DE3830854C2 - Process for optimizing the infeed when grinding cams of a camshaft - Google Patents

Description

The invention relates to a method for optimizing the infeed when grinding cams of a camshaft by means of a numerically controlled camshaft grinding machine, in which the camshaft is rotatably arranged in a workpiece holder with a predetermined angular velocity in predetermined angular steps about its longitudinal axis and a grinding slide with a grinding wheel in one Axis perpendicular to the longitudinal axis of the camshaft can be set in predetermined steps, the grinding wheel being selected with regard to its properties depending on the respective initial geometry, the material and the desired surface properties (surface roughness (R _Z ), shape error (f _m )) of the cams .

A method of the type mentioned above is generally known. For example, in DE-Z "Werkstatt und Betrieb", 1985, pages 443 to 448; 1986, pages 655 to 660; 1987, pages 269 to 274 and 1988, pages 201 to 206 described different methods, with which production cam form grinding machines are dependent of various parameters, u. a. also the geometry of the cams as well as the camshaft and the material used become.

Finally, from Yegenoglu's dissertation "calculation of topography parameters for the design of CBN grinding processes ", Faculty of Mechanical Engineering of the Rheinisch-Westfälische Technical University of Aachen, 1986, a mathematical model known to topography characteristics of external cylindrical grinding processes to determine and strategies for process design forward.

In the initially mentioned methods, such as those for Cam shape grinding have been used, attempts have been made certain individual aspects of cam shape grinding through math to record mathematical models and derive process parameters from them lead, but the focus of these efforts was on Shape retention, d. H. the dimensional accuracy of the ground cams, while economic criteria are marginalized at best have been viewed.  

Yegenoglu's work also includes economic ones Considerations have been taken into account, but that relates known model on general external cylindrical grinding and there is no closed system for the found models to implement in a production strategy.

In contrast, the invention is based on the object To further develop methods of the type mentioned at the beginning, that the physical mechanisms of cam shape grinding with tool specifications and process parameters in one closed sphere of activity to be brought under host economic aspects, d. H. with minimal grinding time, with the fullest possible use of the physical Possible to find an optimum.

This object is achieved by the following procedure Steps solved:

• - First determine a theoretical minimum grinding time (t _hmin ) per revolution of the cam from the geometry of the cam and the maximum angular velocity (ω _max ) according to the cut size equation: where ϕ _G , ϕ _F and ϕ _{S are} the circumferential angles in the area of the base circle, the flanks or the tip and ω _{G max} , ω _{F max} and ω _{S max} which, considering the cam geometry (base circle radius (R _G ), tip radius (R _S ), mean flank radius (R _Fm ), survey value (S)) and the grinding wheel data (radius (r _S ), speed (v _S ), speed quotient (q)) are theoretically maximum angular speeds in these areas;
• - then determine a maximum related _{chip removal volume} (Q ′ _wmax , ie machined material _volume per unit of time and per mm grinding wheel _width ) depending on the maximum drive power (P _max ) of the grinding wheel drive according to the cut size equation: where b is the width of the cams and K₁ and K₂ are constants, for which preferably applies: K₁ = 1.754 and K₂ = 2.788;
• - further determine a maximum machined workpiece _volume (V ′ _wmax ) from the minimum grinding time (t _hmin ) and the maximum _{machined volume} (Q ′ _wmax ) according to the formula: V ′ _{w max} = Q ′ _{w max} · t _{h min} ;
• - and finally calculate the maximum, optimized infeed (a _max from the maximum machined workpiece _volume (V ′ _wmax ) and the geometry of the cams according to the formula: where k is a running parameter for the number of flank radii (R _F ) that is specified in a case-by-case manner and runs from 1 to n.

The object on which the invention is based is achieved in this way completely solved. It is the first time that the two of them most critical sizes of the grinding process, namely the maximum possible angular velocity of the so-called C-axis on the one hand and the drive power of the grinding wheel on the other hand, about the special geometry of the machined Cam of the camshaft a maximum related chip removal volume as a critical parameter of the method according to the invention to investigate. This maximum obtained chip removal volume is determined then again the geometry of the cams maximum delivery and in such a way that when setting this Infeed the grinding machine just at the limit of yours possible performance data is operated. About specifying a finite amount of actually available grinding wheels can then ever according to the desired surface quality, d. H. depending on the desired Surface roughness, an associated grinding wheel can be determined, to then run the cam shape grinding process.  

In a preferred further embodiment of the method according to the invention, in which the chip filling degree (f _g ) is also taken into account, the following steps are additionally used:

• - Determine the chip _{filling degree} (f _g ) from the maximum _{drawn chip removal volume} (Q ′ _wmax ) according to the formula: where V _{ES is} the individual chip _volume and V _{SR is} the chip space _volume dependent on the maximum obtained chip _{removal volume} (Q ′ _wmax );
• - Comparing the determined chip filling degree (f _g ) with an allowable limit (K₁₁), for which preferably K₁₁ = 0.75 applies;
• - Reduce the maximum amount of chip _removal , (Q ′ _wmax ) until the determined chip _{filling degree} (f _g ) does not exceed the limit value (K₁₁); and
• - Determine the associated optimized infeed (a _opt ) from the reduced maximum _{obtained chip removal volume} (Q ′ _wmax ).

These measures have the advantage that in addition to that already mentioned limit data of the maximum angular velocity in the C-axis and the performance of the grinding wheel drive the physical process of cutting by cutting the grain of the grinding wheel is taken into account in the way that the chip filling degree, d. H. The relationship of individual chip volume and chip space volume, a certain one Limit should not exceed. Flow here as well physical processes again the topography of the grinding wheel over the chip space between the grains of the grinding wheel on the one hand and the size of the material chips removed.

In a further preferred embodiment of the invention, in which the individual grain force (F _K ) is also taken into account, the following further steps are used:

• - Determine the individual grain force (F _K ) from the maximum _{obtained chip removal volume} (Q ′ _wmax ) according to the formula: where F _{C is} the cutting force, N _{kin is} the area-related kinematic cutting edge number, which is dependent on the maximum _{relative chip removal volume} (Q ′ _wmax ), and A _{K is} the contact area between the grinding wheel and the cam;
• - Comparing the determined single grain force (F _K ) with an allowable limit value (F _Kzul );
• - Reducing the maximum amount of _{chip removal obtained} (Q ′ _wmax ) until the individual grain force (F _K ) does not exceed the limit value (F _Kzul ); and
• - Determine the associated optimized infeed (a _opt ) from the reduced maximum _{obtained chip removal volume} (Q ′ _wmax ).

This measure has the advantage that as a further process parameter the resilience of the grains of the grinding wheel is used, to prevent a premature excessive wear of the grinding wheel occurs. In this case too, it is in the interest of fulfilling this Additional condition is a certain reduction in grinding performance accepted.

In a further preferred embodiment of the fiction According to the method, at least one further boundary condition is used determined time span volume and compared this with the previously determined maximum or reduced maximum related time span volume and the smaller time span volume to determine the optimized delivery used when grinding the cams.

