EP1704963B1 - Methods for manufacturing or measuring of rotationally symmetrical workpieces - Google Patents

Abstract

The method involves treating a workpiece with optically effective surfaces, whose symmetry axis is parallel to an aligned Z-axis and parallel to the moveable Z-axis. A rotary, rotationally symmetric sharpener (1) is provided, its rotation axle parallel to the Y axis and aligned and parallel to the X axis. The workpiece (2) rotates around its symmetry axis. The tool is on one level, which is parallel to the X-Z-level and is separated by a distance of the rotation axle of the workpiece, with constant Y-value moving. An independent claim is included for a grinding or polishing tool.

Description

The invention relates to a method for processing a rotationally symmetrical workpiece, in particular for machining a workpiece with optically active surfaces, the axis of symmetry aligned parallel to the z-axis and which is movable parallel to the z-axis, with a rotating, rotationally symmetrical grinding or polishing tool Alignment axis is aligned parallel to the y-axis and which is moved parallel to the x-axis, thereby touching the surface of the workpiece with a machined surface, wherein the workpiece rotates about its axis of symmetry, and a method for tactile measuring such a workpiece. The genera of the claims 1,3 and 13 corresponding methods are for example from DE-A-100 38 415 known.

The invention is preferably used for machining aspherical workpieces with optically active surfaces, in particular lenses or mirrors, which have a non-workable zone, for example a conical elevation in the middle of the workpiece.

The production of aspheres is done in two steps, first by grinding or turning to produce the mold and then by polishing to achieve the required surface finish.

In the prior art, both steps are carried out by means of grinding, polishing or lathes, which are controlled by CNC.

When grinding, the tool spindle is aligned horizontally parallel to the y-axis at right angles to the workpiece spindle. The workpiece is mounted on a designated as a mandrel holder and tensioned in the workpiece spindle. Both tool and workpiece are rotated by means of the spindles. The workpiece can be up and down be moved parallel to the z-axis. The tool can be moved forward and backward parallel to the y-axis to adjust it to the center of the workpiece, and left and right parallel to the x-axis to perform the operation.

The grinding tool is an initially cylindrical grinding wheel, the grinding surface being the jacket of the cylinder. On it diamonds are applied in a metal or plastic bond. The grinding wheel is formed into a narrow spherical cutout with the highest or thickest point in the median plane of the wheel. For exact machining, it is absolutely necessary to always grind with the highest point of the grinding wheel. Due to wear, there is a risk that, instead of the highest point, a depression forms whose two edges touch the workpiece. In addition, the grinding can be affected by impact of the grinding wheel. To avoid these two sources of error, the grinding wheel is dressed after installation. For this purpose, a so-called dressing stone is glued and clamped on a mandrel instead of the workpiece to be ground. The grinding wheel is located exactly vertically above the truing stone, the center of its spherical section, ie the virtual center of the associated ball, lies on the extension of the tool axis. Then, the grinding wheel is moved very slowly into the dressing stone along the z-axis, with both the dressing stone and the grinding wheel rotating. By appropriate choice of the hardness of the stone and the rotational speeds both the stone and the disc are removed. The result is a spherical cavity in the stone and a spherical segment shape of the grinding wheel. Due to the mechanical and geometric conditions, the highest point of the grinding wheel is located exactly in the center of rotation of the dressing stone.

The grinding takes place by the tool traveling in the x-direction over the diameter of the workpiece. While driving is by default the z-position of the workpiece generates the desired shape of the workpiece. The path is then divided into small line segments, for which the x-values for the tool and the z-values for the workpiece are transferred via a CNC program. The y-position of the tool is determined by dressing so that the center of the grinding wheel, ie its highest point, travels over the center of rotation of the workpiece, and remains constant during machining. As a result, the machining can be understood as a radial cut through the workpiece for the calculation, in which the grinding wheel is abstracted as a circle.

