MACHINERY ' S REFERENCE SERIES
EACH NUMBER IS ONE UNIT I N A COMPLETE LIBRARY OF MACHINE DESIGN AND S HOP PRACTICE REV I SE D AND REPUBLISHED FROM MACHINERY
NUMBER 133
HOBS AND GEAR HOB G
B y J OH N E DGAR
CON TE N TS
Intro duction :P rinciples of the H obbing P roce ss
Bobs f or S pur and S piral Gears
S pecial H ob - tooth S hapes
The Centering of the H ob in Ge ar I;I obbing
e ar H obbing v s . M illing of G s
b h M A C H I N E R Y p r h t 1 91 4 T h e n d s t r a P re ss , P s e rs , C , o y ig , I u i l u li of
- L e t S t re e t N e w Y r% t 1 4 0 1 4 8 a fay t e , o Ci y Othe r boo%s in this series dealing with the subje ct o f Ge aring are as follows:
—WORM GE R N G N o . l A I — E R N G , N o . 1 5 SPUR G A I — P1 RA E R NG N o . 20 S L G A I —B EV EL GE R N G N o . 37 A I
M ACHI NERY
The L e adin g Mech an ic al Jo u rnal
M ACH IN E DE SIGN CON STR UCTION S HOP PR ACTICE
TH E IN DUSTRIAL PRESS
- 1 4 0 1 4 8 L afayett e St . N e w Y o r% Cit y
- e Lo ndo n 51 52 Chance ry L an , “ I N TR ODUCTHHJ
PR IN C I P LE O F TH E H O B B IN G PR O C E S S
The hobbing proc e ss for cutting the teeth in spur and spiral gears
e is beginning to be very widely used . The principl of this method is
shown diagrammatically in the accompanying illustration . In the lower part Of the illustration is shown an imaginary rack ( in dott e d
h e o f are lines ) ; this rack is in mesh with the ge ar , t e te th which
e as Of a to be formed , and if the blank could be imagin d made plastic
e material , the rack , i f moved along as indicated by the arrow , whil
e ee the ge ar rotate d to correspond , would form theor e tically corr ct t th
th e in the gear blank . The teeth of this rack coincide with outlines
o f the worm shown in full lin e s , this latter having been set at such an angle as to make the teeth o n its front side parallel with the axis Of h the gear . In other words , it has been set at the angle of its elix ,
e measured at the pitch line . This worm , when properly flut d , forms
e o f th e the hob for cutting the gear t e e th . It will be s en that the teeth
e e . h ob , when set in this position , corr spond with the t eth of the rack
th e If, now , the hob and blank be rotated at the ratio required by number o f thr e ads in the hob and the number o f teeth in the gear , this movement will cause the teeth of the hob to travel lengthwis e in exactly the same way as the t e eth o f the imaginary rack would trav el ,
s if in mesh with the ge ar , th e t e eth of which are to be c ut . It will thu be seen that th e h ob fulfills the r e quir e m e nts nec e ssary for molding h the t e eth o f the ge ar to the proper form . In practice t e hob is f rotate d in th e r e quir e d ratio with the work , and e d gradually through - it from one side Of the face to th e other . When it has passed through
‘
e . once , the work is complet d Of the great number o f machines built during the past few years
e S e involving this principle , many are arrang d for cutting piral g ars r Of as well as spur ge ars . Of cou se , all of the machines capable T cutting spiral ge ars are capabl e of cutting spur gears also . h e spiral gear- hobbing machine bears ab out th e s ame r e lat ion to the plain spur g ear- hobbing machin e that th e universal does to the plain mill
me e ing mac hine . The added adjust nts and mechanism r quired in e ach case tend to somewhat limit the capacity of th e machine in tak ing heavy cuts although th e y add to its usefuln e ss by e xte nding the n range o f work I t is capabl e o f p e rformi g.
R e q uire m e n t s o f G e a r H o b b in g Ma c h in e s
Th e requirem e nts o f the succe ssful gear hobbing machin e are
e First . A frame and m e chanism of gr at rigidity .
e e m S e cond . D urabl e and pow rful driving m chanis .
e . Third . Accurate indexing m chanism
o n The first requirem e nt is e of gr e at importanc e , not only in its influ e nc e o n th e h e avin e ss o f the cut to b e take n and th e cons e qu e nt 3 4 7 5 9 7 NSJEM OB S SAN D GE AR HO B B I N G o o f o n cc utput work , but the matter Of a uracy as well . The co n n ecti on between the h ob and the work , through the shafts and gea ring, is liable to be so complicated that the irregular cutting action Of th e
c hob produ es torsional deflections in the connecting parts , leading to serious displacement from the desired relation between the hob and
the teeth being cut . This displacement fro m the desired position f results in teeth o inaccurate shape , weak and noisy at high speeds .
In its effect o n the output, rigidity is even more imp orta nt in the
D i a gram illu strat in g th e P rin ciple of th e H obbin g Proc ess of Formin g S pur Ge ars
A hobbing machine than in the orthodox automatic ge ar cutter .
On heavier cut is taken , since a greater numb e r of teeth are cutting
the work at once . The numb e r o f joints between the cutter and the
“ - - w o rk supporting table and spindle must , therefo re , be reduced , to a
minimum , and the matter o f overhang both for the work and the
cutter must be car e fully looked o ut for . The r e duction Of overhang is hampered at the cutter head by the necessity fo r a strong drive
- and an angular adjustment . In the case o f th e work supporting parts , it is difli cult to bring the cutting point close to the b e aring on a o c ount o f the necessity for plenty o f clearance below the work for the
hob and its driving gear . S PUR AN D S PI R AL GE AR HOB S 5
Th e matte r o f design Of the driving me chanism for th e hob and th e
o t o work is a difficult one . N nly must it be rigid for th e sak e o f ac
- curacy , as pr e viously explained , but car e ful attention must b e given to durability as well . It requires gr e at skill to design a durable — mechanism for the purpose within the limitations imposed i n the
e cutter h ad by the necessity for reducing the ov e rhang, and in the
e e e work tabl by the high sp ed r quired for cutting small ge ars . S ince th e ind e xing wheel works constantly and und e r considerable load , both the wheel and worm must be built o f such materials as
e e c will pr serve th ir ac uracy after long continued use . Particular attention should be giv e n to th e homogen e ity o f the mate rial o f the
- index worm wheel , to make sure that it does no t wear faster on o n e side than o n the other .
e The fi ld of the hobbing process for cutting spur gears has , perhaps , n o t yet been definite ly determined . In some work it appears to have great advantage s over the usual type Of automatic gear—cutting
machine , while in other cases it seems to fall behind . It will doubt
a f less require continued use , with variety o work , and fo r a con si de rable length of time , to determine just what cases are best suited fo r the hobbing machine , and for the machine with the rotating disk t cutter . It is quite probable that in the fu ure neither o f them will o ccupy the field to the exclusion o f the other .
CHAP TE R I
H O B S F O R S PU R A N D S PIR A L G E A R S
In explaining the methods used in the design Of hobs for spur gears , it is best to assume a practical example . S uppose that the 1 t ge ars are to be cast ir on , with 1 20 t eeth , 6 diametral pi ch and
e . inch width o f face . The pitch diameter , henc , is inches The
' hole in the hob for th e spindle is to be 1 14 inch in diameter with a
1 - e e e . A square inch keyway , the hob to b run at high sp d
F o rm a n d D ime n s io n s o f To o t h
The first thing to be settled is the form and dimensions o f the tooth
e or thread secti on o f the hob . If the form is to be the standard shap
- i m n for the involute syst em with a degre e pressure angle , the d e
sions o f the hob tooth would be as shown in Fig . 1 . A modification
f m e o this shap e may in so e cases b e advisable , and will be r ferred to
- late r in this chapter . The standard rack tooth shape with straight
- sides , as shown in Fig . 1 , how e ver , is the easiest to produce , and it is
o f e ntire ly satisfactory , unless gears with a very small number teeth
re a to be cut . 1 33— B A D E AR B B 6 N o . HO S N G HO I N G
The circular pitch corresponding to 1 6 diametral p itch is o f inch , which is obtained by dividing by 1 6 . The thicknes s
- the tooth o n the pitch line is o ne half of the circular pitch , o r The height o f the tooth above the pitch line is equal to the reciprocal
“ o f the diametral pitch plus the clearance , which latter is equal t o
o f Of the thickn e ss at the pitch line . Hence , the height the tooth above the pitch line equals inch . This dis
tance equals the space in the gear below the p itch line . T h e depth Of the too th Of the hob below the p itch line is usually made great e r than the distance from the pitch line to the top Of the
t o o n e - n tooth . The extra depth should be equal from half to o e times n the clearance . On small pitches , o e times the clearance is no t to o great an allowance , and , th e refore , the depth below the pitch line is made equal to making the whole depth o f
F i g. 1 . S t an dar d H ob Too th D imen sions tooth equal to The extra d epth at the root Of the thread is to f allow o r a larger radius at the root , so as to prevent c racking in hardening . The radius may then be made equal to two times the ill i clearance , if desired . In th e ustrat o n , however, the radius is made O o f o f equal to the whole depth the tooth . The top c orner o f the tooth is rounded o ff with a corner tool to a radius about equal t o the
clearance , or say inch . This c orner is ro und ed to avoid unsightly
steps in the gear tooth flank near the root . Having Obtained the hob tooth dimensions , the principal dimensions o f the hob may be worked o ut with relation to the relief , the diameter o f the hole and the size of the keyway .
R e li e f o f H o b To oth
The proper relief for the too th is a matter generally decided by
exp erienc e . We may say that , in general , it should be great enough to give plenty Of clearance o n the side o f the too th , and o n hobs o f
- degree pressure angle the peripheral relief is , roughly speaking,
about four times that on the side . F o r cutting cast iron with a hob
o f the pitch in question , a peripheral relief Of inch will give m i satisfactory res ults ; for steel , this clearance should be s o ewhat n S PUR AN D S PI R AL GE AR HOB S 7
m e e e e crease d . The a ount of relief d p nds , n c ssarily , also upon the diameter o f the hob .
With a p e riphe ral relief of inch , th e gr e ate st depth o f the tooth space in th e h o b must be The gash
e o r 20- will b e made with a cutt r tool with a degree included angle ,
inch thick at the point , and so formed as to produce a gash with
- a half circular s e ction at the bottom . Th e depth of the gash should f b e inch deeper than th e greatest depth o the tooth space , o r about
inch .
T e v ash r t s Fig . 2 . H ob wi th w l e G e s o Flu e
Th i c % n e ss o f Me t a l a t % e y w ay
The radius Of the hob blank should be e qual to the thickness o f the stock between the keyway and th e bottom Of the
use 3- 2 e flute . If we a inch bar , we can turn a hob blank 94 inch s in ufii i n diameter from this , which wo uld allow s c e t stock to be turn e d
e from the outer portion o f the bar to remov the decarbonized surface .
