Process for torque free outer circumference grinding of a cylindrical journal

A process for grinding a cylindrical journal is provided, in which the workpiece is rotationally drivably received and held in a work spindle. The grinding disk, which is cylindrically trimmed on its outer circumference, is brought into engagement with the journal to be ground. In order to be able to avoid twist structures during the cylindrical grinding, or at least to keep them within tolerable limits, while approaching the desired circumferential speed of the grinding disk and that of the workpiece within a respectively permissible spread, the rotational disk speed under a load during the grinding and/or the rotational workpiece speed under a load is/are continuously changed during each grinding operation and/or adjusted such that the ratio of the rotational disk speed to the rotational workpiece speed is disharmonic to as high a degree as possible; that is, that integral or simple fractional ratios of the disk rotational speed to the workpiece rotational speed are avoided. During the trimming of the grinding disk, a trimming advance of from 0.05 to 0.415 mm per revolution of the grinding disks is maintained, in which case the grinding disk is trimmed only in one advancing direction. The axes of rotation of the workpiece and the grinding disk are aligned precisely in parallel to one another.

BACKGROUND AND SUMMARY OF THE INVENTION 
This application claims the priority of German Patent Application No. 197 
40 926.1, filed Sep. 17, 1997, the disclosure of which is expressly 
incorporated by reference herein. 
The invention is based on a process for the outer circumference grinding of 
a cylindrical journal on a workpiece. The workpiece is received in a work 
spindle in a rotatable manner and is rotationally drivable at a defined 
rotational workpiece speed and a defined circumferential speed. A grinding 
disk, which revolves at a defined rotational disk speed and at a defined 
circumferential speed and which is cylindrically trimmed on the outer 
circumference, is brought into a grinding engagement with the journal to 
be ground. 
For a secure sealing function at shaft passage points through housing 
walls, in addition to the sealing ring provided with a ring-shaped radial 
sealing lip, the characteristics of the journal-side counterrotation 
surface must also be taken into account. As a rule, these are 
circumferentially ground journal surfaces. In addition to certain 
roughness values, the designing engineer also requires a torque free 
characteristic of the grinding structure for the shaft journal. A "torque 
free" characteristic means that the grinding structure is situated 
precisely in the circumferential direction and superimposed regular shaft 
portions are absent. 
Using a rubber-elastic sealing edge, the radial sealing lip of the sealing 
ring rests against the surface of the shaft journal with a defined radial 
force and on a defined radial width. By means of the rotation of the shaft 
journal, the contact area of the sealing lip is deformed to a varying 
extent in the circumferential direction as a function of the local radial 
contact pressure. Smaller deformations are situated close to the edge and 
larger circumferential deformations are situated more in the center area 
of the contact strip. This results in a sensible tribological and 
Theological equilibrium with an oil flow which, on the one hand, ensures 
the lubrication of the contact zone and, on the other hand, a return 
mechanism which maintains the sealing function of the ring seal. This 
equilibrium must not be disturbed by the formation of a torque or twisting 
in the microstructure of the counterrotation surface. A torsional 
conveying effect in one or the other direction is to be avoided. In the 
case of a torque-induced conveying effect into the sealed interior of the 
housing, the seal would run dry. Exterior dirt would be conveyed into the 
contact zone and the seal would wear out prematurely and become leaky. 
Although a conveying effect directed to the outside would prevent a 
running-dry of the seal, it would result in a discharge of oil at the 
sealing point, which for various reasons must be more or less strictly 
rejected. 
So far it has been widely assumed that the so-called plunge-cut grinding 
process results in torque-free structures. However, even by means of the 
insecure so-called thread method, it can be proven that, at least in the 
case of a certain combination of working parameters, also in the case of 
the plunge-cut process, torque structures can be formed on a workpiece 
surface which is finely machined in this manner. Without the targeted use 
of the special knowledge of the formation of twists and countermeasures 
derived therefrom, the plunge-cut grinding of torque-free structures is 
more a question of the accidental meeting of favorable process parameters. 
With respect to the cylindrical grinding of shaft journals, surprisingly, 
the formation of possible torque structures has not been considered 
significant or significant enough. The cause of premature seal failures is 
assumed to lie more with the seal and less with the journal surface and 
its microstructure. 
Although by means of a so-called "sparking-out" after the termination of 
the grinding operation, as demonstrated by the applicant's investigations, 
a torque structure in the ground surface can be avoided, the shop term 
"sparking-out" relates to a continued operation, without a feeding motion, 
of the grinding wheel on the rotating workpiece until the emitted sparks 
are extinguished in the case of a dry grinding and for a correspondingly 
long period during a wet grinding. The longer the sparking out takes 
place, the lower the twist formation. However, for the torque-free 
sparking-out of the workpiece, it is required to maintain the operation of 
the sparking-out for at least 20 to 30 s. This would impair the cycle time 
of the grinding operation to an unacceptably high extent. 
