[0001] This invention relates to methods of grinding blade tips of turbine/compressor rotors.
[0002] Most aircraft gas turbine engines, as well as axial flow turbo-machines used in many
other applications have within them disks or rotors which carry a multiplicity of
removable or fixed blades. Such structures are used in both compressor and the turbine
parts of the engine to respectively compress and expand the working fluid. In some
instances the rotating blades have shrouds at their outermost tips and are connected
at these locations. More commonly, modern engines have blades that lack shrouds and
are only supported at their roots in a rotor disk or drum.
[0003] For high efficiency, it is desirable to have the closest possible fit between the
tips of the rotating blades and the sealing structure of the circumscribing case of
originally manufactured engines. During use, especially during the manoeuvres which
aircraft accomplish, there is occasionally rubbing between the blades and the circumscribing
abradable sealing ring. In addition, other degradation of the blades occurs as an
inevitable result of long hours of use. As a result, the clearance between the blade
tips and the case are increased and it is an object of engine overhaul to restore
these clearances. To achieve good fits the rotor blades must be precisely ground to
within ±0.001'' (±0.025mm) or less so that they are all at a constant radial distance
from the centre line of the engine. This presents a substantial machining problem,
both in original parts manufacture and in overhaul.
[0004] While the tolerances sought currently are tighter than previously, there has always
been a desire to have bladed rotors fit well. In the main this has been achieved by
separately machining rotors and blades to close tolerances but this has resulted in
an accumulation of tolerances greater than now is acceptable. Consequently, it is
currently preferred to machine blades while they are a part of a disk or drum and
blade assembly. As the blades are removable type, they necessarily fit somewhat loosely
in the rotor disk or drum. Thus, during machining, shims have been placed under the
blades to thrust them radially outward to approximately the position they assume during
use. Low speed workpiece rotation, common in cylindrical grinding, also tends to have
the same effect but in neither case is the seating comparable to that obtained during
high speed engine rotation. Typically, horizontal rotary grinding machines have been
used to grind the assemblies while they rotate at no more than a few hundred revolutions
per minute.
[0005] However, the forces accompanying slow rotation or from use of shims are not powerful.
It has been found that the older tip grinding process produces a variation in length
at individual blades which is too great, much more than ±0.001'' (±0.025mm) on an
18'' to 39'' (450mm to 1000mm) diameter rotor assembly. Additionally, the modern type
rotor construction the slot which receives the multiplicity of blades runs circumferentially
around the rim of the disk or drum. With this configuration, it is not practical to
insert shims.
[0006] Thus, during machining either the blades and their retention slots have been configured
to limit radial inward movement or resilient cushions have been used to sandwich the
rotor and thus capture the blades during machining. For the reasons indicated above
neither of these approaches is entirely satisfactory in producing the desired accuracy.
[0007] The clearance between the rotor blade tips and the outer housing has a critical bearing
on engine performances. The main advantages are, improved specific fuel consumption
and increased thrust. In some cases as much as 1%. Additionally, closer running tolerances
result in significantly reduced engine noise.
[0008] In order to achieve accurate clearance with minimum stock removal the grinding process
has to simulate in so far as is practical, the operating conditions of the engine
and also hold the blades out with sufficient force to withstand the grinding forces
imposed on the blades for grinding to take place.
[0009] The grinding action produces radial grinding force (FN). The centrifugal force (Mw²r)
generated even by the lightest blade at high rotating speed must be able to compensate
the grinding force applied. In addition grinding process produces a burr on each blade
which has to be removed.
[0010] The methods previously used have involved conventional, universal or modified grinding
machines. These methods have been extremely inaccurate and time consuming. A normal
universal grinder is not suitable, due to the fact the wheelhead pivot axis is remote
from the grinding wheel, resulting in a need to provide for angular adjustment to
a high accuracy to establish the correction required in both radial and longitudinal
axes for the various stage angles. The problem is further amplified by the fact the
blade assemblies are referenced to a longitudinal dimension from which a datum and
angular accuracies are required to be held within ± 2 minutes of arc.
[0011] A further problem involves the means for measuring the diameter of a rotor assembly.
This function is required before, during and after the grinding operation. The measuring
system has to take readings of individual blades while the workpiece is rotating at
a relatively high velocity of typically 2000 in/sec. (50.8 m/sec.).
