Evaluating a toothed work piece for machining based on accumulated pitch variation

A method of evaluating a toothed workpiece for machining according to a predetermined machining process. A workpiece spindle is rotated to bring selected leading and/or trailing tooth flanks each into a predetermined position relative to a probe to generate a signal indicative of the instantaneous rotational position of the spindle and the instantaneous rotational spindle positions corresponding to each generated signal are recorded. Theoretical spindle positions corresponding to each selected tooth flank are provided, and the difference between respective recorded spindle positions and the theoretical spindle positions for each selected tooth flank is calculated to yield a measured error value. The maximum and minimum measured error values for leading tooth flanks and/or trailing tooth flanks are selected and a maximum accumulated pitch variation (P.sub.V) is calculated for the leading tooth flanks and/or trailing tooth flanks. The maximum accumulated pitch variation (P.sub.V) is compared to predetermined pitch variation tolerance limits comprising an abort tolerance (T.sub.A) and a modified process tolerance (T.sub.M) whereby the predetermined machining process is aborted if P.sub.V .gtoreq.T.sub.A, the predetermined machining process is modified if T.sub.M .ltoreq.P.sub.V .ltoreq.T.sub.A, and the predetermined machining process is carried out if P.sub.V <T.sub.M.

RELATED APPLICATIONS 
This application is Provisional Application No. 60/014,345 filed Mar. 29, 
1996. 
FIELD OF THE INVENTION 
The present invention is directed to machining of toothed articles such as 
gears and the like. Particularly, the present invention relates to a 
method of evaluating a workpiece to determine the appropriate procedure to 
be followed in machining the workpiece. 
BACKGROUND OF THE INVENTION 
In machining processes for toothed workpieces such as finish grinding 
processes for spur and helical gears or bevel and hypoid gears, the 
presentation of a succession of workpieces for machining provides a 
variety of workpiece geometries to be machined by a tool, such as, for 
example, a threaded grinding wheel for spur or helical gears. 
The geometry of a workpiece prior to final machining can be affected in 
many ways. For example, workpiece geometry is influenced by runout, 
cutting blade sharpness and positioning accuracy in a cutting tool, the 
mounting position of the workpiece on the cutting machine spindle, the 
precision of machine axes motions of the cutting machine itself, 
distortions caused by heat treating subsequent to cutting, or, assembly 
errors when the workpiece is fastened to another rotational member. 
Inaccuracies in a gear degrade its quality and performance and can lead to 
undesirable stresses under load, transmission errors, noise and vibrations 
when rotating. 
Regardless of how inaccuracies are introduced into a workpiece prior to 
final machining, the final machining process must contend with a range of 
workpiece conditions with the expectation that the workpiece, after final 
machining, will meet the geometrical requirements of a finished workpiece. 
In some instances, attempting to grind a workpiece with excessive runout, 
whereby excessive stock material is present on a portion of the tooth 
flanks, can lead to burned tooth flank surface finish and accelerated wear 
on the tool thus requiring more frequent dressings and diminishing the 
useful life of the tool. If too little stock exists on the tooth flank 
surfaces or runout is excessive, some surfaces of the teeth will not be 
properly finished by the machining process. 
One approach to analyze gear quality is to detect the amount of runout 
present in the gear. Runout is a measure of the radial eccentricity of a 
gear, but runout may also be of the type known as "hidden runout" which is 
identified by the accumulated pitch variation present in a gear. Hidden 
runout may exist apart from radial runout. A discussion of hidden runout 
and its detection by use of accumulated pitch variation data is discussed 
by Smith, Robert, et al., Detection of "Hidden Runout", AGMA Technical 
Paper, 95FTM1, October, 1995. 
Another method of analyzing a workpiece for errors due to runout and heat 
treat distortions is disclosed in U.S. Pat. No. 5,136,522 to Loehrke. A 
gear is rotated past a non-contacting probe and the work spindle 
rotational positions of leading and trailing flanks are recorded, compared 
to theoretical spindle positions, and measured error values based on the 
difference between actual and theoretical readings are computed for each 
set of leading and trailing flanks. The measured error values for each set 
are then analyzed using fourier transform techniques to generate a first 
harmonic comprising a set of modified error values indicative of runout. 