For machining, it is important that the position of all three axes is exactly defined. The x-axis is largely adjusted by the manufacturer of the grinding machine, so that at an x-value specified by the factory, the axis of the grinding wheel is above the axis of the workpiece. If this is not the case, there is a form error, from which one has to manually recognize and correct the misalignment. For this a specimen is usually processed. The position of the z-axis must be determined by probing and only determines the thickness of the workpiece, which can generally be measured directly. The position of the y-axis is similar to the x-axis largely adjusted by the manufacturer. However, since the grinding wheel is plugged in and tightened in the y-direction, there is always a mechanical tolerance. Only removing and re-screwing will change the y-position. If the highest point of the tool does not go exactly through the center of the workpiece, another, not exactly known point touches the workpiece, resulting in a further shape error of the workpiece. By renewed, short dressing the misalignment is corrected with respect to the y-axis.

This known method is not suitable for machining workpieces in which a predetermined by the radius of the grinding wheel Area in the middle of the workpieces can not be edited, for example, due to non-removable structures in this central area.

When turning the CNC, a small plate, the insert, is screwed onto the turning tool, which contains the actual cutting edge. To increase the service life of the plate, its edges are rounded off. The considered from above radius between the parallel to the axis of rotation of the workpiece and the perpendicular edge is called cutting radius. This is the area of the insert that is directly engaged. For accurate machining, it is important to know exactly the cutting radius or the deviation from the ideal shape. In particular, when turning cones or more complex shapes such as spheres or aspheres, it must be taken into account that the bit must be delivered further because of this radius than would be the case with an unrounded cutting tip. Modern CNC lathes allow you to enter the cutting radius and adjust the CNC program accordingly. It is assumed that the radius is exactly maintained, ie no deviation from the ideal form exists.

This procedure reduces the possible accuracy of the machining.

For the measurement of rotationally symmetrical bodies tactile measurements with profilometers are used. To do this, a probe with a ruby ball or a diamond tip is pulled over the workpiece and the movement of the probe is converted into a height image. After subtracting the nominal shape, the error of the DUT is obtained. The probe is usually a two-bar right angle, at its vertical, lower end is the ruby ball or diamond tip, and whose horizontal bar is suspended in a rocker. The tilt angle of the rocker is measured and the position of the measuring ball or tip and above it the shape of the workpiece is calculated. In the case of rotationally symmetrical workpieces, a travel over the diameter of the workpiece in the x direction is thereby carried out. The z position of the measuring system remains constant, it is only pulled in one direction.

For workpieces with a central elevation or a hole, this procedure is not feasible.

Due to the principle, the absolute position of the workpiece in the x-direction in a tactile measurement is unknown. In particular, the measuring system is moved away with each measurement in order to be able to remove the workpiece, so that there is no constant position of the measuring system over several measurements. One of the objectives of the measurement evaluation is therefore the determination of the workpiece position with respect to the x-axis and, in particular for rotationally symmetrical workpieces, the determination of the center point. One possibility is to approximate a system of equations using the least squares method.

However, this presupposes that the desired shape of the workpiece can be represented adequately analytically. However, this is not possible, especially with aspheres.

The invention has for its object to provide methods with which a simple, fast and accurate machining and / or measurement of rotationally symmetrical workpieces is possible.

According to the invention the object is achieved by methods which contain the features specified in claim 1, 3 or 13.

Advantageous embodiments are specified in the respective subclaims.

According to the invention, in a first method, the grinding or polishing tool is moved with a constant y value in exactly one plane which is parallel to the x-z plane and which is spaced from the axis of rotation of the workpiece. The tool is thus moved along a chord of the workpiece. For workpieces with central, non-processable zones, this also allows machining of surfaces in the vicinity of non-workable zones without touching them.

The fact that for each x-position of the tool is determined at which y-position, the machined surface when moving parallel to the z-axis, the workpiece first touched, and the x-position belonging to this z-position is approached, the method easy and with conventional grinding or polishing machines are performed.

