EP0543079B1 - Method for NC grinding the cam of a camshaft - Google Patents

Description

The invention relates to a method for grinding cams of a camshaft, in which the camshaft is rotated about its longitudinal axis and at the same time, depending on a predetermined cam contour, a first grinding wheel is fed in a direction perpendicular to the longitudinal axis, the cam contour in the start-up area and in the run-out area of the cam has a concave curvature, and a second grinding wheel is used to grind the concavely curved regions, the radius of which is smaller than the minimum radius of curvature of the concave curvature, while the radius of the first grinding wheel is very much larger than the minimum radius of curvature of the concave curvature.

A method of the type mentioned above is known from document DE-C-678 981.

The known method is a copy grinding method, in which the camshaft is rotated in a conventional manner together with a so-called master cam, which is arranged in an extension of the camshaft and is connected to it in a rotationally rigid manner. Using a suitable button on the master cam, the grinding spindle on a rocker is moved perpendicular to the longitudinal axis of the camshaft, while the camshaft is rotated at a constant speed. In this way you achieve that the point of engagement of the grinding wheel generates the circumferential profile of the master cam on the cams to be ground by this mechanical sequence control.

In the known method it is stated that previously it was known for grinding cams with concavely curved sections to use grinding wheels with a very small radius which is smaller than the minimum radius of curvature of the concavely curved region. However, it was considered to be disadvantageous that these very small grinding wheels, when used to grind the entire cam, are subject to rapid wear.

According to the known method, two steps are therefore used. During a first processing step, only the concavely curved area of the cam circumference is processed, while in a second processing step only the remaining peripheral area is ground.

Two different variants are specified for the first processing step. According to a first variant, a grinding wheel is used which is spherical on its circumference. This grinding wheel is rotated around an axis that is perpendicular to the camshaft axis. The grinding wheel is fed with its parallel circumferential surface in a direction radially to the camshaft axis and then guided in a direction parallel to the camshaft axis through the concave curved region of the cam, which is stationary for this purpose.

According to the second variant, a grinding wheel is also used to grind out the concavely curved section, the axis of which is perpendicular to the camshaft axis. However, the grinding wheel is designed as a shaped wheel, the circumference of which is adapted to the entire concavely curved section of the cam is. Otherwise, the procedure is the same as for the first variant.

In the second step, only the remaining cam circumference is machined with a grinding wheel, the radius of which is much larger than the minimum radius of curvature of the concave section. This grinding wheel of the second machining step is rotated about an axis that runs parallel to the camshaft axis.

In the known method, two grinding wheels are therefore required according to both alternatives, one of which (first machining step) lies with its axis perpendicular to the axis of the camshaft, while the second grinding wheel (second machining step) is arranged parallel to the camshaft.

In the DE book "The control of gas exchange in high-speed internal combustion engines" by W.-D. Bensinger, Springer-Verlag, 1968, include Described cam shapes in which the flanks, i.e. the connecting sections of the base circle and secondary circle do not have the usual convex shape, but rather a concave shape, which is also referred to as a "hollow flank" (DE book, page 31, FIG. 40c).

A CNC control of a grinding machine is known from the document "RESEARCH DISCLOSURE", No. 272, December 1986, New York, USA, page 735. The control system controls two identical grinding spindles that are aligned symmetrically to each other along a common axis. The common axis is parallel to the longitudinal axis of a camshaft to be ground. With the known device it is possible to grind two cams of the camshaft at the same time by simultaneously controlling both grinding slides.

A camshaft grinding machine is known from the document "WORKSHOP AND OPERATION", volume 110, no. 9, September 1977, Munich, DE, pages 623 to 630, with which cams with concave areas can also be ground. It is stated that the grinding wheel radius should be at most two thirds of the smallest radius of curvature in the concave part of the cam.

The invention is based on the object of developing a method of the type mentioned in such a way that cams with a hollow flank, that is to say concave curvature, can be ground quickly, that is to say with high drive power and with a precise cam contour.

According to the method mentioned in the introduction, this object is achieved in that the cam is first grinded with the first grinding wheel over the entire circumference of the cam under numerical control of the infeed of the grinding wheels and the rotation of the camshaft, the first grinding wheel being guided along a first cam contour which is modified in the area of the concave curvature with respect to a cam end contour, such that its minimum radius of curvature is greater than or equal to the radius of the first grinding wheel, so that a zone lying within the modified first contour remains in the area of the concave curvature, and then grinding with the second grinding wheel.