This measure has the advantage that in addition to that already mentioned boundary conditions again via the central process variable, namely the obtained chip removal volume, further boundary conditions be taken into account, which results from empirically determined dependencies. In this case too in other words, in the interest of considering further boundary conditions some reduction in grinding performance, i. H. an increase the processing time to accept additional boundary conditions depending on the expediency.

These additional wheel conditions can be expanded in more ways the method of roughness of cams  and grinding wheel or the shape error of the cams or the Cutting performance of the camshaft grinding machine or the Wear of the grinding wheel or the peripheral zone temperature Cams or the machined workpiece volume.

If all the above boundary conditions are taken into account as limits of the attainable optimum of grinding time, this is how one arrives finally a closed concept for cam form grinding, in which the theoretically possible of the composite from camshaft grinding machine, grinding wheel, conditioning the grinding wheel and workpiece in terms of its geometry and material is reached. Individuals can now selectively Boundary conditions in turn are neglected, then under Accepting certain restrictions is another reduction to achieve the grinding time.

The method according to the invention is particularly suitable for the user-controlled operation of a camshaft grinding machine via an on-screen menu control with graphics dialog, where screen masks in succession to the user of the grinding machine be specified in which the missing values of the can use the respective processing task. The numeric Control of the grinding machine then selects from the fixed default as well as the variably entered parameters the optimal one Grinding wheel from a saved catalog is actually available Grinding wheels and automatically creates the necessary ones Process parameters of the camshaft grinding machine, in particular that is, the movement of the C axis, i.e. H. the axis of rotation of the camshaft and the X axis, i.e. H. the travel path of the grinding slide, a.

It has been shown in practical experiments that the one with the Optimization of grinding achievable according to the inventive method  processes to drastically reduce grinding times leads, so that camshafts in the production process with a significantly increased output can be sanded, whereby at the same time the grinding wheel has an optimally low ver exposed to wear and conditioning of the grinding is optimally integrated into the grinding process.

Further advantages result from the description and the attached drawing.

An embodiment of the invention is in the drawing shown and is described in more detail in the following description explained. It shows

Figure 1 is a side view, extremely schematic and partly in section along the line II of Figure 2, a camshaft grinding machine, as can be used to carry out the method according to the invention.

Fig. 2 is a plan view of the cam form grinding machine shown in Fig. 1;

Figure 3 is a detailed view on a greatly enlarged scale, on a cam in progress to explain various operating parameters.

Fig. 4 is a side view of a camshaft, as it can be processed by the inventive method;

Figure 5 in a very greatly enlarged scale as used in modern grinding wheels a per-perspective view of an octahedral CBN grain.

6 is a partial view in section and a greatly enlarged scale the surface of a CBN grinding wheel.

Fig. 7 is a perspective view for explaining a abgespanten workpiece volume;

FIG. 8 shows a representation similar to FIG. 3, to explain the speeds of the grinding wheel and cam effective in the method according to the invention;

Fig. 9 is a diagram for explaining constraints, as they are in the inventive process taken into into account;

Fig. 01/10 to 12/10, a flow chart for explaining an embodiment of the inventive method.

The aim of the method according to the invention is the bear processing task taking into account the material that Raw and finished part geometry and surface quality in implement a machining concept in which a prediction the tool specification, the conditioning parameters, the  Technology parameters, process flow and processing time can be taken without experimental trials perform. The determined information on form grinding the camshaft are controlling a camshaft grinding machine shown in a form that allows editing of the proposed numerical control program according to DIN 66 025 enables.

The method according to the invention preferably relates to the field of CBN grinding, in which grinding wheels with a Abrasive material made from CBN (cubic boron nitride) crystals be used. It becomes a quantitative connection between the physical processes of CBN cam shape grinding as a closed circuit with the process parameters of the camshaft grinding machine.

To do this, the machining task is first defined. When The workpiece with material, oversize and Geometry specified. The criteria are used as a disturbance variable Vibrations and temperature are given and finally as a starting point the limit criteria, d. H. the formal error and defines the surface quality.

The technology follows from the machining task, both in terms of machining kinematics as well as machining kinetics. The former means the Process variables of the infeed, the cutting volume, the angular velocity, the cutting speed, the contact length and the equivalent grinding wheel diameter as manipulated variables, while under the second one the cutting volume, the cutting force, performance, process time, wear and tear understands dynamic stiffness as process variables.  

The processing task and the technology then become that Tool determined according to design and conditioning. Under the former is understood as the state variables of the specification and the topography, while under the second the core sizes, d. H. the delivery and the speed strategy of the Dressing understands.

The technology and the tool ultimately follow the processing concept, for which the results, namely the cutting value optimization for minimal grinding time and the control variables for the NC program according to the raw / finished part description, Manufacturing data, processing sequence, conditioning strategy and execution instructions are issued.

In summary, this means that with the invention First process the workpiece data (material, oversize and geometry) as input variables and the limit criteria (Shape error of the cam contour, surface quality, thermal Edge zone influence) can be specified as output variables, to determine the machining strategy from it. As a result of Relationships between machining kinematics as manipulated variables with the numerical consideration of the design of a grinding disc topography and processing kinetics as process variables a machining concept is defined so that a minimal Grinding time is made possible with optimal cutting values determine the NC program as the control variable as the result variables. It is an essential part of the proposed method the specification of the physical mechanism of action of the Processing process with an analytical view of the Cutting movement when grinding and the interaction of the Individual components at the cutting point.  

The method according to the invention is preferred as a graphic dialog on the camshaft grinding machine in one for the user of the Grinder illustrated in an easy-to-use manner. So can one first advantageously a group of materials specify because experience has shown that the camshafts to be ground consist only of a finite number of materials. Of the Users of the grinding machine therefore only need one To specify a certain standardized material. The geometry parameters of the cam contour are determined using multiple derivation after the time kinetodynamically analyzed and represented as process parameters, as is known per se is.

Also the toolpaths in the X axis and the perpendicular one Z axis are graphically represented and can be viewed by the user the grinding machine depending on the application.

When considering the machining kinematics, it is assumed that the grinding wheel with its peripheral cutting edges moved relative to the workpiece on an orthohypocycloid, the Path from the superposition of the peripheral speed of the Grinding wheel and the workpiece speed results. The successive othohypocycloids run during the Surface creation in the contact area for material removal, the size of the infeed, the cutting volume, the Contact length and the equivalent grinding wheel diameter is determined.

The specified roughness depth of the cam contour to be machined defines the grain size and thus the concentration of the CBN Grinding wheel.  

In summary, the theoretical is now expressed first Grain protrusion derived and then by means of the grain spacing determines the chip space volume. Here it is assumed that the CBN grain in the grinding wheel bond by cylindrical Binding webs are bound, which the grain with a stiffness depending on the modulus of elasticity (2-10 × 10⁴ N / mm²), bending strength (25-150 N / mm²) and compressive strength (100- 1000 N / mm²) anchored in the binding. It is important here that preferably ceramic in the context of the present method Binding of CBN grains can be used.