If we make the blank inch e s in diameter we have inch of
stock over th e keyway , which is sufficient .
N umb e r o f F lut e s
T o f o r o n he number gashes flutes depends many factors . In Fig .
e 2 is shown an end vi w of a hob with tw e lve gash e s . This number giv es plenty o f cutting te e th to form a smooth tooth surface o n the t gear without showing prominent ooth marks . A large r number Of 8 — H B A N O. 1 33 O S N D GE AR HOB B I N G
gashes will not , in practice , give a better tooth form , but simply i n creases the liability to inaccuracies due to th e forming p rocess and t o distortion in hardening . This number o f gash e s also leaves plenty o f stock in the teeth , thus insuring a long life to the hob .
S t ra igh t o r S p ir a l F lut e s
The qu estion whether the gashes should be p arallel with the axis o r o n n o ' e asil normal to the thread helix is e that is t y answered . It
o f must be admitted that when the angle the thread is great , the cutting action at both sides Of the tooth is not equal in a hob with a f straight gash ; but in cases o hobs for fine pitch gears , where the hobs
are o f comparatively large diameter, thus producing a small thread angle , the p arallel gash is more practical because it is much easier to
- Fig . 3 . D iagram f or D erivat ion of Formula f or S pirally flut ed H ob s
sharpen the hobs , and the long lead necessary for spiral gashes , in such cases , is not easily obtained with the regular milling machine
equipme nt . However , when it is desired to Obtain the very best
results from hobbing , especially in cutting steel , the gash should be
o r 3 spiral in all cas e s when the thread angle is over degrees . In o ur case the thread angle figured at the pitch diamete r o f the blank is equal to 1 degree 22 minutes; hence , straight flutes are not
Obj ectionable .
S p ir a l - fl ut e d H o b A n g l e s
As mentioned , it is d esirable that hobs should be fluted at right
o e c angles t the direction o f the thread . S ometimes , however , it is n es
sary to modify this requirement to a slight degree , because the hobs cannot b e relieved unless the number o f teeth in on e revolution , along the thread helix , is Such that the relieving attachment can b e properly
geared to suit it . In the following ( from an article by G . H . Gardner in MACH IN E R Y ) it is propos e d to S how how an angle o f flute can be selected that will make the flute come approximately at right angles
to the thread , and at the same tim e the angle is so selected as to meet
the requirements of the relieving attachment . S PUR AN D S PI R AL GE AR HOB S 9
’ L e t C pitch circumfe renc e ; T : d e v e lop e d l e ngth Of thread in o n e turn ; N numb e r of t e eth in o n e turn along thread h elix ; F numb e r o f flute s ;
2 a angle Of thread h elix .
The n ( see Fig . 3 )
0 + l e o n ngth of each small division pitch circumfer e nce .
' —F a e ( C ) X cos l ngth of division on develop e d thread .
0 cos a T.
H e nce z —- ( C z F ) Cos a c o s a
o a. N w, if 30 d e gr e e s , N 1 F
a 4 5 d e grees , N 2 F ;
a 4 6 0 degrees , N F .
In most cases , however , such simple relations are not obtained .
for i— = 3 = S uppose example that F 7, and a 5 degrees . Then N
e c ec e and no g ars ould be sel t d that would relieve this hob .
B i a n o f y a very slight change in the sp ral gle the flute , however , we can change N to 1 0 or in either cas e we can find suitable ge ars
for the r e lieving attachment .
The rul e for finding the modified spiral l e ad of the flute is
M lti l th a o h F n i i u p y e le d f t e h o b by , a d d v d e th e pro duct by th e
n s a l n differe ce b e twe en th e d e i re d v ue of N a d F .
e N 1 H e nce , the lead o f flute r e quir e d to mak 0 is
Lead Of hob ( 7 +
= 1 e T O mak e N 1 0 A) , we hav — L e ad of flut e = lea d Of hob X ( 7 2
‘ o f e e From this th e angle the flut can asily b e found .
That th e rule giv e n is corr e ct will b e und e rstood from the follow
e o f t e e A ing consid e ration . Change th e angl h flut helix 6 so that G
contains the r e quire d numb e r of parts N desir e d . Then E G contains
— B = B D — E D ' an d o m N F parts ; but co t , , by the law f si ilar triangles : F B D and E D N
'
e C co t . The l e ad Of th e spiral of th flute , however, is X fi
e e S e H e nc e , the requir d l ad of piral of the flut F C X co t fi L N — F
This simple formula make s it possibl e always t o flute hobs so that
h e e th e y can b e conveniently r e li e v e d , and at th e same time have t flut s th at a pproximately right angles to e thread . 33— B 1 0 N O. 1 HO S AN D GE AR HOB B I N G
G ra ph ic a l Me t h o d
The angle o f the flutes, determined so as to a void di fii culti es in
e : r lieving , may b e found graphically as follows First , lay Off a base AA 4 f ' o e . line , Fig . , any convenient l ngth Then erect the perpen di cular A O making it equal to the develop e d length Of the p itch ci r cumf r n f D e e ce o the hob . From 0 draw line C parallel to the base line AA f and o f a length equal to the lead o the hob . N o w drawn diagonal n AD which repre sents the thread . D ivide A O into as ma y equal parts as there are flutes in the hob , as a , b and c . From 0 and a draw lines AD E through and at right angles to the diagonal , as C and OF . Then length E F equals the pitch Of the flutes on the thr e ad when the gash
Fig . 4 . Graphica l M ethod of Fin din g Gashin g Angle an d N umb er of Flut es f or which B ac%in g -off At t a chment sh ould be set f or S pira l -flut e d H ob s
AD ing is at right angles t o the thread . T o proceed , divide into a
certain number o f equal parts , the length o f these parts to be as near
F Off o n AD to the length E as possible . S tep these divisions , and
C’ to through the division nearest to E , as at G, draw a line from the 'B base line intersecting the base line at B . This line C r e presents the
AB o f gash , line the lead the gash , and the number Of divisions in the line AD equals the number o f flutes t o o n e revolution o f the hob , fo r
which we must gear the machine .
To get the exact length Of AB , divide the number Of divisions in AG by the number of divisions in GD and multiply the result by th e
e a length o f the line CD o r the lead o f the hob . The angl which is i the angle for gashing can be found by scaling the d agram . F o r 2 example , let the hob be inches pitch diameter , lead 5 inches , and number Of flutes 8 . A We first drawn base line A , and the line A O inches long which
ow is the pitch circumference . N draw CD 5 inches long, and then S PUR AN D S PI R AL GE AR HO B S 1 1
AD draw line . We now divid e A C into eight e qual parts and draw lines from G and a through and at right angles to AD int e rs e cting AD , ,
E F . S s E F e o ff AD at and etting the divider , to length we st p lin e and find that this length E F will go into AD a little ov e r thirteen
e e AD e tim s ; so we divide this lin into thirteen qual parts . It is now n e cessary to gear the mach ine for thirteen flutes to o n e revolution o f
the hob .
Th e E division nearest to is G, so by drawing a line from 0 through
G we e e th e e B int rs ct bas line at . In the line GD there are fiv e
divisions , and in th e lin e A G
e are th re eight divisions . The
o f i lead the hob is five nc h e s , so that th e length of the l e ad fo r 8 — the gash o r AB is X 5 : 8 5 B inches . y measuring o n the diagram with a scale we find the gashing angle is 38 14 de
e grees . Th refore , we will gear the machin e used in backing o ff the hob for 1 3 flut es to o n e
revolution , and we will gear the milling machin e to cut a lead of 8 inches , and at a gashing angle 38 1 of 4 degre es .
Th r e a d in g t h e H o b
The linear pit ch of the hob and the circular pitch o f the
gear , when considered in action , are to each other as 1 is to the Fig . 5 . Thr ea din g Tool f or H ob o f cosine the thr e ad angl e . In the present case th e y do not diffe r apprecia bly and may be considered w f as equal . In cases here th e di fe renc e is over the true linear pitch should be used .
The change -ge ars for the lathe may be figured by the formula
G ear on l e ad -s cr ew l e ad o f lead - screw
Gear o n stud linear pitch o f hob
e - e e r On a lathe with a l ad scr w of six threads p inch , or a lead o f
o r inch , the gears that would give accurate enough r e sults
2 - fo r the present hob would be 8 teeth o n the lead screw, and 33 teeth
n o the stud .
Th re ad R e li e v in g To o l
In Fig . 5 is shown the hob thread relieving tool . Th e front Of the
20- e are tool is relieved with a degree rake for clearanc e . The sid s
- ground straight at a degree angle t o form the sides Of the thread , O 33— B A D R B B 1 2 N . 1 HO S N GE A HO I N G and are at an angl e o f 1 degree 22 minutes with the v e rtical to clear f A the sides o the thread . tool make like this can be sharpened by
grinding across the top without lo sing its size o r form . If the gashes
w e re made o n the spiral , the top of the tool should be ground to the
angle o f the thread , as shown by the dotted line AB . In cas e s where
the angle Of the thread is considerable , the angle o f the sides of the
e - tool must be corrected to give the prop r shape to the hob tooth .
’ H N E R Y 1 905 or M A OH I N E RY S R e B ( S ee MAC I , May , , ference ook N O. 32 ,
% Formula for Planing Thread Tool s ) The point o f the too% should be stoned to give the proper r adius to the fillet in the bottom Of th e hob tooth space .
H e a t - t re at m e nt o f H o b The best practice in making the hob is to anneal it after it has been
bored , turned , gashed and threaded , the annealing taking place before
B - relieving the teeth . efore hardening, the h o b ought to be re gashed
n Fig . 6 . S p ec i al H ob Tooth D imen si o s o r milled in the groove , removing about inch o f stock from the , front side o f the tooth to eliminate chatter marks and the effect due o the to the spring in the tool , which always leaves the front edge f o o teeth without r e li e f . In hardening, do not atte mpt to get the hob t hard , as the required high heat and quick cooling would distort the
te eth badly .
M o d ifi e d To o t h S h a p e i n H o b
case 1 2 - f In the . 0 tooth ge ar is to run with a pinion o a small number
o f of teeth and is the driver , as in small hand grinders where gears
this size are often used , it would be advisab le to make the tooth shape
as shown in Fig . 6 . This shape will obviate undercutting in the pinion and relieve the p oints o f the teeth in the gear so as to Ob tain
- a free running combination . This shape is more difficult to produce
f - e . o and requires more car in, forming If the hob is made high speed steel , it should run at about 1 1 5 revolutions per minute for cutting an ordinary grade Of cast iron with a feed o f inch p er revolution f O the blank . The feed may be incr e ased considerably if the gear
e blank is well support d at the rim . The best combina tion o f sp e eds and feeds in each case can be found only after considerable
experimenting .