The object underlying the invention is completely achieved in this way.

According to the invention, namely - as is known per se from document DE-C-678 981 - the machining of the cam is divided into two sections, but the conventional large grinding wheel in a first machining step removes the essential portion of the oversize and is deliberately in Kauf takes that in the area of the concave curvature remains the said zone, which cannot be reached for the large grinding wheel due to its large radius. This zone is then removed in a second step by means of the small grinding wheel known per se, which at the same time takes over the finishing of the desired cam contour in a subsequent step.

With the method according to the invention, it is therefore possible for the first time to grind cams with hollow flanks on an industrial scale with processing times such as are currently state of the art in the case of cam grinding of conventional camshafts, that is to say with convexly curved flanks, that is to say about 3 to 4 seconds each Amount to cams without affecting the service life of the grinding wheels.

In a preferred embodiment of the method according to the invention, the cam is stopped after grinding with the first grinding wheel and the zone with the second grinding wheel is essentially ground out in plunge grinding.

This measure has the advantage that practically the entire zone can be ground out in a very fast operation, a time-consuming web operation not being necessary because the cam stands still during this phase of processing and the second, small grinding wheel only dips into the zone in the feed operation . Since the cam contour in the area of the concave curvature usually has the shape of an arc of a circle, the remaining zone can be almost completely ground out by immersing the second grinding wheel once.

In a further development of the exemplary embodiment mentioned above, the cam is rotated again after plunge grinding and is ground with the second grinding wheel along a second contour lying within the first contour.

This measure has the advantage already mentioned above that the last machining operation, namely usually the finishing grinding, is carried out by the second, small grinding wheel, which is neither problematic from the point of view of the machining time nor from the point of view of the tool life, because with this last one Grinding process only very small material volumes can be machined.

Further advantages result from the description and the attached drawing.

It goes without saying that the features mentioned above and those yet to be explained below can be used not only in the combination indicated in each case, but also in other combinations or on their own without departing from the scope of the present invention.

Fig. 1

eine Seitenansicht eines Ausführungsbeispiels eines Nockens mit hohlen Flanken (nicht maßstäblich);

Fig. 2

eine Seitenansicht einer Vorrichtung zur Durchführung des erfindungsgemäßen Verfahrens;

Fig. 3

eine Draufsicht auf die in Fig. 2 gezeigte Anordnung;

Fig. 4 bis 7

vier Phasenbilder zur Erläuterung von Schritten des erfindungsgemäßen Verfahrens.

An embodiment of the invention is shown in the drawing and is explained in more detail in the following description. Show it:

Fig. 1

a side view of an embodiment of a cam with hollow flanks (not to scale);

Fig. 2

a side view of an apparatus for performing the method according to the invention;

Fig. 3

a plan view of the arrangement shown in Fig. 2;

4 to 7

four phase images to explain steps of the method according to the invention.

1 shows a cam 10 (not to scale) as it is used for camshafts of motor vehicle engines.

The cam 10 is rotatable about an axis of rotation 11, which is also the longitudinal axis of the camshaft, not shown.

The cam 10 has in a known manner a base circle section 12 with a radius R _G , the center of which coincides with the axis of rotation 11. The base circle section 12, which takes up a circumferential angle φ _G in the cam 10, is followed by a concave flank section 13a on the start-up side via the pre-cam region 15a / 15b and a second concave flank section 13b of the cam 10 on the opposite discharge side, each of which has a circumferential section φ take _k . The pre-cam sections 15a and 15b of the cam 10 have a convex curved area as a transition between the base circle section 12 and the flank sections 13a and 13b at a circumferential angle φ _v . The cam contour then has a convex section 14 in the tip region, which section is variable. Radius ρ _S has. The tip circle section 14 takes a circumferential angle φ _S.

As can be clearly seen from Fig. 1, the cam 10 is designed in its contour so that the start-up section 13a and the outlet section 13b, i.e. the cam flanks are not convex in the usual way, but rather are concavely curved. This phenomenon is also called "hollow flanks".