In a second method, the tool is moved to its point of contact with the workpiece in exactly one plane, which is parallel to the yz plane and in which the axis of rotation of the workpiece lies, with a constant x-value. The tool is thus moved radially over the workpiece. Due to the predetermined orientation of the tool, this allows for workpieces with central, non-workable zones, the processing of the surfaces in the vicinity of the non-editable zones, without touching them, because the overlap of tool and workpiece in the radial direction is minimized.

Advantageously, a tool is used whose machining surface is a rotationally symmetrical spherical surface section of a virtual sphere whose center lies on the axis of symmetry of the tool and which is asymmetrically shaped with respect to each mirror plane which is perpendicular to its axis of symmetry and therefore the virtual sphere center outside the median plane of the working surface lies. Thus, with little wear, adaptability to the particular shape and optimum working surface, a steep cross-section of the tool can be used so that always the working surface rests in parallel on the surface to be machined.

If a tool is used, which is a torus section, wherein the cut is made in a plane perpendicular to the axis of symmetry, the cross-section of the tool can also be used, with slight wear, so that the machined surface rests in parallel on the surface to be machined.

By orienting the tool for concave portions of the workpiece with the largest increase side of the machining surface away from the rotational axis of the workpiece and for convex portions of the workpiece with the largest increase side of the machining surface toward the rotational axis of the workpiece; It is also possible to edit surfaces in the marginal area with minimally unworkable rest.

Characterized in that for each point on a section parallel to the y-axis through the axis of rotation of the workpiece, the increase of the workpiece surface is determined, for this point, the location of the tool is determined, where the machined surface has the same slope and the tool so is positioned so that the point and the place coincide, an exact machining of the workpiece is guaranteed.

If the tool also touches the workpiece away from the center plane of the working surface, depending on the control, a point can be used with an optimum rise to the touch for the workpiece.

If the tool consists of a thin disk with the working surface on the narrow side, the control of the grinding or polishing machine is very simple.

If a tool is used, which is a cone or a truncated cone, which has the machined surface at the location of the largest radius of the conical surface on the jacket, it is also possible to machine the entire, mechanically machinable surface of the workpiece.

By orienting the tool with the side of the largest radius of the cone sheath toward the axis of rotation of the workpiece, surfaces near the center of the workpiece can be machined with non-machinable remainder.

CNC makes it easy to control the machining process.

In the measuring method according to the invention, the measuring probe of a profilometer is moved to its point of contact with the workpiece in exactly one plane which is parallel to the xz plane and which is spaced from the axis of rotation of the workpiece, with a constant y value. The probe is thus moved along a chord of the workpiece. This allows for workpieces with central, non-scanning zones to measure.

By converting the approached x position to the associated radius of the workpiece for each measuring point, a virtual section through the diameter can be determined.

If the data determined for determining the center of a rotationally symmetrical body are split into two parts at potential center points, one part of which is mirrored and then the correlation is determined by the mirrored and the non-mirrored part and the point which is the largest is determined as the actual center Correlation value results, the center can be determined independently of the desired shape of the workpiece, with an analytical representation of the surface profile is not necessary. The method is therefore insensitive to strong deviations from the desired shape, as long as there is sufficiently strong symmetry.

The invention is explained in more detail below with reference to an embodiment.

Figur 1

eine schematische Darstellung des Bearbeitungsverfahrens, bei dem das Schleifwerkzeug entlang einer Sehne parallel zur x-Achse bewegt wird

Figur 2

eine schematische Darstellung des Bearbeitungsverfahrens, bei dem das Schleifwerkzeug radial parallel zur y-Achse bewegt wird

Figur 3

eine schematische Darstellung des Vermessungsverfahrens

Figur 4

die perspektivische Ansicht eines Schleifwerkzeugs,

Figur 5

das Herstellen eines Schleifwerkzeugs,

Figur 6

einen Schnitt durch das fertige Werkzeug,

Figur 7

einen Schnitt durch ein weiteres Beispiel für ein fertiges Werkzeug,

Figur 8

ein alternatives Verfahren zur Herstellung eines Werkzeugs,

Figur 9

ein nach dem in Figur 8 gezeigten Verfahren hergestelltes Werkzeug

Figur 10

eine schematische Darstellung des Verfahrens zur Bestimmung des Werkstückmittelpunktes
und

Figur 11

eine schematische Darstellung des Verfahrens zur Vermessung von Drehmeißeln.