1 4 — N o . l 33 HOB S AN D GE AR HO B B IN G
r spaced , o there may have been an error in the gears o n the relieving lathe influencing the form ; the hob may also have been distort e d in hardening ; it may have been improperly handled in the fire o r bath , o r it may have been so p roportioned that it could n o t heat or cool uniformly ; the grinding after hardening may be at fault ; the hole n o t may have been ground concentric with the form , thus causing the
on o n e o f to on teeth side the hob cut deeper than the other . Any on e or a combination Of several Of these conditions may have thrown th e t out o f eeth the true helical p ath .
. 7 Fig illustrates the difficulty of thick and thin teeth . The tooth A t o o B is thick and is too thin , the threading tool having sprung over A B from and gouged into . Fig . 7 also shows a develo ped layout o f the At 0 hob . is shown the effect that thick and thin teeth may have o n
T Figs . 7 and 8 . D i st ort ion of H ob e eth an d it s E ffe ct
— the tooth being cut in the ge ar that of producing a flat on the tooth . This flat may appear on eith e r side o f the tooth and at almost any
point from the root to the top , d e pending upon whether the particular
hob tooth happens to come Ce ntral with the gear o r not . If it does
come central o r nearly so , it will cause the hob t o cut thin te e th in
the blank . The only practical method to make a hob of this kind fit
- for use i s to have it re formed . A I n F i g. 8 is shown at the result of unequal spacing of the teeth f around the blank . Owing to the nature o the r e lief, the unequal spacing will cause the top of the teeth to be at differ e nt distanc e s from
the axis o f the hob . This would produce a s e ries o f flats o n the gear
‘ n e s B tooth . O e r sult Of di tortion in hardening is shown at Fig . 8 ,
' where the to oth is canted over to o n e si de so that one c orner I S o ut o f
t f o duces the helical path . This defec also p a flat and shows a
- f peculiar under cutting which at first is di ficult to account for . S ome times a tooth will distort under the effects o f the fire in the manner
8 . D . indicated at , Fig S PUR AN D S PIR AL GE AR HO B S 1 5
e Th se defe cts may be avoid e d by proper care and by having th e e ste l in good condition before forming . The blank should be roughed o ut b e - , ored , thread d , gashed and then ann e aled before fin i sh forming
e and hardening . The annealing r l ieve s th e st resses in the ste el due to
the rolling process .
The proportions o f the hob have a direct effe ct o n distortion i n , hardening . This is especially notic e able in hobs o f large diam e t e r fo r
fine pitch e s . Fig. 9 shows the results Obtained in hard e ning a 4 - inch
1 0 1 1 - hob , pitch , with 4 inch hole . Ther e is a bulging o r crowning of e A c the t eth at . This is a counted for by the fact that the mass o f B n o t o metal at does co l as quickly as that at the ends . Cons equently , when the hob is quenched , the ends and outer shell cool most quickly and become set, preventing the mass at B from contracting as it would
9 0 Figs . an d 1 . D i st ort ion of H obs and R e sult on t he S h a pe of t h e T e et h if it could come in direct contact with the cold bath and cool Off as
n quickly as the r e st of the metal . The effect o f this distorti on o the
shap e of the ge ar t e eth is indicate d in Fig . 1 0, where the tooth A is unsymmetrical in shap e due to th e fact that th e t e eth near th e c e nte r
- n of the h o b cut d e e p e r into the blank , under cutting the tooth on o e
side and thinning the point . This e ffe ct is produc e d whe n the gear
is ce ntere d near th e e nds of the hob . If the ge ar is cent e re d midway f Of th e length o the hob , th e tooth shape produc e d is as shown at B ,
h - Fig . 1 0. This tooth is thick at t e point and under cut at th e root . A hob in this condition makes it impossible to obtain quiet running
e e e e gears . In this case , it would be us l ss to ann al and r form the hob , m as the same r e sults would be cert ain to be e t with again , on account o f the proportions Of the hob . H e nce , defe cts of this kind are prao tically impossible to correct , and th e hob should either be entirely
- re made o r discarded .
1 2 e Figs . 1 1 and show in an exagg rated manner two common
defects due to poor workmanship . In Fig . 1 1 the hole is ground o ut
Of true with the outside o f the tooth form . The hol e may run eith e r
f o parallel with the true axis o the hob , r it may run at an angle to it ,
2 o f as seen in Fig . 1 . The effect the first condition is to produce a — B AN D E AR B B N 1 6 N O. 1 33 HO S G HO I G
h tooth shaped like that shown by th e full lines at B in Fig . 1 0, and t e
e h ob effe ct o f that in Fig . 1 2 is about the same , xcept that the will
e cut thin t e eth when cutting to full depth . Gears cut by eith r hob f m will lock with m e shing g e ars , and instead O s ooth rolling, the action will be jerky and int e rmitte nt . Gashes which originally w e re equally spaced may have b e come
' un e qually spac e d by having more ground Off the face of so me t e e th
e m e e than o f oth e rs . The gr eat r the a ount of r li f, the more particular o n e must be in having th e gash e s e qually spac e d .
G rin d in g t o Co rre c t H o b D e fe c t s
Th e se various faults may be corrected to a great e r or less e xtent in the following manner :Place th e hob o n a true arbor and grin d the outside as a shaft would be ground ; touch all Of the te e th j ust enough
o n so that the faintest marks of the wheel can be seen the tops . The
h e t er H e ut O Tr e th th e Figs . 1 1 an d 1 2 . H ob s with t e C n ol o f u wi Out sid e of th e Tooth F orm
t e eth that are protruding and would cause troubl e will , of course , show
a wide ground land , whil e o n those that are low , the land will b e
hardly visible . N o w grind the fac e o f each tooth back until the land
on each is equal . This will bring all th e t e e th to the same height
and the form will run true with the hole . To keep the hob in con
r - dition so that it will n o t be spoiled at the first e S harp e ning , grind
o f fi n r- the backs the teeth , using the face as a ge guide , the same as
wh e n sharpening milling cutters , so as to r e move enough from the B back of each tooth to make the distance A , Fig . 1 1 , the same o n all
e . e the t eth Then , wh n sharpening the te e th in the future , use the
fi r- back of the tooth as a n ge guide . I f care is taken , the hob will then
cut good gears as long as it lasts . It is poor practice to use the index
head when sharpening hobs , because the form is n e ver absolutely tru e
e e with the hole , and unl ss the hob has been pr par e d as just described ,
th e th e re is no reliable way to sharpen it . If hob , after having been
e e e e e e f prepared as d scrib d , is sharpen d on c nt rs by m ans o indexing ,
it will be brought back to the original condition .
1 2 e The defect shown in Fig . is correct d in the same manner . The gash when so ground will not be parall e l with th e axis in a straight
flute d h ob , nor will it be at an exact right angl e with th e thread helix S PUR AN D S PI R AL GE AR HOB S 1 7
- - in a spiral flute d hob , because the t e e th at th e right hand e n d are high while those at the l e ft- hand e n d are low and the amount that must b e gr ound o ff the faces o f the hob teeth W I I I be greater at o n e end than
h e t e . o f at other The angle will be slight , how ver , and no cons equence .
S h a pe o f H o b Te e t h
The first thing that is questioned when a hob does not produc e n smooth run ing gears is the shape of the hob tooth . Th e poo r b e aring obtain e d when rolling two ge ars together would in many cases s e em , , e to indicat that the hob tooth was Of improper shape , but in nearly
HOB TOOTH GEAR TOOTH PRODUC ED
° I 4 x PRESS URE ANGLE
Fig . 1 3 . Forms of H ob Te eth and Gear Te eth Pr oduc e d every case the trouble is the result of o n e o r more o f the defects already pointed out .
Theoretically , th e shape of the hob too th should be that of a rack
tooth with perfec tly straight sides . This shape will cut good gears
i - from th rty teeth and up , in the degree involute system , but gears under thirty teet h will have a reduced bearing surfac e as a result
- o f under cutting near the bas e circle , which increas e s as the number
of teeth grows smaller . The shape produced by such a hob , if
m e chanically perfect , would be a correct involute , and the gears should interchange without difficulty . In order that th e beginning o f
h h e contact , however , may take place without jar , t e points of t teeth
should be relieved o r thinn e d , so that th e contact takes place gradu
ally , instead Of with full pressure . This is accomplished by making
‘ the hob tooth thicker at the root , starting at a point considerably 1 33— B A D 1 8 N O. HO S N GE AR HO B B I N G
t below the pitch line . This is illus rated in the upper portion o f Fig .
1 3 w S B - , hich shows the standard hape adopted by the arber C olman Co . S The Shape o f the tooth produced is also hown . The full lines show
the shape generated , and the dotted , the lines O f the true involute . The amount removed from the points is greater o n large gears and
less o n small pinions , where the length o f contact i s n o n e t o o great ' even with a full shaped tooth , and where any great reduction must
o f be avoided . This S hape hob tooth does not , however , r educe under
- cutting o n small pinions . The fact that hobbed gears have under cut teeth in small pinions , while those out with rotary cutters have radial flanks with th e curve above the p itch line corrected to mesh with
Fig . 1 4 . Illu st ratin g E ffect of F e e d in H obbin g them is the reason why hobbed gears and those out with rotary ,
cutters will not interchange . f In the lower part o Fig . 1 3 is shown a hob tooth S hape which will
- p roduce teeth in p inions without under cutting , the teeth , instead , hav
fl- f ing a modified radial ank . The radii o the correction curves are such that the gear tooth will be slightly thin at the point to allow
an easy approach o f contact . The shape shown is approximately that which will be produced o n hobs the teet h Of which are generated from the shape o f a gear tooth cut with a rotary cutter , which it is desired to reproduce .
D i ame t e rs o f H o b s
The diameters o f h obs is a subject which has been much discussed . Many favor large hobs because the larger the h ob the greater the
number o f teeth obtainable . This , however, has already been shown to be a fault , because the greater is the p ossible chance Of some Of the f teeth being distorted . For the same feed , the o utput o a small hob f is greater , because o being inversely prop ortional to the diameter . The number Of teeth out is direct ly propo rtional t o the number Of S PUR AN D S PI R AL GE AR HOB S 1 9
f o m e revolutions per minut e o th e h b . Th e nu b r of r e volutions de ’ f h pends o n the surfac e spe e d O t e hob ; th e r e fore , the small hob will produce more gears at a given surface spe e d .
o n It may b e argued that , account of the large diam eter , th e large hob can be give n a greate r fe e d per r e volution of the blank than the
' o f small e r hob , for a given quality tooth surface . This argum e nt is
analyz e d in Fig . 1 4 . Let R be th e radius of the hob and F th e feed B o f the hob per revolution of the blank . Then may be called th e f rise o feed arc .