The purpose of this measure is, when actuating the bucket tappets for the valves of the engine, a faster start-up or sequence to reach from the secondary circuit section 14, so that the filling behavior of the combustion chambers is improved.

In Fig. 1, ρ _{k is} the radius of curvature of the sections 13a, 13b, it being clear that this radius of curvature ρ _k is opposite to the radii of curvature R _G and ρ _S of the base circle section 12 and the tip circle section 14. It is understood that the radius of curvature ρ _{k is} not constant. The minimum radius of curvature ρ _{k min of} the sections 13a and 13b is therefore an important variable for the machining of these sections 13a and 13b.

For example, it is readily apparent that sections 13a and 13b can only be ground using a grinding wheel whose radius is smaller than the minimum radius of curvature ρ _{k min} , because otherwise there would be shape errors. In practice, the radius of the grinding wheel is selected to be significantly smaller in order to keep the osculation smaller, so that the contact between the grinding wheel and the workpiece in the concave region corresponds to a contact line.

In the other areas of the cam contour, namely in the base circle section 12, in the pre-cam section 15a / 15b and in the tip circle section 14, the radius of the grinding wheel does not play a role from the point of view of shape retention, because these areas are convexly curved and therefore at least theoretically with grinding wheels of any radius can be ground.

In FIGS. 2 and 3, a grinding machine is shown - extremely schematically - which is designated 20 overall.

In the grinding machine 20, a first grinding slide 22 is arranged in a conventional manner in the direction of an arrow 23 on a machine frame 21, not shown.

The arrow 23 indicates the so-called X-axis in the technical language of grinding machine construction.

A first drive motor 24 is located on the first grinding carriage 22 and drives a first grinding wheel 26 with a large radius via a first belt drive 25. The first grinding wheel 26 is mounted in a first headstock 27.

In this respect, the grinding machine 20 is of conventional construction.

However, a second grinding slide 30 is now arranged on the top of the first headstock 27. For this purpose, the second grinding slide 30 is, for example in the side view of FIG. 2, L-shaped with a horizontal leg and a vertical leg.

By means of a corresponding longitudinal guide with a feed device, the second grinding carriage 30 can be moved relative to the first grinding carriage 22 along an arrow 32 which runs parallel to the X axis (arrow 23).

The horizontal leg of the second grinding carriage 30 carries a second drive motor 33, which drives a second grinding wheel 35 via a second belt drive 34. The second grinding wheel 35 is mounted in a second headstock 36, which is located at the front on the vertical leg of the second grinding carriage 30. The second grinding wheel 35 has a substantially smaller radius than the first grinding wheel 26.

In the position shown in FIG. 2, the second grinding carriage 30 has moved into its right end position in its position relative to the first grinding carriage 22, with the result that the second, small grinding wheel 35 projects to the right over the outer circumference of the first, large grinding wheel 26 .

In the plan view of FIG. 3, however, the situation is reversed, because there the second grinding slide 30 relative to the first grinding slide 22 is in its retracted, i.e. in FIG. 3 the upper end position has been moved, in which the first, large grinding wheel 26 protrudes forward (downwards in the illustration of FIG. 3) beyond the outer contour of the second, small grinding wheel 35.

In this position, which is indicated in FIG. 3, the first, larger grinding wheel 26 is in engagement with a cam 41 of a schematically illustrated camshaft 40. The camshaft 40 is clamped in the usual way and rotatable about its longitudinal axis 42, the so-called C-axis, such as indicated by an arrow 43.

For grinding the cam 41, the camshaft 40 is rotated in the direction of arrow 43 about the C axis 42 in the manner customary for numerically controlled grinding of cams, while at the same time the first grinding slide 22 in the direction of arrow 23, i.e. is moved forward and backward along the X-axis so that the first grinding wheel 26 engages the surface of the cam 41 along a predetermined cam contour when it is rotated.

The special feature of the grinding machine 20 shown in FIGS. 2 and 3 is that, alternatively, the first, larger grinding wheel 26 and then the second, smaller grinding wheel 35 can be brought into engagement with the cam 41 and the other cams of the camshaft 40. For this purpose, the camshaft 40 is clocked relative to the first and second grinding carriages 22, 30, that is to say in the direction of its longitudinal axis 42, which runs parallel to the Z axis (arrow 45), by an increment which corresponds precisely to the distance between the grinding wheels 26, 35 Direction of the longitudinal axis 42 (arrow 45) corresponds.

