METHOD FOR PRODUCING ROTATIONALLY SYMMETRICAL, NON-CYLINDRICAL BORES WITH A HONING TOOL, AND HONING MACHINE WHICH IS DESIGNED AND EQUIPPED FOR MAKING A CYLINDRICAL BORE INTO A CONICAL BORE

Abstract

A method is proposed for honing conical bores.

Claims

1. A method for producing a rotationally symmetric, non-cylindrical bore using a honing tool comprising the following steps: honing of the bore with a stroke of the honing tool, wherein the stroke (H) is limited by an upper reversal point (OP) and a lower reversal point (UP) (H=OP?UP), permanent detection of the actual diameter (D.sub.IST) of the bore, which varies over the length of the bore to be machined during the honing process in a region between the reversal points (OPn, UPn) of the honing bars of the honing tool. permanent comparison of the actual diameter (D.sub.IST) of the bore to the specified target diameters D.sub.SOLL (OPn, UPn) for at least one of the reversal points (OPn, UPn) and permanent limitation of the stroke (H) to the region or regions (L-b) of the bore in which the actual diameter (D.sub.IST) is smaller than the target diameter (D.sub.Soll (L-b); wherein the stroke (H) of the honing tool is reduced step-by-step corresponding to the measured actual values of the diameter (D.sub.IST) of the bore, so that it is still only the regions (L-b) of the bore that are machined in which the actual diameter (D.sub.IST) of the bore is still smaller than the target diameter corresponding to the measured actual values of the diameter (D.sub.Soll).

2. The method according to claim 1, characterized in that the stroke (H.sub.n) is reduced to a stroke (H.sub.n+1) if the actual diameter (D.sub.IST, n) is equal to the target diameter (D.sub.SOLL, n (OPn, UPn) for at least one reversal point and that the honing bars of the honing tool having the reduced stroke (H.sub.n+1) no longer machine the point or the region ((OPn, UPn)).

3. The method according to claim 2, characterized in that the reduced stroke (H.sub.n+1) is equal to the stroke (H.sub.n) minus a specified amount (DeltaH) (H.sub.n+1=H.sub.n?DeltaH).

4. The method according to claim 3, characterized in that the stroke (H.sub.n+1) is further reduced if, at a reversal point (OP.sub.n+1, UP.sub.n+1) of the honing tool, the actual diameter (D.sub.IST) of the bore section honed last is equal to the target diameter (D.sub.SOLL) (OP.sub.n+1, UP.sub.n+1) of the bore at one of the reversal points (OP.sub.n+1, UP.sub.n+1) of the honing tool.

5. The method according to claim 2, characterized in that at least one new reversal point OP (.sub.n+2) is determined by a new target diameter (D.sub.SOLL, n+2) being determined (D.sub.SOLL, n+2=DeltaD+D.sub.SOLL, n+1) based on the (current) actual diameter (D.sub.IST) by addition of a diameter increment (DeltaD) to the current target diameter (D.sub.SOLL, n), and that the at least one new reversal point OP (.sub.n+2) is located where a target diameter (D.sub.SOLL (y)) is equal to the target diameter (D.sub.SOLL (.sub.n+2)).

6. The method according to claim 5, characterized in that the stroke (H.sub.n+2) of the honing tool is further reduced if the actual diameter (D.sub.IST (OP(.sub.n+2)) at a reversal point (OP.sub.n+2) of the honing tool is equal to the target diameter (D.sub.SOLL (OP(.sub.n+2)) of the bore at this reversal point (OP(.sub.n+2)).

7. The method according to claim 1, characterized in that the bore is initially honed along its entire length (L).

8. The method according to claim 1, characterized in that a corrected target shape of the non-cylindrical bore takes into account the radial widening (Ar) of the cylinder bore during the honing process.

9. The method according to claim 8, characterized in that the corrected target shape (42) of the overlay of a target shape (36) corresponds to the non-cylindrical bore without radial widening and the elastic radial widening (A.sub.r) occurring during the honing process.

10. The method according to claim 1, characterized in that a target shape of the non-cylindrical bore is specified as a function of a longitudinal axis (Y-axis) of the bore, in particular as an nth order polynomial.

11. The method according to claim 1, characterized in that the target shape of the non-cylindrical bore is specified in a table of values.