According to the applicant's experiences with a process developed by the 
applicant for determining torque or twist structures on finely machined 
cylinder surfaces, on the one hand, and with tightness and durability 
tests on installed seals, on the other hand, an absolute freedom from 
twisting is not the only device for achieving tightness and a high 
durability expectation on radial shaft sealing rings. Slight formations of 
a twist structure and/or a high number of threads with a respective low 
conveying cross-section also lead to tolerable results. 
Twist formation during grinding takes place, on the one hand, by way of the 
trimming operation of the grinding wheel or by way of deviations of 
parallelism between the grinding wheel axis and the workpiece axis. The 
applicant therefore differentiates between various types of torques. 
In the case of the trimming torque, a single-thread trimming spiral is 
first formed on the grinding disk by means of the trimming using a 
so-called nonwoven or using a single diamond grain. During the grinding 
process, corresponding to the lower rotational speed of the workpiece, 
this trimming spiral leaves a flatter line on the workpiece, which 
generally is transferred to the workpiece as a multiple-thread twist 
structure. In the case of a zero twist, the waviness, which is formed in 
the cross-sectional shape similar to that of the trimming twist, is 
situated precisely in the circumferential direction; that is a "twist" 
formation is observed which has the peculiarity that the twisting angle is 
precisely equal to zero. With respect to their formation, the trimming 
twist and the zero twist are to be assigned to the waviness and are 
superimposed on the grinding structure. 
The grinding structure must clearly be differentiated from the waviness. 
The term "grinding structure" here relates to the grinding traces of the 
individual grains of the grinding disk on the workpiece surface. 
Corresponding to the circular path of the grinding disk circumference and 
correspondingly of the passing-by of the workpiece circumference, the 
abrasive grains in each case engage only temporarily with the workpiece 
surface. The grinding structure is formed of a plurality of 
surface-covering superimposed lens-shaped or fish-type notches of a length 
of approximately 0.5-1 mm and a width of about 1/10th of it, which are all 
aligned in parallel to one another. The grinding structure is therefore 
interrupted repeatedly and contains a high stochastic form proportion. In 
contrast, the waviness of the trimming twist and the zero twist is 
uniformly formed along the whole sealing surface and has the 
characteristic of an interconnection. This means that the path of a twist 
extends continuously along the circumference. The interconnection will 
exist as long as the waviness proportion of the twist is at least formed 
to the same extent as the roughness proportion of the grinding structure. 
The cause of the offset twist is an offset angle according to DIN 8630 as a 
deviation from the parallelism between the axis of rotation of the 
grinding disk and that of the workpiece. In the microstructure of the 
workpiece surface, the offset twist can be recognized in that the--not 
interconnected--grinding structure is sloped at a small angle with respect 
to the circumferential direction of the workpiece. Because of the slope of 
the grinding structure with respect to the circumferential direction, this 
surface structure--irrespective of the interconnected trimming twist -, in 
the interaction with a sealing lip, also has an axial conveying effect 
which may impair the durability of the shaft sealing ring. 
Irrespective of whether it is a trimming twist or an offset twist, a twist 
formation will impair the sealing function of the surface the more or the 
higher the twist angle, the lower the number of threads and the larger the 
surface cross-section or the depth of one or several threads or of the 
grinding structure. In the case of a twist structure with a low number of 
threads, the individual threads have the tendency to be deeper, thus 
larger in the cross-sectional surface than in the case of higher thread 
numbers. So far, a large number of sealing surfaces with a twist structure 
were measured and a large variety was discovered in the twist formation. 
It is an object of the invention to improve the process for the cylindrical 
grinding of shaft journals on which this application is based in that 
twist structures on grinding surfaces are avoided or can at least be kept 
within tolerable limits without a subsequent "sparking-out" in the case of 
all workpieces to be machined in one cycle. 
According to the invention, this object is achieved by the process for the 
cylindrical grinding of a cylindrical journal on a workpiece. The 
workpiece is received in a work spindle in a rotatable manner and is 
rotationally drivable at a defined rotational workpiece speed and a 
defined circumferential speed. A grinding disk, which revolves at a 
defined rotational disk speed and at a defined circumferential speed and 
which is cylindrically trimmed on the outer circumference, is brought into 
a grinding engagement with the journal to be ground. During the trimming 
of the grinding disk, an axial trimming advance of 0.05 to 0.15 mm per 
grinding disk revolution is maintained and/or while approaching the 
desired circumferential speed of the grinding disk and of the desired 
circumferential speed of the workpiece within a respective permissible 
range, the rotational disk speed under a load during grinding and/or the 
rotational workpiece speed under a load during each grinding operation 
is/are continuously varied and/or adjusted such that the ratio of the 
rotational disk speed to the rotational workpiece speed is non-integral or 
does not represent a simple fractional ratio. 