[0012] Many manufacturing and overhaul facilities use conventional gauging associated with
machine shops, including in recent times the use of various non-contact electro-optical
measuring systems which allows measurements to be taken while the workpiece is rotating
at low velocity of about 150 in/sec. (3.8 m/sec.). Individual blade dimensions measured
under static or trivial rotational speeds will not be indicative of those in a rapidly
rotating structure.
[0013] This invention provides a method of grinding blade tips of a turbine or compressor
rotor, comprising the steps of spinning a rotor naving one or more sets of blades
to be ground on its axis, providing a grinding wheel which is narrower than the blades
to be ground and having a convexly curved grinding periphery as seen as cross section,
rotating the grinding wheel about an axis parallel to the rotor axis and moving the
grinding wheel and rotor relative to one another in a traverse direction parallel
to the axis of the rotor and wheel and a feed direction orthogonally to the axis of
the rotor and wheel to grind the blade tips of the rotor to a required dimension and
profile which is flat, angled, convexly or concavely curved with a simple or complex
curvature.
[0014] Preferably, the grinding wheel is moved simultaneously in the feed direction with
movement of the rotor in the traverse direction to create said tapered or curved forms.
[0015] The wheelhead and or rotor may be moved incrementally in micro steps in grinding
a blade tip to the required profile.
[0016] Preferably, the grinding wheel is moved with a varying rate in relation to traverse
of the rotor to create said curved profiles.
[0017] It is further preferred that the blade tips of the rotor are ground to a required
dimension and profile in a series of grinding operations.
[0018] In any of the above methods, the grinding wheel may be dressed between grinding operations.
[0019] In addition a deburring operation may be carried out on the blade tips after grinding.
[0020] In a specific method according to the invention the blade lengths may be measured
between grinding operations to determine the remaining amount of material to be removed
in a succession of operations.
[0021] The following is a description of some specific embodiments of the invention, reference
being made to the accompanying drawings, calculations and tables in which:
Figure 1 is a perspective view of a grinding apparatus for grinding blade tips of
a multi-stage turbine/compressor rotor.
Figure 2 is a diagramatic illustration of an existing process for a stage without
angle that is with parallel blade tips;
Figure 3 is a diagramatic illustration of an existing process for a particular stage
and blade tip angle;
Figure 4 is a diagramatic illustration of the process according to the invention for
grinding the blade tips to a requested angle for a particular rotor stage;
Figure 5 is a similar illustration to Figure 3 for stage with parallel blade tips;
Figure 6 is a diagrammatic illustration of part of a multi-stage rotor on which significant
dimesnions are indicated;
Figure 7 is a diamgrammatic illustration of two blades in successive stages on which
significant dimensions are indicated;
Figure 8 is an illustration of the forces acting during cylindrical grinding;
Figure 9 is an illustration of a grinding wheel profile according to the invention
on which significant dimensions are identified; and
Figure 10 is a diagram showing stock removal on a rotor at stage 3 utilising the method
of the invention.
[0022] Reference is made firstly to Figure 1 of the drawings which shows a computer controlled
machine tool suitable for grinding blade tips of a multi-stage turbine or compressor
rotor. The machine tool comprises a rigid base 10 on which an elongate table 11 is
mounted for linear movement in the direction of the axis denoted by the letter z on
Figure 1. At one end of the table a work drive unit 12 is mounted including a rotary
chuck 13 to receive one end of the rotor shaft and having a motor drive 14. At the
other end of the table there is a pedestal 15 on which a freely rotatable chuck 16
is mounted in alignment with chuck 13 to support the other end of the rotor. Both
the work drive unit and the pedestal are adjustable along the table to cater for different
rotor lengths.
[0023] A wheelhead unit 17 is mounted part-way along the table on a further base 18, the
wheelhead including a rotatable grinding wheel 19 having a motor drive 20, de-burr
unit 21 and dresser unit 22. A blade measuring unit 23 is provided on the oppositie
side of the table to the wheelhead.
[0024] The wheelhead is mounted on the base for feed/withdraw movement in the direction
of the axis denoted by the letter x on Figure 1 towards and away from the work piece.
The grinding wheel itself is retractable on the wheelhead unit in the direction indicated
by the arrow A to engage with the dresser unit located at the rear of the wheelhead
for dressing the wheel when required. The grinding wheel is rotated in the direction
indicated by the arrow B on the wheel by the drive motor so that the blade tips at
each stage move continuously past the grinding wheel to be ground by the wheel.