12. The method according to claim 11, characterized in that the the target shape of the non-cylindrical bore is determined by interpolation between the reference points of the value table.

13. The method according to claim 1, characterized in that the speed of the honing spindle is increased as the stroke (H) decreases.

14. The method according to claim 1, characterized in that the honing bar contact pressure is increased as the stroke H decreases.

15. A honing machine that is designed and arranged for conifying a non-cylindrical bore using a honing tool, wherein the conifying comprises the following steps: Means for honing of the bore with a stroke (H=OPn?UPn; where n=1 to m), Means for detecting the actual diameter (D.sub.IST) of the bore during the honing process in a region between the reversal points (OPn, UPn) of the honing bars of the honing tool. Means for comparing the actual diameter (D.sub.IST) of the bore to the specified target diameters D.sub.SOLL (OPn, UPn) in at least one of the reversal points (OPn, UPn) and limitation of the stroke (H) to the region or regions (L-b) of the bore in which the actual diameter (D.sub.IST) is smaller than the target diameter D.sub.SOLL (L-b); wherein the stroke (H) of the honing tool is reduced step-by-step corresponding to the measured actual values of the diameter (D.sub.IST) of the bore, so that it is still only the regions (L-b) of the bore that are machined in which the actual diameter (D.sub.IST) of the bore is still smaller than the target diameter corresponding to the measured actual values of the diameter (D.sub.Soll).

16. The honing machine according to claim 15, characterized in that the honing machine is designed and arranged so that the stroke (H.sub.n) is reduced to a stroke (H.sub.n+1) if the actual diameter (D.sub.IST, n) is equal to the target diameter (D.sub.SOLL, n (OPn, UPn) at at least one reversal point and that the honing bars of the honing tool having the reduced stroke (H.sub.n+1) no longer machine the point or the region ((OPn, UPn)).

17. The honing machine according to claim 16, characterized in that the honing machine is designed and arranged so that the reduced stroke Hub (H.sub.n+1) is equal to the stroke Hub (H.sub.n) minus a specified amount (DeltaH) (H.sub.n+1=H.sub.n?DeltaH).

18. The method according to claim 17, characterized in that the honing machine is designed and arranged so that the stroke (H.sub.n+1) is further reduced if, at a reversal point (OP.sub.n+1, UP.sub.n+1), the actual diameter (D.sub.IST) of the bore section honed last is equal to the target diameter (D.sub.SOLL) (OP.sub.n+1, UP.sub.n+1) of the bore at one of the reversal points (OP.sub.n+1, UP.sub.n+1) of the honing tool.

19. The honing machine according to claim 18, characterized in that in that the honing machine is designed and arranged so that at least one new reversal point OP (.sub.n+2) is determined by a new target diameter (D.sub.SOLL, n+2) being determined (D.sub.SOLL, n+2=DeltaD+D.sub.SOLL, n+1) based on the (current) actual diameter (D.sub.IST) by the addition of a diameter increment (DeltaD) to the current target diameter (D.sub.SOLL, n), and that the at least one new reversal point OP (.sub.n+2) is located where a target diameter (D.sub.SOLL (y)) is equal to the target diameter (D.sub.SOLL (.sub.n+2)).

20. The honing machine according to claim 19, characterized in that the honing machine is designed and arranged so that the stroke (H.sub.n+2) of the honing tool is further reduced if the actual diameter (D.sub.IST (OP(.sub.n+2)) at a reversal point (OP.sub.n+2) of the honing tool is equal to the target diameter (D.sub.SOLL (OP(.sub.n+2)) of the bore at this reversal point (OP(.sub.n+2)).

21. The honing machine according to claim 15, characterized in that the honing machine is designed and arranged so that the bore is initially honed along its entire length (L).

22. The honing machine according to claim 15, characterized in that the honing machine is designed and arranged so that a target shape of the non-cylindrical bore is specified as a function of a longitudinal axis (Y-axis) of the bore, in particular as an nth order polynomial.

23. The honing machine according to claim 15, characterized in that the honing machine is designed and arranged so that the corrected target shape takes into account the radial widening (Ar) of the non-cylindrical bore during the honing process.

24. The honing machine according to claim 15, characterized in that the honing machine is designed and arranged so that the target shape of the non-cylindrical bore is specified in a value table.