Accordingly, the invention starts with the causes of the formation of the 
two different types of twists and suggests different countermeasures for 
avoiding twists or torques. Indirectly, the invention recommends a twist 
formation which is as low as possible on the grinding disk itself during 
trimming and a large number of threads on the workpiece-side twist 
structure. For this purpose, the grinding disk and the workpiece are 
driven at rotational speeds whose ratio is disharmonic to as high a degree 
as possible. This can be achieved, among other measures, by avoiding 
integral or simple fractional ratios of the participating rotational 
speeds of the grinding disk and the workpiece. Thus, ratios should also be 
avoided which correspond to an integral number plus the value of a simple 
fraction with numbers below six in the numerator and/or denominator. A 
change of at least one of the participating rotational speeds during a 
grinding operation is also conceivable for achieving this object. By this 
measure, a tumbling synchronization of twist threads generated on the 
workpiece side with the disk-side trimming spiral is to be avoided. 
In German Patent document DE 37 37 641 C2, with a view to achieving optimal 
surface roughnesses during plane grinding, certain ratios of the 
circumferential speed of the grinding disk and the workpiece are to be 
maintained, but the technical context is completely different there than 
in the present case. Although the known process involves a simultaneous 
grinding of a cylindrical circumferential surface, on the one hand, and a 
wavy shoulder, on the other hand, by means of a biconically trimmed 
grinding disk whose axis of rotation is sloped at a large angle with 
respect to the workpiece axis, the known grinding disk carries out a 
periodical axial lift corresponding to the wave shape of the wavy 
shoulder. In contrast, when grinding sealing surfaces according to the 
invention, no axial relative movement is to take place between the 
grinding disk and the workpiece. The cited prior art does not indicate the 
problem of an insufficient sealing effect of ground cylinder surfaces and 
its elimination. 
A careful trimming of the grinding disk with a slight advance recommended 
according to the invention already causes a twist structure to slightly 
form on the workpiece. The measure, which is to be recommended 
additionally or as an alternative, of providing highly fractional 
rotational speed ratios of rotational disk speeds to rotational workpiece 
speeds aims in the same direction. The more complicated the fraction of 
the rotational speed ratio at least at the end of the grinding operation, 
the more threads the twist structure will have and the weaker the 
construction of its individual threads. 
According to the invention, the trimming twist can be reduced at least to 
tolerable measurements by the careful trimming of the grinding disk and/or 
by avoiding integral or simple-fraction ratios of the rotational speeds. 
However, independently of the above, a possible offset twist will still 
exist which is caused by a parallelism defect of the grinding disk axis 
and the workpiece rotation axis. An occurring offset twist can be avoided 
in that the cause of its formation is eliminated; that is, that the axis 
of rotation of the workpiece and that of the grinding disk are aligned 
precisely in parallel to one another. 
The advantages of the invention are, that through the use of the targeted 
adjustment of machine parameters during plane or cylindrical grinding, a 
twist structure on finely machined journal surfaces can be avoided or be 
kept within tolerable limits, without any increase of the machining time. 
After the above, more general explanations concerning the invention, the 
measures will be explained in the following which are possible according 
to the invention for avoiding or reducing twists, partly by means of a 
numerical example and partially with reference to the technological 
sequences.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
A first--but not only--prerequisite for a twist-free plane grinding of a 
cylindrical journal is the fact that the journal surface is ground without 
an axial advance but only by means of a radial advance of the grinding 
disk. The grinding disk must therefore be wider than the axial length of 
the cylindrical journal surface to be machined in the grinding process so 
that the grinding of the cylinder surface can be finished by means of a 
simple radial feeding movement of the disk onto the workpiece. 
The workpiece is received in a precisely rotatably disposed work spindle of 
the grinding machine which rotates at a relatively low rotational 
workpiece speed. As a result, the workpiece surface to be ground is to be 
provided with a certain rotating-past or circumferential speed which was 
previously optimized for the workpiece material and disk material 
combination. In addition to the feeding speed, this workpiece-side 
circumferential speed is responsible for the removal rate of the grinding 
process. The circumferential speed in the case of a defined material of 
the workpiece and of the grinding disk has the tendency to be constant in 
a first approximation along the different workpiece diameters. During the 
grinding, small workpieces therefore rotate at high rotational speeds and 
large workpieces rotate at low rotational speeds. 
The grinding disk is rotatably disposed in a spindle head of the grinding 
machine, in which case--apart from certain parallelism defects which, as a 
rule, are not intended--the axis of rotation of the grinding disk is 
aligned in parallel to the workpiece axis. In addition to an axial 
displaceability, which is not of interest here, of the spindle head 
carrying the grinding disk for the adjustment of the correct axial 
relative position of the workpiece and the grinding disk, the spindle head 
can mainly be moved at a distance from the workpiece and is provided with 
a sensitively variable feeding drive. In the case of each newly chucked 
workpiece, the grinding engagement is established by the careful 
approaching of the rotating grinding disk or its circumference to the 
surface of the workpiece to be ground. By the extent of the radial feeding 
movement of the rotating grinding disk into the moved workpiece surface, 
on the one hand, and by the circumferential speed of the workpiece 
surface, on the other hand, the amount of the removal rate is determined 
which is essential for the grinding process. On the one hand, a high 
removal rate is desirable for achieving short cycle times; on the other 
hand, this removal rate must not be too high because, despite the 
intensive cooling of the workpiece by cooling water, there is the danger 
of a local overheating of the material. This mainly also concerns grinding 
disk conditions of several grinding operations after a trimming of the 
disk in which the disk during the grinding has a higher frictional effect 
than in the freshly trimmed condition and will then also--as a result of 
the friction--carry more waste heat into the workpiece. 