Show this

FIG. 1

a schematic representation of the machining process in which the grinding tool is moved along a chord parallel to the x-axis

FIG. 2

a schematic representation of the machining process in which the grinding tool is moved radially parallel to the y-axis

FIG. 3

a schematic representation of the surveying process

FIG. 4

the perspective view of a grinding tool,

FIG. 5

the production of a grinding tool,

FIG. 6

a cut through the finished tool,

FIG. 7

a section through another example of a finished tool,

FIG. 8

an alternative method of making a tool,

FIG. 9

a tool manufactured according to the method shown in FIG. 8

FIG. 10

a schematic representation of the method for determining the workpiece center
and

FIG. 11

a schematic representation of the method for measuring turning tools.

In the illustrated schematically in Figure 1. The process Fig. 1 a) shows the top view, and FIG. 1 b) the side view. The coordinate system is drawn for each sub-figure. The grinding tool 1 moves, as already known, in the direction of the x-axis, but is spaced from the center of the workpiece 2, around which the elevation 3 is located. The movement thus takes place along a chord of the workpiece.

Another method is shown in FIG. 2 , again in plan view and side view with indication of the coordinate system. The grinding tool 1 moves the surface of the workpiece 2, which has the elevation 3, in the y and z direction instead of in the x and z directions. The x-position is chosen so that the workpiece and tool axes intersect during machining. As a result, the overlap of the tool 1 and workpiece 2 in the radial direction is minimized.

Although the known, conventional grinding wheels can be used in principle with these two alternative methods, but have the great disadvantage that they reach very far to the center of the workpiece 2 because of their relatively flat shape. The machining is therefore only partially possible outside a predetermined by half the thickness of the grinding wheel area.

Therefore, a grinding tool 1 is preferably used in which the grinding surface is asymmetrically shaped as a spherical surface portion and with respect to each mirror plane perpendicular to the axis of symmetry. Since the virtual sphere center point is therefore outside the center plane of the grinding surface, the highest point of the grinding wheel is closer to one of the two edges of the grinding wheel, which expediently for concave workpieces 2 that of the axis of rotation of the workpiece 2 facing edge and convex workpieces 2 that of the axis of rotation of the workpiece 2 facing away from the edge. As a result, the distance to be maintained by a raised center of the workpiece 2 is reduced and thus a larger part of the workpiece 2 can be achieved.

When grinding a concave workpiece 2 on a chord or radially parallel to the γ-axis should therefore, when the disc 1 is viewed in the γ-direction behind the center of the workpiece 2, the highest point on the center side facing the disc. 1 are located. The aim is that always the working surface rests in parallel on the surface to be machined. Therefore, the increase of the workpiece 2 determines the necessary increase of the grinding tool 1. For example, if a mirror 2 to be produced has a radial rise of 10 ° to 30 °, the grinding wheel section must also have an increase of at least 10 ° to 30 °. The exact position of the virtual center and also the necessary or allowed thickness of the disk body 1 always depends on the shape of the workpiece 2, more precisely on the required climbs as described above. In addition, as with conventional grinding, in concave surfaces, the surface curvature of the virtual sphere must be greater than the strongest curvature of the workpiece 2.

Similar conditions arise when using toroidal grinding tools 1, wherein in turn the torus center must be moved in order to achieve the desired increases.

Alternatively, a cone or truncated cone with grinding surface on the mantle can be used at the large radius. In principle, the orientation of the largest radius to or from the axis of rotation of the workpiece 2 is possible here, wherein preferably the first variant is used for concave and convex workpieces.

Another alternative form is the use of an extremely narrow disk similar to a cutting wheel in which only one edge is used for machining. In the same way, the large radius of a cone or truncated cone can be used.