25. The honing machine according to claim 24, characterized in that the honing machine is designed and arranged so that the target shape of the non-cylindrical bore is determined by interpolation between the reference points of the value table.

26. The honing machine according to claim 15, characterized in that the honing machine is designed and arranged so that the speed of the honing spindle and/or of the honing bar contact pressure is increased as the stroke H decreases.

27. A workpiece having a conified bore, characterized in that the conifying of the bore was carried out using a honing tool that comprises honing bars whose length is less than ? of the length (L) of the bore to be machined and conifying the bore comprises: Means for honing of the bore with a stroke (H=OPn?UPn; where n=1 to m), Means for detecting the actual diameter (D.sub.IST) of the bore during the honing process in a region between the reversal points (OPn, UPn) of the honing bars of the honing tool. Means for comparing the actual diameter (D.sub.IST) of the bore to the specified target diameters D.sub.SOLL (OPn, UPn) in at least one of the reversal points (OPn, UPn) and Means for limiting the stroke (H) to the region or regions (L-b) of the bore in which the actual diameter (D.sub.IST) is smaller than the target diameter D.sub.Soll (L-b)); wherein the stroke (H) of the honing tool is reduced step-by-step corresponding to the measured actual values of the diameter (D.sub.IST) of the bore, so that it is still only the regions (L-b) of the bore that are machined in which the actual diameter (D.sub.IST) of the bore is still smaller than the target diameter corresponding to the measured actual values of the diameter (D.sub.Soll).

28. A workpiece having a conified bore, characterized in that, when conifying the bore, the stroke (H.sub.n) is reduced to a stroke (H.sub.n+1) if the actual diameter (D.sub.IST, n) is equal to the target diameter (D.sub.SOLL, n (OPn, UPn) for at least one reversal point (OPn, UPn) and that the honing bars of the honing tool having the reduced stroke (H.sub.n+1) no longer machine the point or the region (OPn, UPn).

29. The workpiece having a conified bore according to claim 28, characterized in that the reduced stroke Hub (H.sub.n+1) is equal to the stroke Hub (H.sub.n) minus a specified amount (DeltaH) (H.sub.n+1=H.sub.n?DeltaH).

30. The workpiece having a conified bore according to claim 28, characterized in that the stroke (H.sub.n+1) is further reduced if, at a reversal point (OP.sub.n+1, UP.sub.n+1, the actual diameter (D.sub.IST) of the bore section honed last is equal to the target diameter (D.sub.SOLL) (OP.sub.n+1, UP.sub.n+1) of the bore at one of the reversal points (OP.sub.n+1, UP.sub.n+1) of the honing tool.

31. The workpiece having a conified bore according to claim 28, characterized in that at least one new reversal point OP (.sub.n+2) is determined by a new target diameter (D.sub.SOLL, n+2) being determined (D.sub.SOLL, n+2=DeltaD+D.sub.SOLL, n+1) based on the (current) actual diameter (D.sub.IST) by the addition of a diameter increment (DeltaD) to the current target diameter (D.sub.SOLL, n), and that the at least one new reversal point OP (.sub.n+2) is located where a target diameter (D.sub.SOLL (y)) is equal to the target diameter (D.sub.SOLL (.sub.n+2)).

32. The workpiece having a conified bore according to claim 30, characterized in that the stroke (H.sub.n+2) of the honing tool is further reduced if the actual diameter (D.sub.IST (OP(.sub.n+2)) at a reversal point (OP.sub.n+2) of the honing tool is equal to the target diameter (D.sub.SOLL (OP(.sub.n+2)) of the bore at this reversal point (OP(.sub.n+2)).

33. The workpiece having a conified bore according to claim 28, characterized in that the bore is initially honed along its entire length (L).

34. The workpiece having a conified bore according to claim 28, characterized in that a target shape of the non-cylindrical bore is specified as a function of a longitudinal axis (Y-axis) of the bore, in particular as an nth-grade polynomial.

35. The workpiece having a conified bore according to claim 28, characterized in that the target shape of the non-cylindrical bore is specified in a value table.

36. The workpiece having a conified bore according to claim 35, characterized in that the the target shape of the non-cylindrical bore is determined by interpolation between the reference points of the value table.

37. The workpiece having a conified bore according to claim 32, characterized in that the speed of at least one of the honing spindle and the honing bar contact pressure is increased as the stroke H decreases.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Shown are:

[0025] FIGS. 1a and 1b: Schematic illustration of an originally cylindrical bore that is conified using the method according to the invention.

