1、 STD-AGUA 75FTM2-ENGL 1775 m Ob87575 000Lib5b 754 m I , from Separation of Runout Elemental Inspection Data by: Irving Laskin, Consultant and Ed Lawson, American Sykes Company American Gear TECHNICAL PAPER COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Servic
2、es STD-AGMA 95FTM2-ENGL 1775 Ob87575 000Lib57 bTO Separation of Runout from Elemental Inspection Data Irving Laskin, Consultant and Ed Lawson, American Sykes Company Fe statements and opinions contained herein are those of the author and should not be consued as an officiai action or opinion of the
3、American Gear Manufacairers Association. Abstract As reported previously (AGMA 93FTM6),Runout due to eccentricity influences Index, Pitch andn.ofie inspection data for spur and helical gears and Tooth Alignment inspection data for helical gears. This paper reviews the numerical procedure currentiy u
4、sed with index and Pitch data to determine the magnitude and direction of the Runout and to replot the inspection data with the Runout influence removed. It also introduces a speciai numerical procedure to perform the same function with Profile and Tooth Alignment inspection data. This new numerical
5、 procedure is effective in the presence of such tooth geometry features as slope variation (e.g., pressure angle Variation in Profile and helix angle variation in Tooth Alignment), non-linearity (e.g., tip relief in ProNe and crown in Tooth Alignment), and waviness. The numerical procedure is demons
6、trated for Index, Pitch, and Profiie inspeCon data taken from a test gear. Copyright O 1995 American Gear Manufacturers Association 1500 King Street, Suite 201 Aiexandria, Virginia, 223 14 October, 1995 ISBN 1-55589450-2 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information
7、Handling ServicesSTD.AGMA 95FTM2-ENGL 1995 m b87575 04b58 537 Separation of Runout from Elemental Inspection Data Irving Laskin, Consultant, Sharon, MA Edward Lawson, American Sykes Co., Beavercreek, OH Introduction. In the manufacture of gears, one of CL.? common variations from ideal gear )metry i
8、s the presence of Runout. In the ladest use of the term, Rumut covers Axial Runout (wobble) and Radial Runout, with the latter as a combination of Eccentricity and Out-of-Roundness. Each of these variations detracts in its own way from ideal performance of the gear and each deserves to be studied. T
9、his paper, as did a previous paper l for which this is a continuation, deals with the Eccentricity component of Runout in spur and helical gears. The previous paper showed quantitatively how this Runout, expressed by the magnitude and direction of eccentricity, influences the inspection results for
10、the Elemental Variations of Profile, Index, Pitch, and Tooth Alignment (the last, on helical gears only). It was notea that any system of tolerances for such inspection results should consider the information in these relationships. This is especially true when the procedures for inspection data int
11、erpretation simply lump together the effect of eccentricity with all other sources of variations. The present AGMA interpretation procedures, as defined in AGMA 2000-A88, Gear Classification and Inspection Handbook, does just this, as, for example, in its use K-charts for evaluating Profile and oth
12、Alignment inspection data. A better approach to analyzing such inspection data is to separate out the individual components of the total measurement and to judge the gear quality accordingly. This approach is partially applied in IS0 standards for gear quality 121 which establish tolerances for indi
13、vidual components of an inspection record. However, the separation process described in these standards is incomplete and approximate. This may be a result of the limitations of traditional inspection equipment. The introduction and increasingly widespread use of computer controlled inspection machi
14、nes, with their internal data processing capabilities, now make it possible to thoroughly and more accurately define procedures for separating the component Variations. This paper describes such procedures for separating the Runout eccentricity component from Index (and similarly for Pitch), Profile
15、, and certain cases of Tooth Alignment. Runout Eccentricity and Gear Quality. separating this Runout from other types of gear geometry variations is not merely an academic exercise, or even just a diagnostic tool. Inspection results are used to predict how well the gear will perform in its intended
16、application. It is a waste to reject a manufactured gear for exceeding any of these elemental tolerances because of the unseparated contribution of eccentricity, when the eccentricity itself will not significantly affect performance. It should be pointed out that 1 COPYRIGHT American Gear Manufactur
17、ers Association, Inc.Licensed by Information Handling ServicesSTD-ALMA 95FTMZ-ENGL 1995 It is similarly a waste to specify tighter quality classes, and the more expensive manufacturing processes they demand, because of a failure to distinguish the true critical quality features. To judge the relativ