A machining overmeasure is provided on the workpiece for implementing a 
cylindrical surface with a high accuracy of measurements and form, as well 
as a high surface quality. This machining overmeasure is removed in 
several workpiece rotations under a radial feeding of the grinding disk. 
The removal rate may be selected to be slightly higher at the start of the 
grinding operation. Toward the end, that is, when the finished measurement 
of the workpiece is reached, a reduction of the feeding movement and thus 
a reduction of the removal rate can be recommended. By means of a careful 
adjustment of the working parameters toward the end of the grinding 
process, a better surface quality is achieved on the workpiece. At the end 
of the machining, within each grinding operation, in each case at least 
one complete workpiece rotation must be carried out without a feeding of 
the grinding disk in order to change from the spiral approaching of the 
finished measurement to the desired cylindrical shape of the grinding 
surface. 
The grinding disk is driven at a defined circumferential speed which was 
also empirically optimized with respect to the given pairing of workpiece 
material, on the one hand, and the type and material of the grinding disk, 
on the other hand. In order to constantly ensure a precisely cylindrical 
disk shape and to continuously expose new sharp abrasive grains at the 
disk circumference, the grinding disk must be trimmed again after 
several--for example, ten--grinding operations, which is carried out by 
means of a trimming tool--a so-called diamond nonwoven or a single diamond 
grain--in the manner of a turning operation. By means of this trimming, 
the outside diameter of the grinding disk is gradually reduced. In order 
to be able to maintain the desired circumferential speed of the grinding 
disk despite the diminishing disk size, to the extent of the reduction of 
the diameter, the rotational speed of the disk must be increased during 
the grinding. The drive of the grinding disk is therefore provided with a 
continuous rotational speed control. In the case of modern grinding 
machines, this takes place by means of an electric control of the driving 
motors. 
In order to obtain, during the grinding, a twist structure of a formation 
which is as slight as possible, it is recommended according to the 
invention that the grinding disk be trimmed as carefully as possible, that 
is, with a slight advance per grinding disk rotation. However, in this 
case, it is not optimal to trim infinitely slowly. On the one hand, the 
trimming advance must not become too small because the trimming operation 
would be too long and impair the productivity of the grinding machine. On 
the other hand, an extremely small trimming advance would result in very 
finely broken abrasive grains in the working surface of the grinding disk. 
As a result, the grinding disk would act as a finer-grained grinding disk 
and, under the working parameters selected for the actually 
coarser-grained disk, result in overheating. An optimal lower limit of the 
trimming advance cannot be indicated as a generally valid value. On the 
contrary, in this respect, the optimum of a lowest-possible trimming 
advance must be determined empirically as a function of the workpiece 
material and of the disk material. However, a good orientation value for 
the lower limit of the trimming advance would be in the proximity of 0.05 
mm per disk rotation. In order to be able to trim a grinding disk with a 
grinding width of 50 mm in the case of a trimming advance of 0.05 mm per 
revolution, the grinding disk would therefore have to carry out 1,000 
revolutions. In the case of a rotational disk speed of 1,500 revolutions 
per minute, approximately 40 seconds would be required for this purpose. 
From a productivity aspect, the user would naturally like to trim much more 
rapidly. However, the applicant's experiences with the above-mentioned, 
very precisely operating twist structure determination process demonstrate 
clearly that, starting from a certain upper limit of the trimming advance, 
the twist structures forming on the workpiece surface become so deep that 
running-surface-caused leaks of the sealing rings or reductions of 
durability cannot be excluded. In this respect, it is better to indicate a 
generally valid limit value, specifically the above-mentioned 0.15 mm per 
disk rotation. According to the above-mentioned numerical example, the 
essential operating time of the trimming operation would only amount to 
one third of the above-mentioned time, thus to approximately 13 seconds. 
Naturally, a twist-related deterioration in the case of larger trimming 
advances will start only gradually but the twist structure has the clear 
tendency to become deeper with an increasing trimming advance. 
According to the applicant's experiences, it is not advantageous to trim 
the grinding disk by a forward movement and backward movement of the 
trimming tool. This only leads to an "asymmetrical" cross structure on the 
grinding disk surface, in which case the trimming spiral produced by the 
returning trimming tool is more pronounced. This cross structure forms 
completely analogously to the single spiral on the workpiece surface. 
Disadvantages of the double trimming with a forward movement and a 
backward movement are an increased wear on the trimming tool, an increased 
grinding disk shrinkage by trimming and a lengthening of the trimming time 
and therefore a reduction of the productivity. It is therefore recommended 
according to the invention that a trimming of the grinding disk take place 
in only one respective passage. 
As mentioned above, the trimming spiral of the grinding disk is formed 
corresponding to the lower rotational speed of the workpiece in a multiple 
and steeper manner on its circumference. Specifically, in this case, the 
rotational speed ratio of the grinding disk to the workpiece is decisive. 
