32 GEA R TE CHN OlOGY Computerized Hob Inspection & Applications of Inspection Results Part I Yefim Kotlyar Gea!f Process!ing '& Metrol!og-y Consulitant Sk,okiie.IIL - -- Fi!!l.l /\ Introoocti()D Can a gear profile generated by the hob- bing method be an ideal involute? In strieUy theoretical lenns - no, but in practicality - ye . A gear profile generated bylhe hobbing method i an approximation of the involute curve. Let's review a classic example of an approximation. Do regular polygons and circles have any- thing in common? Yes. One can appruximate a circle imply by increasing the number of sides of a polygon. Let' a sume that one has scissors and can cut only a traight line. Let's cut the simplest. polygon, a triaagle, from a piece of paper. It hardly resembles a circle (Fig. 1). he haded area shows the vallation between a triangle and a circumseribed circle. But i.f the number of the sides of a polygon is doubled (Fig ..2), the variation between a polygon and a circle is reduced dramatically, Yet, if the number of ide. is doubled once again, the variation can hardly be eel] (Fig. 3), By increasing the number of sides of a poly- gon further, it is possible 10 get so dose to a circle that the variation becomes negligible - the difference CaJJlIIot be seen or even measured. The process of generating a gear .0111 a hob- bing machine is baed on a similar idea of approximation. Hobbing is a process that gen- erates a number of connected lines which approximate an ill volute curve. Fig.2 Fi!!l.3 -- -
Introoocti()DCan a gear profile generated by the hob-
bing method be an ideal involute? In strieUytheoretical lenns - no, but in practicality -ye . A gear profile generated bylhe hobbingmethod i an approximation of the involutecurve. Let's review a classic example of anapproximation.
Do regular polygons and circles have any-thing in common? Yes. One can appruximatea circle imply by increasing the number ofsides of a polygon.
Let' a sume that one has scissors and cancut only a traight line. Let's cut the simplest.polygon, a triaagle, from a piece of paper. Ithardly resembles a circle (Fig. 1). he hadedarea shows the vallation between a triangleand a circumseribed circle. But i.f the numberof the sides of a polygon is doubled (Fig ..2),the variation between a polygon and a circle isreduced dramatically, Yet, if the number ofide. is doubled once again, the variation can
hardly be eel] (Fig. 3),By increasing the number of sides of a poly-
gon further, it is possible 10 get so dose to acircle that the variation becomes negligible -the difference CaJJlIIot be seen or even measured.
The process of generating a gear .0111 a hob-bing machine is baed on a similar idea ofapproximation. Hobbing is a process that gen-erates a number of connected lines whichapproximate an illvolute curve.
Fig.2
Fi!!l.3-- -
Involute Generation. ona. Robbing Maehine
A bobbing machine cannot cut curves, but itcan cut lots of straight lines in a certain pattern.Therefore. the idea of approximation is utilizedin order to generate an involute. Every cuttingedge of a hob cuts a straight line. The numberof straight lines (enveloping cuts) should belarge enough so that the difference between theinvolute and the combination of straight linesbecomes negligible.
Figs. 5 and 6 show gear profile generation asseen 'by an observer who rotates with the gear.
Fig. 5 shows an approximation of an involutegenerated by only three cutting edges of a hob.
The shaded area illustratesthe variation betweenthe involute and the approximating cuts.
If the number of cutting edges is increased,as in Fig. 6, the variation becomes less appar-ent. The involute variation generaled by anideal hob can be calculated as follows:
Profile Variation = [1t2• Zo· Mil· sin(NPA)]I
(4· Z2· (2)
Zo - Number of hob startsMil - Normal module
NPA - Normal pressure angleZ2 - Number of gear teethi-Number of hob gashes
As one can see from the formula, an expo-nential. reduction in variation can be obtainedby increasing the number of gashes. A geargenerated by means of an idea] hob, an idea]machine and an ideal future will have a profilecurve that. is an approximation of an involute.in the same way alii equilateral polygonapproximates a circle. The whole topology of agear tooth consists of numerous cuts in leadand involute direction (Fig. 7).