[0026] FIG. 2: an exemplary embodiment of the method according to the invention,

[0027] FIGS. 3 and 4: two alternatives for the stroke reduction,

[0028] FIG. 5: an illustration similar to that in FIG. 2 and FIGS. 6a to d: an additional embodiment of the method according to the invention.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

[0029] FIG. 1 is a cylinder bore, shown schematically, having a diameter D (y) that increases in the direction of the longitudinal axis of the bore (Y-axis). On the upper end, bore 1 has a diameter D.sub.0. Diameter D.sub.0 corresponds to the diameter of the bore after pre-honing if the bore is still cylindrical. After pre-honing, the bore has the diameter D.sub.0 along its entire length L.

[0030] It is the object of the method according to the invention to produce a bore that is primarily conical. In the example illustrated in FIG. 1, after the implementation of the honing according to the invention, the bore is conical over the entire length L. The contour line of the conically honed bore is indicated using 1 in FIG. 1. It is generally valid for all figures that the same reference characters are used for the same components or methods and only the differences are explained for each.

[0031] It has been found, surprisingly, that by using the method according to the invention, conified or other non-cylindrical bores can be produced in the shortest time process stable and with high precision. A variety of contour lines can thus be specified.

[0032] Exemplary different bore shapes or contour lines are illustrated in FIG. 1b that can be produced using the method according to the invention.

[0033] The largest diameter D.sub.Max is found on the lower end of the bore in the exemplary embodiments having numbers 1 to 4. The example having the number 5 illustrates that even rotationally symmetrical bores whose largest diameter is located neither on the upper nor the lower end can also be produced. The largest diameter D.sub.MAX in this example is located between the upper and the lower end of the bore.

In FIG. 2, the production of a non-cylindrical, rotationally symmetric bore is illustrated in four steps (a, b, c and d).

[0034] The contour line of the bore is provided with reference character 1. In a non-cylindrical bore, target diameter D.sub.SOLL is a function of the longitudinal axis Y (D.sub.SOLL=f(y)).

[0035] In the exemplary embodiment represented in FIG. 2, the bore has a cylindrical section on its upper end and an additional cylindrical section c on its lower end. The diameter in the region of the upper section b is smaller than diameter D.sub.Soll in lower section c.

[0036] The starting point of the method according to the invention is a cylinder block in which the bore has been pre-machined so that it has a cylindrical shape with diameter D.sub.Ist,0. In this state, the machining according to the method of the invention begins by a honing tool having a honing bar (not shown) being inserted into the bore with diameter D.sub.Ist, 0. The bore is honed along the entire length of the bore. The reversal points of the honing tool or its honing bars are designated with OP.sub.1 and UP.sub.1 (see FIG. 2a).

[0037] By means of the honing process, diameter D.sub.IST of the bore is enlarged uniformly over its entire length starting from D.sub.Ist,0 until the still-cylindrical bore has the diameter D.sub.Ist,1.

[0038] It is evident from FIG. 2b that diameter D.sub.Ist,1 of the bore in this state is equal to target diameter D.sub.Soll, 1 in region b. The actual diameter of the bore is preferably determined according to the invention during the honing process and compared to target diameter D.sub.Soll in region b of the bore.

[0039] As soon as the diameter of bore D.sub.Ist is equal to target diameter D.sub.Soll, 1 in region b, the method according to the invention provides that the stroke of the honing tool is reduced in such a manner that region b is not machined further.

[0040] This is achieved in this dislocated by upper reversal point OP (see FIG. 2c) being displaced in the direction of lower reversal point UP so that new upper reversal point OP.sub.2 is located below region b. Below region b, target diameter D.sub.Soll, 2 is larger than target diameter D.sub.Soll, 1 in region b. Therefore, the region below region b must be further honed in order to achieve the desired bottle-shaped or bottle-neck shaped contour line 1.

[0041] During the honing process with reversal points OP2 and UP (see FIG. 2c), a new target value D.sub.Soll, 2 applies for the part of the bore that is yet to be machined. The actual value of the region of the bore being machined during the machining is compared to target value D.sub.Soll, 2. As soon as actual value D.sub.Ist is equal to target value D.sub.Soll 2, the stroke is further reduced or the machining is ended if the desired contour line 1 has been produced.

