Journal of Mechanical Working Technology, 1(1977/1978)215--230 215 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

A W O R K A B I L I T Y A N A L Y S I S O F T H E C O L D F O R G I N G OF G E A R S W I T H I N T E G R A L T E E T H

MARK ROBINSON

Paul D. Merica Research Laboratory, International Nickel Company, Inc., Sterling Forest, Suffern, N.Y. (U.S.A.)

and

HOWARD A. KUHN

Department of Metallurgical and Materials Engineering, University of Pittsburgh, Pittsburgh, Penn. (U.S.A.)

(Received February 3, 1977; in revised form July 19, 1977)

Indus t r i a l S u m m a r y

The cold forging of gears with integral teeth offers advantages over more conventional gear-manufacturing methods. However, a limiting factor in forging complex shapes is surface cracking during deformation. A workability analysis that can predict the likelihood of surface cracking is applied to the types of deformation that would occur during cold forging of a gear.

The forging of a gear from a ring preform is simulated by a two-stage sequence: ring upsetting followed by gear-tooth formation. Using model materials, the workability analysis is applied to both stages to determine the effect of process variables on the likelihood of surface cracking. The process variables considered in this study are preform geometry, die geometry and die-workpiece friction.

Results of the study are used to formulate preform-design guidelines for different types of gears, including pinions, ring gears, and spur gears. A criterion to predict wall instability during upsetting of a ring is also presented.

I n t r o d u c t i o n

Cold forging o f gears wi th integral t ee th of fe rs s o m e advantages over machin ing . T h e cu t t i ng o f gear t e e t h requires long mach in ing t ime, skil led labor , and resul ts in cons iderab le mate r ia l waste. The surfaces o f cu t gear t e e th also have an un favo rab l e o r i en t a t i on to the f iber o f the mater ia l . How- ever, co ld forging can be accompl i shed a t re la t ively high ra tes wi th min ima l mate r ia l loss. Fo rged gear t e e th are s t r eng thened b y f low lines t h a t fo l low the t o o t h profi le .

Sur face f r ac tu re is a m a j o r l imi t ing f a c t o r in the forging o f c o m p l e x shapes. Dur ing forging, a f ree ly e x p a n d i n g sur face m a y exh ib i t a tensi le c o m p o n e n t o f s t ra in and poss ib le f rac ture , as s h o w n in Fig. 1. This is s imi lar t o the c rack

216

formation in upset compression of cylinders. If the effects of process param- eters on the surface strain state are known, they can be utilized to reduce the likelihood of surface cracking during deformation. The present s tudy was undertaken to determine these effects for the process of gear forging.

Workability can be defined as the ability of a material to deform in any given metalworking process wi thout fracturing. A workabili ty analysis which brings together the characteristics of both the material and the process has previously been developed for predicting the likelihood of free surface cracking during bulk deformation processes [ 1 ]. The material is characterized by a total-strain fracture criterion, or forming limit. This is determined by upset compression tests and the technique is reported elsewhere [ 1]. Process effects are reflected in experimentally determined surface str: ~n states. Changes in the process parameters are reflected in changes in the shape of the surface strain path. Comparison of the strain path to the forming limit yields a graphical representation of workability.

The forging of a gear with integral teeth in a closed die is basically a two- step sequence. The initial step is simple upsetting of the ring preform. As the ring height decreases, the outer diameter increases. This step ends when the outer diameter of the ring has expanded enough to contact the tooth- root sections of the die and material starts to flow into the tooth cavities. Tooth formation is the second step in gear forging.

The approach taken in this s tudy is to determine the effect of process parameters on the surface strain states in each step of gear forging. By varying the die geometries, different gear types are simulated: ring gears, pinion gears*, spur gears with a beveled face, and spur gears with a hub. Model

Fig. 1. Surface cracking of a partially forged P/M gear.

*In this s tudy, the term pinion gear is used to describe a gear with a large body thickness relative to the tooth length. Therefore, it does not necessarily correspond to the widely accepted definition of a pinion gear.