With the grain distribution model on which this is based assumed that the grains cut in a statistical distribution in a square arrangement on concentric levels lie. This gives the possibility to use the surfaces related kinematic number of cutting edges, the grain density, the Single chip volume, the grain load, as well as the chip space filling degree of computation to then calculate the characteristic Characteristics of grinding wheel topography with machining to coordinate kinetics. Using the calculated tool data a CBN grinding wheel with its name from the tool file recommended.

The conditioning parameters are based on the theoretical Grain wear and the theoretical stock removal ratio determined.

Overall, an optimization strategy is pursued with the aim of a minimum grinding time while observing certain Achieve secondary conditions and thus the cutting data exactly to describe.  

Finally, the determined values for the user of the cam shape grinding machine by means of a Log shown.

Before the special peculiarities of an embodiment of the method according to the invention should be described first briefly explains the underlying physical model become. Supplementary to the already mentioned dissertation by Yegenoglu to refer to the further explanations about the physical processes involved in CBN grinding.

The parameters of a multi-stage grinding process, which determine the machine setting for cam shape grinding in the plunge process as a control variable, are the cutting speed v _C , the workpiece angular velocity ω _W and the infeed per workpiece revolution a.

The cutting speed v _C can be regarded as a constant parameter which is determined in a multi-stage process in accordance with the respective grinding task. The cutting speed corresponds in the first approximation to the peripheral speed of the grinding wheel. The cutting speed v _C can be calculated from the relationship using the cosine theorem:

Where

v _w = 2 π r _in / 60 000 (m / s) (2)

With

n = ω _w / 360 (min ^-1 ) (3)

is determine. Values of v _C = 60-140 m / s are common practice. Compared to the cutting speed v _C , the workpiece circumferential speed v _W is smaller by at least two powers of ten and the speed ratio is given by the equation

q = v _c / v _w (4)

given. The length of the engagement arc results from the curvatures of the grinding wheel and workpiece as well as from the radial feed. The radial feed corresponds to the infeed amount of the grinding wheel per workpiece revolution. The geometric length l _g over which each cutting edge is in engagement with the workpiece is calculated

With

The contact lengths for cam shape grinding are usually between l _g = 0.1-5 mm. Larger values result in particular on the cam flank.

The cutting volume is due to the cam geometry and the Infeed given per workpiece revolution:

Where b is the cam width, ϕ _G the base circle angle, R _G the base circle radius, ϕ _F the flank angle, R _K the flank radius for an interval, ϕ _S the tip angle and R _S the tip radius. The grinding time per cam revolution can be calculated using the equation

t _h = (φ _G x 60) / ω _G + 2 (φ _F × 60) / ω _F + (φ _S x 60) / ω _S (8)

to calculate.

The following applies to the machining kinetics:

If the grinding allowance is specified, it depends on roughing to remove as much material as possible in the shortest possible time, without fear of thermal damage to the peripheral zone.

The chip removal volume can consist of the cutting volume and the grinding time per cam revolution:

Relative to a grinding wheel width of 1 mm:  

Usual related chip removal volumes are in the range of Q ′ _w = 0.1-5 mm³ / mms for finishing. Surface roughness R _z = 0.5 µm to 4 µm can be achieved. Extremely high chip removal volumes Q _w ′ = 85-110 mm³ / mms can be made possible during roughing. These values depend on the material, the grain size, the concentration and the cutting edge load.

The cutting performance can be calculated from the chip removal volume Q _w . The equation is:

P _c = kQ _w ⁿ (11)

Here k means a constant and n an exponential Coefficient representing the respective workpiece-related ratio between chip formation and friction energy taken into account.

A comparison of the constant k and the exponent n for the same class of materials, namely chilled cast iron, pearlitic ferrous cast iron and malleable cast iron, shows that the type of Conditioning the grinding tool a distinction in their sizes:

This applies to synchronous conditioning without sharpening k = 1.903 and n = 0.384, with synchronous conditioning with sharpnesses k = 1.824 and n = 0.384, while with one counter running conditioning without sharpening k = 1.869 and n = 0.36 as well in the case of countercurrent conditioning with sharpening k = 1.754 and n = 0.36.  

The cause of this phenomenon is the chip space formation as well as in the generation of the cutting geometry.

The specific cutting energy

can be done in a similar manner depending on the amount of chip removal represent.

The cutting force at a constant chip removal rate is through the equation

given. With constant cutting performance and increasing cutting speed decreases the cutting force degressively. This Ultimately, this is related to reducing the span cut back.

The cutting force is determined as the sum of the individual forces currently acting on the cutting edges in the cut. The individual force components of a collective of cutting edges of a grinding wheel for external plunge grinding are the cutting tangential force F _ct and the cutting normal force F _cn .

The cutting force F _c can then be described by the relationship

The normal cut force F _cn can be found in the relationship

determine, with the proportionality factor µ the cut represents power ratio

Since µ from the chip formation mechanisms on the grain edges is determined, the cutting force ratio mainly corresponds Lich the shape of the edge of the kinematic number of edges, the Stress cross section, the grain material, the workpiece material as well as the coolant conditions.

With CBN discs, a cutting ratio of µ = 0.36 to 0.45 is assumed and there is a loading angle of the cutting edge α _b = arctan µ = 19.8 ° to 24.2 °.

The greater the ratio of tangential force to normal force is, the lower are those running in the contact zone Rubbing, shearing and cutting processes, resulting in a sharp cut indicates the state with coordinated chip spaces. With careful Coordination of the grinding wheel specification and the conditioning on the grinding process it is possible the topography the grinding tool so that only very small Deviations in the initial cutting force ratio before stationary area occur.

The following applies to the tool:  

In order to interpret the specification, the roughness must first be closed take into account that for the respective grinding task in is generally prescribed. However, the roughness is once from the specification of the CBN grinding tool and on the other depending on the intervention conditions. According to the procedure becomes the specification of the CBN grinding tool according to grain size and concentration selected, so that among those still to be explained kinematic and kinetic conditions the roughness requirement can be met. The specification of the Grinding tool determines the initial effective roughness; for small ones Grain sizes and increasing concentration decrease the initial effective roughness. A large grain and decreasing concentration increases the initial effective roughness.

For CBN grinding wheels available today, for example specify the following table of corresponding parameters:

The grain size and the concentration of a CBN grinding wheel gives the surface quality of the grinding tool, so that between the peripheral CBN grains for the resulting Chips sufficient space is available.

The type and hardness of the binding influences the Grinding wheel topography and on the breaking out of the CBN Grains from the bond (ceramic). With a harder bond the CBN crystals remain in the bond longer, so that in the first Line a dulling of the cutting takes place in the grinding process.  

This not only changes the grain shape, but also that Number of cutting edges.

The type of bond in a grinding wheel specification is dependent on the grain density C _K , which is selected as the grain size to describe the number of grains per mm³ volume of grinding surface. the equation

with the value of q = 1.41 _m for an octahedron represents the dependence on the mean particle diameter and concentration. ³ W _m is the theoretical volume of an octahedron.