For control purposes, in the case of a cutting disk, its cross section is abstracted as a dot. This results in a simple calculation of the CNC program. For each point of the workpiece on the radius in the y-direction or on the chord, the disk must be positioned directly vertically above it.

More complicated is the control when using a spherical surface section as a grinding surface. In the case of machining parallel to the y-axis, for each point on the radial section of the workpiece 2, the increase must be calculated, the point on the grinding tool 1 must be determined with the same slope, and the grinding tool positioned so that these two points coincide. When grinding on a chord, although the grinding tool 1 travels parallel to the x-axis, a chord with a constant y-value, but moves the point of contact in the y-direction. For each x-position of the tool 1, therefore, it must be determined at which y-coordinate the grinding surface first moves when moving the workpiece in the z-direction is touched. In the CNC program, the associated z position must then be approached at this x position.

Of course, the processing methods according to the invention can be used analogously on machines with differently constructed coordinate systems.

Likewise, they are equally applicable to workpieces made of metal or other materials such as semiconductors.

Similar to grinding, the same methods can also be used for polishing if the grinding tool is replaced by a polishing tool.

FIG. 3 schematically shows a method for measuring rotationally symmetrical workpieces 2. A travel path via a chord of the workpiece is selected, ie the measuring system with measuring probe 4 is pulled parallel to the x-axis with a constant y value on a line spaced from the center of the workpiece 2 so that it does not touch Survey 3.

For each measurement point, the approached x-position must be converted to the corresponding radius in order to again obtain a section along the diameter, which is then virtual.

With tactile measurement, the grinding tools themselves and other rough bodies can be measured. In order to avoid damage to the probe, a uniformly thick layer is first applied to the grinding surface or other rough surfaces, in particular adhesive strips or films, on which the probe can be used.

For grinding away from the average axis parallel to the x-axis through a workpiece, rather than a conventional grinding wheel where the highest point is exactly in the midplane transverse to the axis of symmetry of the disk, a rather steep cross section of the disk is desirable where the highest point is as far as possible at the edge of the disc. When grinding a concave workpiece on a chord or radially parallel to the y-axis should therefore, when the disk is in the y-direction behind the center of the workpiece is the highest point on the center-facing side of the disc. The aim is that always the working surface rests in parallel on the surface to be machined. Therefore, the increase of the workpiece determines the necessary increase in the grinding tool. If, for example, a mirror to be generated has a radial rise of 10 ° to 30 °, the grinding wheel cross-section must also have an increase of at least 10 ° to 30 °.

For this purpose, for example, a grinding tool 1 is used, as shown in FIG. 4 within a virtual ball shell 1.3, whose center lies in the middle of one of the two side surfaces 1.2 of the grinding tool 1. It is a grinding wheel which has been brought into the shape according to the invention. The spindle, with which the tool 1 is rotated, may alternatively be located on both sides of the disc 1, depending on whether convex or concave workpieces or workpiece areas are to be processed.

In this case, the grinding surface 1.1 is a spherical segment, which forms the edge of the grinding tool and represents a section of the virtual ball 1.3. The virtual center of the sphere 1.3 lies outside the median plane of the disc with respect to its thickness, so that the disc is asymmetrically shaped. The center may even be outside of the disk body.

The exact position of the virtual center and the necessary or allowed thickness of the disk body depends on the shape of the workpiece, more precisely on the required climbs as described above. Just as with conventional grinding, the surface curvature of the virtual sphere 1.3 must also be greater than the strongest curvature of the workpiece in the case of concave surfaces.

For polishing away from the axis parallel to the x-axis through a workpiece, a polishing tool of the same shape can be used analogously.