The modified error values are subtracted from the measured error values to 
yield a set of adjusted error values indicative of distortions due to 
other factors such as heat treating. The largest and smallest modified 
error values are utilized to simulate an effective tooth spacing which is 
compared to the desired tooth spacing and a correction value is generated 
by which the angular position of the workpiece spindle is adjusted to 
ensure accurate machining. 
It is an object of the present invention to provide a process wherein tool 
wear and the number of rejected workpieces are reduced. 
It is a further object of the present invention to provide a process 
wherein a toothed workpiece is evaluated to determine the suitability of 
the workpiece flanks for subsequent machining and providing alternatives 
or modifications to the intended machining process depending on the 
results of the evaluation. 
In this way, a given workpiece can be determined to be suitable for a 
predetermined machining operation, or alternatively, the machining 
operation can be modified to bring the workpiece within an acceptable 
range for machining without having to reject the workpiece. 
SUMMARY OF THE INVENTION 
The present invention comprises a method of evaluating a toothed workpiece 
for machining according to a predetermined machining process. The toothed 
workpiece includes a plurality of teeth with each tooth having a leading 
flank and a trailing flank with respect to a direction of rotation. 
The inventive method comprises mounting the workpiece to a rotatable 
spindle on a machine tool and providing a probe means positioned whereby a 
signal is produced when a leading or trailing flank of the workpiece is 
located in a predetermined position relative to the probe, the signal 
produced by the probe being indicative of the instantaneous rotational 
position of the spindle. 
The workpiece spindle is rotated to bring selected leading and/or trailing 
tooth flanks each into the predetermined probing position to generate a 
signal, and the instantaneous rotational spindle positions corresponding 
to each generated signal are recorded. Theoretical spindle positions 
(relative to the first tooth flank) corresponding to each selected tooth 
flank are provided and measured error values are determined by the 
difference between respective recorded spindle positions and the 
theoretical spindle positions for each selected tooth flank. The measured 
error values are recorded. 
The maximum and minimum measured error values for leading tooth flanks 
and/or trailing tooth flanks are selected and a maximum accumulated pitch 
variation (P.sub.V) is calculated for the leading tooth flanks and/or 
trailing tooth flanks. The maximum accumulated pitch variation (P.sub.v) 
is compared to predetermined pitch variation tolerance limits comprising 
an abort tolerance (T.sub.A) and a modified process tolerance (T.sub.M) 
whereby the predetermined machining process is aborted if P.sub.V 
.gtoreq.T.sub.A, the predetermined machining process is modified if 
T.sub.M .ltoreq.P.sub.V &lt;T.sub.A, and the predetermined machining process 
is carried out if P.sub.V &lt;T.sub.M.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The details of the present invention will be discussed with reference to 
the preferred embodiment. 
The present inventive method may be carried out on any machine tool capable 
of probing a workpiece and adjusting the relative rotational position 
between the tool and workpiece in response to information acquired and 
manipulated as a result of the probing. 
FIG. 1 schematically illustrates one type of machine tool as set forth 
above comprising a computer controlled machine 10 for grinding spur and 
helical gears with a threaded grinding wheel. Machines of this type are 
known in the art and are readily available. 
The machine includes a base 12 and a work column 14. A work table slide 16 
is arranged on the work column 14 for linear movement along an axis 
(Z-axis). Mounted for rotation to work table slide 16 is work support 18 
which is rotatable about an axis (A-axis) for setting the proper helix 
angle required for grinding a particular gear. A work gear 20 is mounted 
to a rotatable spindle 22 by appropriate work holding equipment for 
rotation about the work gear axis (C-axis). Also shown is non-contact 
probe 24 positioned adjacent the tooth surfaces of workpiece 20. 
Non-contacting probes are well known using electric or magnetic fields, 
air jets, or light beams to generate trigger signals whenever the flank of 
a workpiece passes within some predetermined distance from the probe. 