To look at the grinding wheel topography, these are area-related kinematic number of cutting edges, the machining volume per cutting edge, the chip space volume and the chip space filling degree to consider. This creates the opportunity a theoretical coordination between analytical parameters the volumes of the cutting process on the one hand by means of the Technology parameters and the tool on the other hand Perform topography with a defined specification. At the same time, workpiece wear is examined, but not only by changing the grain geometry, but also by the Breaking out the grains at high grain load and not coordinated Strength of the binding material arises.

For the area-related kinematic number of cutting edges, based on the dissertation of Yegenoglou, chapter 6.2, pages 51 to 61 and chapter 6.33, Page 60, describe the following context:

where K is the volume-related concentration, W _{m is} the mean mesh size for the grains, ie 1.42 times the grain diameter d _k for an octahedron and finally q is the speed ratio, as already shown above. The area-related kinematic number of cutting edges has the dimension mm ^-2 . The term "area-related kinematic number of cutting edges" is also explained in the DE book by König, W. "Manufacturing Processes, Volume 2 - Grinding, Honing, Lapping", VDI-Verlag, Düsseldorf.

The individual chip volume can be dependent on the cut conditions and the grinding wheel specification by the equation

determine. The single chip volume receives the dimension µm³ if you choose the exponents with m₁ = 0.598, n₁ = 0.201 and p₁ = 0.798 and use W _m in µm, Q _w in mm³ / mms, d _eq in mm and v _c in m / s .

To determine the chip space volume, the theoretical mean grain protrusion and the grain spacing be determined. The theoretical average grain protrusion between the peripheral grain tips and the binding material is through the equation

given, the exponents with m₂ = 0.05, y = 0.25, n₂ = 0.1 and p₂ = 0.4 can be specified.

The mean grain protrusion is then simplified by the relationship

Zr = 0.62 Z _th (µm) (21)

certainly.

The grain spacing can then be determined by the equation

to calculate.

The chip space volume then results from the following relationship

V _SR = (l _k - Z _r · 1.41) · Z _r ² (μm³) (23)

The ratio between the individual chip volume and the associated one Chip space volume is called the so-called chip space filling degree Are defined

The degree of chip filling depends largely on the type to be machined the material if you assume that the specification as well as the topography the requirements of the cutting conditions is adjusted. Depending on the material and material condition the chips different shapes. In the real grinding process the chips require a larger chip space volume than you own volume. From this it can be deduced that the chip space degree of filling a certain limit, for example 0.75 must not exceed if the grinding is overloaded to be avoided.

In this regard, radial grain wear is permitted that by means of the equation

r _s = (0.75 - f _g) .DELTA.b _s · Z _r (microns) (25)

is calculated, where Δb _s = 1.42 corresponds to the grain coverage factor.

The stability of the grinding tool is when plunging grinding of great importance. Exceeds radial wear a certain permissible dimension, the required form can only can be generated again by conditioning (dressing). The Conditioning interval is often used to assess grinding process. It is called the ratio of worn work volume of material for radial grinding wheel wear due to the so-called grinding ratio specified or referred to as the stock removal ratio G. The one for calculating the Stock removal necessary total wear of the grinding disk obeys the relationship:

V _vs = π · d _s r _s · b · 10 ^-3 (cc) (26)

The machined volume of material within one conditioning intervals can be calculated using the equation

V _WG = V _w · N _w · T _s (cm³) (27)

calculate, where V _{w is} the machining volume per workpiece, N _{w is} the number of machined workpieces per hour and T _{s is} the stand interval between two conditions.

With this, the transfer ratio becomes too

As a result of the grain dulling, the individual grain force F _K increases due to increased friction. On the other hand, the bond to the grain base is more strongly eroded at higher cutting capacities, which in turn leads to a decrease in the grain breaking force F _Kmax .

The load on the individual grain is determined by the number of Cutting determined on which the cutting force due to Grinding wheel specification and the process parameters distributed.

The individual grain force is calculated

in which

A _K = l _g · b (mm²) (30)

the contact area is.

The effective cutting edge spacing l _K and the engagement length are dependent on the infeed and the cutting speed in addition to other influencing variables. The effect of the change in the kinematic quantities v _s and v _w on the chip thickness a _n is determined by the relationship

shown.

If you increase the grinding wheel peripheral speed with constant intervention sizes, there are decreasing Chip thickness. Because fewer cutting edges are engaged, however, the total cutting force drops. By shortening it the contact time between abrasive grain and workpiece at one high thermal conductivity of the grain can the Kon cycle zone temperatures can be reduced. So is the thermal Conductivity of CBN grain, for example, 700 W / m ° C and is much higher than that of conventional aluminum oxide.

Conditioning is another process parameter Note grinding wheel.

As is well known, grinding wheels lose both due to wear their original starting profile as well as their cutting ability. There is a change in the grinding wheel topography as a function of grinding time. The task of conditioning  is to put the topography of the sanding back into the Bring original form. Coming as conditioning tools Diamond form rollers or sharpening rods are used.

The conditioning parameters regarding the rotating diamond The mold sizes are: profile shape, specification (grain density, Settlement scheme) as well as the setting variables: infeed per conditioning process, peripheral speed of the roll, axial side feed and speed quotient.

You define the degree of coverage with

V _d = a _pd / f _ad (32)

as the quotient of the effective width of the roller profile and side feed of the roller per grinding wheel revolution, these values for V _d lie between 1 and 6, so that the theoretical axial ripple

is minimal.

The speed quotient

results from the peripheral speed of the diamond roller v _R and the grinding wheel v _S. Changing directions of rotation of the roller (co-rotation and counter-rotation), the speed quotient and the axial side feed influence the initial effective roughness.

Having the underlying physical processes have been explained in a summarized representation, should now Embodiment of the invention are explained in detail in the process based on the processes described above cutting value optimization is carried out. This cutting value optimization has as its goal the theoretically derived Relationships between the processing technology, the tool and the work result against determined dependencies transfer, taking into account the performance limit the machine tool and the grinding tool. It should be from it for any infeed workpiece speed combinations optimal chip removal volumes are calculated to a minimum Allow grinding time.

In Figs. 1 and 2 in an extremely schematic way a numerically controlled cam shaft grinding is shown which is in total designated with the reference numeral 10.

In a workpiece holder 11 , a camshaft 12 is clamped. The camshaft 12 is rotatable by means of the rotating workpiece holder 11 about its longitudinal axis 13 , the so-called C axis, in defined angular steps, as indicated by an arrow 14 . The angular velocity of the workpiece holder 11 is identified by ω. As a result of the actually existing drives, with the required precision of the angle of rotation adjustment of the C-axis 13, only a certain maximum angular velocity ω _{max is} possible, which can vary in regions over the cam contour, as will be shown below.

A grinding carriage 17 carries a grinding wheel 18 which can be driven by means of a drive motor 19 . The power of the drive motor 19 is denoted by P.

The grinding carriage 17 with grinding wheel 18 can be advanced along an axis 20 , the so-called X axis perpendicular to the C axis 13 of the camshaft 12, in defined X steps.