[0025] The forces acting during cylindrical grinding are illustrated on the diagram of Figure
8 and are as follows:
FN - Radial Grinding Force
FT - Tangential Grinding Force
FA - Axial Grinding Force
FG - Resultant Grinding Force
[0026] The cutting force in cylindrical grinding are resolved into tangential, radial and
axial force components relative to the workpiece and wheel.
[0027] The tangential force together with the peripheral speed of the wheel mainly determines
the power required for grinding.
[0028] The radial force, which is normally the largest component, is of importance because
of its direct effect on the machine and workpiece deflections.
[0029] The axial force on the other hand is generally very small by comparison with the
tangential and radial components and therefore need not be considered.
[0030] Grinding forces have been the subject of much study. Investigations have shown that
the radial force lies between 2.5 to 3 times the tangential force.
[0031] Conventional blade tip grinding machine tools currently in use employ a square profile
grinding wheel having a width in excess of the width of the blade tip to be ground
so that the whole of the tip can be acted at once by a simple feed movement of the
grinding wheel transverse to the direction of axis of rotation of the rotor. This
is illustrated diagrammatically in Figure 2 of the drawings in which the grinding
wheel is indicated at 25 and the blade tip at 26. The axis of rotation of the grinding
wheel extends parallel to the axis of rotation of the rotor and the grinding wheel
is fed in the direction of the x-axis into the blade tips to remove the stock indicated
at 27. In a typical turbine/compressor rotor, the blade tips of certain stages along
the rotor will be parallel to the rotor axis and others will be angled to conform
to the encircling casing. The wheelhead is rotatable about the vertical or y-axis
to angle the grinding wheel as illustrated in Figure 3 to grind the angled ends of
the blade tips at each stage along the rotor. The arrangement for angling the wheelhead
may, for example, be in accordance with the construction described and illustrated
in U.K. Patent No. 2076323.
[0032] These arrangements enable only a limited range of profiles to be formed on the tip
blades, that is parallel or angled cut, and in many instances it would be beneficial
to be able to form other profiles including curved profiles to ensure that the blade
tips conform closely to the profile of the encircling casing in which they operate.
[0033] The electric motors for creating the movement of the wheelhead in the direction of
the x-axis and the movement of the table in the direction of the z-axis have controllers
operated under the direction of the machine computer which provide both rapid traverse
for feed/withdrawal between grinding operations and precision incremental movement
at constant or varying rates in accordance with the profile of the blade tip to be
ground. The simplest blade form is a blade without an angled end, that is a blade
end parallel to the rotor axis as illustrated in Figure 3. In this case, the blade
tip is reduced to the required dimension by a series of passes in which the table
is traversed with a continuous movement past the blades with incremental advances
of the wheel between passes until the tips of the blades at that stage have been ground
to the requested dimension. Figure 4 shows an angled blade end and in this case the
grinding wheel is advanced to a location offset to the shorter said of the blade to
a location corresponding to the full depth of cut required on the blade at that end.
The grinding operation is then commenced with the table moving the blade into the
wheel continuously or incrementally at a constant rate and the wheel head retracting
continuously or incrementally at a constant rate determined in accordance with the
rate of movement of the table. Again the blade tip is subjected to a succession of
grinding operations until the tip has been ground to the requisite depth of cut and
angle on the blade end as illustrated in Figure 4.
[0034] The following table refers to the dimensions of the grinding wheel identified on
Figure 9 and relates the depth of cut h to the length of grinding area 1.
Depth of Cut h in (mm) |
Angle α Deg |
Length of grinding area ℓ in (mm) |
0.050 (1.270) |
15° |
0.392'' (10.0) |
0.005 (0.127) |
4.7° |
0.123'' (3.1) |
0.002 (0.051) |
3° |
0.079 (2.0) |
0.001 (0.025) |
2.1° |
0.055 (1.4) |
0.0005 (0.013) |
1.5° |
0.039 (1.0) |
0.0002 (0.005) |
1° |
0.026 (0.7) |
0.0001 (0.002) |
0.7° |
0.019 (0.5) |
[0035] For curved blade tips the table and wheelhead are moved incrementally in microsteps
and a number of points up to and in some instances in excess of ninety are calculated
which the wheel periphery must reach on the blade tip taking into account correction
for changes in wheel radius angle of contact. The table and wheelhead rates of movement
are calculated so that the wheel periphery and blade tip reach each point simultaneously.