217

materials were used to simulate the flow of metal in each stage. Using this information, guidelines for preform design that lead to the most favorable surface strains are formulated for the various gear types considered. The most favorable surface strains, as indicated by the workability analysis [1], are those which avoid biaxial tension, and which most closely approach homogeneous compression (slope of negative one-half in the tension--com- pression quadrant o f strain space).

Ring upset forging

The upsetting of rings has been extensively characterized by experimental studies [2--4], upper bound analysis [5--7] and stress analysis [8]. These studies indicate that radial expansion and bulging of the outer surface of an upset ring depend on the ring geometry, die--workpiece friction and mandrel-- bore clearance. The local strains on the outer surface which control fracture are dependent on the bulging and radial expansion of the free surface. To maintain a low slope of the local surface strain path, and therefore avoid fracture, the die--workpiece friction should be low. Also, ring H/Do ratios should be large and the wall thickness should be large to avoid buckling. Combinations of ring geometry and friction should be chosen so that the neutral radius is as large as possible to minimize outward expansion. Finally, a clearance should exist at the bore to accommodate the inward flow caused by the large neutral radius position.

Unfortunately, these factors are not independent, and the desirable values are not all compatible. For example, large aspect ratio, large wall thickness and large clearance may not be possible for any given volume of material. The neutral radius at its maximum position is in direct opposition to low friction and to rings with large aspect ratio and large clearance. Since not all the opt imum values can co-exist, some must be chosen at the expense of others. However, first principles cannot predict which of these factors will dominate.

In light of this, ring-forging experiments were carried out to determine the variables that are most important in controlling local surface strains. Aluminum alloy 5052 was used as a model material. The surface strain paths were deter- mined by measuring the dimensional change of a 1.6 mm square grid with a toolmaker 's microscope. Grids were electrochemically etched on the surface of the preform with the Electromark system. All ring-upset~forging strains were measured at mid-height, the maximum bulge diameter. Details of the experimental technique are reported elsewhere [9]. Two values of aspect ratio (H/Do), two values of wall thickness to inner diameter ratio (T/Di) and two values of bore-clearance-to-thickness ratio (C/T) were considered, resulting in the six ring geometries listed in Table 1. A schematic view of the testing setup is shown in Fig. 2. By upsetting the rings on two sets of dies, one polished (~ = 0.12) and one knurled (p = 0.4), rings with neutral radii within the ring or bore, or initially within the bore but moving into the ring during

218

deformation, resulted. The aforementioned coefficients of friction were measured using the ring-test method of Male and Cockcroft [10] ; these are for the model material upset on unlubricated dies. No lubricant was used during the experiments because the incremental nature of the deformation would necessarily disturb any lubricant film, altering its lubricity and, there- fore, result in a varying coefficient of friction during the test. Consideration of the results of the upset forging tests will reveal the relative effect of each of the variables on the surface strains during forging.

Figures 3 and 4 clearly show the effect of friction. Regardless of ring geometry, all of the rings tested under conditions of high friction (knurled dies) exhibit strain paths that deviate greatly from the desired case, homoge- neous compression, whereas lower friction (polished dies} causes some of the rings to exhibit a more desirable strain path. For high friction, large-aspect- ratio rings have strain paths of slightly lower slope than low-aspect-ratio rings. Wall thickness also exerts a minor effect. Within each aspect ratio grouping, the ring of greatest wall thickness has the strain path of lowest slope. Bore clearance and mandrel contact during deformation exhibited no effect on the surface strains.

Low-friction ring forgings lend insight into the relative importance of other variables. The low-aspect-ratio rings and the thick-walled rings having large aspect ratios have surface strain paths of considerably lower slope than either the thin-walled rings of large aspect ratio or any of the high-friction

TABLE 1

Geometric factors of forged rings

Upset forgings

Ring No. H/D o T/D i C/T Die and friction condition code*

1 1/2 1/2 0 a, b 3 1/2 1/2 2/5 a, b 5 1/2 1 0 a, b 6 1 1/2 0 a, b, c 8 1 1/2 2/5 a, b, c

10 1 1 0 a, b, c

Hubbed die forgings

Ring No. H/D o T/D i C/T Area under punch (in 2 (ram2))

1 1/2 1/2 0 0.036 (23.4) 2 1/2 1/2 1/4 0.380 (245.1)

26 1/3 3/4 0 0.479 (309.1) 27 1/3 1/2 2/9 0.479 (309.1)

*Die and friction condition code: a = flat, polished dies, b = flat, knurled dies, c = conical, polished dies.