As shown in FIG. 2 in dashed lines, the grinding wheel 18 can be moved toward the camshaft 12 for machining the surface of the camshaft 12 in this way.

The grinding wheel 18 rotates about its axis 21 , which coincides with the so-called Z axis. The grinding slide 17 or the workpiece holder 11 are namely additionally displaceable in the direction of the Z-axis 21 so that the grinding wheel 18 can process the individual cams of the camshaft 12 in succession.

It is understood that the above illustration is only an example is to be understood and the invention is not thereby is restricted. So is the invention of course can be used in grinding machines where the axis the grinding wheel is inclined to the workpiece axis and the Instead of a cylindrical grinding wheel, a conical grinding surface has and the like. More.

In the cam form grinding machine 10 according to FIGS . 1 and 2, an NC control device 25 is provided, to which input parameters 26 can be supplied. From this, the NC control unit 25 derives control signals which are fed to the drive of the workpiece holder 11 and the drive of the grinding carriage 17 via data lines 27 and 28 . A distinction is made here between the so-called "delivery operation" and the so-called "rail operation". In the infeed mode, the grinding wheel 18 is advanced along the X axis 20 to the camshaft 12 in order to achieve a certain material removal during grinding. In rail operation, however, the grinding wheel 18 is adjusted along the X-axis 20 depending on the respective rotational position of the camshaft 12 about the C-axis 13 so that the point of engagement or the line of engagement on the grinding surface of the grinding wheel 18 is always at a desired point Cam contour of the camshaft 12 is present. By superimposing the infeed mode and the track mode, the cams of the camshaft 12 can be ground along a spiral grinding path that begins on the raw surface of the unprocessed cam and ends on the contour of the finished surface of the cam. These processes are known per se and are therefore not to be explained again here.

Fig. 3 shows a cam 30 of the camshaft 12 with further details.

The cam 30 has a so-called base circle 31 , a tip 32 and side flanks 33 .

In a first point 34 , the grinding wheel 18 engages with a surface line on the surface of the cam 30 . In second points 35 , the base circle 31 merges into the flanks 33 . The second points 35 thus define the so-called base circle angle ϕ _G. The radius of the base circle is designated R _G.

Third points 36 mark the transition from the flanks 33 to the tip 32 . You thus define the so-called flank angle ϕ _F and the tip angle ϕ _S. The radius of the tip is labeled R _S.

A fourth point 37 denotes any point, for example on the tip 32 , at which a tangent 38 is placed on the cam contour. If a parallel tangent 39 is drawn to the base circle 31 in relation to the tangent 38 , the distance between the parallel tangents 38, 39 gives the so-called survey value E.

A fifth point 40 and a sixth point 41 denote any points on the contour of the cam 30 , shown using the example of two points on the flank 33 . The radii of curvature of points 40, 41 are denoted by R _{F i} and R _Fn . This is to say that the radius of curvature varies with R _Fi or R _Fn in the area of the flanks 33 , ie over the flank angle ϕ _F , while the radius of curvature with R _G in the area of the base circle 31 over the base circle angle ϕ _{G is} as constant as with R _S over the tip 32 or the tip angle ϕ _S.

Various forms of tables can be set up to analytically define the cam contour. The contour of the cam 30 can thus be represented, for example, as a table of polar coordinates, but forms of representation are also common in which a so-called survey value table is specified, which represents the survey value E over an angle R.

In both cases, the table specified in each case is converted into control commands for the angle of rotation of the C-axis 13 and the drive unit for the X-axis 20 of the grinding carriage 17 in order to determine the rail operation, taking into account the grinding wheel diameter.

In FIG. 3, the oversize by which the raw contour shown in solid line in FIG. 3 is to be removed in order to obtain the finished contour shown in dashed lines is also designated by a.

Finally, FIG. 3 shows in a section 42 with a greatly enlarged representation the roughness depth R _Z which is to be generated on the surface of the cam 30 by grinding. In addition, the material used is symbolized in section 42 with W.

The material symbolized with W is not continuous variable size. For the practical applications of the erfin Rather, the inventive method can be a limited number of materials, as they are usually used as camshaft materials be used. Above all, this includes the Chilled cast iron, malleable cast iron, pearlitic cast and it is also take into account whether these materials are case hardened or are induction hardened. This finite number of options can in practice be determined by a finite number of Symbolize symbols used by the user of the invention Procedure can be selected.

Fig. 4 shows a camshaft 12 as it can be processed with the method according to the Invention. In the general illustration in FIG. 4, the camshaft 12 has n cams 30/1, 30/2. . . 30 / n on. Typically, camshafts 12 with a total of 8 cams can be ground according to the method according to the invention.

At the beginning of the grinding process, the grinding wheel 18 is set in the Z-axis so that it faces the first cam 30/1 . The distance of the grinding wheel 18 from the first cam 30/1 in the X axis 20 is an initial value X _A. This value must be specified for the method according to the invention so that the cam shape grinding machine can travel through this initial infeed path at the beginning of the method before the grinding wheel 18 comes into contact with the first cam 30/1 .

Furthermore, the above-mentioned initial adjustment of the grinding wheel 18 along the Z axis 21 must be specified, which is characterized by the initial dimension Z _A.

In the subsequent processing of several cams 30/1, 30/2 . . . must then the so-called cam jump Z _s , ie the distance between the cams 30/1, 30/2 . . . be specified in the Z axis 21 . Finally, after machining the last cam 30 / n, the grinding wheel 18 has reached its axial end position Z _E , which is also to be specified.

The cam width must also be used to determine the process parameters b can be entered.

In order to illustrate the grinding wheel parameters, a CBN grain 50 , ie a crystal of cubic boron nitride, is shown in FIG. 5, which ideally has the shape of an octahedron. The diameter of the CBN grain 50 is denoted by d _K and its volume by V _K.

As FIG. 6 shows, several of these grains 50 , namely grains 50/1, 50/2 , are in a real grinding wheel 18 . . . 50 / n embedded in a ceramic bond 55 . The concentration of the grains 50 is denoted by K.

The distance between two grains 50/1 and 50/2 is 1 _K and the theoretical grain projection is Z _{r on} average. The chip space volume V _SR between two grains 50/1, 50/2 can be determined from this.

Finally, with F _K , the effective grain force is shown in FIG. 6, which occurs during grinding on the grains 50/1 . . . acts.

Fig. 7 shows a perspective view of the illustration, a volume 60 , as is machined on a cam when an infeed a is set at a cam width b. As can be easily seen from FIG. 7, the volume V _w results as the product of oversize a, width b and circumference of the cam, as will be explained below with reference to FIG. 9.

Fig. 8 shows the relationships at the effective speeds during the cam shape grinding.

As indicated by arrows 62, 63 , the cam 30 and the grinding wheel 18 rotate in opposite directions. At the point of engagement 34 , the workpiece speed v _W and the grinding wheel speed v _S , each represented as peripheral speeds, are effective. The directions of the speed vectors v _W and v _S result from the respective radii R _{S of} the grinding wheel 18 and R _{n of} the cam 30 , as has already been explained above for FIG. 3 for the cam 30 .