The curve is therefore created by a succession of a large number of very small flats.
The computer has a radius/circular interpolation program which calculates the points
which the grinding wheel must reach in traversing the end of the blade tip and for
controlling the incremental movement of the wheelhead and table with the table moving
at a constant feed rate and the wheelhead feed rate varying in order to produce the
requisite curved profile on the blade tip. Thus the program calculates the feed rate
of the wheelhead and this changes in order to make the line of wheel contact move
from one point to the next as the table moves at a fixed feed rate. Again the table
is moved in a succession of passes with respect to the grinding wheel until the blade
tips at that stage have been ground to the required profile and dimension.
[0036] Figure 6 illustrates a typical rotor and the following is a table of typical data
for such a rotor.
Stage |
Angle K |
Radius J in (mm) |
Dia D in (mm) |
Dim H in (mm) |
Grinding R.P.M. |
Surface Speed ft/min (m/s) |
Surface Speed in/sec |
1 |
14°04' |
11.848'' (300.94) |
23.696'' (601.88) |
-0.221 (-5.61) |
1615 |
10 019 (50.9) |
2004 |
2 |
13°48' |
11.133 (282.78) |
22.266 (565.56) |
2.809 (71.35) |
1723 |
10 043 (51) |
2008 |
3 |
10°01' |
10.643 (270.33) |
21.286 (540.66) |
5.387 (136.83) |
1800 |
10 030 (50.9) |
2006 |
4 |
10°56' |
10.258 (260.55) |
20.516 (521.10) |
7.750 (196.85) |
1855 |
9 965 (50.6) |
1993 |
5 |
8°36' |
9.987 (253.67) |
19.974 (507.34) |
9.788 (284.62) |
1901 |
9 940 (50.5) |
1988 |
6 |
5°16' |
9.711 (246.66) |
19.422 (493.32) |
11.892 (302.06) |
1954 |
9 935 (50.5) |
1987 |
7 |
4°39' |
9.591 (243.61) |
19.182 (487.22) |
13.579 (344.91) |
1978 |
9 933 (50.5) |
1987 |
8 |
2°22' |
9.516 (241.71) |
19.032 (483.41) |
15.259 (387.58) |
2000 |
9 965 (50.6) |
1993 |
9 |
0°00' |
9.488 (241.00) |
18.976 (481.99) |
16.939 (430.25) |
2000 |
9 936 (50.5) |
1987 |
[0037] Figure 7 illustrates a pair of typical blades in successive stages of the rotor and
the following is a table of typical data for the blades.
Stage |
Blade Width W ins (mm) |
Dim V ins (mm) |
Dim U Gap between blades ins (mm) |
Blade Weight Wg lbs (grammes) |
Radius Rg ins (mm) |
Centrifugal Force lbf (N) |
Number of Blades per stage |
1 |
1.22 (31) |
0.57 (14.4) |
1.950 (49.5) |
0.2 (90.7) |
9.13 (232) |
135 (602) |
38 |
2 |
1.04 (26.5) |
0.56 (14.3) |
1.70 (43.3) |
0.1 (45.35) |
9.03 (229) |
75 (338) |
53 |
3 |
0.83 (21.1) |
0.39 (9.8) |
1.66 (42.3) |
0.05 (22.68) |
9.03 (229) |
41 (185) |
60 |
4 |
0.71 (18) |
0.32 (8) |
1.40 (35.4) |
0.05 (22.68) |
8.90 (226) |
43.5 (194) |
68 |
5 |
0.65 (16.5) |
0.29 (7.4) |
1.50 (38.0) |
0.04 (18.14) |
8.90 (226) |
36.5 (162) |
75 |
6 |
0.57 (14.4) |
0.27 (6.9) |
1.21 (30.6) |
0.03 (13.6) |
8.82 (224) |
28.6 (127) |
82 |
7 |
0.50 (12.7) |
0.23 (5.9) |
1.16 (29.6) |
0.03 (13.6) |
8.82 (224) |
29.3 (130) |
82 |
8 |
0.50 (12.7) |
0.23 (5.9) |
1.18 (30.0) |
0.02 (9.07) |
8.82 (224) |
20 (89) |
80 |
9 |
0.50 (12.7) |
0.23 (5.9) |
- |
0.02 (9.07) |
8.82 (224) |
20 (89) |
76 |
[0038] The automatic cycle is fully controlled by the NC (numeric control) part program.