219

forgings. This occurs because the low-aspect-ratio rings and the thick-wailed rings of large aspect ratio have lower wail-slenderness ratios (H/T) than the other rings of large aspect ratio. Thus, wail stability is important at lower friction. As in the high-friction case, clearance and mandrel contact have no effect on the surface strain path.

The effect of neutral radius position is also shown in Figs. 3 and 4. The initial position of the neutral radius is within the bore for the low-friction forgings and half of the high-friction forgings, and within the ring wail for the other half of the high friction forgings. However, all the high-friction ring forgings exhibited strain paths of similar slope and the low-friction forgings had strain paths of two different slopes. Therefore, the position of the neutral radius, while strongly affecting the mode of flow in the bore, has little effect on the strain state on the outer free surface.

Rings of large aspect ratio were also upset forged in dies having a 20 ° conical bevel. Along with these flat-ended rings, rings with a 20 ° conical bevel, whose ring height at mid-radius was equal to the corresponding flat-ended rings, were also upset in the beveled dies. The resulting surface strain paths are shown in Fig. 5. The beveled ring results are similar to the results for the corresponding flat rings forged on the knurled dies. The results for the flat- ended rings forged in the beveled dies are similar to the corresponding smooth die forgings. Figure 6, a replot of the strain paths for rings of large aspect ratio forged on polished and knurled dies, is shown for comparison.

Rings of four geometries, see Table 1, were forged in dies with a hub recess,

HIGH FRICTION TESTS 1 0.5

-o; -oi, "o "r' - - ° o M,NOR STRA, N,Ez

Fig. 2. Schemat ic of exper imenta l set up and parameters describing ring geomet ry . H is ring height, D O and D i are ring inner and outer diameters, T is ring wall thickness and C is bore clearance.

Fig. 3. Surface strain paths of rings upset on knurled dies. Open symbols indicate H / D o = 1, closed symbols indicate H I D o = 1/2.

220

LOW FRICTION TESTS

& C3

-0.5 -0.4 -0.3 -0.2 -0.1

MINOR STRAIN, E z

0.5

0.4 c~

Z

0.3 ~. 03

f r O

0.2 ~E

0.1

Fig. 4. Surface strain paths o f rings upset on polished dies. Open symbols indicate H / D o = 1,

closed symbols indicate H / D o = 1/2 .

with and wi thout a radius at the hub-flange comer. Strains were monitored on the outer surface and on the hub top surface. In every case, no deforma- t ion occurred in material in the hub. No surface strain occurred on the top of the hub. The surface strains on the outer free surface are shown in Fig. 7. As the amount of die contact area increased, the slope of the surface strain path increased. The radius at the hub-flange corner had no effect on the surface strains. The ring with the least amount of die contact area (Number 1),

CONICAL DIE TESTS

~ 0 •

• IoC Io T o • hiC l o t • IoC hi T

• FLAT RING o BEVELED RING

I

0.5

0.4

i

0.5

0.2

O.t

I I I 1

-0.5 -0.4 -0.3 -0.2 -0.1 0

MINOR STRAIN,E z

Fig. 5. Surface strain paths of rings upset in conical dies. Open symbols indicate beveled preforms, closed symbols indicate flat preforms.

221

FLAT DIE 0.5

TESTS 1 H/Do -- I

/' 0.4 • D

0.5

• IoC I o T ~ " ~ , ~ • hiC loT 0.2 • IoC hiT I

-2

• LOW FRICTION 0.1 o HIGH FRICTION

I I I I I -0.5 -0.4 -0.3 -0.2 -0.1 0

MINOR STRAIN, E z

Fig. 6. Replot of surface strain paths of rings of H/Do = 1, Open symbols indicate forgings on knurled dies, closed symbols indicate forgings on polished dies.

exhibited no surface strains. In this case, the mode of deformation was similar to machining or shaving rather than upset forging.