By moving the grinding slides 22 and 30 in the direction of the arrows 23, 32 relative to one another, one or the other grinding wheel 26, 35 can then be brought into engagement with the cam 41 in order to then grind the surface of the cam 41 along a predetermined contour .

The procedure is now to be explained in more detail using the phase images according to FIGS. 4 to 7.

To process the cams 41 of a camshaft 40 according to FIG. 3, the raw camshaft 40 is first clamped in a known manner, and the camshaft 40 is clocked relative to the grinding carriages 22 and 30 such that the first cam to be machined has the first, larger grinding wheel 26 is aligned. The grinding carriages 22 and 30 are moved relative to one another in such a way that the configuration shown in FIG. 3 arises, in which the first, larger grinding wheel 26 protrudes and therefore becomes effective when the first grinding carriage 22 along the X-axis 23 hits the camshaft 40 to proceed.

Fig. 4 shows that the cam 41 has a raw contour 50 in the initial state, which corresponds to the raw surface of the camshaft blank. An intermediate contour 51 marks the final state after the cam 41 has been roughed, while an end contour 52 denotes the final state after the cam 41 has been finished. It goes without saying that the illustration in FIGS. 4 to 7 is not to scale, because the oversize between the rough contour and the intermediate contour, ie the oversize for the roughing process, is of course significantly larger than the oversize between the intermediate contour 51 and the end contour 52, ie the oversize of the finishing process .

4 now shows a state in which the first, larger grinding wheel 26 is already in engagement with the cam 41 and has already ground from the raw contour 50 onto the intermediate contour 51 over a certain part of the base circle section. It goes without saying that FIG. 1 only shows the situation in a simplified manner, because of course the grinding from the raw contour 50 to the intermediate contour 51 usually takes place in several stages and not only in one stage, as FIG. 4 shows.

For this purpose, the grinding wheel 26 was advanced in the area of the base circle in the infeed mode from the raw contour 50 to the intermediate contour 51, while rail operation is not necessary in this area, since the base circle radius (cf. FIG. 1) is constant in this area. Only after leaving the base circle section is a path operation required, in which the rotation of the cam 41 about the C-axis 42 is superimposed on an oscillating movement of the grinding wheel 26 in the direction of the X-axis 23.

4 that the minimum radius of curvature ρ _{k min is} significantly smaller than the radius R _{S1 of} the grinding wheel 26. Thus, for example, the minimum radius of curvature ρ _{k min} is a factor 10 lower than the radius R _{S1 of} the grinding wheel 26 .

For the reasons already explained above, it is therefore not possible to grind the intermediate contour 51 exactly with the grinding wheel 26, because the large grinding wheel 26 in the concave region cannot reach to the bottom of the intermediate contour 51, without shape defects in the adjacent pre-cam section and to create the top circle section.

For this reason, the grinding process according to FIG. 4 is carried out so that the grinding wheel 26 is not guided along the intermediate contour 51, but rather along a modified intermediate contour 51 '. The modified intermediate contour 51 'is designed such that its minimum radius of curvature is greater than the radius R _{S1 of} the grinding wheel 26. The modified intermediate contour 51' can therefore be ground using the large grinding wheel 26 without any form errors.

However, the modification of the intermediate contour 51/51 'means that in the area of the concave curvature, i.e. Zones 55a, 55b remain in the run-up section 13a and in the run-off section 13b of the cam (cf. FIG. 1), which lie outside the intermediate contour 51 desired per se.

When the first grinding wheel 26 has finished grinding the modified intermediate contour 51 ′, the camshaft 40 is clocked relative to the grinding wheel 26, and the second and further cams to be machined are ground in the same way along modified intermediate contours until all the cams of the camshaft 40 have been machined . The grinding wheel 26 is moved in rapid traverse in the direction of the X-axis 23 into the starting position by means of the carriage 22 (FIG. 5).