S ince the surfac e of the tooth is produc e d by th e side , the actual ,
d e pth of the fe e d marks is D , which depends on the angle Of th e sid e
Fig . 1 5 . Dia gram sh owi ng Com Fig . 1 6 . Di agra m showin g Com parat i v e F e e d s f or H ob s of parat iv e Out put Of H ob s of V ariou s D iamet ers V ari ou s D ia me t ers b a se d on 3 -in ch H ob
- o of the tooth , th e d epth being greate r for a 20 d e gree to th than it
- would be for a degre e tooth for the sam e amount of feed . The
F R B b e e e e as r e l ations between , , and may xpr ss d follows
— 2 F = 2 %%Z R E B
B 2 S inc e B is a very small fractional quantity , would b e much
a small e r and can , therefore , be disregarded , giving the very simple p
2 proximat e formula F 2 V 2R B . A rise Of inch would mean a
- e depth D of about inch on a d egree tooth . Th e allowabl f e ed is inch for a 4 -inch hob and inch for a 3- inch hob for a
1 5 e inch rise . The curve in Fig . shows the fe ds for this rise for
3- various hob diameters . Fig . 1 6 shows a curve based on a inch hob
e that shows th e comparative output for an equal rise . This curv shows that the smaller hob is superior in matter of product ion . The larger hobs are also more liable to distortion in hardening — B A D 20 N O. 1 33 HO S N GE AR HOB B I N G and they do not clear th emselves as well as the smaller ones when
- cutting ; consequently , they need a greater amount o f relief . Large
t - o f e f hobs also require a grea er over run f ed at the start o the cut . When cutting spiral gears Of l arge angles this greatly reduces the
o f h e output , as the greater amount feed required before t hob enters t o full depth in the gear is a pure waste . The question o f whe ther the gashes or flutes should be parallel
with the axis o r at right angles to the thread helix has two sides .
From a p ractical point Of view , it appears to make very little difference m in the results Ob tained in hobs Of s all pitch and angle o f thread .
In hobs Of coarse pitch , however , the gashes should undoubtedly be
normal t o the thread . The effect o f the straight gash is noticed when
ifli - cutting steel , in that it is d cult to Obtain a smooth surface o n o ne
side Of the tooth , e sp ecially when cutting gears coarser than 1 0 pitch .
What has been said in the foregoing, however, applies equally to straight and spirally fluted hobs .
— 22 N O. 1 33 HOB S AN D GE AR H OB B IN G
4 - . The interference in gears with thirty two te eth o r less when in
Of As 1 mesh with those a greater number Of te eth . the 1 4 743 degree formed gear - cutters are based o n the twelve -tooth pinion with radial
flanks , a rack tooth to mesh with this radial flank tooth can be made wit h the straight sides extending only to a po int inch outward
f n from the pitch line in a ra ck o o e diametral pitch . The remainder
o f the t oot h must be eased off fro m this point outward , sufficiently to
clear the radial flank Of the pinion t o oth . This rounding Off Of th e r ack tooth may b e made by using the cycloidal curve from the inter i l ference point, with a rolling c rc e o f a diameter equal to that Of th e
l J o A r twe v e t oth pinion . ci cular arc tangent to the toot h side , drawn from a c enter o n the pitch line at the point o f intersection o f the normal to the tooth side at the point o f
interferenc e , will be a near approximation
to the cycloidal curve . The hobs used extensively today are n ot made t o produce t eeth in any near approximation to the shape pr o duced by
the milling cutter. The only correction
that is made , in many cases , is to mak e the teeth of the hob a trifle fuller at the base o r ro o t to eas e the approach ; even d this is one only in a few instances . Th e
F i 1 m ar s n b et een g . . Co p i o w difference between the hobbed tooth and R obbe d a n d M i ned Gear Teeth c that produ ed by milling is seen in Fig . 1 . The hobbed tooth is shown in full ; this shape was traced from an actual
- e . n hobbed tooth , photograp h d and enlarged The gear had tw e nty o e % f teeth . The hob used was corrected for the thinning o the tooth
e o f at the point , but in a g ar this diameter the effect would no t sh o w
to any grea t e xtent . The dotted lines are drawn from actual milled
c tooth curves and show the differen e bet ween the two forms of teeth .
Attention is called to the fullness Of th e milled tooth at the root , and
the thinning Of the tooth at the point . The diffe rence would be
- greater in the case o f a twelve to oth pinion .
The filli ng- i n Of the flank o f the to oth is n o t done to any rule based
o n a proportion to the numb er o f teeth in the gear . The curve selected is made to fill the spa ce at the r o ot to just clear t h e corrected rack h tooth . N either is the thinning o f the tooth at t e point proportional
e o f - to the diam ter in the sense that the curve the hobbed t ooth is . E ach form o f the cutter syste m is made and varied to the extent
o f necessary for smo o th action , and the curves th e entir e system can
not be produced by the hobbing process with a single hob . To ac curat ely reproduce the form Of the milled to o th , a specia l ho b would
f ro x i m be necessary for ea ch numb er o teeth . However , a close app a
tion may be obtained , wit hin a narrow range Of teeth , with a hob
generat ed from a milled tooth . This is being done in the automobile
industry with good results . The necessity for interchangeability makes the duplication o f the milled tooth imperative when the
originals were made with the formed cutter , and t h e int roduction o f S PE CIAL HO B S 23
the hobbing machine , in such cases , dep e nds o n th e successful dupli
is n o cation o f th e se forms . It exceptional thing to see the hobbing proce ss used in conjunction iv i th the automat ic gear—cutter in the
o f m production interchangeable transmission and ti ing gears . The Of shapes produced by the standard s ets cutters , from a rack to a
- e t e tw elve tooth pinion , cannot , howev r , be genera d by a singl e hob , a o f because the shapes are only an approxim tion the correct curve .
T h e ge ars mentioned above as being successfully hobbed are , th e r e
e fore , when milled , cut with sp ecial cutt rs for each number o f te e th , o f b as in this way only can a curve correct shape be O tained .
s b are Of - e A s stated above , mo t ho s the straight sid d sh ap e , and the tooth hobbed is Of pure involute form . In gears o f less than
- t hirt y two teeth , the flank is undercut to a considerable extent . This undercutting does n o t involve any incorr e ct action in the rolling o f
o f - the gears , but in the case the twelve tooth gear , for example , th e
Fig . 2 . H ob Tooth d e signe d t o gen erat e t h e Approx imat e S h a p e Of a -d egre e Inv olut e M ille d Tooth
involute is cut away at th e base lin e close to the pitch line , giving
but a line contact at a point which is subjected to heavy we ar . This e T f ventually develops backlash . h e t e eth o the gears also come into
. action with a degr e e of pr e ssure that is continuous throughout th e time o f cont act ; this results in a hammering which in time develops
into a humming noise .
S p e c i a l H o b s fo r G e a r Te e t h
To overcome these objections a hob tooth may be developed to gen
e rate a curve which will closely resembl e that of th e form e d tooth . 2 S uch a hob tooth is shown in Fig . . Theoretically , t h e correction for interference or und e rcutting should begin at a point locat e d abov e the pitch line a dista nce as determined for a twelve -tooth pinion by the expression
X P in which N number o f t e eth in the small e st gear to be hob bed ;
P diametral pitch of gear .
However , to begin the correction for interference at this point would r e duc e th e l e ngth o f th e true involute and r e sult in t o o full a 24 33— B N O. 1 HO S AN D GE AR HOB B I N G
e tooth , causing noisy g ars . Therefore , a compromise is made and
e e - the corr ction is Obtain d for a minimum o f twenty o ne teeth . To
s th e the o compen ate for extra fullness of tooth at the ro t , the point o f the tooth is thinned down in proportion , and this is done by leaving the tooth o f t h e hob full below t h e pitch line by striking an are from
o n a center the p itch line , and also employing a large fillet having a 4 —P radius equal to 0 5 ( see Fig . It will be noticed that th e radius o f the are at the top o f t h e hob tooth is smaller than the radius
th e t o f o o at bot om the h b t oth . This Will thin the t ooth o f the gear f in excess o the amount necessary t o clear the flank , easing the action m and eliminating the ham ering effect due to the theoretical contact .
It will be seen from the illustrat ion that the thinning Of the teeth do e s
- e not affect the twelve tooth gear to any appr ciable extent, but is f gradually increased with t h e number o te e th . The fact that a twelve t o ot h gear will mesh without int e rfe renc e at the point o f the teeth
’ - Fig . 3 . H ob Tooth f or gen eratin g a 20 d egre e Inv olut e M ill e d Tooth
makes the t hinning unn e c e ss ary ; besides , th e small pinions are usually
th e drivers .
3 - d Fig . shows a twenty degr e e hob tooth with standard a dendum and
- e corrections for non interferenc e . The curve of the tooth b gins at a
o f a p oint inch from th e pitch line , in the case a one di m etral
- pitch toot h , and is based o n non interference wi th a ll teeth from twelve teeth up .
Fig . 4 shows the shape Of the hob tooth to reproduce the stub teeth
o f the gears ge nerat e d o n the Fellows gear shap e r . The particular
tooth in the figure is a pitch tooth , and the proportions are give n
' in terms Of the pitch numbers so as to be easily appli e d to the o ther p i tches ; thus the height of the tooth above the pitch line is stated as
8 o f t . where is the addendum number . the pitch designa ion 8 The shape o f the rack or hob tooth to roll with the gears produced
e by the gear shap r should be gen e rated from the cutter used . The
Fellows cutters have perfect involutes above the base line , with radial m flanks , so that the hob tooth would be straight only a distance fro
N —:i n o f the pitch line equal to X P , where N is the umber teeth in the cut ter ; in most cases the cutter would have m ore than seven
h ob - teen teeth and the tooth would be straight sided to the point . In S P E CI AL H OB S this syste m the radial flank o f cutters with mor e than seventeen teeth
f e o f does not affect the shape o the fac the tooth , as the involute por
e e e tion o f the cutter tooth gen rat s a pur involute . The straight side
of th e hob tooth should extend to the root in such cas es . T o reproduce gears of some standard the exact shape of which is
- e not k n own , the hob tooth shap can be easily generat ed from the gear tooth o n the milling machine , as will be explained in a subsequent
part of this chapter .