A center of every single generating cut lieson the line of action (Fig. 8). The dashed linesdepict hob cutting edges (rom the point. of viewof an. observer rotated the gear.
After a hob with a sufficient number of cut-ting edges is selected. the hob should be ableto generate an ideal involute or at least aninvolute with a predictable variation. Whydoes it ometimes :fail? Well, because we livein an imperfect world, especially when itcomes to a hobbing machine. a work-holdingfixture. a blank or a hob. all of which effect
Fig.4
Fig.5
Figl.6
rr * Z * M .. Sin(NPA)Profile variation '" 0 n-
hZ2* j2
Zo - Number of hobs startsMn - Normal moduleNPA - Normal pressure angleZ2- Number of gear teethj - Number on hob gashes
Fig.7
~efim Kotlyalris a gear processing andmetrotogy consultant.He lias also worked forAmerican Pjower. L. P..Loves Park, Il; and Roto-Technology, Inc .• Dayton,OH. He is the author ofltt/mtrOlts papers 011
gearillg subjects.
MAY/JUNE 1994 33
Une of Action
Fig.8 -I
TotalLength
Fig. 9 _
All hob geometrycharacteristics arereferenced to proofflanges,
the hobbing process.Our discussion, however, will be limited to
reviewing the effects or hob errors on the accu-racy of involute generation.
Hob Geometrical CharacteristicsThe ultimate goal of hob inspection is to
make sure that during the hobbing process, thecutting edges of a hob have a minimum devia-tion from their theorericalposirions.
There are several hob geometrical charac-teristics. Some of them, like the line of action,show the direct variation of cutting edges fromtheir theoretical positions at the points wherethey generate gear involutes. Most characteris-tics, however, can only show the displacementof cutting edges indirectly.
Commonly accepted characteristics that ahob manufacturer or a hob user might checkinclude the following: Radial. runout of proofflanges, face runout, rake, flute index, flutelead, lead and thread-to-thread variation, out-side diameter, pressure angle, line of action,radial and axial relief and tooth thickness.
Radial Runout of Proof FlangesMost bobs have ground proof diameters or
hubs on both sides (Fig. 9). These diametersare used by operators to Indicate a bob whenmounting it on the machine (Fig. 10). AI] hobgeometrical characteristics are referenced toproof diameters. Usually proof diameters arechecked first,
Excessive hub runout cau es a gear profileerror that can be approximately calculated asshown in Fig. I].
Fig, 12 shows the effect of hob radial runouton gear involute. Fig. 13 shows the leastquares method for determination of a circle's
center and eut-of-roundness. This methodallows one to determine concentricity and out-of-round amount very precisely.
A CNC inspection machine will automati-cally check the hub's runout at a specifiedposition (Fig. 14).
Evaluation should include the determinationof total runout, out-of-round and concentricityerrors (Fig. 15). The results of inspection andevaluation can also be pre ented in circular formas shown in Fig. 16. This chart shows a roundsurface that is magnified 2000 times. The dis-tance to the center of the best fit circle has the
Gear ()O
Rightflank
Leftflank
(Gear Root
Effect of hob radial runout on gear involute------
Fig.12
Eccentric;ity
Out-af-round
Machine CenterCenter of least squared circle
Fig.13
Distance from cutting edgeFor c ecking upper 'hub
Distanc from cutting edgeFor check,ingllower hub
Fig.14
Probe
Scale O.4ll
Hob 10 4191 Left Contact
Serial 001
Operal0r Ed
N,D,P, 7,2.36461 Left NPA
