Method for cylindrical surface grinding of workspaces

A method serves for cylindrical surface grinding of workpieces. A grinding wheel engages a workpiece which rotates in the opposite direction and is fed at a given feeding speed parallel to the axis of the workpiece. The grinding wheel rotates about an axis which is inclined at an angle relative to the axis of the workpiece. In order to achieve workpiece surfaces of low roughness at high machining speeds, in particular surfaces without spiral-shaped surface grooves, one first determines from the given surface roughness, by empirical means, a contact ratio serving as an auxiliary value whereafter the axial length of the first surface is determined and adjusted using a formula. The method is used within a range of values where workpiece diameters of 5 to 250 mm are encountered, the grinding wheel rotates at a speed of 100 to 300 m/s, the workpiece rotates at a circumferential speed of 65 to 200 m/s and the speed of the axial feed is between 150 to 2000 mm/min.

BACKGROUND OF THE INVENTION 
The present invention relates to a method for cylindrical surface grinding 
of workpieces having a workpiece diameter (d.sub.w) wherein a grinding 
wheel rotating at a circumferential speed (v.sub.s) engages a workpiece 
rotating in the opposite direction at a circumferential speed (v.sub.w), 
while the grinding wheel and the workpiece are fed relative to each other 
at a feeding speed (v.sub.fa) along directions extending parallel to the 
axis of the workpiece, the grinding wheel rotating about an axis extending 
at an angle relative to the axis of the workpiece and the grinding wheel 
comprising first and second conical circumferential portions so that a 
first surface of the first circumferential portion engages a helicoidal 
material removal surface, while a second surface of the second 
circumferential portion engages an axial circumferential surface of the 
workpiece. 
Methods of the type described before have been generally known and are used 
as a rule for an operation known as "plunge-cut grinding". In conventional 
plunge-cut grinding, relatively low circumferential speeds are selected 
for the grinding wheel and the workpiece, for example circumferential 
speeds in the range of 40 m/s. 
It has been further known to use the method described before for peel 
grinding, which means that the outer circumference of the workpiece is 
ground from a raw dimension to a desired dimension, at relatively high 
material removal rates, by feeding the workpiece in the axial direction. 
The speed of the axial feed is extraordinarily low in this case, i.e. in 
the range of a few mm/min. 
On the other hand, a high-speed grinding method has been known where a 
grinding wheel of relatively small thickness (for example 8 mm) is used 
and inclined in such a manner that one end face engages a radical shoulder 
face of the workpiece between the raw dimension and the final dimension, 
while its circumferential surface is inclined relative to the finished 
axial circumferential surface of the workpiece at a relief angle. 
Although relatively high material removal rates can be achieved with the 
aid of these known high-speed grinding methods, the known method is 
connected with the drawback that due to the practically point-shaped 
contact between the grinding wheel and the foot of the radial end face of 
the workpiece at the transition to the finished circumferential surface, a 
spirally grooved surface of the workpiece is obtained which is 
unacceptable for many applications. 
SUMMARY OF THE INVENTION 
Now, it is the object of the present invention to improve a method of the 
type described above in such a manner that a uniform and 
precision-finished surface without any surface spirals and with a 
predetermined surface quality can be obtained at high material-removal 
rates. 
This object is achieved by the steps of determining from a given surface 
roughness (R.sub.z) of the workpiece a contact ratio (u) of the grinding 
wheel, and selecting thereafter the axial length (l.sub.N) of the first 
surface using the formula 
##EQU1## 
wherein (q) is the quotient (V.sub.s /v.sub.w) of the circumferential 
speeds of the grinding wheel and the workpiece and the following value 
ranges are preferably selected: 
d.sub.w =5 to 250 mm 
v.sub.s =100 to 300 m/s 
v.sub.w =65 to 200 m/min 
v.sub.fa =150 to 2000 mm/min. 