A pplic at i o n s o f t h e H o b b in g Pro c e ss
t h e The hobbing process is not limited to production of gears , but can be us e d to generate teeth of almost any shape , such as the te eth o f c t e e rat h e s , milling cutters , r am rs with equally spaced teeth , chuck
e s m ing drills , multiple splined shafts for automobil transmi sions , ca s ,
4 H ob T th f or a . 5 D a ram sh n h w H ob Fig . . oo Fig . i g owi g o Pit ch Fe llows Sy st em ma y b e use d f or gen erat i n g S t ub Ge ar Tooth Or din ary R at ch et Te eth
e a o f sprockets , etc . Fig . 5 shows th sh pe hob tooth to generate the
‘ a e t e e th o f ratchets . There is no shape of tooth th t will gen rate the radial te eth of ratch e ts of th e typ e shown at A ; the nearest that can b e obtained is th e modified shape at B with th e fille te d root . S hould the toot h o f the hob be made straight and normal to the axis of the
’ hob , the tooth produc e d would be undercut as shown at C . ' Th e shap e shown is generated from a 1 2-tooth radial ratchet and would produce a nearer approach to the radial form in ratchets of
a larger number o f t e eth . The back of the t e eth would be con cave
o f e f i nstead straight in the case of larg r numbers o t e eth . A good
compromise would be to make the back of the hob tooth straighter ,
th e being obtained by gen e rating from a rat che t o f, say , forty .shape f eight teeth . The back o the teeth of ra tchets of a smaller numb er
o f t e eth would then be convex in shape . Hobs o f this kind have been
used successfully in hobbing milling cutt ers , a single hob c overing a m f li ited range of sizes . The di ficulty in having a hob cov e r a wide range o f cutte r sizes is the fa ct that the pitch o f the tee th is no t con t stan , as in the case of gearing . When ma king cutters in quantiti e s , the cost o f the hob is soon covered by the saving in the manufacture
of the cutters over the cost of milling . In the case of spiral cutters , t h e angl e can be alt ered to make it possible to make the h ob cover a O 1 33— H B A D 26 N . O S N GE AR HOB B IN G
b . greater ra nge o f sizes . The hob ing process is especially adapted to
the making o f spiral milling cutt e rs .
The form o f hob shown in Fig . 6 is a cross be tween a hob and a formed milling cutter , and can be employed profitably in the milling ' s o f radial teet h by the hobbing p roce s . The form is made with a
- normal face and is generated back as in the case just shown . Th e hob
‘ is set so as to be all o n one sid e of the center of the blank being cut ,
“ a f s shown . The radial face o the tooth is formed with the face o f
o fl - t the hob t oth acting as a y cu ter , the form of the face being a re
o f production the face of the last hob tooth , which is set radial with o f the axis the blank . The fronts of the h ob te e th are relieved o n the sides ; this can be done by using the combined side and radial relief
. 6 . T e H ob f ra t n h T Fig yp of or gen e i g R a t c e t e e th . F i g . 7 . V i e w showin g th e R eli ef i n t he H ob f or gen erat in g R at ch e t Te eth
o r c a ms , , if that combination is n o t available , th e s ide relief can be f given as a separate operation . The latter will cause a widening o f the top o t h e too th as the h o b wears back in sharpening . Fig . 7 shows
‘ a V i e w of the hob . The convex shape o f the generated form o f the ho b tooth will have the same effect on the shap e o f the back of th e
o f t r to th as stat ed above in the case o the genera ed h ob . This po tion
- o f the tooth cannot be made to act as a fly tool , as it cannot be set o n t h e radial line and must generate the form . by a regular generating
actio n . A form of h ob that can be used to advantage in the automobile i n dustry is that for forming the splines o n the transmission shaft . This
o f shaft commonly has six splines , as shown in Fig . 8 . The face the
i o f splines o r teeth have a negat ve rake , being set ahead the radial
line , and for that reason can be fo rmed with the hob if the depth and
thickn e ss are n o t too great in proportion to th e diameter . In the
- illustration the proportion is six to o n e , and the hob form is such as to give a very close approximation to the desired form ; howeve r, if h the s afts are to be used as left by the hob , that is , without grinding, it would be well to make the broach by the same p rocess to insure a S PE CIAL HOB S 27
e w duplication of shape in the k y ays in th e gears . In all thes e special forms the pit ch is take n from the outside of the blank ; if taken inside of this point , the hob to ot h , if radial , would have no t to be undercut , which is
pract ical .
o In Fig . 9 is sh wn another shape that could b e used t o advant age fo r hobbing
squar e s . H obs for this pur pose could be used i n Squar ing the ends of such shafts
as , for instanc e , th e ends o f
- milling machine fe e d s cre ws ,
- cro ss scr ews , and the elev at ing shafts . I f th e re is a job that is handled to di sad vantage o n the milling ma i chine , t is the squaring of
these shafts and screws . A similar h ob c o uld be de
8 H ob t t h f or en erat n v elope d fo r th e hobbing Of Fig . . oo g i g a S i x -splin e S haft hexagons and ot her polygon
shapes o n the e nds of shafts , o r fo r the heads of bolts . Th e great disadvanta ge of the hobbing of the shapes jus t men ti on e d is the low numbe r of
“ % teeth or divisions , which necessitate s a rapid travel o f the index gear and high ratio gears t o give th e
p roper s pacing, and also
the long lead of th e hobs . The latte r is not so ob jecti o n able in the case o f the small squar e s and h exago ns
gen e rally used , as the lead in most cases can be lower
than o n e inch . The examples given do n o t exhaus t the fi eld fo r th e
hobbing process , but give an . array o f cases which are o ut o f the ordinary and show t h e application o f the proc r F i g ' 9 ° H °b f % gen e at in g ess t o other than the ordi
- nary work o f gear cutting .
The shap e s have been laid o ut on the d rawing-board in each i h en erat stance , but a far more accurate way to obtain them is by g is ing th e m o n th e milling machine . This generating process in ' — 28 N O. 1 33 HOB S AN D GE AR HOB B I N G
t o f the b r e ality a duplica ion ho bing process , but in generating the
fo r h ob tooth shape the the process is reversed , that is , the shape to
h ob - be generated by the is used in generating the hob tooth shape .
G e n e rat i ng H o b - t o o t h S h ape s
s In Fig . 1 0 is shown a milling machine e t up for generating the hob
- n t o o th templet . This is done on the u iversal milling machine or on
the plain milling machine if the screw can be connected up w1 th the
worm o f the dividing head , as in milling spiral work . The spindle of
f or a n ut th ha e Fig . 1 0. M illing M a chin e set up l yi g o e S p of a H ob Tooth
the dividing head is set v e rtical , and the master gear or templ e t of the shape it is desired to produce by hobbing is mounted on an arbor
in the S pindle . In making the mast er t e mplets , care shoul d be taken to produce t h e correct shape and to b e sure that the shape is true
m a with the hole ; if the te plet is no t true , the shape gener ted will not
be accurate , of course .
The gearing connecting the f eed -scr e w and th e dividing head must be for a lead equal to th e circumfer e nce of the pit ch circle o f the
g e ar from which the hob templet is ge n e rated . ‘ T o prov i de a rest o n which the to ol templ e t to be laid o ut may be
clamped , a parallel is bolte d t o t h e out e r arbor support so as to be horizontal and parallel with the milling machin e table and at right
angles t o the machine spindle . The rest may also be in the form o f m an angle plate cla ped to the face of the column , but the former typ e
30 — B A D AR B B N N O. 1 33 HO S N GE HO I G
done the lines on the templet will resemble that in Fig . The
e lin e s should now be etched in and the plate polish d . The combined o n the plate will be seen to d e scribe the rac% “ lines - th tooth shape o f the hob te e th in a clear cut mann e r , if e operation has
c been carefully carried o ut . If the gear tooth from whi h the lin e s f t were taken is th eore tically correct , the sides o the ou line on th e plat e will be straight a gr e at e r p ortion of the way from the point o f the toot h to the edge o f the plate ; the lines dive rge from the straight line at a point near the edge of the pl ate , as shown by the dotted
lin e s in Fig . 1 2 . This point will be found to be , in the case o f th e
- e d o f N P degr e tooth , at a istance from the pitch line X ,
f an d P th e e where N is the numb e r o teeth in gear diam tral pitch . If
1 L Fig . 2 . ine s scrib e d on th e H ob Tooth Templ et from a. H obb e d Gear
th e hob to be made from this form is to b e used for N te e th o r less , th e o f h e shape t e t mplet will be correct , but if the hob is to cut gears
of a larger number of teeth , th e straight portion of the tooth must be carried down to the edge o f the plate in order that the teeth o f the
larger gears will not be cut a way too much at the p oi n ts .
In making a templ e t in this way for any other shape than for ge ars ,
t o i n it should be cut the lines on the plate , as no correction can be
lli e n tl h e t e g y made in those cases . S om e success has been made in t layout of t e mplets for a h ob tooth for ge ars o f a limite d range of teeth by using the space b e low the pitch line of the small e st gear in the set and th e space above th e p itch line o f th e large st gear in t h e
h e e set as t shap in generating a hob tooth templet . This is of value in generating a hob -tooth shap e to reproduce a set o f gear-s milled
e with form d cutters . However , the best and e asi e st method is to
e e tak the small st ge ar in the set as the o n e from which to gen e rate , and prolong the straight port ion of the hob tooth to the edge o f the
e A plate , asing the side at , to point the t e e th slightly . The teeth o f the hob are generally made with an extra cl e arance at the bottom as S PE CIAL HOB S 31
a e w i e shown . This is a m tt r on h ch authorities differ , som preferring
to have th e h ob cut the top o f th e te e th , to make th e t e et h of standard
ra length if th e blanks should b e ov e r siz e ; how e v e r , the general p c tice is to make the tooth the same length both abov e and below th e 3 2 . pitch lin e as in Figs . and
If the form is for a ge n e ra t e d ge ar and results in the straigh t-sided
e s e tool in Fig . 1 2 , all that is n ce sary is to m asure the angle and make - h a threa d tool that will cut a thread of this s e ction . S hould t e shap e t urn out to be a compound o f curv es , as will b e the case in repro
e h o e o ut e duci ng the milled tooth , the templ t s uld be fil d to the lin s , making a fe mal e ga ge to which a planing tool is made , the planing
- a e tool b e ing a duplicate o f the hob t ooth sh pe . The thr ading tool is
h e o n o pla n e d up with this tool . In making t thread t ol , it is t usual
m t h e e e to make it of fe ale shape , that is , like t mpl t , but p ointed as
e usual , planing th e sides with the opp osite sid s of the planing tool . T h e prop e r corr e ctions should be mad e in the thread tool to cor
e o f re spond to the angle of th e threa d , and the s tting the tool and
e e the fluti n g o f th e hob , wh e ther it is gash d parall l to the axis or
normal to the thread h e lix .