The camshaft 40 now moves with its last machined cam into the position of the grinding wheels 35, although the Camshaft 40 is clocked by the distance that corresponds to the distance between the grinding wheels 26, 35 in the direction of the longitudinal axis 42 (arrow 45). At the same time, the grinding carriages 22 and 30 are moved relative to one another along the X axis 23 in such a way that the smaller, second grinding wheel 35 now projects (cf. FIG. 2). At the same time, the camshaft 40 is brought from the starting position at high speed (arrow 43) to an angular position (FIG. 6a) in which one of the zones 55a, 55b, in the example of FIG. 6a the zone 55a, is in the direction of the X- Axis 23, based on the line of engagement of the second, smaller grinding wheel 35, is located.

In this rotational position, the camshaft 40 is stopped, ie the turning process is ended. The second, smaller grinding wheel 35 has a radius R _S2 that is smaller than the minimum radius of curvature ρ _{k min} in the region of the concave curvature of the cam 41. The second, smaller grinding wheel 35 is now advanced according to FIG. 6a in the direction of arrow 23 on the cam 41, so that the zone 55a in the position of the grinding wheel 35 according to FIG. 6b is essentially completely ground out by plunge grinding.

The grinding wheel 35 is then moved in rapid traverse in the direction of the X-axis 23 into the starting position by means of the carriage 22.

The cam 41 is now rotated at high speed in such a way that the other zone 55b is also ground out by plunge grinding when the cam 41 is stationary. 6c shows this process. The grinding wheel 35 is then moved in rapid traverse in the direction of the X-axis 23 into the starting position by means of the carriage 22, as shown in FIG. 6a.

7 now shows the final process in which the cam 41 is ground in a conventional manner from the intermediate contour 51 to the end contour 52 by means of the second grinding wheel 35, which is now guided exactly along the end contour 52. In FIG. 7, the punctures are indicated by 60, which were previously made during plunge grinding according to FIG. 6. As a result of the piercing, the material in the region of the zones 55a, 55b was machined so far that, with the finishing according to FIG. 7, so little material can be machined in the region of the concave curvature that this can be done in one operation.

It is also understood that the grinding from the intermediate contour 51 to the finished contour 52 can also take place in several stages and not only in one stage, as shown in FIG. 7. The same process, plunge grinding with a stationary workpiece (Fig. 6a, b, c) and finish grinding (Fig. 7) is now repeated by clocking the camshaft 40 relative to the second grinding wheel 35 on all other cams of the camshaft 40, so that finally, the camshaft 40 is ground on all cams.

In a practical application, a 450 mm diameter CBN grinding wheel is used as the first grinding wheel 26 in order to grind cams 41 of a steel camshaft 40.

4, the first grinding wheel 26 is operated at a peripheral speed of v _S = 100 m / s, which corresponds to a speed of approximately n = 4,300 rpm. However, the cutting speed v _S can also be varied, for example in the range between 50 and 300 m / s.

The camshaft 40 is rotated about the C axis 42 at an angular velocity ω. The angular velocity ω is gradually changed. During the machining of the base circle section 12 it is, for example, 35,000 degrees / min, during the machining of the tip circle section 14 15,000 degrees / min and during the machining of the flanks 13a, 13b, for example 8,000 degrees / min.

The allowance between raw contour 50 and between contour 51 during roughing is e.g. 0.55 mm, which are removed in six revolutions of the camshaft 41, so that an infeed of approximately 0.09 mm results in each revolution.

If the minimum radius of curvature ρ _{k min} in the concavely curved areas 13a, 13b of the cam 41 is, for example, 50 mm, then a CBN grinding wheel with, for example, 80 mm diameter can be used as the second grinding wheel 35, the radius of which is thus smaller than 40 mm the minimum radius of curvature.