The cutting speed v _C results from the geometric addition of the vectors v _W and v _S and can be calculated in terms of the amount with the aid of the cosine theorem.

Fig. 9 finally shows a diagram in which the grinding time t _h for a cam is plotted against the related chip removal volume Q ' _W.

As is known, the grinding time t _{h is} equal to the quotient of the machined workpiece volume V _w (see FIG. 7) and the related chip removal volume Q _w '. The circumference of the cam 30 is calculated as the sum of the products of circumferential angles ϕ and radii R, as in FIG. 9 with the relationship

is specified. Since the cam width b is constant, the machined volume V _w therefore only depends on the variable oversize a. The relationship between grinding time t _h and related chip removal volume Q _w 'is thus expressed in a hyperbolic curve, which is parameterized according to a, as shown in Fig. 9 for two examples a₁ and a₂.

However, it is 'not free because the adjustable relative metal removal rate Q _w' in the choice of the specific removal rate Q _w is limited by various process parameters.

These additional conditions can be met without any claim for complete naming - based on empirically obtained Functions explained as follows:

A first boundary condition is the achievable roughness depth R _{t of} the workpiece and R _{t0 of} the grinding wheel 18 . With these two variables as well as the concentration K of the grinding wheel 18 and the cutting speed v _c , a first relationship for a limit value of the related chip removal volume Q _w 'can be represented as follows

The second boundary condition is the shape error f _{m of} the cam, which is known to be the quotient of cutting force F _c and system rigidity C _g . Then, taking the cam width b into account, the following relationship results:

With

As a third boundary condition, the grain wear r _s depending on the chip filling degree f _g and the grain coverage factor Δb _s can be specified as follows:

where Z is an auxiliary variable and the relationship

obey.  

The fourth boundary condition can be given as the difference between the temperature T _M at the cutting point and the room temperature T _R. The relationship is:

where c is the specific heat, ρ is the density of the material and K * the conversion factor between heat and energy units is.

As a further boundary condition, taking into account a drive power P of the motor 19 of, for example, 22 kW and taking into account maximum angular velocities ω _max of 10,000 ° C./min in the survey area and 30,000 ° C./min on the base circle, the relationships

depending on the cam width b as well as the relationship

Q ′ _w6 = 0.694 · V _w ′ (43)

depending on the machined workpiece volume V ′ _w .

A range of the permissible values is shown hatched in the illustration in FIG. 9, with straight lines 65/1. . . 65 / n represent the boundary conditions Q _w ′ explained above and their intersections 66/1. . . 66 / n lie on a straight line with the a-hyperbolas.

Depending on which and how many of the above-mentioned boundary conditions are to be taken into account, the limiting boundary condition in each case is the one with the lowest related chip removal volume Q _w ′, in order to then determine the infeed a as a minimum but optimal value, which is then at the minimum grinding time t _hmin leads.

The control provided for carrying out the method according to the invention will now be explained on the basis of the flow diagram of FIGS . 10/1 to 10/12.

In a first block 70 , a determination program is started by first entering the input data either individually in block 71 or calling it up from machine-specific files.

The maximum power P _{max of} the drive motor 19 of the grinding wheel 18 of, for example, 22 kW is called up as grinding machine data. Next, the maximum Winkelge speeds of the workpiece holder 11 of the C-axis 13 are called up, which can be between 10,000 and 30,000 ° / min. Finally, the rigidity C _{g of} the machine has to be taken into account.

Material W is first called up as cam data using the table of typical camshaft materials already mentioned. Furthermore, the overall oversize A and the number of cams n of the camshaft 12 are specified. With regard to the cam contour, the base circle radius R _G and the contour itself are to be specified, for example in the form of the data collection table E _(R) already mentioned. The cam width b is to be entered, as is the adjustment path X _{A of} the grinding wheel 18 in the direction of the X axis 20 and the starting position Z _{A of} the grinding wheel 18 in the direction of the Z axis 21, as well as the end position Z _E in this axis 21 and the cam jump Z _S .

The roughness depth R _Z and the shape error f _{m are} specified as cam specifications. With regard to the thermal boundary zone influence, symbolized by ϑ _RZ , the user can make a yes / no decision with Y / N, with the effect that the further determination of the parameters is carried out either with or without taking into account the thermal boundary zone phenomenon.

The grinding wheel data are also specified in tabular form for a finite number of CBN grinding wheels available in practice. The grinding wheel diameter d _S as well as the grain size d _K and the concentration K can be specified for each of these grinding wheels in the known manner. A polyhedron constant q _m , which in the case of an octahedron is 1.4, is also given, as is the theoretical polyhedron nerve volume W _m , which can also be tabulated according to the type of polyhedron provided that different polyhedra are provided for different grinding wheel coverings.

Furthermore, the grain coverage factor Δb _s , the permissible maximum grain force F _Kzul for the grinding wheel and, as conditioning parameters, the dressing setting a _d and the speeds of the dressing roller v _fd , v _{fd ′} in the opposite direction are to be specified.

The grinding wheel circumferential speed v _S , the number of workpieces to be machined per hour N _w and finally the conditioning interval of the grinding wheel T _{s are} to be specified as constant processing parameters.

Finally, in the course of the method according to the invention Numerous constants are required, most of which are empirical won and can therefore fluctuate within certain limits. In the following explanation of the invention These constants are used as concrete numbers values specified, however, it is understood that these numerical values for the reasons mentioned, they are also subject to certain fluctuations can.

From the input variables specified in block 71 , the cam geometry is first calculated in block 72 according to further characteristic values. The workpiece diameter d _W , the flank radius R _F in the form of a table, the tip radius R _S , the maximum elevation value E _max and the base circle angle ϕ _G , the flank angle ϕ _F and the tip angle ϕ _{S are} determined.

Depending on the survey table and the maximum angular velocity of the C axis 13 , the cam circumferential speed v _W is now calculated in block 73 .

In block 74 , the cutting speed v _{C of} the grinding wheel 18 is determined by means of the vectorial addition from the circumferential cam speed v _W and the grinding wheel speed v _S.

In block 75 , the values R _G , R _F , R _S , E _max , ϕ _G , ϕ _F , ϕ _S , b, X _A , Z _A , Z _E and Z _{S are} output in the menu already mentioned at the beginning -Technology in the form of a graphic dialog with the user of the method according to the invention. For this purpose, the camshaft can be represented in two side views in a mask, the values listed in block 75 being illustrated graphically.

Parallel to the output in block 75 , the ratio of cutting speed v _C and workpiece speed v _{W is} calculated as a quotient q in block 76 .

In block 77 , an effective diameter d _eq is determined as an auxiliary variable from the diameters of the workpiece d _W and grinding wheel d _S.

In block 78 , the cutting force F _{C is} determined using an empirical formula from the maximum power P _{max of} the drive motor 19 .

With the help of the relationship already specified and explained in FIG. 9, the theoretically minimum grinding time t _h min is now determined in block 79 from the cam geometry and the achievable angular velocities ω.