M a % in g a Ma st e r Pla n i n g To o l fo r a H o b
A master planing tool can b e mad e in th e following manner , with o u o f e s e t the use the scrib ed line t mplet . It is nece s ary to hav a
e universa l milling attachm e nt for the milling machin e . Th e spindl of the attachment is set in the horizontal positi on with the axis
o f fl - e parallel with the direct ion the table movem e nt . A y tool hold r
is th e n placed in the spindl e , in which the blank planing tool is to
be held . This t o ol should be roughly fo rmed to the shape to which
it is to b e finish e d . Th e t op o f th e tool should be radial , that is , it f th f should b e in the plane o e center o the spindle . Th e gear o r other master templet that it is desired to duplicate by hobbing must be
e o hard ned and ground to a cutting edge on n e face , pr e ferably the f top face when mount e d in th e spindle o the dividing head , so that th e
o f a p ressure the cut will be downw rd . The kn e e should be adjusted to bring the ground face of the ge ar to the level o f the cent er of the
spindle of the attachment . The dividing head and the table screw
e th e ' same e are conn cted in way as pr viously describ e d , but in this c ase the pow e r feed can be us e d and the saddle can be fed in t o depth as needed , care being taken to use the power feed , in ge nerating the n tool , only in o e direction , as the backlash in the ge ars and screw will throw th e tool and dividing head out of rela tive position if used in the opp o sit e direction . As many cuts can be taken as r e quired to f obtain a tool o the correct sha pe .
a If the tool is to be used in making more th n one thr e ading tool , as might be th e c as e in many insta nc e s , th e planing to o l can b e made in th e shap e o f a circular tool which can b e ground indefinite ly with o u - t losing the shap e . In this case the fly tool hold e r would give place
th e to standard milling ma chine arbor . This method is th e most a c 32 O — A B B N . 1 33 HOB S AN D GE R HO IN G
cura te way of ma king the master planing tool , and where the
universal milling attachm e nt is available , it should be used where
accurate results are desired . I t eliminates the human el ement and the amount o f skill required in making the master templet . The inaccuracy o f the ma chine is the only element that is likely to cause
e rror . One point that is likely to cause difficulty is the rel ati on o f the
e generated tool shape to the thread shape , as it app ars in the normal s th e o ection o f the hob tooth . The simple fact is that master t ol
f a shape , as generated by the direct method o m king the maste r plan ing tool , o r the shape as outlined o n the hob tooth templet in th e
- n o f h ob o n first method , is the shape of the cross sectio the , thread a plane normal to the h ob thread helix . This relation should be kept m f in ind throughout the process o making the tools and h ob . This statement also clears any hazin ess regarding the question o f the lead , as in single -threaded hobs this must be such that the normal pitch f o f the thread is equal to the circular pitch o the teeth hobbed . In the case o f hobs o f small thread angles , the normal and axial leads are
practically the same , and may be treated as such in cases where the angle is less than 2 degrees and the p itch less than lé inch ; an error
n o t e o f more than inch should be exce ded in any case . The e ffect of the error is apparent in the case o f a 6 diametral pitch h ob
3 inches in diameter , when the axial lead is ta ken as the ci rottia r
e pitch of the teeth , as it results in an error of more than on e half
o f degree in the pressure angle the hobbed tooth . Only in extreme
o f cases should the ang le the hob thread be more tha n ten d egrees .
a e diffiCul m H obs with gre ter angl s than this are t to ake and use . In hobs o f long lead the diameter should be proportioned so as to obtain f a r e asona ble angle o thread . However , the extr e me in diameters is as bad as the steep angles , and in cases where the two extr emes are
met a compromise is the only solution . The method used in laying o ut the tooth shapes on the drawing
board is an interesting study , but the method of generating the tool
as described is the most useful , and ca n be relied o n for accurate results ; th is is not the case with the drawing -board method which
o f is value only as a means of getting an approximate shape . CHAP TE R I II
TH E C E N TE R I N G OF TH E H O B I N G E A R H O B B IN G
Whether o r not it is necessary to center the hob in order t o get
satisfactory results in gear hobbing, is a question tha t is n ot so
r e adily answered as it might appear . For the s ake of making the matter clea r to thos e who have not the time to ma k e a study of the
subject , the results o f an investigation conducted by the writer will
e no doubt be o f interest . Theoretically spea king, th re should be no
o r . difference in the results whether the hob is centered not However, practical mo difications enter into the actual conditions and exert peculiar effects upon the results produced . To briefly explain the
th e action of the hob , we may say that generating operation consists
h Fig . 1 . D i a gram s owin g P oint s of Int erse ct ion of th e Pr essure L in es with the H ob Te eth e qu a lly sp a c e d at e a ch S ide of th e Pit ch Point o f a succe ssive trimming of the te e th o f the gear by those cutting
edges of the hob that are located in the generating path . The por tion of the cutting edge that forms th e tooth of the gear lies o n the pressure lin e of the hob , inte rsecting the pitch point , and the maxi mum l e ngth o f th e hob in this gen e rating space is 23 tan where 3 e quals the addendum o r the reciprocal o f the diametral pitch a n d (15 e quals the pressur e angle ; in case of small pinions this length ma y b e f as short as the circular pitch o the teeth . The point where th e two opposite pressur e lines cross the pitch line is the c e nt e r of the hob , and the object of centering is to get corresponding portions o f th e gen e rating edge s at equal distance s on h e ach side of t e cente r , so that the si de s o f the teeth gen e rated will m be sym etrical . Thus in Fig . 1 , the point s wh er e the pressure lines
e A A B B intersect the te th of the hob at , , , , and 0 , 0 1 , are at an equal
o r distance o n each side of the center pitch point , and at a like dis
' tance from the axis o f the hob wh e n the pitch point li e s in th e c e nter
of a tooth or space as shown . If the pitch point is shifte d out of th e
c e nt e r o f the tooth or spac e , the radial distanc e s of the r e spective
e e A n points of int rs ction are not equal , the points , B a d 0 being a
e e e e th e h A B gr at r or l ss distanc from axis than t e points 1 and C, . 4 1 33— B A D 3 N O. HO S N GE AR HO B BI N G
There are defects in the h ob that cannot be compensated for by any f amount o centeri ng, and the generating o f symmetrical teeth cannot A be insured . mong these we may cite the defects due t o distortion in hardening, unequal tooth thickness due to springing o f the tool
in forming, and errors in size resulting from ca reless workmanship . The defect that can be favored in the setting o f the hob is that in which the eccentricity o f the fo rm an a x i s causes the teeth to run out . This eccentricity may be caused by the use of an inaccura te mandrel in the backing-off operation or by n o t truing up the h ob properly in grinding the hole ; it may also be caused by an untrue h o n b ar bor o the hobbing machine itself . These defects can be de termi ned and proper allowance ma de to counteract the natural results by a careful setting o f the hob . B y knowing what result will be obtained with these eccentric hob conditions the defect can be
a nt ere Fig . 2 . Case I . H ob wi th L ow Tooth and H igh S p c e c e d . Full L in es show H igh S id e and D ott e d L ine s show L ow S id e
e diagnosed and a remedy applied , o r, at least , the setting can be mad
to favor the defective conditions . Let us take the most common condition— the case where the axis — o f the form and that of rotation are eccentric and parallel an d treat
it a s follows :Case I . Hob with low tooth and high space centered .
C . Case II . H ob with high tooth or low space centered . ase III Hob
o f wo n o t centered , but half way between the conditions the t p re ceding cases .
Cas e I fo r F o urt e e n a n d On e - h a lf D e gr e e Te e t h
The method o f treatment is to take a normal gear and show it in
h e e : mesh with the eccent ric hob in t d sired position in this case , with
“ ’ f on o the high spa ce cent e red . This setting brings the tooth the p po si te side of the hob in the center if the number o f gashes are even ,
“ % and this opposite side is the low side o f the hob . This is shown
in Fig . 2 . In each c ase , the high side is shown in full lines and the
low o r opposite s ide in dot ted lines . The intermediate teeth which range from high to low are not shown except in the central p osition n n in Figs . 2 and 5, and in the extreme p ositions in Fig . 8 . A i spection o f Fig . 2 will show that th e pitch line o f the hob , considered in its CE N TE R IN G T H E H OB 35
relation to the tooth itself, does n o t lie along a straight line pa rallel
o f o n t the axis o the hob , but a zigzag line that is shown broken . This
e o f line represents the pitch location of the right sid the hob tooth ,
“ o f and may be termed the line equal tooth thickness . It will have a drop for each pitch length of the hob for every convolution of the , e thread . In reality , the line inst ad of being zigzag should be a r e verse curve .
In the central p osition indicated by the full lines , the contact b e
o f h ob tween%the teeth the and gear is normal and correct . If the
- hob be given o ne half revolution , the p osition taken is indicated b y the dotted lines and it will be noticed that the gear and hob do not come into contact as they should at the p oints B and B the spac e A A widening from the p oints o f contact and I to the points B and B 1 . From this we may rightly assume that the hob would fo rm the teeth
Figs . 3 an d 4 . Tooth Outlin e s sh owin g h ow Flat s are forme d at the Pit ch L in e an d at th e Point i n C as e I o f the gear with a fullness at the point , as indicated by the full line 4 A t o o f th e from B in Fig . 3 . The dotted line shows the normal curve tooth . If the hob is giv e n a quarte r turn fr o m th e full line position , the rela tive position o f the teeth o f both the gear and hob is at the . dotted line position shown in the cente r o f Fig . 2 , midway between
‘ the teeth instead o f giving the normal contact at the pitch point on
o f the pitch line both gear and hob . This should d e velop a fullness o f the gear tooth at the pitch line diminishing again to normal at A the p o int . B ut the normal position o f the h o b tooth at the point A
brings the edge of the hob tooth inside of this bulge , so that it would
e f - e r move the greater portion o it shown in cross section in Fig . 3, l av
e ing a flat from the p oint A extending to the pitch line . In e xaggerat d cases , in cutting large numbers of teeth , the flat will extend past the
pitch line to the base o f the involute .
e Wh n the projected arc of action shown in Fig . 2 is gr e ater than
twice the p itch of the teeth , which is the case when cutting gears with f a greater number o teeth than 36 , the trimming o f the involute p ortion o f the teeth takes pla ce through two o r more turns o f th e h ob instead o f o n e . This brings the tooth o f the hob more nearly into 3 O 33— B 6 N . 1 HO S AN D GE AR HO B B IN G
e n the normal p osition at the d of the gear tooth , tending to make the point o f the tooth nearer to the proper thickness; but the correct thickness is never reached as it would be neces sary for the contact to continue to the position 0 , which is the case o f a gear o f infinite diameter . This develops a flat at the point o f the tooth for the same
reason as that given for the flat produced at the pitch line . Th e r e sult o f this action o n gears with teeth gre ater in number than 36
e 4 - is illustrat d in Fig . , where the cross s e ctioning shows the excess
metal removed , resulting in the production o f the flat . The effect o n the flank o f the tooth need n o t be taken into consideration ; as th e hob leaves it , there is ample clearance fo r the gear tooth o f the mating gear , it being only in the ca se of a gear meshing with a rack
that the flank would be apt to give trouble .
