z-direction. The second line of best fit results from the Z-axis position of the reference elements on the first wall 10 (stepped triangle) in the X-direction and the position deviations thereof in the X-direction. Subsequently, the angle a between the two lines of best fit is calculated. The determined deviation can be used directly as a correction value for error compensation in the control unit 9.

[0098] The perpendicularity between the Y-axis and the Z-axis is calculated in the same way. In this case, the first line of best fit results from the Y-axis positions of the reference elements on the base plate 8 along the Y-direction and the position deviations thereof in the Z-direction. The second line of best fit results from the Z-axis positions of the reference elements on the second wall 20 in the Y-direction and the position deviations thereof in the Y-direction. The deviations of the perpendicularity between these two straight lines can again be used directly as a correction value for error compensation.

[0099] The actual position of all the reference elements is then adjusted, in the measurement data, according to their Z-position, on the basis of the perpendicularity error, such that the measurement data no longer contain any X-Z-perpendicularity errors or any Y-Z-perpendicularity errors.

[0100] In a further step, the geometric deviations of the Z-axis are calculated. For this purpose, the reference elements (reference holes and ground stepped surfaces) of the three walls 10, 20, 30 are used. Since the errors of the X-axis and Y-axis, and the three perpendicularity errors, have already been eliminated from the measurement data in the preceding evaluation, it is assumed in this step that a displacement in the X-direction or Y-direction, which is necessary for measuring the steps, does not influence the geometric deviations of the Z-axis.

[0101] Thus, the position deviation of the Z-axis is determined in that the differences of the actual position and target position of the reference position in the Z-direction, on the first wall 10, are evaluated. Since the zero point of the measurement body 2 and the position of the reference elements relative to the zero point are known, the determined differences can be associated with Z-axis positions of the 3-axis machine tool. Thus, a table of Z-axis positions results, which positions can thus be used directly as correction data or an error compensation of the 3-axis machine tool. As in the case of the X-axis and the Y-axis, the data can be further processed or used directly as correction data. Here, too, the correction data can be extrapolated with a corresponding mathematical function.

[0102] As in the case of the other axes, the straightness deviations of the Z-axis are determined in the same way. In this case, the position deviations in the Y-direction or X-direction are associated with the Z-axis positions. In this case, the differences between the actual position and target position result from the determined centers of the holes. The further processing of the straightness deviations can take place identically to the position deviations of the Z-axis.

[0103] In this way, all relevant geometric errors, including sheering, pitching and rolling, can be checked and corrected with the aid of the measurement body 2. The method is suitable in particular for the correction of a 3-axis machine tool geometry after a change in the thermal conditions, since in this case in general linear errors occur, which can be easily extrapolated. In addition, this method can also be used for adjusting the geometry of the 3-axis machine tool to materials having different coefficients of thermal expansion if a temperature different from the reference temperature prevails in the working space.

[0104] In addition to the above written description of the invention, for the additional disclosure thereof reference is hereby explicitly made to the illustration of the invention in FIGS. 1 to 6.

LIST OF REFERENCE NUMERALS

[0105] 1 3-axis machine tool [0106] 2 measurement body [0107] 3 working space [0108] 4 spindle [0109] 5 measuring device (3D measuring sensor) [0110] 6 machine table [0111] 7 reinforcement element [0112] 8 base plate [0113] 9 control unit [0114] 10 first wall [0115] 11 upper, exposed region [0116] 12 step-shaped region [0117] 13 steps [0118] 14 row of step holes [0119] 15 hole [0120] 20 second wall [0121] 21 upper, exposed region [0122] 22 first row of wall holes [0123] 23 holes [0124] 30 third wall [0125] 31 upper, exposed region [0126] 32 second row of wall holes [0127] 33 holes [0128] 71 first slat [0129] 72 second slat [0130] 81 first edge [0131] 82 second edge [0132] 83 third edge [0133] 84 fourth edge [0134] 101 first row of holes [0135] 101a holes [0136] 102 second row of holes [0137] 102a holes [0138] 103 third row of holes [0139] 103a holes [0140] 111 first straight line [0141] 112 second straight line [0142] 113 third straight line [0143] d spacing [0144] G straightness deviation [0145] R perpendicularity error [0146] P position deviation [0147] x X-axis [0148] Y Y-axis [0149] Z Z-axis [0150] perpendicularity deviation