A typical cycle is as follows:-
1. Load the rotor into chucks in the floor mounted loading fixture.
2. Transfer the rotor and chucks to the machine and fasten into machine pedestals.
3. Check the runout of the rotor and adjust using the chucks if necessary.
4. Fasten pedestal half caps and secure rotor sliding guard.
5. Press the machine cycle button to start machining.
6. The machine will check that all cycle start conditions are valid.
7. The control will request the grinding wheel to be started if a grind is to take
place and the grinding wheel is not already running.
8. The work motor will be started after a time period when the chuck bearings have
been lubricated.
9. The rotor will run up to programmed speed.
10. The table slide will traverse to the start grind position plus the distance set
above finished size for the particular stage (stage 1).
11. The wheelhead slide will advance from the clear point (retracted) position to
the start grind position plus the distance set above finished size.
12. The table and the wheelhead slides will traverse the grinding wheel across the
stage face (linear interpolation) grinding the blades at programmable rates and distance
set up in the part program.
The distance set at this point say 0.015 ins.
(0.38mm) above the final size.
13. The wheelhead is retracted to the clear point position.
14. The wheelhead slide will traverse to dress position. Dressing is from a rotating
diamond roller mounted to the underslide at the rear of the grinding wheel. After
dress cycle the wheelhead slide will traverse to the clear position.
15. Steps 9 to 14 will be repeated for each stage to be ground.
16. The grinding wheel and the rotor will stop.
17. The de-burr unit mounted on the wheelhead slide is advanced into position (in
front of the grinding wheel).
18. The de-burr will run to speed and the rotor will run up to programmed de-burr
speed.
19. The table slide will traverse to the start de-burr position for the particular
stage (stage 1).
20. The wheelhead slide is advanced until the brush makes contact with the blades
at a programmable torque value set in the part program.
21. The table and the wheelhead slides will traverse the de-burr brush across the
stage face (linear interpolation).
De-burr takes place in both directions of rotation of the brush for a programmable
time.
22. The wheelhead is retracted to the clear point position.
23. Steps 19 to 22 will be repeated for each stage to be de-burred.
24. The de-burr brush and the rotor will stop.
25. The de-burr unit is retracted.
26. Steps 8 to 13 will be repeated for Stage 1. The distance set at this point say
0.010 ins.
(0.254mm) above final size.
27. The table size is positioned for laser gauge calibration.
28. The gauge is calibrated against gauge calibration blocks which are fitted on the
table.
29. The table slide is positioned and the gauge slide is advanced to measure the radius
of each blade. Using the gauge measurement, the wheelhead slide position is determined
and updated.
30. The gauge slide is retracted.
31. Step 14 will be repeated.
32. Steps 10 to 13 will be repeated.
The distance set at this point say 0.005 ins.
(0.127mm) above final size.
33. Steps 26 to 32 will be repeated for each stage to be ground.
34. Steps 16 to 25 will be repeated for each stage to be de-burred.
NOTE: At this point of the machine cycle each stage to be ground is 0.005 ins. (0.127mm)
above final size and de-burred.
35. Steps 9 to 12 and 29 to 30 will be repeated with feed increments of:-
0.003 ins. (0.076mm);
0.001 ins. (0.025mm);
0.0005 ins. (0.013mm);
0.0002 ins. (0.005mm);
0.0002 ins. (0.005mm);
0.0001 ins. (0.002mm);
to final size using the previous gauge measurement as a target to determine the size
position (in-process gauging).
36. Step 14 will be repeated.
37. Steps 35 to 36 will be repeated for each stage to be ground.
38. A printout is produced showing the radius of each blade in a stage. Any blades
out of tolerance are identified on the printout together with the average, maximum
and minimum.
39. Steps 16 to 22 will be repeated for Stage 1.
40. Step 39 will be repeated for each stage to be de-burred.
41. Steps 24 to 25 will be repeared.
42. The table size is positioned at a location suitable for the rotor to be unloaded
from the machine.