Ca s e I I fo r F o urt e e n a n d On e - h a lf D e g r e e Te e t h
e e The high tooth c nt red , as illustrated in Fig . 5, shows the normal
e a n d B contact betw en the teeth at the points B 1 . With the hob
n r Fig . 5 . Ca se II . H ob with H igh Te eth and L ow S pa c e c e t e e d . Full L in e s sh ow H igh S id e an d D ot t e d L i n e s show L o w Sid e
- revolved o n e half turn , the low space comes into the central p osition , A but there is n o contact between the teeth at the points and A, . In the central position where the pitch lines o f the gear and hob are f ta ngent , instead o the normal contact we have a space between the
h ob e teeth . A gear generated with the set in this position would hav A teeth of the form illustrated in Fig . 6 , with fullness at the points
h e e and a perc e pt ible flat below the pitch line , which extends t o t bas
e circle in gears with a larg e number o f teeth . In the case of g ars B with more than 36 teeth , the normal contact at the points B and , develop s into a space and results in a flat at the point o f the teeth , as
shown in Fig . 7 . The two pr e ceding cases give the two extremes in setting the hob central and show th e results o f eccentricity of the axis o f form and
e the axis of rotation . Of the two methods , the latter is the mor
B h t e o pra ctical . y cente ring the high to oth t e d e p h is asily btained ,
whereas in the first cas e with th e high space centered , the depth is not so easily obtained because the c e nter e d tooth is the low tooth and if
3— B AN D E AR B B 38 N O. 1 3 HO S G HO I N G
A f the hob tooth in the p osition , o Fig . 8 will leave a flat at this point f f covering considerable o the right side o the tooth face . The cross f sectioned areas show portions o the bulges cut away , leaving flats . T h e method outlined in Case III has the same effect as centering
any o f the teeth o f the hob except the high o r low tooth , so that the usual proce dure o f shifting the hob to bring new cutting p oints into position will result in unsymmetrical teeth being dev e loped in the
gear if the hob runs out o f true with the axis of rotation . The actual amount o f the distortion in the teeth generated will depend upon the amount o f eccentricity o f the hob form and is approximately on e
n o f fourth o f the eccentricity o ea ch sid e the tooth . In Fig. 3, for B example , the amount that the tooth is thick at the point , for a hob a o inch eccentric , will be inch on e ch side r inch
th e altogether . The amount of the space at pitch line would be the
8 Fig . . C ase III . H ob c ent ere d midwa y b et w een Positions in Case 1 and Case 1 1
o f o n e- result only half the eccentricity , as the tooth is in the mean
p osition at this point .
Co n s id e rat io n o f Ot h e r Ca s e s
S e b e e everal cas s could treat d in this way , as for instance , the case where the axis o f form is not parallel with the axis o f rotation but
e m where these axes int rsect . The only re edy that would make it pos sible t o ob tain symmetrical teeth would be to find the p oint o f inter of w section the axes and set the hob central ith that point . B ut
e o f r Fi inst ad setting the high tooth cent al , as in g. 5 , the hob should be set in such a p osition that the axis of the form lies in the same
o n plane as the spindle which the gear is placed , and the hob should
o f c o f be set central irresp ective the lo ation the teeth of the hob .
That is , the hob should be set so that the point of intersection o f the two axes will lie directly in line with the a xis o f the work spindle o f o r n o t o f the machine , whether the tooth the hob comes centra l .
’
Of course if a tooth comes into this position , so much the b e tter for the symmetry o f the teeth of the gear . This setting is illustrated in
Fig . 1 1 . The unsymmetrical results sure to be developed by any other w setting are quite obvious ithout further exposition . CE N TE R I N G TH E H OB 39
D e fe c t s in H o b s The preceding treatment of three typical cases throws some light o n the cause o f the poor shape of the te e th so often complained o f
h e in t results obtained from the hobbing machine , and while this dis cussi o n do e s n o t include all of th e defects that will produce similar ‘ results , it does emphasize the fact that more care will be necessary in th e e th e h ob e pr paration of than has formerly be n the pract ic e .
E ventually we shall have the ground hob , with the defe cts o f harden ing and careless forming eliminated by grinding the hard e ned hobs o n precision machines in which the human el e m e nt will be reduced
n to a minimum , so far as its effect o the accuracy o f the h ob is
th e concerned . When such hobs are available , hobbing process will meet with little or no opposition b as e d on the unreliable results oh
tai ne d by it . Ho wev e r , until the ground hob is perfected , flats and
Figs . 9 and 1 0. Tooth Out li ne s showin g Flat s produc ed by H ob set a ccordin g t o Condit ions of C ase III unsymmetri cal to oth outlines will be a source o f worry to the user o f the hobbing machine and he will meet the results already p ointed o ut e in Chapt r I . In that chapter , a remedy is given to reduce the
o f effects careless workmanship , and a further means o f correc ting such defects and distortions of the hob teeth is outlined in the follow
ing paragraphs . This consists o f the more direct process of grinding o ut the di stor
tion of the teeth from the narrow helical path , and o f bringing their cutting edges back into the pr o per helical relation with each other . — All that is neces sary for the operation is a to olpo st grinder pr e fer an a bly electric machine . Of cours e it goes without saying that the more carefully the p e rformance is carried o n , the more satisfactory will be the results obtained . The proc e dure is simply this :S et the lathe to the proper lead o f
o ol o o n - the hob , with the t p st grinder the slide rest , and with a clean cutting wheel grind the edge o f the side of the teeth into the proper
n o heli cal relation . It is necessary to be careful t to grind too much from the side o f the teeth ; just let the wheel touch the teeth all the
o n way a round , and if the mandrel which the hob is held is running e true , the hob thread will be straightened up . It will be notic d that 4 0 O 1 33— N . HOB S AN D GE AR HO B B I N G the land left by the wheel is not uniform and the amount that the teeth are o ut of true is directly proportional to the width of this land . It will also be noticed that some rows o f teeth will have wid e land while those of the opposite side o f the hob will have narrow la nds ; this is the res ult o f the eccentricity of the axis o f form with the axis o f rotation and should be corr e cted by grinding the t e eth back
o f until the lands are uniform width . This is the same tr e atment that wa s given for the correction o f car e less spacing and improper sharpen
t o f ing in the firs chapter this treatise . B esides this regular variation
o f in the width the ground lands , other irregular lands will be
Fig . 1 1 . M et hod of set t in g H ob wh en Ax e s of Form an d R ot a t ion int erse ct
t no iced which are the result of singly distort ed teeth , due to car eless
forming or to distortion in hardening . If the land left by the wheel is not so wide as to cause th e teeth to drag o n account o f the relief
o being gr und away , th e y may be allowed to r e main in the condition as
o left by the wheel , r they may be treated singly by grinding back as
in sharpening . The r e sults obtained by this treatment more than pay fo r the time m and expense , and where a h ob is giving trouble this remedy is re co
mended . A hob thus trea ted need not be centered as the te e th gen era te d by it will be symmetrica l by the most rigi d test usually ap
plied to c o mmercial work . The treatment will have to be repeated o f at each sharpening , however , to insure the continuance the good
r esults . In choosing the change gears for the lathe , the axial lead corresponding to the normal pitch o f the teeth must be used ; and as a B B N HO I G V S . MILLI N G 4 1
n o f h th e e o f diffe re ce inc is noticeable in angl the te e th , the e lead must be closely followed . S om such treatm e nt as this is n ece s
' sary with th e i rregular hobs now obtainable .
Co n c lus io n
:S th e e % The answer to the question hould hob be cent red thus , is that with the unground hob in which the e ccentricity is an unknown
a s quantity , but may be t ken a sure to exist , it is well to center the
high to o th as in Case II ; and with the accurate hob , that will be
available when the methods of grinding the teeth are perfected , it will be unnecessary to center the hob i f the hob has be e n carefully sharpened and the hob arbor runs true on its axis . Wh ile the results revealed by the treatment of the three cases seem to be unfavorable to
the hobbing p rocess , it is such studies as these that bring the truth
to light and lead the way to the remedy which , when applied , brings to the hobbing process the share o f consideration it deserves as one o f the simplest and most efficient methods for the production of the te e th o f gears .
CHAP TE R I V
B B H O IN G V S . M IL LIN G OF G E A R S
The adve rse criticism o f the gear mobbing proc ess has been the m cause of many interes ting investigations , and one o f the most i portant of these has been th e comparative study o f the condition of
o r the surfaces produced by the h b and by the rota y cutter . In mak
ing such a compa rative study , it is necessary that the investigator poss ess the required practical knowledge , and also that he be willing
h e to admit a point , even though his favorite p rocesses may suffer by t
comparison .
F e e d M ar %s p ro d uce d b y R o t at in g Milli ng Cut t e rs While both the gear hobbing machine and the automatic gear cutter i use rotat ng cutting tools , the operations cannot be placed o n a com
mon basis and cons idered as similar milling operations , although they
x e may , t o a certain e tent, be compar d as such . In comparing the
o f th e qualit y the surfaces produced by two processes , consider first
the milled surface produced by an ordinary rotary cutter . This sur
o f e face h as a series hills and hollows at r gular intervals , the spacing between these d epending upon the fe e d per revolution o f the cutter,
- an d the depth o n both the feed and the diam e ter o f the cutte r . The ridges are more prominent wh en coarse feeds and small diameter
e o f cutters are used . These feed marks are the r sult the convex path
- e o f the c utt ing edge and the slight running o ut o f the cutt r , which 4 2 - N o . 1 33 HOB S AN D GE AR HO B B I N G
b is inevitable in all rotary cutters with a num er of t e eth . As is well known to those familiar with milling operations the sp acing the , o f marks does n o t dep e nd on the number o f teeth in the cutter Theo .
' re ti c ll a y , e on it should dep nd this number , but as it is p ractically i m p ossible to get a cutter which will run absolutely true with the axis
o f o n rotation , only e mark is produced fo r each revolution and hence , , , o the spacing bec mes equal to the feed per revolution . The ecce n tri ci ty of the cutter with the axis o f rot tion is therefore the factor a , , t which , toge her with the diameter o f the cutter and the feed p er revo l i ut o n , o f determines the quality the surface, other conditions being
equal .
The depth o f the holl o w p roduced by th e high side o f the revolving
o r o f cutter is equal to the height rise a circular arc , the radius o f t h e o f which equals radius the cutter , and the chord o f which equals
the feed per revolution . ( S ee Fig. The length o f the chord or the fe ed per revolution may be exp ressed
F = 2 X 2 H R — H 2
in which F = feed per revolution ; H height o f arc ; R = r adius o f cutter .
H % S ince is a very small quantity , it may be discard e d in the ex
pression , which is then simplifi e d to read
F = 2 X V H D
in which D diamet er o f cutter .
a Transposing this expression , we obtain H which is an p 4 D proximately correct expression o f the depth o f the hollows produced
A - by milling . s an example , take an 8 pitch rack cutter , with straight
-s 3 rack haped sides , inches in diamete r, milling with a feed per revo luti o n o f r o f inch . The depth o f the feed ma ks at the bottom the o ut will be equal to
inch . 4 X 3
f The working surface o the tooth , howev e r , is produced by the side
o f of the cutter , as illustrated in Fig . 2 , and the depth the feed marks
is normal t o the surface , and is expressed as
d : H X sin a
a in which d depth of the feed marks o n the side o f the to oth , and
(1 e the angle o f obliquity . In the example given , the depth would qual
- inch , for a degree involute tooth . The depth o f the feed marks is inversely proportional to the diameter o f the cutter , an d is , therefore , greater at the point o f the
m e u tooth than at t h e root . In the exa ple giv n , the depth wo ld be
inch at the extreme p oint o f the rack tooth . It is thus ap B B N L HO I G V S . MI L I N G 4 3 parent that the quality of the surfac e at any position along the tooth from the root to the point depends upon th e diam ete r and form o f l the cutter a n d th e feed per revo ution .
o f - In Fig . 3 is shown the outline a N o . 6 standard degree i n
volute ge ar cutt e r . This outline , at the point close to the e n d of th e
e tooth o f the ge ar , is a tang nt inclined at an angl e o f 4 5 degrees as , indicated . H e nc e , th e d e pth of the r e volution marks is
° 4 5 e X sin inch , inst ad of inch , as in th e 4 X o f case the straight rack tooth . It is evident that to produce an equal
e o f d gree finish with that left by the rack cutter, the feed must be
N o considerably less for a . 6 involute gear cutter than fo r th e rack
cutter . In Fig . 5 is shown the full range o f cutter profil e s from N o s .