Also located on base 12 are a pair of tool slides 30 and 32. Tool slide 30 
enables movement of the tool along the length of the base (X-axis) and 
tool slide 32 enables movement of the tool across the width of the base 
(Y-axis). Machine axes X, Y, and Z are mutually perpendicular to one 
another. 
Attached to tool slide 32 is tool support 34 to which tool 36 is mounted 
for rotation about a tool axis (S-axis). 
A dressing wheel table 38 is located on tool slide 32 and is movable along 
perpendicular dressing axes (U-axis and V-axis). A dressing tool support 
40 is mounted to dressing wheel table 38 and a rotary dressing tool 42 is 
mounted for rotation to dressing tool support 40. Dressing tool support 40 
is angularly adjustable on table 38 in order to position the dressing tool 
42 to the lead angle of the grinding wheel 36. V-axis motion is utilized 
to traverse the dressing tool 42 along the width of the grinding wheel 36 
and U-axis motion is used for infeeding of the dressing tool to position 
the dressing tool 42 at contact points along the profile of the grinding 
thread surface. 
Movement about or along the described axes is imparted by separate drive 
motors (not shown). The movable machine components named above are capable 
of independent movement with respect to one another and may move 
simultaneously with one another. Each of the respective motors is 
associated with either a linear or rotary encoder (not shown) as part of a 
computer numerical control (CNC) system which governs the operation of the 
drive motors in accordance with instructions input to a computer (not 
shown). The encoders provide feedback information to the computer 
concerning the actual positions of each of the movable axes. 
The method comprises mounting a toothed workpiece 20, such as a helical 
gear, to the rotatable spindle 22 on grinding machine 10 and providing the 
probe 24 positioned whereby a signal is produced when a predetermined 
height position of a leading or trailing flank of the workpiece is located 
in a predetermined position relative to the probe 24. The signal produced 
by the probe 24 being indicative of the instantaneous rotational position 
of the spindle. The workpiece spindle 22 is rotated to bring selected 
leading and/or trailing tooth flanks each into the predetermined probing 
position to generate a signal and the instantaneous rotational spindle 
positions corresponding to each generated signal are recorded. Probing in 
this manner is known from previously mentioned U.S. Pat. No. 5,136,522 the 
disclosure of which is hereby incorporated by reference. 
FIG. 2 illustrates probing the tooth flanks of workpiece 20 with 
non-contacting probe 24. As workpiece 20 is rotated in the direction of 
arrow 26, a position at a predetermined flank height "h" (usually the 
mid-height point of the tooth) on a first leading tooth flank T.sub.1 
passes probe 24 and a signal is generated to record the rotational 
position of the work spindle 22. As the workpiece continues to move past 
probe 24, the first trailing flank T.sub.1 would also trigger probe 24 to 
generate a signal to again record the instantaneous work spindle 
rotational position. Rotation of the workpiece 20 continues as the next 
leading flank, L.sub.2, and trailing flank, T.sub.2, pass the probe 24 to 
trigger recording of the respective work spindle positions. Rotation of 
workpiece 20 continues until all teeth have passed probe 20 and the work 
spindle positions for all leading and trailing flanks have been recorded. 
It is to be understood that although it is preferred to probe all teeth of 
workpiece 20 as stated above, the present invention may be practiced with 
as few as four, preferably equidistantly spaced, leading and trailing 
tooth flanks. 
The measured work spindle rotational positions for the leading and/or 
trailing flanks are then compared to corresponding theoretically correct 
flank positions. The first measured leading and/or trailing tooth flanks 
function as the "zero" position and the theoretically correct flank 
positions of all subsequent flanks relative to the first-scanned tooth 
flanks are generated based upon the first measured flank. The difference 
between respective measured spindle positions and theoretically correct 
positions are determined to yield a measured error value for each probed 
flank. 
As an example, a left-hand helical gear having 65 teeth and a pitch radius 
of 53 mm was mounted to a work spindle on a grinding machine such as shown 
in FIG. 1. The gear was rotated past a non-contact type probe and the 
leading and trailing flanks of all teeth were probed at a consistent tooth 
height "h" at about the mid-height of the teeth. The positional 
information obtained by probing, along with the respective theoretical 
position data relative to the first leading and trailing flanks and 
calculated measured error values for a portion of the teeth, are 
illustrated in the Tables below. Position and Error values are listed in 
degrees. FIG. 3 graphically easured error for the leading flanks of all 65 
teeth. 