The object underlying the present invention is solved in this manner fully 
and perfectly. The preferred value range with the extremely high 
circumferential speeds and speeds of feed permits to achieve material 
removal rates which are equal to the material removal rates of 
conventional machining processes using defined cutter faces (turning, 
milling). On the other hand, however, one achieves the advantages 
connected with machining methods using nondefined cutter faces (grinding), 
the grinding process giving rise only to very small granular chips, 
whereas the other machining processes using defined cutter faces, in 
particular turning processes, give rise to relatively big and long chips 
which may make themselves felt during turning as so-called coiling chips 
which--at least according to the present state of the art--exclude any 
automatic production processes which include turning operations. For, even 
modern turning machines require the presence of an operator who will clear 
the workpiece from coiling chips by means of a hook, in case coiling chips 
should occur. 
The method according to the invention, therefore, can be described as a 
longitudinal-feed circumferential grinding process where the material is 
removed by geometrically undefined cutters. The machining oversize 
provides for a big cutting depth which is approximately 100 to 1000 times 
bigger than in the case of conventional longitudinal grinding. During 
circumferential grinding, one main cutter edge acts as end face of the 
grinding body, the axial feed being approximately 10 to 100 times greater 
than in the case of conventional longitudinal grinding. During surface 
grinding, a smoothing effect is achieved by a secondary cutter face, the 
axial length of the secondary cutter face being determined by 
qualification of the technological operating mechanisms. 
Given the fact that this is not necessary in the case of the method 
according to the invention, the method of the invention opens up 
absolutely novel perspectives for automatic production operations which 
heretofore were exclusively reserved to drilling and milling processes. 
A particular advantage is seen in this connection in the fact that the 
desired surface roughness can be predetermined within broad limits in the 
before-mentioned value range. For, it is the desired surface roughness 
from which a contact ratio is determined by means of empirically 
determined relations, which contact ratio serves as an auxiliary value 
from which the axial length of the first surface can be derived, using the 
geometry and the operating parameters of the workpiece and the grinding 
wheel as additional values. The length so determined can then be adjusted 
by appropriate selection of the grinding wheel so that minimum radial 
pressures, corresponding to the axial length of the first surface, will 
have to be exercised for achieving the desired surface roughness. 
Other advantages of the invention will appear from the following 
description and the attached drawing. 
It is understood that the features which have been described above and will 
be explained below may be used not only in the described combinations, but 
also in any other combination or individually, without leaving the scope 
and intent of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In FIG. 1, reference numeral 10 designates a rotational-symmetrical 
workpiece having a longitudinal axis 11. A first portion 12 of the 
workpiece 10 comprises a first circumferential surface 13 of a raw 
dimension, a second portion 14 of the workpiece 10 is already finished, 
and its second circumferential surface 15 exhibits the desired final 
dimension. 
Between the portions 12 and 14, one can see a helicoidal material-removal 
surface 16, the oversize being indicated at a. 
The workpiece 10, which has a diameter (d.sub.w), can be rotated about an 
axis 11 in the direction indicated by a first arrow 17 (z axis), the 
rotational speed selected for the purposes of the present invention 
corresponding to a circumferential speed of 65 to 200 m/s for workpiece 
diameters (d.sub.w) of 5 to 250 mm the arrow 17 representing any 
conventional, well known in the art, apparatus for providing a means to 
rotate the workpiece 10. 
The workpiece 10 can be displaced relative to a grinding wheel 30. 
Preferably, the workpiece 10 is displaced axially in the direction 
indicated by a second arrow 35, the arrow 35 representing any 
conventional, well known in the art, apparatus for providing a means for 
displacing the workpiece 10 relative to the grinding wheel 30. The speed 
of feed v.sub.fa of the workpiece 10 is equal to approx. 150 to 2000 
mm/min. The coordinate system x-y-z usually employed is likewise shown in 
FIG. 1. 