In Figure 5 , the production of the shape of a grinding tool is shown schematically. The cylindrical grinding wheel 1, which has the grinding surface 1.1 on the cylinder surface, rotates about its axis of symmetry and is moved into the dressing stone 5. The grinding wheel 1 is positioned transversely to the axis of symmetry of the axis of rotation of the Abrichtsteins 5 in the direction of the axis of symmetry of the grinding wheel 1 with respect to its center or its center plane, thus spaced in the coordinate system of a grinding machine in the y direction of the axis of rotation of the dressing stone 5.

FIG. 6 illustrates the result of this procedure. The Abrichtstein receives as in conventional dressing a spherical section-shaped trough, but the grinding wheel is replaced by the shape of a non-centric ball section. The grinding surface 1.1 thus receives the shape of a spherical surface segment.

If necessary, the distance between the center of the disc 1 and the axis of rotation of the dressing stone 5 can be selected so far that the grinding wheel 1 does not touch the axis of rotation of the dressing stone 5 at all. The Abrichtstein then has, as shown in Figure 7 , in the middle of a untouched area, the steepest slope on the grinding surface 1.1 is steeper here than in the example from FIG. 6.

The necessary area of the ball section is calculated on the basis of the desired inclinations and depending on the travel of the tool, and taking into account the condition that the virtual center of the virtual ball 1.3 lies on the extension of the axis of rotation of the disc 1, the disc is parallel to the y -Axis, thus along the axis of rotation of the disc 1, shifted as the virtual sphere center was calculated from the center of the grinding wheel.

From the cylindrical grinding wheel so the spherical section, grinding tool is made.

FIG. 8 shows another possible procedure. Here are two identical grinding wheels 1 arranged together, preferably pressed together. They are centered in the dressing stone 5 driven.

As indicated in FIG. 9 , again a depression is formed in the dressing stone, while the grinding tools 1 thus produced have asymmetrical grinding surfaces 1.1 with respect to each plane perpendicular to the axis of rotation and symmetry of the tool 1.

The method illustrated in FIG. 10 serves to determine the center point or the axis of symmetry of rotationally symmetrical workpieces. The measurement data of the profile 7 are successively divided into two parts at all potential center or symmetry axis positions 8 and mirrored one or both parts at the respective position, in the example by the position 10. Then, these mirrored parts 11 with the original parts 7 determines the correlation, ie the scalar product of both divided by the product of the norm of the respective parts calculated. This value is greatest when the cutting position 10 coincides with the actual center point 9. In the example, the curve 12 shows the course of the correlation as a function of the selected axis.

Figure 11 illustrates a method of determining the cutting edge shape of a turning plate 13. A sample 14 is rotated in which the continuous shape of the workpiece is replaced by a piecewise linear approximation. Within a cone piece 15, only a certain point of the cutting edge is engaged, depending on the slope of the cone 15. In addition, in the same step, a flat reference surface 16 is rotated against the sample 14. The sample 14 is then measured, and by comparing the positions of the cones 15 with the reference surface 16 or the conical pieces 15 with each other, the exact position of the working point of the cutting edge can be determined as a base of the cutting edge shape.

From these interpolation points, one per conical piece, the shape of the cutting edge can then be determined by interpolation and the CNC program can be adapted accordingly. Alternatively, a mean cutting radius can be determined from the determined interpolation points.

LIST OF REFERENCE NUMBERS

1

grinding tool
1.1 grinding surface
1.2 side surface
1.3 Virtual Ball

2

workpiece

3

survey

4

probe

5

truing

6

trough

7

Measured profile

8th

Possible symmetry axes

9

Actual axis of symmetry

10

Selected axis

11

Mirrored profile

12

correlation function

13

insert

14

specimen

15

cone segments

16

plane surface

Claims (14)