[0042] As soon as actual diameter D.sub.Ist of the bore in the region between OP.sub.2 and UP is equal to the target value at the upper reversal point OP2, the stroke is further reduced (not shown in FIG. 2c).

[0043] FIG. 2d shows three different target diameters, D.sub.Soll 1, D.sub.Soll, 2 and D.sub.Soll 3, from which desired contour line 1 is assembled. It is clear from this illustration that contour line 1 is approximated by a plurality of cylindrical sections having diameters D.sub.1, D.sub.2 and D.sub.3. The illustrations in FIGS. 2a to d are greatly exaggerated.

[0044] The differences between diameters D.sub.Soll, 1, D.sub.Soll, 2 and D.sub.Soll, 3 and the corresponding actual diameters D.sub.1, D.sub.2 and D.sub.3 are only a few thousandths of a millimeter. Because of the permanent measuring, a permanent stroke extension also takes place with the smallest variations in travel, so that a continuous, stepless shape is produced. The respective variation in travel is only limited by the resolution of the position sensor for the stroke movement that is substantially smaller than the local slope of the desired shape. During the subsequent smooth-honing that takes place along the entire length of the bore, the previously prepared shape is machined to the desired final roughness profile. The steps in FIGS. 2c and 2d are shown greatly exaggerated and only serve for better understanding of the control. Because of the pneumatic permanent measuring, a permanent stroke dislocation takes place, whereby there are continuous local shape changes.

A first variant of the reduction of the stroke according to this invention is illustrated using FIG. 3. This variant is designated as default constant DeltaH for the determination of DeltaX.

[0045] The honing tool or the honing bars 5 belonging to the honing tool are shown very schematically once at the upper reversal point OP and once at the lower reversal point UP. The stroke of the honing bars corresponds to the spacing of OP1 and UP if the bore is honed along its entire length.

[0046] An air-measurement nozzle that belongs to the honing tool is provided with the reference character 7 in FIGS. 3 and 4. Air-measurement nozzles 7 are only shown at the upper reversal point of the honing tool. Because the air-measurement nozzles are integrated into the honing tool, they complete the same movements as honing bars 5. If actual diameter D.sub.IST of the bore has reached diameter D.sub.SOLL, 1, stroke Hub H1 (=OP1?UP) is reduced by an amount DeltaH.

[0047] The amount of DeltaH can be specified by the operator of the honing machine as a parameter in the control system.

[0048] Because the bore in region b, where reversal point OP1 is located, already has desired target diameter D.sub.Soll (1), upper reversal point OP2 is dislocated downward in the direction of lower reversal point UP. New reversal point OP2 is obtained by the displacement of previous upper reversal point OP1 by the amount DeltaH in the direction of lower reversal point UP.

[0049] A second target diameter D.sub.Soll,2 is associated with a new second reversal point OP2. Second target diameter D.sub.Soll,2 is equal to the target diameter of the bore at reversal point OP2.

[0050] New diameter D.sub.Soll, 2 at reversal point OP2 can also be determined based on diameter D.sub.Soll (1) using the formula D.sub.Soll,2=D.sub.Soll, 1+DeltaX.

[0051] The amount of DeltaX is not constant, but depends upon the slope of the contour line at upper reversal point OP1 and new upper reversal point OP2. Because the contour line of the bore is stored in the machine controlsfor example, as a polynomial or a table of valuesthe corresponding target diameter at the reversal point can be determined for each reversal point OP, UP.

[0052] The strokes of the honing tool over the time t are plotted in the right-hand part of FIG. 3. It is clear that a larger stroke H.sub.1=OP1 and UP takes place in the first machining step. In the second step, stroke H.sub.2 is significantly smaller. (H=OP2?UP).

[0053] The variant default constant DeltaH for the determination of DeltaX is represented in FIG. 4 and explained below. In this variant, based on a diameter D.sub.Ist or D.sub.Soll,1, a constant DeltaX is added to target diameter D.sub.Soll,1. New upper reversal point OP2 is determined from the cutting point between contour line 1 and new target diameter D.sub.Soll, 2=D.sub.Soll, 1+DeltaX. In this variant, the stroke between OP1 and OP2 or between OP.sub.n and OP.sub.n+1 is not reduced by a constant amount. The reduction of the stroke is greater or lesser depending upon how greatly the contour line in the region between current upper reversal point OP.sub.n and new upper reversal point OP.sub.n+1 changes.