18、e significance of the Runout eccentricity in evaluating gear performance, consider first that during gear operation, eccentricity by itself does not change basic tooth geometry. It simply continually moves the location of the true center of that geometry in a circular pattern. Consider next what the
19、 different Elemental variations are presumed to reveal about gear performance and whether this changing center location can affect these performance characteristics, as follows: - Profile variations, in the form of excessive slope differences from the specified ideal, are understood to predict addit
20、ional impact at load transfer and other undesirable dynamic load conditions during the tooth-meshing-cycle. These slope variations, by introducing a mis-match in base pitch between mating gears, can cause reduction in gear life or unacceptable vibration and noise at frequencies based, typically, on
21、tooth meshing rates. However, consider a gear which is otherwise ideal but has some eccentricity which appears as apparently excessive Profile variation. Such a gear has no variation in true base pitch and will not suffer the same kind of tooth-meshing-cycle dynamic effects. There may be some dynami
22、c influence from the eccentricity, but only at the much lower frequency based on rotation rate and, therefore, generally with a much lesser effect on gear life, vibration, or noise. - Pitch variations (or differences in successive Index measurements) also suggest life-reducing impact during meshing
23、tooth load transfers. Here again, the otherwise ideal gear, with enough eccentricity to show an apparently excessive maximum Pitch variation, will experience none of this presumed impact. departure from uniform tooth load distribution and a resulting reduction in gear life. In otherwise ideal helica
24、l gears, for which pure radial eccentricity can create an apparently excessive Tooth Alignment variation, the true base helix angle is unchanged and there is no loss in uniform tooth load distribution. - Tooth Alignment variations suggest a It is true that eccentricity has its own set of undesirable
25、 effects on gear performance, such as variation in backlash and angular position accuracy, which may be critical in some gear applications. The necessary response, therefore, is not to ignore eccentricity, but to identify its scale and avoid its possibly misleading influence on other features of gea
26、r geometry quality. b87575 00Yb59 Y73 Axial Runout (Wobble) of gear performance may be indifference to Radial Runout caused by eccentricity do no generally apply to Axial Runout. Axial Runout will adversely affect tooth load distribution and can introduce additional undesirable dynamic effects. Outs
27、ide of some brief comments, this paper does not consider Axial Runout and how it might be revealed in Elemental inspection procedures. This important issue has been left to future study. The above comments on how some aspects Effect of Runout Eccentricity on Inspection Measurements. The previous pap
28、er 111 developed the following equations that relate the eccentricity to the Element variation measurements. The symbols and directional conventions used in these equations are shown in Figure 1 and Table 1. Index measurements on the left and right flanks: e - sin 180 + 8elM - Mm - cos Mt EEq 21 Pit
29、ch measurements on the left and right flanks: 2 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 95FTM2-ENGL 1975 Profile measurements on the left and M+,. = e sin M+ = e sin 1 (- eel, - aPgt)l + right flanks: (eelM - apat) + r(k-1) + 1) EEq 51
30、 -I(k-l) + E,) EEq 61 Tooth Alignment measurements on the M = e(cos + (Mt - apt)1 + r(k-1)+(36o0/L) x.1) Eq 71 MR = e(cos + ) sin I C180 + Bei - (Mt- apWldl + r(k-l)+( 360“/L) xm 1) Eq 81 left and right flanks (of helical gears): sin 1 ceel + All of these equations show that the measurements derived
31、 from eccentricity will, when plotted, follow some portion of a sine curve of the form: The semi-amplitude of each such sine curve is defined by the coefficient (C) preceding the sine function. The magnitude of the eccentricity (e) is alway part of each coefficient and, except or the Profile measure
32、ments, is modified by a factor based on the gear data and the inspection Set-up. The angle of the sine function consists of a number of terms, the final one, represented by y in Equation 9, contains the independent variable in each measurement function. Each of these variables contains (k-l), the nu
33、mber of teeth spaced from the first tooth. For the Index and Pitch measurements, there are no other components since only one point is measured on each tooth. For Profile, the second component is the roll angle at the measurement location (E,). For Tooth Alignment, it is the distance along the tooth