wobei ρ_{k min} der minimale Krümmungsradius im konkaven Bereich des Nockens 41 ist, der z.B. 50 mm beträgt. d² S_N/dφ² ist die Umfangsbeschleunigung der Eingriffslinie der zweiten Schleifscheibe 35 am Nocken 41 und beträgt bei der vorgegebenen Nockenkontur beispielsweise 0,0164 mm/Grad². ω_k ist die Winkelgeschwindigkeit des Nockens 41 bei der Drehung um die C-Achse 42 im Bereich der hohlen Flanken. Wenn ω_k 8.000 Grad/min ist, beträgt somit der Radius R_S2 der zweiten, kleineren Schleifscheibe 35 nur das 0,76-fache des minimalen Krümmungsradius ρ_{k min}, während bei einer Winkelgeschwindigkeit ω_k von 4.000 Grad/min das 0,87-fache anzusetzen ist.For a more precise determination of the permissible radius of the second grinding wheel 35, it is assumed that the dynamic relationships to the cam contour in the controlled contact point must be taken into account in order to keep the osculation at the cutting point small. This leads to the formula $${\mathit{\text{R}}}_{\mathit{\text{S2}}}\text{=}\mathit{\text{f}}{\text{(ρ}}_{\mathit{\text{k}}\text{min}}\text{;}\frac{{\mathit{\text{d}}}^{\text{2nd}}{\mathit{\text{S}}}_{\mathit{\text{N}}}}{{\text{dφ}}^{\text{2nd}}}{\text{; ω}}_{\mathit{\text{k}}}\text{)}$$

where ρ _{k min is} the minimum radius of curvature in the concave region of the cam 41, which is, for example, 50 mm. d² S _N / dφ² is the peripheral acceleration of the line of engagement of the second grinding wheel 35 on the cam 41 and is, for example, 0.0164 mm / degree² for the given cam contour. ω _k is the angular velocity of the cam 41 when rotating about the C axis 42 in the region of the hollow flanks. If ω _{k is} 8,000 degrees / min, then it is Radius R _{S2 of} the second, smaller grinding wheel 35 is only 0.76 times the minimum radius of curvature ρ _{k min} , while 0.87 times is to be used for an angular velocity ω _k of 4,000 degrees / min.

In order to more precisely determine the form given above for the permissible radius R _{S2 of} the second grinding wheel 35, the exact functional relationship can be determined on the basis of an analytical view. For this purpose, the elevation angle φ _E1 at the beginning of the elevation and the elevation angle φ _Ei at the points of the maximum circumferential acceleration d² S _N / dφ², the line of engagement of the second grinding wheel 35 on the cam 47, are initially considered as further output variables. $${\text{Δφ = φ}}_{\text{egg}}{\text{- φ}}_{\text{E1}}\text{.}$$

so läßt sich die oben angegebene Formel für den Radius r_S2 wie folgt schreiben: $${\mathit{\text{R}}}_{\mathit{\text{S2}}}{\text{= ρ}}_{\mathit{\text{kmin}}}\text{(1-}{\mathit{\text{b}}}_{\text{max}}\frac{{\text{ω}}_{\mathit{\text{k}}}}{\text{Δ}{\mathit{\text{C.v}}}_{\mathit{\text{x}}}}\text{)}$$

wobei ΔC das eingestellte Winkelinkrement im konkaven Bereich und v_x die maximale Achsgeschwindigkeit in Richtung der X-Achse sind.Let us consider a further auxiliary variable b _max $${\text{b}}_{\text{Max}}{\text{= (i.e.}}^{\text{2nd}}{\text{S}}_{\text{N}}{\text{/ dφ}}^{\text{2nd}}{\text{) (Δφ / π)}}^{\text{2nd}}{\text{(Δφ / φ}}_{\text{egg}}{\text{)}}^{\text{2nd}}$$

the formula for the radius r _S2 can be written as follows: $${\mathit{\text{R}}}_{\mathit{\text{S2}}}{\text{= ρ}}_{\mathit{\text{kmin}}}\text{(1-}{\mathit{\text{b}}}_{\text{Max}}\frac{{\text{ω}}_{\mathit{\text{k}}}}{\text{Δ}{\mathit{\text{Cv}}}_{\mathit{\text{x}}}}\text{)}$$

where ΔC is the set angle increment in the concave area and v _{x is} the maximum axis speed in the direction of the X axis.