TABLE I 
______________________________________ 
Leading Flanks 
Measured Theoretical Measured 
Tooth # Position Position Error Value 
______________________________________ 
1 2.54710 2.54710 0.00000 
2 8.08280 8.08556 -0.00276 
6 30.23105 30.23941 -0.00836 (min.) 
11 57.94550 57.93172 0.01378 
16 85.65400 85.62402 0.02998 
21 113.37950 
113.31633 0.06317 
26 141.10825 
141.00864 0.09961 
31 168.80130 
188.70095 0.10035 
36 196.51285 
196.39325 0.11960 
41 224.20815 
224.08556 0.12259 (max.) 
46 251.87825 
25i.77787 0.10038 
51 279.54600 
279.47018 0.07852 
56 307.20855 
307.16248 0.04607 
61 334.87985 
334.85479 0.02506 
65 357.00980 
357.00864 0.00116 
______________________________________ 
TABLE II 
______________________________________ 
Trailing Flanks 
Measured Theoretical Measured 
Tooth # Position Position Error Value 
______________________________________ 
1 5.12595 5.12595 0.00000 
2 10.65865 10.66441 -0.00576 
6 32.80460 32.81826 -0.01366 (min.) 
11 60.50610 60.51057 -0.00447 
16 88.21600 88.20287 0.01313 
21 115.93230 
115.89518 0.03712 
26 143.66035 
143.58749 0.07286 
31 171.35780 
171.27980 0.07800 
36 199.06770 
198.97210 0.09560 
41 226.77245 
226.66441 0.10804 (max.) 
46 254.44735 
254.35872 0.09063 
51 282.11825 
282.04903 0.06722 
56 309.78190 
309.74133 0.04057 
61 337.44915 
337.43384 0.01551 
65 359.58870 
359.58749 0.00121 
______________________________________ 
The maximum and minimum measured error values for leading tooth flanks 
and/or trailing tooth flanks are selected. Tooth #6 exhibits the minimum 
measured error value of -0.00836 for the leading flank and -0.01337 for 
the trailing flank. Tooth #41 exhibits the maximum measured error value of 
0.12259 for the leading flank and 0.10804 for the trailing flank. 
Maximum accumulated pitch variation (P.sub.v) of the leading tooth flanks 
and/or trailing tooth flanks is calculated utilizing any known method, the 
following equation being preferred: 
EQU P.sub.v =E.sub.max -E.sub.min !.times.(.pi./180).times.(R.sub.p).sub.work 
where 
EQU E.sub.max =maximum measured error value (degrees), 
EQU E.sub.min =minimum measured error value (degrees), 
EQU (R.sub.p).sub.work =pitch radius of workpiece (inches or mm). 
Thus, for the leading flanks in the example above, the maximum accumulated 
pitch variation is determined as: 
EQU P.sub.V =0.12259-(-0.00836)!.times.(.pi./180).times.53 mm 
EQU P.sub.V =0.12118 mm 
As an alternative, the amount of runout for the leading and/or trailing 
tooth flanks may be calculated using known techniques (such as fourier 
transformation, for example) and the results analyzed according to the 
procedure described below. 
The maximum accumulated pitch variation (P.sub.V) is compared to 
predetermined accumulated pitch variation tolerance limits comprising a 
process-abort tolerance (T.sub.A) and a modified-process tolerance 
(T.sub.M) whereby the predetermined machining process is aborted if 
P.sub.v .gtoreq.T.sub.A, the predetermined machining process is modified 
if T.sub.M .ltoreq.P.sub.V &lt;T.sub.A, and the predetermined machining 
process is carried out if P.sub.V &lt;T.sub.M. Workpieces with P.sub.V values 
equal to or in excess of the abort tolerance TA have considerable runout 
such that no amount of grinding can bring the condition of the workpiece 
to an acceptable form and therefore, the workpiece is rejected. Workpieces 
with P.sub.V values less than the modified-process tolerance T.sub.M 
exhibit little or no runout and as such can be machined by relatively fast 
standard grinding cycles programmed into the machine tool computer. If the 
P.sub.V value exists in the range of from equal to or greater than T.sub.M 
to less than T.sub.A, a significant amount of runout is present but with a 
modification of the standard machining cycle, the runout condition can be 
effectively addressed and the workpiece can be brought to an acceptable 
form. 