43. Unsecure the rotor sliding guard and pedestal half caps.
44. The rotor is removed from the machine, placed in the floor mounted loading fixture
and chucks unclamped.
[0039] Figure 10 illustrates a succession of grinding operations on a rotor stage and the
following is a table of data for a typical grinding cycle:

[0040] The machine auto cycle is controlled by a different part program for each rotor.
These part programs are kept as a library of canned cycles, graphically illustrated,
and selected using soft keys on the control, providing a user friendly man/machine
interface. The library of screens or canned cycles is a self-contained module for
grinding, dressing, de-burring and gauging.
[0041] Data is entered into the parameter column on each screen in response to clear text
language prompts displayed at the bottom of each screen page. This is designed in
such a way that subsequent alterations and modifications to suit changes in rotor
size and to suit other rotors may be carried out by personnel who are not familiar
with the machine part programming language.
[0042] The task of new and repair grinding has been specifically treated in the machine
control. Program blocks (or screens) may be summed together as required enabling the
operator to choose which stages of a rotor need to be ground, de-burred or measured.
[0043] A typical repair sequence will be put to a rotor in the machine and do a measurement
cycle. It may be necessary to use the de-burr to clean up each of the stages to be
measured if the reflectivity of the balde tips is too low for a reliable determination
of size by the laser gauge. The blades or stages to be replaced will then be identified
from the laser gauge print out and the rotor removed for the necessary work to be
undertaken. The rotor will then be re-ground, only the stages that have been re-worked
will need to be ground but a full measurement cycle should be undertaken to provide
a complete documentation of the rotor.
[0044] There is provision in the control for a small offest to be applied to any stage of
the rotor being ground. The size of the offset is designed to allow for the clean
up of blades in a repair grind situation on blades that may not need replacing.
ADVANTAGES
[0045] Reduced contact between the blade and the grinding wheel accordingly reduces the
grinding force (FN) and the residual stresses on the blade. An element of great importance
in blade tip grinding.
* Reduced machine content,
3 axis machine against 6 axis required for the existing process.
Reduction in the cost of the machine hence fast return on investment.
* One wheel profile able to grind different rotors, thus reducing tooling cost and
change-over time, i.e. different width wheels, diamond rollers, diamond roller spindles,
wheelflanges, etc.
DISADVANTAGES
[0046] * Increased time cycle.
1. A method of grinding blade tips of a turbine or compressor rotor, comprising the steps
of spinning a rotor having one or more sets of blades to be ground on its axis, providing
a grinding wheel which is narrower than the blades to be ground and having a convexly
curved grinding periphery as seen as cross section, rotating the grinding wheel about
an axis parallel to the rotor axis and moving the grinding wheel and rotor relative
to one another in a traverse direction parallel to the axes of the rotor and wheel
and a feed direction orthogonally to the axis of the rotor and wheel to grind the
blade tips of the rotor to a required dimension and profile which may be flat, angled,
convexly or concavely curved with a simple or complex curvature.
2. A method as claimed in Claim 1, wherein the grinding wheel is moved simultaneously
in the feed direction with movement of said rotor in the traverse direction to create
said angled or curved forms.
3. A method as claimed in Claim 2, wherein the grinding wheel is moved with a varying
rate in relation to traverse of the rotor to create said curved profiles.
4. A method as claimed in any of the preceding claims, wherein the wheelhead and/or rotor
are moved incrementally in microsteps in grinding the blade tip to the required profile.
5. A method as claimed in any of Claims 1 to 4, wherein the blade tips of the rotor are
ground to a wherein the blade tips of the rotor are ground to a required dimension
and profile in a series of grinding operations.
6. A method as claimed in Claim 5, wherein the grinding wheel is dressed between grinding
operations.
7. A method as claimed in Claim 5, wherein the grinding wheel is dressed during grinding.
8. A method as claimed in any of the preceding claims, wherein a deburring operation
is carried out on the blade tips after grinding.
9. A method as claimed in any of Claims 1 to 7, wherein the blade tips are de-burred
during grinding.
10. A method as claimed in any of the preceding claims, wherein the blade lengths are
measured between grinding operations to determine the remaining amount of material
to be removed in a succession of operations.
11. A method as claimed in any of Claims 1 to 9, wherein the blade lengths are measured
during grinding to determine the remaining amount of material to be removed in successive
grinding operations.