From this, in block 80, as the central variable of the method _according to the invention, the maximum related _{chip removal volume} Q ′ _{wmax is determined} using an empirically obtained formula from the maximum power P _{max of} the drive motor 19 of the grinding wheel 18 .

The maximum machined workpiece _volume V ′ _Wmax can be determined from the two values of blocks 79 and 80 thus obtained (block 81 ).

With the help of the complete relationship shown in FIG. 9 and explained, a maximum infeed a _{max of} the grinding wheel 18 is now determined in block 82 as an output variable for the method according to the invention.

This maximum infeed a _max should now be checked in the further procedure to determine whether it is permissible in relation to various restrictions of the system used.

In order to accomplish this, the maximum reference time span _volume Q ′ _{wi is again} specified as the maximum value Q ′ _wmax in a block 83 as the central calculation variable.

As indicated at 84 , this maximum output value Q ′ _{wmax can} still be decremented in the following method by various loop passes, as will be explained in more detail below.

In the first process loop, a specific type of grinding wheel is selected in block 85 from the predetermined roughness depth R _Z for the finished cam surface by means of the grinding wheel table, with which said roughness depth R _Z can be achieved. As a result, the grain size B and the concentration K and thus also the grain diameter d _{K are} fixed. The determined type of grinding wheel is output in block 86 and in turn is shown in the graphics dialog of the menu control.

The rest of the procedure is now based on the equations (1) to (42) explained in detail above. These equations are referred to below.  

In block 87 , the grain density C _{K is} calculated using equation (17).

In block 88 , the area-related kinematic cutting edge number N _{kin is determined} using equation (18).

In block 89 , the individual chip volume V _{ES is} calculated using equation (19).

In block 90 , the theoretical grain protrusion Z _{th is} determined therefrom using equation (20).

With the help of equation (21) the real grain protrusion Z _r follows in block 91 , with the help of equation (22) the block distance l _K follows in block 92 and finally with the help of equation (23) in block 93 the chip volume V _SR .

With the help of equation (24), the chip filling degree f _g can finally be determined in block 94 .

In decision block 95 , it is now checked whether the chip space fill level f _{g is} less than or equal to a predetermined limit value of, for example, 0.75. If this is not the case, i.e. if the chip space volume V _{SR is} not large enough to accommodate the individual chips with their individual chip volume V _ES , the output variable of this process loop, namely the related chip removal volume Q ′ _{wi, is} decremented via a block 96 , namely by a predetermined amount Δ Q ' _w . With this decremented value, the method returns to the already explained point 84 behind block 83 in order to carry out the above-described method steps until the obtained chip removal volume Q ' _{wi has been} decremented to _{such an} extent that the chip filling degree is sufficiently dimensioned.

As soon as this is the case, the method continues its steps and calculates the grain wear factor r _s in block 97 using equation (25).

With the help of equation (26) the total wear V _VS is then calculated in block 98 and with the aid of equation (27) the machined material volume V _{WG is} determined in block 99 .

This results in block 100 with the help of equation (28) and in block 101 with the help of equation (5) the contact length l _g .

In block 102 , the contact area A _K is calculated using equation (30) and in block 103 , using the equation (29), the individual grain force F _{K is} finally calculated.

In decision block 104 , it is now checked whether the individual grain force F _{K is} less than or equal to an allowable single grain force F _Kzul . If this is not the case, that is, in other words, the load of the individual grain is too high, the central process variable, namely the relative metal removal rate Q is in turn _'wi by the amount Δ Q' _wi decremented in block 105, wherein the Dekrementierungsbetrag Δ Q _wi can be the same as that of block 96 or differently sized. In this case too, the program returns to point 84 via the loop in order to continue calculating with the decremented value for Q ′ _wi until the individual grain force F _K has dropped to the permissible value F _kzul .

It should be inserted at this point that the two process loops explained above are to be understood as options by which the process can be operated. Thus, as already mentioned, it is entirely possible to abort the method described above with block 85 and to proceed using the grinding wheel determined there, but then neither the chip space filling ratios nor the individual grain load ratios are taken into account. If, on the other hand, the method is continued, the chip filling ratios up to block 95 are first taken into account, upon reaching which the method according to the invention can alternatively be terminated. The determined chip removal volume Q _{w '} determined at the yes output of block 95 can then be converted with the aid of blocks 81 and 82 into a maximum infeed a _{max of} the grinding wheel 18 , which is then of course smaller than the amount when the invention was first run through Procedure at the output of block 82 was determined.

If you now grind the camshaft 12 with the grinding wheel 18 while setting the uniquely reduced infeed a, the restriction specified in block 80 is, on the one hand, the maximum power P _{max of} the drive motor 19 of the grinding wheel 18 as well as the restriction with regard to the chip space filling ratios of the Blocks 94 met.

If, on the other hand, the method according to the invention is also run through the second loop up to block 104 and, based on the twice-decremented reference chip volume Q _w 'present at the output of block 104, an oversize a reduced accordingly twice, its specification leads to the real one Grinding a camshaft 12 to a grinding process, which also takes into account the restriction of the individual grain load.

It goes without saying that with increasing consideration of restrictions and thus progressive reduction of the related chip removal volume Q _w ′ and the infeed a, an increase in the grinding times t _{h also} occurs.

Corresponding considerations apply to those below specified restrictions, either individually or in any combinations can also be taken into account.

In block 106 , the roughness depth is used as a restriction criterion with the aid of equation (36) and a value of the related _{chip removal volume} Q ′ _{wl is} calculated therefrom. In decision block 107 , it is now checked whether the value Q _wl ′ determined in this way is greater than or equal to the process value Q ′ _wi currently applied, which was determined after the procedure had been carried out up to block 83 and possibly up to block 95 and / or block 104 .

If the result is that the newly determined value Q _wl 'is smaller, this new value Q _wl ' must be _specified via block 108 as a new process _parameter for Q _wi 'if the roughness depth is to be taken into account as a restriction _criterion .

However, if the newly determined value Q _wl 'is greater than the currently pending value Q _wi ', the restriction criterion of the roughness depth can be ignored because its effects lie within the range of the process parameters already taken into account.

To take into account the next restriction criterion of the shape error f _m , this must first be calculated in block 109 using equation (38). The next restriction criterion is then set in block 110 with the aid of equation (37) and a decision is again made via blocks 111, 112 , as was explained previously for blocks 107, 108 .

In block 113 , the next restriction criterion, tool wear r _s , is taken into account with the aid of equation (39), and a decision is again made via blocks 114, 115 .

In block 116 , the temperature T _{M is} taken into account as the next restriction _criterion with the aid of equation (41) and the corresponding decision is made in blocks 117, 118 .

Block 119 determines the next restriction criterion with the aid of equation (42), the machine data with subsequent decision in blocks 120, 121 and in a corresponding manner block 122 calculates a further restriction criterion using equation (43) on the basis of machine data with subsequent decision in the Blocks 123 and 124 .