At a rotational speed ratio of ten to one, the trimming spiral of the 
grinding disk forms ten times on the surface of the workpiece. After each 
tenth rotation of the grinding disk, at this rotational speed ratio, the 
workpiece has just completed a rotation. During the eleventh rotation of 
the grinding disk, the workpiece has just completed 1.1 rotations, and the 
disk-side trimming spiral will then just fit back again into the first 
disk-side "image" of the spiral and hollow it out more. 
The applicant was able to observe that--when viewing the cross-section of 
the twist threads in the axial direction--the flank angles of the threads 
are relatively small and remain within a narrow value range, which is 
explained by the formation method of the threads. However, this means that 
few threads of a twist structure are relatively deep and wide, 
specifically because the individual threads are met again by the trimming 
spiral of the grinding disk during each workpiece rotation. If, for 
example, ten workpiece rotations are required for a grinding operation and 
the rotational speed ratio is ten to one, this means that each thread of 
the workpiece-side twist structure is in each case met ten times by the 
disk-side trimming spiral and the thread is correspondingly wide and deep 
and thus contains a large conveying cross-section. 
As explained above, at a rotational speed ratio of ten to one between the 
rotational speed of the grinding disk and the rotational speed of the 
workpiece, a ten-thread twist structure is formed. At a rotational speed 
ratio of 11:1, the number of threads is 11; at 12:1, there are 12 threads, 
and so on. The number of threads of the forming twist structure is 
therefore--at least at integral rotational speed ratios--a true image of 
the rotational speed ratio of the rotational disk speed to the rotational 
workpiece speed existing during the grinding operation. It is understood 
that the rotational speeds and their ratio which actually exist are 
important here, that is, exist under a load. In the case of non-integral 
rotational speed conditions, the situation involving the thread numbers is 
somewhat more complicated--the reason is that the threads can occur only 
as integrals in a twist structure. 
If, in contrast, the load--rotational speed ratio of the grinding disk and 
the workpiece in the mentioned example (10:1) is changed by only 5%, thus, 
from 10,0 to 10,5, this means that the trimming spiral of the grinding 
disk arrives in a thread of the twist structure already existing on the 
workpiece surface only after 21 rotations of the workpiece. Thus, at this 
rotational speed ratio, a 21-thread twist structure is to be expected. In 
the case of the, for example, ten workpiece rotations within the whole 
grinding operation, each thread would be met only five times by the 
trimming spiral of the grinding disk. The threads would therefore be 
narrower and less deep. By avoiding the rotational speed ratio of 10:1 and 
maintaining an easily changed rotational speed ratio, the number of 
threads of the forming twist structure can therefore be significantly 
increased and the conveying cross-section of the individual threads can 
clearly be reduced. If the on-load speed ratio of the disk rotational 
speed to the workpiece rotational speed were brought, for example, 
precisely to 10.43. --at least theoretically--the trimming spiral would 
arrive back in a thread of a workpiece-side twist structure only after 
1,043 disk rotations. In the case of a rotational disk speed in the 
proximity of 1,500 revolutions per minute, approximately 40 seconds would 
be required for this purpose. Frequently, the whole essential operating 
time of the grinding operation will not be as long. The conclusion can be 
drawn from the above that, in the case of highly fractional rotational 
speed ratios with rotational speeds which are set to the point at the 
grinding disk and at the workpiece and are maintained under a load, the 
effect of a repeated meeting of a twist thread already existing on the 
workpiece side by the disk-side trimming spiral during a grinding 
operation would not occur. 
Because of the trimming-caused reduction of the diameter of the grinding 
disk and because of the requirement to maintain a certain cutting or 
circumferential speed of the grinding disk, during the life of a grinding 
disk, within a certain rotational speed range, there is a passing through 
the spectrum of the rotational speeds. New grinding disks, which still 
have large diameters, are, for example, at first operated at approximately 
1,200 revolutions per minute--under a load. Toward the end of the useful 
life, the reduced grinding disk has to be driven at perhaps 2,000 
revolutions per minute in order to offer the desired cutting speed at the 
circumference. At higher rotational speeds, there is the danger of a 
vibration excitation of the grinding machine by unavoidable residual 
imbalances of the grinding disk. In addition, at these rotation numbers, 
the centrifugal forces, which rise quadratically with the rotational 
speed, have values which represent a certain danger potential. 
In contrast to the variably driven grinding disk, the workpieces are always 
driven at approximately the same circumferential speed and, according to 
the workpiece diameter, at a correspondingly constant rotational speed. 