Axial Lead 0,8661)000 lead Hand
20,000000
Right-
Whole Depth 0,23622 Gash Hand Left1-
O.07847L Number Gashes 10 Required Quality AGMA: B1---- ----
Journal Toler.iotal Runoul 0,00070Oul of RoundEccentricityAverage Diamets r
UpperO,OOOl1:A0,000040,000041.71883
lowero.oOO14:.A0,000090,000051.70886
Fig,15
Hob ID 4191 left Contact N,D,P, 7.23S46~ Left NPA 20.000000:.:.1
Serial 001 Axial Lead 0,8660000 Lead Hand RighI----------~-- ~ --------------1
Operator Ed Whole Depth 0.23ll22 Gash Hand Left--------------1
Probe Q,07814L Number Gashes Ia . Required Duality AGMA: B
2 c:\Roto HobIHBOOO,HOBIMSOO9,MESInspected 04115/93 09:20:48 Number Threads
Metric/InCh Inch Right NPA. 2Q,QOCOOO Magni! 2000.00 Scale 2.00
Hob Journal Inspection
UpperO,OOQll:AO.!Dll40000041.11883
Journal Toler.Total Runout 0,00010Out of Round~ccentricitvAverage Diameter
LowerO,00Q14:AO,ocoog0.00005IJ088Ii
Fig. 16
Hob face runout
Fig. 11
Left flank Right flank
Effect of hob face runout on gear involute
SurfaceVariation
Fig. 18
Hob ID 4191 left Contact N.D.P. 7.236467 LeftNPA 20.000000
Senal 001 Al:ial Lead 0.1m6OOOO Lead Hand RighI
Dperalllf :Ed Wll:ole Depth 0.23622 Gash Hand LehProbe n 07874l NumlMf Gashes 10 Required Qu!l", AGMA:B
Inspected 114115/93, 09:20:48 Number Threads c:lRoto HoblH BDOO.HOBIMSOOS.MESI Me1licllnch Inch Right NPA 20.000000 Meg"i! .2000.00 Scale O.4ll
H!obFace Inspection
Upper0.00006:1\0.l100050.000015.44237'
LowerD.00075:10.00D430.000302.42440
Fig.20
Face Toler.TDtIII Hunout 0.00030OutolAatEccentricityVertical PDsitJon
- -------------- -----
Fig. 19
36 GEAR TECHNOLOGY
----------------------------
IFigl.21
SurfaceVariation
Form
Evalusltion range'~~---- ------~
Fig. 23
same magnification; thus, eccentricity can bescaled. AU the numerical evaluations are alsodisplayed all the chart. The results of hubinspection on both sides are superimposed so therunout inaccuracies can be compared visually.
The evaluation program may have a built-in AGMA, DIN, and ISO hob tolerance sys-tem. If the operator specifies the requiredqUality class, the program should automatical-ly compute the required tolerance.For charac-teristics which have quality classification, theactual quality may also be automatically deter-mined and displayed ..
Face RunoutHob faces are frequently utilized for clamp-
ing during mounting a hob on either a hobbingmachine or a hob sharpening machine. The hobfaces have to be trued (Fig. L7). Excessive facerunout call re ult in involute variation (Fig,18). Inspection and evaluation of face runout
include out-of-flat and eccentricity (Fig. 19).Rake
Some simplificati.on of surface variationmay be useful for process analysi and prob-lem solving.
Gene,.,al Surfacce Variation Components,The variation of any surface from its ideal con-dition can be simplified as a variation of amountainterrain in relation to a flat surface,One could ki ana mountain with a steady andeven drop (Fig. 20), or on a horizontally un-dulating terrain (Fig. 21). But frequently moun-tain terrain is acombination of both (Fig. 22).
The concept of breaking down the total sur-face variation into several components is wide-ly used in many applications, including hobsand gears. Fig. 23 illustrates the least squaresmethod for the determination of form andslope error components. Frequently. slope andform errors are useful even if not specified byDINIA:GMAlISO standards. The breakdown ofthe total value into slope and form componentshelps to determine the sources of errors andbetter identify any needed process adjustments.