34、 face (x,). The remaining terms in the angle, shown within the first set of brackets in each measurement equation and represented by B in Equation 9, collectively designate a phase-shift term. All relate to features of the gear and the inspection Set-up. Included within these is the term identifying
35、 the direction of the eccentricity, namely the angle from the eccentricity to the center of the first tooth at the measurement location, (elw), for Index, Pitch, and Profile, and to the center of the first tooth at the near surface, (Bel ), for Tooth Alignment. Ub7575 0004bb0 195 Solving for Eccentr
36、icity from Measurement Data. The process of extracting the eccentricity data from each set of measurement data would then appear to be quite straightforward, as follows: to the measurement data and note its semi- amplitude and phase-shift angle. 1. Fit the appropriate sine function 2. Set the semi-a
37、mplitude equal to the coefficient term of the corresponding measurement equation (Equation 1 to 8) and solve or e, the magnitude of the eccentricity. the phase-shift set of terms in the corresponding measurement equation and solve for for 8e1 or Bel, the term that locates the direction of the eccent
38、ricity. 3. Set the phase-shift angle equal to 4. Using this eccentricity information and the proper eccentricity measurement equation, calculate the measurements that would result from eccentricity alone. Then subtract these from the inspection data, leaving only the non-eccentricity components. The
39、 following sections describe this process for each type of measurement. Each description also notes difficulties that may be encounted and procedures for overcoming then. The process for Index and Pitch is already known to the inspection equipment industry but, at present, is used in only the most a
40、dvanced Index inspection machines. Even there, the treatment is less complete than the description below. The processes for Profile and helical gear Tooth Alignment are not known to be in use and may be original to this paper. Eccentricity in Index and Pitch Measurements Figure 2 gives the Left Flan
41、k and Right Flank Index and Pitch inspection data on the 15 tooth test gear described in the previous paper il. The data in this figure will be used as an example in describing the calculation process. For a better representation of the Pitch data, the lines with Tooth Number and Index values should
42、 be double spaced with the Pitch values printed on the intermediate lines. This would show that each Pitch value represents a measurement between an adjacent pair of teeth and should be assigned a tooth number corresponding to the mid-value of the pair. Thus, the Pitch values shown in the figure alo
43、ngside Tocth Number 2 are more correctly identified by Tooth Number 1.5. See Table 3 for an example of this representation of tooth numbers. 3 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services STD-AGMA 75FTM2-ENGL 2775 = Ob87575 000qbbL O22 Step 1. Fit
44、a sine function to the data. Since each set of data covers a full sine wave cycle, it is possible to use a well known mathematical procedure, the Fourier analysis, to perform this curve fitting operation. After applying this analysis to the Pitch data, the calculated phase-angle must be reduced by o
45、ne-half the tooth-pitch angle to correct for the first measurement being at the 1.5 tooth number, as explained above. For the example of Figure 2, this analysis gives the semi-amplitude and phase-shift of each sine function in Table 2, listed under Step 1. The Pitch phase- shift values have been adj
46、usted as noted above. The Fourier analysis can simultaneously give information about out- of-round conditions or other geometry variations in the gears. These Considerations are beyond the scope of this paper. Step 2. Find the magnitude of the eccentricity. Each value of sine wave semi-amplitude (C)
47、 is set equal to the corresponding coefficient from Equations 1 to 4, and solved for the eccentricity (e) using the appropriate gear and Set-up data. Values of these gear and Set-up data for the example of Figure 2 were calculate using the equations in Reference ll and are given at the top of Table
48、2. Values of calculated eccentricity for each of the four sets of inspection data are listed in Table 2 under Step 2. to each other. For each flank, the small difference between eccentricity from the Pitch and Index data are due to the rounding errors in the inspection data. Differences between ecce
49、ntricity. from the two flanks are also due to rounding and, possibly, to small measurement error. It may also result from some other slight differences in the flank geometries. Table 2 also shows a comparison with the value of eccentricity intentionally introduced into the test gear by means of an eccentric arbor. The calculated values are each fairly close to the intentional eccentricity. The differences are within the level of quality of the gear as measured without the eccentric test arbor. Note how closely these