Although the rotational workpiece speed can also be varied within 
relatively wide limits by the machine adjustment, as a rule, for grinding 
a certain type of workpiece, these are caused to rotate at a rotational 
speed which remains the same from one workpiece to the next. Small 
workpieces with a grinding surface diameter of, for example, 6 to 15 mm 
are driven at rotational workpiece speeds of from 300 to 500 revolutions 
per minute. If the grinding surfaces have a diameter of approximately 100 
to 150 mm, rotational workpiece speeds of from 100 to 200 revolutions per 
minute are appropriate. If a rotational workpiece speed is, for example, 
120 revolutions per minute under a load, in the case of a rotational speed 
spectrum of the grinding disk of from 1,200 to 2,000 revolutions per 
minute, this means that, during the life of a grinding disk, it passes 
through a spectrum of rotational speed ratios between 10:1 (value 10.0) in 
the case of a new disk, to 100:6 (value 16.66) in the case of an old disk. 
It may be assumed that, at the cutting speed of the disk and at the 
circumferential speed of the workpiece, in each case, a spread of 
approximately .+-.2 to 3% about an optimal value can easily be tolerated. 
Under this condition, certain integral or simple-fractional rotational 
speed ratios of disks to workpieces can be skipped in that values are 
driven which are modified with respect to the optimal values of the 
disk-side and workpiece-side circumferential speed. 
Coming back to the selected numerical example, one would therefore not 
start with a rotational speed ratio of 10.0 but, for example, with 9.57 or 
with 10.43 and would maintain the on-load speeds pertaining to this ratio 
unchanged on the workpiece side and on the disk side until the disk 
diameter has been reduced by approximately 5 to 7%. The mentioned 
"uneven-numbered" ratios can be represented as a true fraction only by 
high numbers in the numerator and/or in the denominator. This therefore 
leads to a high number of threads in a twist structure to be expected 
which, however, because of the high number of threads, is harmless with 
respect to the sealing function. A workpiece which is ground in this 
manner, at least with respect to the sealing result, can be considered in 
the same manner as a twist-free workpiece. 
On the basis of the applicant's experiences, it may be stated that, 
starting from a certain number of threads, the forming of threads in a 
twist structure is so low that the threads are lost in the stochastic 
roughness. The interconnection of the free cross-section of such flat 
threads will be lost in the general surface roughness and is therefore 
acceptable with respect to the sealing effect. It is true that such a 
minimum number of threads, starting from which a twist structure is to be 
judged twist-free, cannot be indicated precisely from the start in a 
generally valid fashion, particularly since in this respect there also 
still seems to be a certain dependence on the diameter. On the 
circumference of a grinding surface of a small diameter, only relatively 
few harmful threads can be accommodated, whereas on the circumference of a 
large grinding surface, there is sufficient space for many harmful 
threads. According to the applicant's experiences, in the diameter range 
of 100 mm, twist structures with 40 and more threads are harmless for a 
perfect sealing effect. In the case of smaller grinding surfaces, this 
result could already be achievable by means of smaller thread numbers. 
Inversely, in the case of larger diameters of about 200 mm, probably 
clearly higher thread numbers would have to be demanded in order to ensure 
a tightness of the ground surface. 
When, in the course of a progressing production, the disk diameter has been 
reduced by approximately 5% by a repeated trimming, a change will be 
made--starting from the value of the example of 10.43--to a new rotational 
speed value (under a load) of, for example, 10.83. The values should be 
selected such that the adjusted rotational speed ratios occurring under a 
load differ from whole or simple-fractional numbers by at least 
approximately 5%. This difference takes into account a certain regulating 
inaccuracy and an uncertainty of the process. 
For all conceivable combinations of workpiece-side and disk-side rotational 
speeds, rotational speed ratios of approximately 3 to 30 may occur, in 
which case the lower value applies to small workpiece diameters and large 
new grinding disks, and the upper value is to be assumed for large 
workpieces and old small disks. In order to obtain ratios which are highly 
disharmonic in the case of the low ratios, significantly more "prohibited" 
ranges must be inserted between two successive whole numbers than at the 
upper end of the spectrum of ratios. In the case of fractional ratios of 
the rotational speeds, this value must be converted into a true simple 
fraction of whole numbers. The number of threads to be expected of a twist 
structure formed during grinding will then correspond to the numerator of 
such a fraction. If the rotational speed ratio under a load is, for 
example, 4.25--as a true simple fraction of whole numbers, this 
corresponds to 17/4--a 17-thread twist can be expected. If the rotational 
speed ratio is 4.125=4+1/8=33/8, 33 threads are formed. At a rotational 
speed ratio of 4.16666=4-1/6=25/6, 25 threads are formed; at 
4.83333=4+5/6=29/6, 29 threads are formed. All these numbers of 
threads--17 or 25 or 29 or 33 threads--would still be harmful. In this 
range of low ratios, values would have to be found which are more 
disharmonically fractional in order to arrive at harmlessly high numbers 
of threads of above 40. This will be illustrated in the following table by 
means of arbitrarily selected examples: 
______________________________________ 
Number of 
Improper Proper Threads to Be 
Decimal Ratio 
Fraction Fraction 
Expected 
______________________________________ 
3.818181 3 + 10/11 43/11 43 
4.090909 4 + 1/11 46/11 46 
4.1000 4 + 1/10 41/10 41 
4.11111 4 + 1/9 37/9 37 
4.3000 4 + 3/10 43/10 43 
______________________________________ 
This shows that, at low ratios of the rotational speeds, these must be 
constantly maintained independently of the load and each separately in a 
very narrow percentage control range in order to be able to ensure a high 
number of threads. The smaller the ratios, the more critical the undesired 
rotational speed changes with respect to the desired rotational speed. 