The grinding wheel 30 comprises an axis 31 which is inclined relative to 
the axis 11 of the workpiece 10 by an angle 32 in the range of 30.degree. 
(preferable 26.degree.34'). The grinding wheel 30 is supported by a shaft 
33 which can be driven to provide means for rotating the grinding wheel 30 
about the axis 31 in the direction indicated by a third arrow 34. 
If the grinding-wheel diameter is in the range of 600 mm, the speed of the 
grinding wheel 30 is adjusted to a value which leads to a circumferential 
speed (v.sub.s) in the range of 100 to 300 m/s. 
The grinding wheel 30 is provided with a first conical portion 40 as main 
cutter face, a second conical portion 41 as a secondary cutter face, and a 
third conical portion 42, starting from its radial end faces. 
The first and the second conical portions 40, 41 define between them an 
angle of 90.degree., while the third conical portion 42 extends at a 
lightly flatter angle than the second conical portion 41. 
As can be clearly seen in FIG. 1, the grinding wheel 30 engages the 
workpiece 10 in such a manner that a first surface 44 of the first conical 
portion 40 (main cutter face) is in contact with the helicoidal 
material-removal surface 16, and a second surface 45 of the second conical 
portion 41 is in contact with the second, finished circumferential surface 
15 of the workpiece 10. Due to the flatter angle of the third conical 
portion 42, its third surface exhibits a relief angle 47 relative to the 
second, finished circumferential surface 15. 
The arrangement is such that the second surface 4645 of the second conical 
portion 41 (secondary cutter face) is in contact with the second, finished 
circumferential surface 15 of the workpiece 10 over an axial length 
(l.sub.N). 
It is now possible to define a contact ratio (u) corresponding to the 
quotient between the axial length (l.sub.N) between the second surface 45 
and the feed in the direction of the third arrow 35, the feed being in 
turn equal to the quotient between the speed of feed (v.sub.fa) and the 
rotational speed of the workpiece. 
The contact ratio (u) so defined provides a direct measure for the surface 
roughness (R.sub.z) achievable when the circumferential speed (v.sub.s) of 
the grinding wheel (30) is also considered for this purpose. The relation 
between the contact ratio (u) and the surface roughness (R.sub.z) can be 
illustrated, using the circumferential speed (v.sub.s) of the grinding 
wheel 30 as a parameter, by a set of curves of the type shown by way of 
example and very diagrammatically in FIG. 2. It can be clearly seen in 
FIG. 2 that the surface roughness (R.sub.z) improves, i.e. reduces, as the 
contact ratio (u) and the circumferential speed (v.sub.s) of the grinding 
wheel 30 rise. 
Now, when a specific surface quality of the workpiece is desired, the 
contact ratio (u) can be determined from the desired roughness (R.sub.z), 
giving due consideration to the circumferential speed (v.sub.s) of the 
grinding wheel 30. The contact ratio (u) so determined is now inserted 
into the formula 
##EQU2## 
One obtains in this manner the axial length (l.sub.N) which is just 
necessary in order to achieve the surface roughness (R.sub.z), considering 
the given operation parameters, i.e. the circumferential speed (v.sub.s 
/v.sub.w) of the grinding wheel 30 and the workpiece 10, the workpiece 
diameter (d.sub.w) and the speed of feed (v.sub.fa). It must, however, be 
considered in connection with the before-mentioned formula that the 
auxiliary value (q) mentioned therein corresponds to the quotient (v.sub.s 
/v.sub.w) between the circumferential speed of the grinding wheel 30 and 
the workpiece 10. 
It is understood that the method described above is meant only as an 
example for cases where the axial length (l.sub.N) of the second surface 
45 has to be determined and set for a given surface roughness (R.sub.z). 
However, it goes without saying that other combinations of process 
parameters may also be given or adjusted according to the method of the 
invention, using the empirical relationships and formulas described above 
for determining mutually the lacking parameters, without leaving the scope 
and intent of the present invention.