In the following block 125 , the grinding wheel specific values d _S , W _m , K, d _K , Z _th , l _g and V _SR are now displayed in the graphic dialog of the menu navigation for the grinding wheel design.

The same applies in block 126 to the output of grinding wheel conditioning values, where, for example, the values a _d , v _fd , v ′ _fd , q, r _s , T _s , G, N _kin , V _ES , f _G and F _K in the Graphic dialog can be displayed.

Finally, in block 127 , the selected material W and, for the grinding wheel type, the values v _C , ω, V _WG , Q ′ _wimax and t _h or taking into account the travel _{paths of} the grinding wheel in the Z and X directions (without machining) the total grinding time.

The determination is then sent out to be taken into account process parameters in block 128 and it will now be transferred 27 and 28 to now the cam 30 of the camshaft 12, the determined values as operating parameters for the cam contour grinding machine 10 in the NC control unit 25 and the output interface of the data lines in to grind the determined shape.

Claims (8)

1. Method for optimizing the infeed (a) when grinding cams ( 30 ) of a camshaft ( 12 ) by means of a numerically controlled camshaft grinding machine ( 10 ), in which the camshaft ( 12 ) in a workpiece holder ( 11 ) with a predetermined angular velocity curve in predetermined angular steps (R) is arranged so as to be rotatable about its longitudinal axis ( 13 ) and a grinding carriage ( 17 ) with a grinding wheel ( 18 ) in an axis ( 20 ) perpendicular to the longitudinal axis ( 13 ) of the camshaft ( 12 ) can be set in predetermined steps, the grinding wheel ( 18 ) with regard to their properties depending on the respective initial geometry, the material and the desired surface properties (surface roughness (R _Z ), shape error (f _m )) of the cams ( 30 ), characterized by the steps:

• - First determine a theoretical minimum grinding time (t _hmin ) per revolution of the cam ( 30 ) from the geometry of the cam ( 30 ) and the maximum angular velocity (ω _max ) according to the cut size equation: where ϕ _G , ϕ _F and ϕ _{S are} the circumferential angles in the area of the base circle ( 31 ), the flanks ( 33 ) or the tip ( 32 ) and ω _{G max} , ω _{F max} and ω _{s max} which, considering the cam geometry (base circle radius (R _G ), tip radius (R _S ), mean flank radius (R _Fm ), survey value (S)) and the grinding wheel data (radius (r _S ), speed (v _S ), speed quotient are theoretically maximum angular velocities in these areas;
• - Then determine a maximum related _{chip removal volume} (Q ′ _wmax ), ie machined material _volume per unit of time and per mm grinding wheel _width ) depending on the maximum drive power (P _max ) of the grinding wheel drive ( 19 ) according to the cut size equation: where b is the width of the cams ( 30 ) and K₁ and K₂ are constants, for which preferably applies: K₁ = 1.754 and K₂ = 2.788;
• - further determine a maximum, machined workpiece _volume (V ′ _wmax ) from the minimum grinding time (t _hmin ) and the maximum _{machined volume} (Q ′ _wmax ) according to the formula: V ′ _{W max} = Q ′ _{W max} · t _{h min} ;
• - and finally calculate the maximum, optimized infeed (a _max ) from the maximum machined workpiece _volume (V ′ _Wmax ) and the geometry of the cams ( 30 ) according to the formula: where k is a running parameter for the number of flank radii (R _F ) that is specified in a case-by-case manner and runs from 1 to n.

2. The method according to claim 1, in which the chip filling degree (f _g ) is additionally taken into account, characterized by the steps:

• - Determine the chip space _{filling wheel} (f _g ) from the maximum obtained chip _{removal volume} (Q ′ _wmax ) according to the formula: where V _{ES is} the individual chip _volume and V _{SR is} the chip space _volume dependent on the maximum obtained chip _{removal volume} (Q ′ _wmax );
• - Comparing the determined chip filling degree (f _g ) with an allowable limit (K₁₁), for which preferably K₁₁ = 0.75 applies;
• - Reduce the maximum related chip _removal volume (Q ′ _wmax ) until the determined chip _{filling degree} (f _g ) does not exceed the limit value (K₁₁); and
• - Determine the associated optimized infeed (a _opt ) from the reduced maximum _{obtained chip removal volume} (Q ′ _wmax ).

3. The method according to claim 2, in which the individual grain force (F _K ) is additionally taken into account, characterized by the steps:

• - Determine the individual grain force (F _K ) from the maximum _{obtained chip removal volume} (Q ′ _wmax ) according to the formula: where F _{C is} the cutting force, N _{kin is} the area-related kinematic cutting edge number which is dependent on the maximum related _{chip removal volume} (Q ′ _wmax ) and A _{K is} the contact area between grinding wheel ( 18 ) and cam ( 30 );
• - Comparing the determined single grain force (F _K ) with an allowable limit value (F _Kzul );
• - Reduce the maximum amount of _{chip removal} (Q ′ _wmax ) until the individual grain force (F _K ) does not exceed the limit value (F _Kzul ); and
• - Determine the associated optimized infeed (a _opt ) from the reduced maximum _{obtained chip removal volume} (Q ′ _wmax ).

4. The method according to any one of claims 1 to 3, characterized in that from at least one further boundary condition a related _{chip removal volume} (Q _w ') is determined and this is compared with the previously determined maximum or reduced maximum related _{chip removal volume} (Q' _wmax ) and that the smaller chip removal volume (Q _w ′) is used to determine the optimized infeed (a _opt ). 5. The method according to claim 4, characterized in that the effective roughness depth (R _t , R _t0 ) of the cam ( 30 ) and grinding wheel ( 18 ) are taken into account and the further boundary condition is: where K is the concentration of the grinding wheel ( 18 ), v _{C is} the cutting speed and K₁₃, K₁₄ constants, for which preferably applies: K₁₃ = -0.8, K₁₄ = 1.25. 6. The method according to claim 4 or 5, characterized in that the shape error (f _m = F _c / C _g ) of the cams ( 30 ) is taken into account and the further boundary condition is: where C _{g is} the rigidity of the camshaft grinding machine ( 10 ), and K₁₅, K₁₆ and K₁₇ are constants, for which preferably applies: K₁₅ = 1.754, K₁₆ = K₁₇ = 2.78. 7. The method according to any one of claims 4 to 6, characterized in that the wear (r _s ) of the grinding wheel ( 18 ) is taken into account and the further boundary condition is: where Z _{r is} the mean grain projection and K₁₈, K₁₉ and K₂₀ constants, for which preferably the following applies: K₁₈ = 0.039; K₁₉ = 0.75; K₂₀ = 2.5. 8. The method according to any one of claims 4 to 7, characterized in that the boundary zone temperature (T _M -T _R ) of the cams ( 30 ) is taken into account and the further boundary condition is: where T _{M is} the average temperature in the cutting point, T _{R is} the room temperature, c is the specific heat, ρ is the density of the material, K * is the conversion factor between heat and energy units and K₂₁ and K₂₂ constants, for which preferably applies: K₂₁ = 419 , 2 x 10³; K₂₂ = 1.563.