In modifying a machining process or cycle, several aspects of the process 
may be changed. For example, any or all of the following process 
parameters may be modified: one or more additional machining passes or 
strokes may be added, the amount of stock material removed per stroke may 
be altered, the infeed position of one or more strokes may be changed, the 
amounts of incremental shift and/or continuous shift may be modified, the 
grinding wheel speed, and, the stroke rate may be adjusted. 
In the above example, P.sub.V =0.12118, the abort tolerance T.sub.A =0.175 
and the modified process tolerance T.sub.M =0.09. Therefore, given that 
P.sub.V lies between the process-abort limit T.sub.A and the 
process-modify limit T.sub.M, more stock material exists on the tooth 
flanks than can be adequately removed by a standard grinding cycle and 
therefore, the actual process utilized to grind the gear was a 
modification of the predetermined standard grinding process for this type 
of gear. Specifically, in the present example, an additional grinding 
stroke was added to reduce wear on the grinding wheel as the excess stock 
material was removed. 
It is to be understood that the tolerance limits T.sub.M and T.sub.A will 
vary for different sizes and types of gears. Generally, the tolerance 
limits can be determined by obtaining the final required gear quality 
specification runout amount for a particular gear (such as AGMA, DIN, JIS 
or equivalent published standards or user specified standards) and 
multiplying this amount by about 3 to obtain the process-modify tolerance 
T.sub.M and by about 6.5 to obtain the process-abort tolerance T.sub.A. 
If the workpiece being probed is a workpiece intended for stock-dividing 
the machine, that is, for "teaching" the machine tool the positioning of 
the tool relative to the workpiece, the above tolerances should be 
tightened since usually a closer tolerance gear (low runout, little heat 
treat distortion, and fewer assembly errors) is desired for stock-dividing 
operations. 
If desired, average maximum and minimum error values may be utilized to 
calculate the maximum accumulated pitch variation. In this instance, the 
maximum and minimum error values and one or more adjacent flank readings 
are averaged to obtain the maximum or minimum error value. For example, 
tooth #6 is the minimum measured error value in the above example and if 
an average error value is desired, the measured error values of teeth #4 
through #8 could be averaged to obtain a minimum error value for either 
leading or trailing flank. 
It should be noted although the minimum and maximum error values in the 
above example occur on the same tooth for both leading and trailing flanks 
(#6 and #41 respectively), this is not always the case. Minimum and 
maximum values for leading and trailing flanks may occur on different 
teeth although usually the teeth will be near or adjacent to one another. 
Although the example discloses two tolerance limits, it is to be understood 
that any number of tolerance values may be included resulting in several 
ranges (T.sub.0 -T.sub.1 -T.sub.2 - . . . T.sub.n) with each range having 
specific process modifications assigned to it. 
While the present inventive process has been discussed with reference to 
helical gears, the invention is not limited thereto but is intended to be 
applicable to any toothed articles such as spur, bevel, and hypoid gears. 
Furthermore, the present invention is not limited to probing with 
non-contacting type probes but may also be effectively carried out with 
contact type probes. 
The present invention represents an enhancement to the prior art approach 
of grind-or-scrap by providing the flexibility to machine heretofore 
non-machinable workpieces and/or to extend the useful life of a tool by 
adapting a process such that tool wear is lessened. 
While the invention has been described with reference to preferred 
embodiments it is to be understood that the invention is not limited to 
the particulars thereof. The present invention is intended to include 
modifications which would be apparent to those skilled in the art to which 
the subject matter pertains without deviating from the spirit and scope of 
the appended claims