In a numerical example: $$\begin{array}{c}\begin{array}{c}{\text{d}}^{\text{2nd}}{\text{S}}_{\text{N}}{\text{/ dφ}}^{\text{2nd}}{\text{= 0.0164 mm / degree}}^{\text{2nd}}\\ {\text{φ}}_{\text{egg}}\text{= 138 degrees}\\ {\text{φ}}_{\text{E1}}\text{= 94 degrees}\\ {\text{ρ}}_{\text{kmin}}\text{= 46.7822 mm}\\ \text{ΔC = 1 degree}\\ {\text{ω}}_{\text{k}}\text{= 8000/4000 degrees / min}\\ {\text{v}}_{\text{x}}\text{= 10,000 mm / min.}\end{array}\end{array}$$

und schließlich der Schleifscheibenradius $$\begin{array}{c}\begin{array}{c}{\text{R}}_{\text{S2}}{\text{= 35 mm (ω}}_{\text{k}}\text{= 8000 Grad/min)}\\ {\text{R}}_{\text{S2}}{\text{= 40 mm (ω}}_{\text{k}}\text{= 4000 Grad/min).}\end{array}\end{array}$$

Then the auxiliary variables result in: $$\begin{array}{c}\begin{array}{c}\text{Δφ = 44 degrees}\\ {\text{b}}_{\text{Max}}{\text{= 0.3274 mm / rad}}^{\text{2nd}}\end{array}\end{array}$$

and finally the grinding wheel radius $$\begin{array}{c}\begin{array}{c}{\text{R}}_{\text{S2}}{\text{= 35 mm (ω}}_{\text{k}}\text{= 8000 degrees / min)}\\ {\text{R}}_{\text{S2}}{\text{= 40 mm (ω}}_{\text{k}}\text{= 4000 degrees / min).}\end{array}\end{array}$$

If the permissible radius R _{S2 of} the second, smaller grinding wheel 35 has been determined in this way, it can be used, for example, with a cutting speed v _S = 100 m / s, which corresponds to a speed n = 24,000 rpm. If one then adjusts the second grinding wheel 35 by 0.1 μm during plunge grinding according to FIG. 6, this results in a feed rate of, for example, 23.9 mm / min and a depth of the zones 55a, 55b of, for example, 0.16 mm at a processing time of 0.4 s.

7, the second grinding wheel 35 is driven at the same speed or cutting speed. The angular velocities for the rotation of the cam 41 about the C-axis 42 are, however, set slightly differently compared to the roughing process according to FIG. 4, namely with 25,000 degrees / min in the base circle section 12, with 8,000 degrees / min in the tip circle section 14 and with 4,000 Degrees / min in the area of the flanks 13a, 13b.

7, the allowance between the intermediate contour 51 and the final contour 52 is, for example, 50 μm, which are ground in ten revolutions of the cam 41.

It is understood that the exemplary embodiment outlined above is only one of many possible exemplary embodiments and therefore the invention is not restricted by the specified numerical data.

Claims (3)

1. A method of grinding cams (12; 41) of a camshaft (40), wherein the camshaft (40) is rotated about its longitudinal axis (42) and a first grinding wheel (26) is concurrently fed in in a direction perpendicular to the longitudinal axis (42) and depending on a predetermined cam profile (50, 51, 52), the cam profile (50, 51, 52) having a concave curvature in the catch area (13a) and in the run-off area (13b) of the cam (10; 41), a second grinding wheel (35) being used for grinding out the concavely curved areas, the second grinding wheel (35) having a radius R_S2 being smaller than the minimum radius ρ_kmin of the concave curvature, whereas the first grinding wheel (26) has a radius R_S1 being very much larger than the minimum radius ρ_kmin of the concave curvature, characterized in that while the feeding-in of the grinding wheels (26, 35) as well as the rotation of the camshaft (40) are numerically controlled, the cam (41) is first ground along its entire periphery by means of the first grinding wheel (26), the first grinding wheel (26) being guided along a first cam profile (51) modified in the concave curvature area as compared to a final cam profile (51'), such that its minimum radius of curvature is greater than or equal to the radius R_S1 of the first grinding wheel (26), such that a zone (55a, 55b) remains in the area of concave curvature within the modified first cam profile (51), and that one then grinds by means of the second grinding wheel (35).
2. The method of claim 1, characterized in that the cam (41) is set stationary after the grinding by means of the first grinding wheel (26), and that the zone (55a, 55b) is ground out by means of the second grinding wheel by plunge-cut grinding when the cam (41) is standing still.
3. The method of claim 2, characterized in that the cam (41) is again rotated after the plunge-cut grinding and that one grinds along a second profile (52) lying within the first profile (51).

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