Buckling or a fold on the bore surface, as seen in Fig.8, was observed for all the forged rings of large aspect ratio. Fifteen rings of widely varying geometries were upset to determine the effect of geometry on buckling. Figure 9 summarizes the test results, along with results from other investiga- tors [3 ,10--12] . The initial ring aspect ratio (H/Do) is plot ted versus the initial ring wall-slenderness ratio (H/T). A clear distinction exists between the values of ring wall-slenderness ratio that lead to buckling (H/T > 3) and those that do not (H/T < 2).

- 0 . 5

HUBBED DIE ( ~ TESTS - 0.4 Q)

z

% t 0.5 1-- O3

SYMBOL RING NO. ~ • or.

o 2 • 2 o -~

• 26

o RADIUS DIE k "~%~'~ -J • NO RADIUS DIE ~..~41..~.~.~~~t.~

I I I - I ~ ~ . ~ i -0.5 -0.4 -0.3 -0.2 -0.1 0

0.1

MINOR STRAIN,E z Fig. 7. Surface strain paths of rings upset in hubbed dies. Ring numbers refer to Table 1. Open symbols indicate radius die forgings, closed symbols indicate no radius die forgings.

222

(a)

(b) I I ...... 11

0.25"

Fig. 8. Sectioned and macroetched rings. Ring (a) shows stable flow in ring wall. Ring (b) shows bore defect and associated flow in ring wall.

The transition from a stable mode of flow in the ring wall to one leading to a bore defect can be explained by the upper bound analysis of Kudo [13]. Figure 10 shows the least-upper-bound deformation modes for slenderness ratios greater than and less than 2.0. Although this analysis is for plane-strain deformation, comparison to the deformation mode shown in the macroetched ring walls indicates good agreement.

In summary, the variables affecting the surface strain state of an upset ring are, most importantly, friction, with ring wall stability of secondary impor- tance. Factors such as the position of the neutral radius, bore clearance and mandrel contact are of no importance. Conical-die forgings yield results similar to high-friction flat-die forgings when the ring ends match the bevel of the dies; these results are also similar to low-friction flat-die forgings when flat-ended rings are forged. The strain path on the outer surface of a ring up- set in hubbed dies is strongly affected by the area of die contact. Ring-wall stability is a function only of the wall-slenderness ratio.

223

0 0 V X7

IO A

~7

o o o x7 H T

o Z o V ~ o ~. S ~ ' ~ ' , \ I "~\,~,~ "CC~

o ..,~-~S~- ''~'~ I* Rob ..... o o o .,,.~-~"\"~'T'~ I A schet

~ : F : : ~ ; ~ I: B.~.~ ..... • " .~.~,~,~ ~ I I / • Male ~Coc~,CFOfl

0 I 2 3 H Do

Fig. 9. Initial H / D o and H I T ratios for buckled and unbuckled rings. Open symbols indicate buckling, closed symbols indicate stable flow in ring wall. Data from other authors is included [ 3,10--12 ].

AFTER INITIAL DEFORMATION RING WALL

!

t

!

t UPPER BOUND

RESULT

E X P E R I M E N T A L

RESULT Fig. 10. Comparison of Kudo's upper-bound analysis [13 ] and macroetched ring walls for the buckled and unbuckled specimens shown in Fig. 8.

224

Gear-tooth forging s tudy

When too th formation starts to occur during gear forging, the preform can be considered to be divided into a number of pie-shaped segments, one per tooth, bounded by radial lines passing through the middle of the root land between each tooth. Each segment supplies material to form only the one tooth with which it is associated, with no flow across the segment boundaries. A gear-tooth die was designed to simulate this type of deforma- tion. As the upper punch descends, material from different-sized rectangular preforms flows outward to form one gear tooth, Fig. 11.