Here, harmonic and low-degree disharmonic ratios, on the one hand, as well 
as high-degree disharmonic ratios, on the other hand, are situated close 
to one another. Although, at high ratios of the rotational speeds, a 
precise maintaining of the rotational speeds is no longer as critical 
because there harmonic and high-degree disharmonic ratios are situated 
farther apart than in the range of lower ratios, it is possible that, in 
the range of ratios which is decisive mainly in the case of large grinding 
diameters, higher numbers of threads than 40, for example, at least 50 or 
60 threads, are to be endeavored in the twist structure of the grinding 
surface in order to be able to achieve a secure sealing effect on large 
journals. This is to be illustrated in several numerical examples in the 
range of ratios of 30 in the following table: 
______________________________________ 
Number of 
Improper Proper Threads to Be 
Decimal Ratio 
Fraction Fraction 
Expected 
______________________________________ 
29.5 29 + 1/2 59/2 59 
29.75 29 + 3/4 119/4 119 
30.0 30 30/1 30 
30.125 30 + 1/8 241/8 241 
30.25 30 + 1/4 121/4 121 
30.1333 30 + 1/3 91/3 91 
30.50 30 + 1/2 61/2 61 
31.50 31 + 1/2 63/2 63 
______________________________________ 
This overview demonstrates that, in the case of high ratios, it is 
sufficient to avoid integral values. With each non-integral ratio, thread 
numbers are reached which are above twice the ratio, which, as a rule, are 
sufficient. 
In general, the following relationship applies to the rotational speed 
ratio of the rotational disk speed to the rotational workpiece speed: At a 
rotational speed ratio V written as in improper fraction of the general 
formula G+Z/N, a thread number of N*G+Z is formed. In this formula, G, Z 
and N are each whole numbers and G signifies the integral of the 
rotational speed ratio V, and Z/N is the fractional remainder of the 
rotational speed ratio V written in the form of a proper, simple, that is, 
no longer divisible fraction; wherein Z=numerator and N=denominator; thus, 
V=G+Z/N. If it is now demanded that the number A of the threads must be 
larger than, for example, 40 (A.sub.min =40) and the approximate amount of 
the rotational speed ratio, thus the integral G of this value, is also 
fixed (for example, G=5), by means of an iterative calculation with the 
modified numbers for Z and N, the precise value of a suitable rotational 
speed ratio can be determined, at which the required minimum number of 
threads is to be expected. By means of the above-selected numerical 
examples for A.sub.min =40 and G=5, many possibilities would be obtained 
by trial, such as: 
5+1/8=5.125 (A=41); 5+1/9=5.111 (A=46); 5+1/10=5.10 (A=51); 5+1/11=5.0909 
(A=56), and so on. 
It should be stressed again at this point that the rotational speed ratios 
are to be formed from actual rotational speeds; that is, from on-load 
speeds. Depending on the type of drive, the no-load speeds may clearly 
differ from the on-load speeds. Rotational speed drops in the case of 
asynchronous drives, depending on the amount of the load, may be at 3 to 
7% of the nominal speed. Since, toward the end of the grinding operation 
before the specified size of the workpiece is reached, a lower feeding 
movement is frequently used, and therefore a load drop is to be expected 
toward the end of the grinding operation, the rotational speeds of the 
grinding disk will also rise here. In particular, toward the end of the 
grinding operation, the recommendation according to the invention with 
respect to "uneven-numbered" rotational speed ratios is to be observed. 
The machine-side condition is that the on-load speed of the workpiece and 
that of the grinding disk can be set with a high precision to arbitrary 
values in a precisely reproducible manner and also independently of the 
load can be held constant at the set value. 
While the previously described approach for solving the twist problems by 
means of "uneven-numbered" rotational speed ratios aims in the direction 
of high thread numbers with an, on the whole, uncritical overall conveying 
cross-section of the surface waviness, a further solution approach of the 
invention goes in another direction. As the result of the continuous 
change of the rotational speed of the grinding disk and/or of the 
workpiece under a load during a grinding operation, a tumbling 
synchronization of the workpiece-side twist threads is to be penetrated by 
means of the disk-side trimming spiral. Because of the speed change of at 
least one of the two surfaces, in an optimal case, the trimming spiral of 
the disk arrives during each disk revolution on a previously not yet 
impacted circumferential point of the workpiece. As the result, a twist 
structure also with a very high twist number can be produced which 
therefore is harmless with respect to a sealing. Although, a continuous 
change of the rotational speed ratio passes through harmonic values, this 
is uncritical because these values are effective only for a short time. 