. 1 . D a r a D th Fig i g am illu st rat in g th e R el Fig . 2 . D i a gram f or findin g ep t n b et e n D m T t h io w e Fe e d , i a e t er of of F e e d M ar%s on S id e of oo Cutt er an d D epth of F e e d M a r%s cut by M illin g Cutt er
- m e 1 to 8, with the angle of the tange nt in e ach cas e which deter in s the quality o f the surface under equal conditions o f feed and diamete r o f cutter . If the depth o f the feed marks is used a s the determining factor in c omparing the condition o f the surfaces produced by a series o f cutters , it is evident that if the surface produced by the rack cutte r
is tak e n as a standard , the feed for cutting a pinion must b e consider ably less than th e feed used for cutting gears with a large number of f d r o . teeth . In fact , if a rack cutter is e inch pe revolution , a N 8 standard involute gear cutter should not be fed mor e than in ch
per revolution to produce an equally good surfac e . Th e fe ed is pro portional to the square root of the reciprocal o f the s ine o f the angle
of the limiting tangent .
If we assume the accuracy o f the surface left by the straight - sided rack cutte r as equal to 1 00 pe r c e nt , then th e relative fe e ds required for cutting ge ars with any formed cutter can be calculat e d . This has
a re b e en done , and the results shown plotted in curve A , in Fig . 6 . This curve i s based o n an e qual depth of the feed marks for the full range of numbers o f teeth in the gears . If, on the other hand , the surfaces 4 3— B A D AR B B 4 N O. 1 3 HO S N GE HO I N G
‘
left by the cutter for a giv e n fe e d per revolution are compared , the depth o f the feed marks will vary with the sine o f the angle o f the
- limiting tangent , and taking the straight sided rack cutter as a basis , th e relative accuracy o f the surfaces is inversely proportional to the
o f B . 6 . sine the angle , and is plotted in curve , in Fig
Co mp ari s o n b e t w e e n S urfac e s p ro d uc e d b y Millin g a n d H o b b ing
A relation has n o wbeen e stablished between the quality o f the sur face and the permissible feeds for cutters for cutting gears with any
number of teeth . We will now consider the condition of the surface
h o produced by a hob in a gear hobbing machine . The b is made with
- - o f straight sided rack shaped teeth and with sides a constant angle ,
o f v and is used to produc e gears with any number teeth . We may there
F i g 3 . n e h h . 4 D a m s A gl w ic Fig . i gra f or d educin g Formulas f or li mi t s th e F e e d an alyz in g Act io n i n Ge ar H obbin g M a chin e
5 - Fig . . Angle s limitin g t he F e ed f or 1 4 % d e gree S t andar d Ge ar Cut t ers
fore assume that it is cutting under the conditions governing the rack
cutter, as just explained , the surface produced being consider ed merely
as a milled surface . If this assumption be c o rrect , then the quality of
the surface produced by a hob , whether cutting a gear o f twelve teeth o r o f h e two hundred teeth , will be the same for a given feed , and t same relation exists between the hob and any formed cutter that
exists between the rack cutter and any formed cutter ; hence , curves
A and B , in Fig . 6 , may b e assumed to sh o w the p e rmissible feeds and the quality o f the surfaces p roduced by formed cutters when co m
pared with the surfaces produced by a hob , provided the surfaces are
e n consider d merely as milled surfaces . However , a co dition enters in the case of the hob which has no equivalent in the case o f the
formed milling cutter , and this influences the condition o f the surface . This condition is the distortion o f the hob teeth in hardening which
“ % causes them to mar the surface o f the tooth by side swiping, pro
i n o f duc g a rough surface . The eccentricity o f the hob with the axis rotat ion also has a diffe rent effect o n the surface than in the case o f a
e formed g ar cutter . The effect is shown in a s e ries of flats running parallel with the bottom o f the tooth , if excessive ; if the eccentricity
3— B AN D E AR B B N 4 6 N O. 1 3 HO S G HO I G
o n th e wh e n th e quality of the tooth surfac e alon e is considered , basis that both proc e sses produce a milled surface .
Th e To o t h Out lin e
Going further into the subject , we will take up the question of the
tooth outline . The tooth of a gear milled with an ordinary milling
e o f cutter must be , or at least is expect d to be , a reproduction the e n o f outline o f the cutter, and since each cutter must cov r a wide ra ge t fo r o ne teeth , the outline is not theoretically correc , except given number o f teeth in the range . Theoretically speaking , the outline of f the hobbed t oo th may be considered as a series o tangents , the tooth surface being composed o f a series o f flats parallel with the axis o f the
o f fo r gear . To show the significance these flats , assume , example , that
- a gear with thirty two teeth is cut with a standard hob , 8 pitch , 3
C O NI P AR I S O N O F T IM E R E %U IR E D F OR CU TTIN G G E AR S O N AU T O M OB IL E G E AR CU TTIN G M ACH IN E S A N D H O B B IN G M ACH IN E S
T inches in diameter , having twelv e flute s . h e length of the p ortion 2 o f the h o b that gene rates the tooth surface is S tan a , where a is 4 the pressure angle , as indicated in Fig . . The number o f teeth fol lowing in the generating path is
X number of gashes
In this case , the generating length is approximately inch , and
e there ar thirty teeth in the generating p ath . The flats of those parts o f the too th outline which each of the h ob teeth form vary in width
f m i m m ' wi dth along the curv e s . They are o i n u at the base line and of f maximum width at the point o the tooth . The width o f the flats at
' o f the pitch circle is proportional to the number teeth in the gear , the
. 8 number of gashes in the hob , and the pressure angle The angle , , to
the left in Fig . 7, which is the angle between each flat , is proportional to the number of teeth in the gear and the number o f gashes in the
- h ob . : In the example given , it is
36 0 X X 4 J i u a B B N I D HO I G v s . M L I HGZ
Th e W id t h o f F i a t Pro d uc e d
The width a o f the flat at th e pitch line is equal to twice the tange nt o f on e-half B times the length of th e pressure line between
o f e : the p oint tangency with the base lin and the pitch point, and is
= 2 a 2 tan B X tan X inch .
This is not a flat that could cause serious troubl e . A s in the case
th e o f e o f the fe ed marks , it is not width the flat alon that is to be
e b e e n consider e d , but the d pth must tak n into accou t ; in fact , th e
' quality o f the surface may be spoken o f as the ratio of the d epth to
o r the l e ngth o f the flat . The depth of the flat is the rise h e ight of th e arc of th e involute and is approximately proportional to the versed
n F e b G ar Fig . 7 . R elat iv e Width an d P o sit io of lat s produc d y e H a r E a h Ge n era t n obbing M a chin e s . A in dic t e s F e e d pe c i g R v t n B an% Toot h ; B , F e ed per e olu io of l
o f th e e sine the angle B, and with the pitch assumed in xample f giv e n , would be inch . It is difficult to conceive o any shock
caused by this flat , as th e gear te e th roll over each other . The action o f th e hob and gear in r e lation to each other furth e r modifies the flat
e a th e by giving it a crowning o r convex shap . In f ct , the wider flat
the more it is crowned . This explains th e fact that hobs with a few gashes produce teeth o f practically as good shape as hobs with a
e large number o f gashes . It is desirabl , th e refore , to use hobs with m as few gashes as possible , b e cause fro a practical point o f vi ew th e errors o f workmanship and those cau se d by warping in hardening m increase with the nu b e r o f flut e s . A peculiar feature o f the hobbed tooth surfac e is shown to the right
th e o n in Fig . 7 , which illustrat e s path a tooth produc e d by a hob in i one revolution . In fact , there are two distinct paths , the first start ng
at the po mt of th e tooth and working down to the bas e line , the
e e o f th cutting dges of the hob tooth th n jumping to . the root e tooth
th e e and working up to base lin , producing the zigzag path shown . ‘ ‘ v n z r i x n * 1 s~ A' N D E AR B B N N a. a Hoes G HO I G
Co n c lusi o n
That the flats so commonly se e n in the results obtained from % the hobbing machine are not due to any faults o f the process that cannot f be corrected , but are due to eith e r carelessn e ss on th e part o the operator in setting up the machine without proper support to the
work o r to the p o or condition o f the hob o r machine , and that nearly all cases o f flats can be overcome by the use of a prop e r hob , may be
me f assu d as a statement o facts . When the hobbing machine will not
give good results , the hob is in nearly all cas e s at fault . If a gear is produced that bears hard o n the point o f the teeth , has a flat at the p itch line o r at any point along the face o f the tooth do not think
h e 1 that t process is faulty in th e ory , o r that the machine s not properly n adjusted , o r that the strain of the cut is causing undue torsion i the
shafts , or that there is backlash b e tw e e n the gears in the train con n e cti n g the work and th e hob ; these things are n o t as likely to cause
o the trouble as is a faulty h b . A fter an e xp e ri e nc e covering all make s of hobbing machines , the writ e r has c o m e to th e conclusion that the real cause o f the trouble
' in nearly every case is a faulty hob . Machine afte r machine has been
tak e n apart , overhauled and r e adjusted , and y et no b e tter r esults have
w et ( b e en obtained until a n e and b ter hob was produced . The faults
m e usually e t with in hobs wer e ref rred to in Chapter I , and the m e ans fo r g e tting th e hob into a good worki n g condition were also
' e to di s r e xplained there . It is not d sired in any way pa age t h e formed cutter process in favor of the hobbing process , but simply t o state the
‘ I v er facts as they app e ar . n e y case , practice seems to substantiate the conclusions arrived at .
THI S B OO% I S DUE ON TH E L A S T DATE S TAM P E D B E L OW
. AN I N ITIAL F I N E o r 2 5 CE N TS W I L L B E AS S E S S E D F O R F AIL U R E TO R ET U R N TH S B O I O % O N TH E D ATE D U E . TH E P E N ALTY W I L L I N C R E AS E TO 5 0 C EN TS O N TH E F O U R TH D A Y A N D TO O N TH E S E V E N TH D AY