1. Procedure for machining a rotationally symmetric workpiece (2), especially for machining a workpiece with optically effective areas, the symmetry axis of which is aligned in parallel to the z axis and which is movable in parallel to the z axis with a rotating rotationally symmetric grinding or polishing tool (1), the axis of rotation of which is aligned in parallel to the y axis and which is moved in parallel to the x axis, touching the surface of the workpiece (2) with a machining area (1.1) while the workpiece (2) rotates around its symmetry axis, characterized in that the tool (1) is moved with a constant y value precisely in one plane which is parallel to the x-z plane and which is at a distance to the axis of rotation of the workpiece (2).
2. Procedure as claimed in claim 1, characterized in that, for every x position of the tool (1), it is determined at which y position the machining area (1.1) touches the workpiece (2) first when moving in in parallel to the z axis, and in that the z position belonging to this x-y position is approached.
3. Procedure for machining a rotationally symmetric workpiece (2), especially for machining a workpiece with optically effective areas, the symmetry axis of which is aligned in parallel to the z axis and which is movable in parallel to the z axis, with a rotating rotationally symmetric grinding or polishing tool (1), the axis of rotation of which is aligned in parallel to the y axis and is touching the surface of the workpiece (2) with a machining area (1.1) while the workpiece (2) rotates around its symmetry axis, characterized in that the tool (1) is moved with a constant x value with reference to its contact point with the workpiece (2) precisely in one plane which is parallel to the y-z plane and which is situated in the axis of rotation of the workpiece (2).
4. Procedure as claimed in claims 1, 2 or 3, characterized in that the workpiece (2) is machined using the tool only outside of a symmetric area which is centred around the axis of rotation of the workpiece (2).
5. Procedure as claimed in any claim 1 through 4, characterized in that a tool (1) is used, the machining area (1.1) of which is a rotationally symmetric spherical surface section of a virtual sphere (1.3) the virtual centre point of which lies on the symmetry axis of the tool (1), is formed asymmetrically with reference to every mirror plane which lies perpendicularly to its symmetry axis, the virtual sphere centre thus being located outside the centre plane of the machining area (1.1).
6. Procedure as claimed in any claim 1 through 4, characterized in that a tool (1) is used which has the form of a torus section where the section has been made in a plane perpendicular to the symmetry axis.
7. Procedure as claimed in claim 5 or 6, characterized in that the tool (1) for concave areas of the workpiece (2) is oriented with the side of the biggest rise of the machining area (1.1) away from the axis of rotation of the workpiece (2), and, for convex parts of the workpiece (2), is oriented with the side of the biggest rise of the machining area (1.1) toward the axis of rotation of the workpiece (2).
8. Procedure as claimed in claims 5, 6 or 7, characterized in that, for every point on a section parallel to the y axis through the axis of rotation of the workpiece (2), the rise of the workpiece surface is determined, the position of the tool (1) at which the machining area (1.1) has the same rise is determined for this point, and in that the tool (1) is positioned such that the point and the position coincide.
9. Procedure as claimed in any claim 5 through 8, characterized in that the tool (1), independently of control, touches the workpiece (2) also away from the centre plane of the machining area (1.1).
10. Procedure as claimed in any claim 1 through 4, characterized in that a tool (1) is used in the form of a thin disk which has the machining area (1.1) at its narrow side.
11. Procedure as claimed in any claim 1 through 4, characterized in that a tool (1) is used in the form of a cone or of a truncated cone which has the machining area (1. 1) at the position of the biggest radius on the cone's lateral surface.
12. Procedure as claimed in claim 11, characterized in that the tool (1) is oriented toward the axis of rotation of the workpiece (2) with the side of the biggest radius of the cone's lateral surface.
13. Procedure for the tactile measurement of a rotationally symmetric workpiece (2), the symmetry axis of which is aligned in parallel to the z axis, having a measuring stylus (4) that is moved in parallel to the x axis, sensing the surface of the workpiece (2) and measuring the surface's z values at measuring points in the process, especially for determining a sectional profile and/or for determining the centre point of the workpiece (2), characterized in that the measuring stylus (4) is moved with a constant y value with reference to its contact point with the workpiece (2) precisely in a plane which is parallel to the x-z plane and which is at a distance to the axis of rotation of the workpiece (2).
14. Procedure as claimed in claim 13, characterized in that, for every measuring point, the approached x position is converted to the appertaining radius of the workpiece (2).

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