[0054] It is clear that the reduction of the stroke can be implemented not only in the region of the upper reversal OP point, but also in the region of lower reversal point UP.

[0055] For reasons of clarity, such an exemplary embodiment is not shown. Refer again to FIG. 1b no. 5. A contour line is illustrated there that requires that upper reversal point OP as well as lower reversal point UP be displaced in order to achieve the desired target contour.

[0056] FIG. 5a to d and FIGS. 2a to d have many similarities. The principle is explained in reference to FIGS. 2a to d; in FIGS. 5a to d, the algorithm according to the invention is highlighted along with the corresponding illustrations.

[0057] The crosshatched surfaces 9.sub.1, 9.sub.2 and 9.sub.3 illustrate where material must still be removed in order to achieve desired contour line 1.

[0058] All figures are schematic illustrations and are not to scale.

[0059] In the method variants described so far, it was assumed that the wall of the (cylinder) bore to be machined is so thick that the forces acting in the radial direction on the wall during the honing process by the honing bars effect no or only small deformations on the wall. The radial force (contact pressure force) with which the honing bars are pressed against the cylinder bore their are caused by the feeding device or the control of the honing machine of the.

[0060] This principle functions for quasi-fixed workpiece structures or workpieces whose wall thickness is constant. These conditions are not always present in practice for modern cylinder crankcases, so that elastic deformations due to machining forces arise because of locally varying wall thicknesses and/or high feeding forces during the machining and the removed material shifts away in the radial direction (radial widening). Because the widening is elastic, the wall springs back as soon as the honing process is completed. In this manner, the achieved actual shape in the tensioned state deviates strongly from the target shape. This circumstance is illustrated in FIGS. 6a and b. Only the half cylinder bore is shown in FIG. 6a. Its central axis is shown as a dot and dash line 30. The length of the cylinder bore in this example comprises a thick-walled section 32 and a thin-walled section 34. The desired target shape is indicated with 36.

[0061] If the bore is now widened radially in thin-walled section 34 during the honing process and the desired target shape is produced corresponding to line 36 according to the method of the invention, the bore then springs radially back after the end of the honing process and results in an actual shape according to line 38 in FIG. 6b.

[0062] It is clear from a comparison of lines 36 and 38 that the actual shape and the target shape in thin-walled section 34 vary significantly from each other.

[0063] A solution according to the invention for this problem is that the target shape becomes, at least locally, a corrected target shape 40.

[0064] The corrected target shape is the shape that the cylinder bore must assume during the honing process in order for it to have the desired target shape 36 after the end of the honing process and without radial widening.

[0065] The corrected target shape is obtained by the radial widening being added to target shape 36 (particularly in the region of thin-walled section 34). The corrected target shape in FIG. 6c has the reference character 42.

[0066] If the cylinder bore is now brought into corrected target shape 42 via the method according to the invention, the deviations between actual shape 38 and target shape 36 of the cylinder bore after the end of the honing process are minimal. This circumstance is illustrated in FIG. 6d.

[0067] In other words: Corrected target shape 42 offsets these local different deformations by additional local material removal. In this manner, it is possible to keep the diameter of the non-cylindric rotationally symmetric cylinder bore within a very narrow tolerance zone between lines 44 along the entire length of the cylinder bore.

[0068] Corrected target shape 42 can be determined empirically or by calculation. In the case of an empirical determination, it is possible to iteratively change from the target shape to the corrected target shape based on the particular results achieved by correcting the target shape in small steps (for example in the range of one of more micrometers) at a plurality of support points until the actual shape (see 38 in FIG. 6c) in the tensioned state corresponds to the target shape (see 36 in FIG. 6c).

[0069] In the case of a calculated determination, the radial widening (Ar) of the cylinder bore in thin-walled region 34 can be at least roughly determined based on the force with which the honing bars are pressed against the cylinder wall and this widening can be added to target shape 36. Starting from the target shape, the respective results achieved can be iteratively changed to the corrected target shape if the target shape is corrected in small steps at a plurality of support points (for example in the region of one or a plurality of micrometers) until the actual shape (see 38 in FIG. 6c) in the tensioned state corresponds to the target shape (see 36 in FIG. 6c).