Ho.b Rake Inspection .. Hob rake is a lineresulting from the intersection of a tooth facewith a plane that is normal to the hob axis. H'this tine crosses the hob center, it is cal1ed a
zero rake.Rake onset is the amount by which the
design rake line i distant from the plane of ahob axis (Fig. 24). Hob rake offset is zero if
Postive Rake Offset Negative Rake Offset
Fig. 24---
~V\
Ra,keInspection
Fig. 25
Correct rake Cutter tooth Gear tooth
~A V Corr,ect
involute
Ip~eerror
Plus
J\ V involut'B
qfJ error
N~tre".r/~ V NegativeinvoMeerror
I
IIConvex rake error
* /\ V Concaveinvoluteerror
Rake Error Effe,cton Gear Involute
Fig. 26
MAVIJUNE 1994 37
Whole Depth
Evaluation Stsrtr-__.--Evaluation End
Measuring End
-
Fig.21 ,
Magnd 2001.00 Scale 25.0
Hob In ~191left Contact
Senal 001
Operator Ed
Probe O.07874L
Inspected D4115193 09:20:48
Metrlcllncil Inch
N.D.P. 7.236467
Axial Lead 0.8660000
Whole Depth 0.23622 GashH8J1d _,LefI_.·_--I
Number Gashes '10 ReqUired Quality: AGMA: II_--II-
~mli::iii:iii~i:ii:iiiiii::::::::::::~~~~+;. - , : 1~ 4/2 r;::;:~::::::::;:~:~~~:::::L:: :::::::~::::::::'::.: :::~:::::::::::':::::::::.q;',::1g t:~::::::~:::::~~:::::::::::::::::~:::~::::::::.:::::::~::::::~::::::::::::::::::~:::t: !~ i i ,
~ ,••.••••••••••••••••••••••• _ ••••••• r ~ ~ •••••••• l 1
latS:0:::~~~~1-0.00004 0.24407
GashJTooth foler. 1/2 412 7f2
Totll 0.00070 O.OOO38:A O.00037:A O.IlOO34:A
Slllcflll - 0.00028 -0.00016 -0.00007
form 0.00019 0.00028 0.000l8
fig. 28
38 GEAR TECHNOLOGY
the rake line cro ses the hob center. The rakeoffseti negative if the rake line make anobtuse angle with the tooth outside diameter,and positive if the rake line causes an acuteangle with the hob outside diameter. Most. hobhave 0° rake, although there ate some hobswith po itive or negative rake. Rake is mea-sured on the tooth face as hown in Fig. 25.The task of inspection is to find out rake devia-[ion from the design geometry.
Rake inaccuracy affects the gear profile.Fig. 26 shows samples of typical rake inaccu-racy and relevant gear profile errors. Theinspection result should identify inspectiondistance in reference to the tip of the tooth(Fig. 27). A ample of rake inspection on ev-eral different teem i hown in Fig. 28. In addi-lion 10 the mea uring and evaluation ranges,the chart should also identify tooth and rawnumber, magnification and scale, requiredstandard, quality .. and tolerance. if any. Inspec-tion of helical flute hobs requires probe contactpoint adjustments, since flute angle changes asthe probe moves from tile root to thetip of thetooth. Evaluation re. ults include the followingcharacteri tic for every measured rake: Totalerror, slope error, form error, and actual qualityper AGMA, DIN or ISO tandard for everytooth. If the sy tern has off-line capabilitie ,the various evaluations could be performedwithout having to recheck a hob .•
Editor's Note: The second hal] of this article. llliUappear in our next issue.Acknowledgements: The author wishes to thallkEd Driscoll for his tulvice, support, and creativitythat inspired and helped l+'I'ilemany parts of thlspaper; 10/m umge. for co-aulllOn'ng a paper on asimilar subject presented at an AGMA symposiumill 1989;' Lauren Bromberr for her meticulou: DIUI
cr;eatil'e editing help; Rachel Huisman; for creal-ing the illustration' that helped simplify thedescription of nlTface variation character! ticsand Richard Considine for computerizing them,and Esther Munsey [or her constructive editorialhelp. Gear inspection charts {Ire courtesy of Roto-Technology, Inc., Day toll, OH. This article wasfirst presented at the AGMA Gear ManufacturingSymposium, held in Detroir, Ml, October, 1993.Refeflence :I. AGMA Standards2. ANSI B94.7. 19803. DIN 3968-1069, 3000=1962, 3960-19804. VDINDE 26065. Kotlyar, Yefim and John Lange. "CNC Inspec-tion and Evaluation of Gear Cutting Tool. ..AGMA,.1989.