A continuous change of the rotational speed ratio of disk rotational speeds 
to workpiece rotational speeds can be implemented in various manners. It 
will be assumed that the rotational speed within a band width of 
approximately 10% of the desired circumferential speed, while taking into 
account the respective existing disk diameter, can be changed during a 
grinding operation without technological disadvantages for the grinding 
process. Under this condition, the rotational speed of the grinding disk 
can be linearly lowered slowly during a grinding operation from 105 to 95% 
of the desired rotational speed. It is also conceivable to keep the 
rotational grinding disk speed in the case of an "uneven-numbered" 
rotational speed ratio in a first phase of the grinding operation with an 
increased removal rate at a first constant and only then linearly lower 
the rotational disk speed. The lowering of the rotational speed may, for 
example, take place by a simple switching-off of the driving motor of the 
grinding disk. It would then be possible to terminate the grinding 
operation by means of the driving energy stored in the grinding disk or in 
an additional flywheel disk at--according to an exponential function--a 
decreasing rotational speed. Naturally, the same advantageous effect of a 
virtually twist-free workpiece surface could also be obtained by means of 
a linearly rising rotational disk speed. The switching-off of the driving 
motor and/or the acceleration, for avoiding switch-on surges or the like, 
should take place by a careful voltage reduction--phase controlling--or by 
a targeted rotational speed control operation. 
In the same manner, it can be assumed that the circumferential speed also 
of the workpiece can be varied within a band width of approximately 10% of 
the desired circumferential speed without technological disadvantages for 
the grinding process during a grinding operation. Thus, also the 
rotational workpiece speed, for interrupting a synchronization of the 
twist structure existing on the workpiece side and of the disk-side 
trimming structure, can be lowered or raised during the grinding operation 
within a 10% bandwidth by a desired rotational speed in a linear manner. 
Also, rotational changes in the opposite direction which supplement one 
another on the workpiece side and on the grinding disk are conceivable. 
In addition to a linear rotational speed change (rising or falling) during 
a grinding operation, a synchronization of the structures can also be 
caused by a periodical rotational speed change. The grinding disk and/or 
the workpiece can be driven by means of a rotational speed which 
fluctuates about a mean value, in which case the rotational speed of the 
grinding disk and/or that of the workpiece under a load fluctuates about 
approximately .+-.3 to 8% of the respective mean value. In this case, the 
rise and fall of the rotational speed can take place linearly or according 
to a harmonic function or according to a time function which is not 
defined in detail. However, this suggestion is suitable only for smaller 
grinding disks or smaller workpieces with a low centrifugal mass. For 
example, such a fluctuating of the rotational grinding wheel speed can be 
carried out by an intermittent energizing of the disk driving motor. When 
the motor is switched off, because of the load moment of the grinding disk 
having a low mass, its rotational speed falls according to an exponential 
function. After another energizing, the rotational speed will rise again. 
This rise and fall can be repeated several times during a grinding 
operation. A fluctuating frequency of the rotational speed occurs in this 
manner. It seems expedient in this context that the fluctuating frequency 
is not constant but itself is varied so that twist-causing synchronization 
effects will not occur by way of this frequency. Instead of being avoided 
by means of a change of the fluctuating frequency, a possible 
twist-generating synchronization effect can also be avoided in that the 
fluctuating frequency is selected such that it is in a fractional 
relationship with respect to the respective participating rotational 
speeds. 
In addition to an offset twist caused by parallelism defects of the axes of 
rotation and a trimming twist generated by the disk-side trimming spiral, 
the applicant could also observe a waviness shape on the grinding surface, 
in the case of which the period length of the workpiece-side waviness 
corresponds precisely to the trimming advance of the grinding disk, in 
which case, however surprisingly, the threads have no slope but extend 
exactly in the circumferential direction. The formation of this twist 
structure, which the applicant calls "zero twist", is uncertain. It can be 
explained by a small undesired axial lift of the grinding disk and/or of 
the workpiece within the scope of a normal free axial play of the grinding 
disk spindle or of the workpiece spindle. By means of the grinding 
engagement of the disk and the workpiece or by means of other, previously 
unknown influences, under certain circumstances, axial forces act upon the 
disk or the workpiece which cause a slight relative axial drift of at 
least one of the two partners. If this axial drift coincides with the 
trimming speed, a so-called zero twist could indeed be formed. 
Although such a zero twist, because of an absence of an axial slope of the 
structure waves, causes no conveying effect on a ground journal surface 
under a sealing lip, the relatively deep wave crests situated in the 
circumferential direction generate an increased sealing lip wear which 
naturally is undesirable. Also, a so-called zero twist should therefore be 
avoided, if possible. This can take place in that a possible free axial 
play of the grinding spindle and of the workpiece spindle is avoided in 
that the spindles are axially prestressed clearly in the direction of a 
respectively assigned and integrated axial bearing. The axial bracing 
should take place by using a force which is higher than the possible axial 
forces occurring during the grinding process, for example, higher than the 
axial forces occurring during the trimming. 
The foregoing disclosure has been set forth merely to illustrate the 
invention and is not intended to be limiting. Since modifications of the 
disclosed embodiments incorporating the spirit and substance of the 
invention may occur to persons skilled in the art, the invention should be 
construed to include everything within the scope of the appended claims 
and equivalents thereof.