Chemical lead was used as a model material because the aluminum alloy used in the ring s tudy would have required forces in excess of the available press capacity. Two too th profiles were considered; rack and involute, with characteristic dimensions of 20 ° pressure angle, diametral pitch of 3 and, for the involute tooth, pitch radius of 5 in (127 mm). A factor relating the preform size to the too th size is defined as RT/TD: Ring Thickness of the gear body (simulated by the preform ring thickness)/Tooth Depth (length of tooth). The tooling was designed for three values of RT/TD; 1/2, 1/1, 2/1. Various upper-punch geometries were available, allowing gear geometries such as flat, beveled face, and hubbed gears to be simulated, F ig . l l . As a result, three factors were considered in this stage of the study: R T/TD, upper-punch geometry, and tooth profile (rack vs. involute).

Prior to testing, it was not known where the most severe surface strains

METAL FLOW

~ / f / i / i /

INITIAL DEFORMED

R T / T D RATIO

112 I / I 2 / I

PUNCH SHAPE

FLAT BEVELED HUBBED Fig. 11. Schematic view of gear tooth forging die showing metal flow during deformation, cavity shape for various RT/TD ratios, and various punch geometries.

225

would occur during too th forging. Therefore, an experiment was run, measuring the strains at various positions on a 1/2 RT/TD involute too th forged with a flat punch. The actual strain paths are reported elsewhere [9], bu t the most severe surface strains occurred at the center of the too th face at mid-height. All subsequent strain measurements were made at this point.

The effect of RT/TD for involute too th forgings is shown in Fig. 12. As RT/TD increases, the magnitude of the strain decreases, and the strain path tends to curl back. Compared to strains occurring during ring upset forging, the overall magnitude of the strains for too th formation is low. Experiments in the rack too th cavity yielded similar results, except that the rack too th forging for RT/TD = 1/2 buckled during deformation.

The effect of upper punch geometry is shown for involute too th forgings in Fig. 13. The insets show the relative punch-preform geometry. As can be seen, a beveled punch increases the severity of the surface strains. When flow can occur into other die recesses, i.e., into a hub recess, the surface strains are more compressive in nature. As before, rack too th profile forgings exhibited similar results.

Summarizing, of the factors considered, die profile has little effect on the surface strain path, while RT/TD and punch geometry have a strong effect. To keep the surface strains low, large RT/TD is desirable. If metal can flow into die recesses away from the too th tip, strains at the too th tip are moder- ated.

INVOLUTE TOOTH INVOLUTE TOOTH FORGINGS FORGINGS

0.2 RT/TD= I / I

-O12

• RT/TD= 1/2 • RT/TD= I / I • RT/TD= 2/ I

-0,1

MINOR STIRAIN,E 2

_z

0.I

-0,4 -0.3 -0.2 -0.I

MINOR STRAIN,E 2

0.3

Z

0.2~ b- (D

nr O

Fig. 12. Surface strain paths for involute tooth forgings of various RT/TD ratios.

Fig. 13. Surface strain paths for involute tooth forgings of various punch-preform geometries. Insets show relative punch-preform geometry.

226

Guidelines for preform design

Some guidelines for design of preforms for the various types of gears arise from results of the present study. By combining geometries of the various ring forgings and gear-tooth forgings, four types of gears may be simulated. Guidelines for the four types are discussed below.

1. Ring gears Ring gears are simulated by ring forgings of low H/Do ratio and involute

tooth forgings having a low RT/TD ratio. The low value of RT/TD ratio associated with ring gears has two detrimental effects. Low RT/TD teeth require large overall height reduction to completely fill the die, necessitating a preform of large height or large wall-slenderness ratio that can cause wall instability during deformation. Low R T/TD teeth also have the most severe surface strains during forging. These two effects can result in a bore defect or cracking at the tooth tips during deformation.

The occurrence of both defects can be minimized by designing the preform to have the largest possible outer diameter and smallest inner diameter allowed by the tooling. This will cause the preform to have the maximum wall thickness and lowest height, resulting in the minimum wall-slenderness ratio and highest RT/TD ratio. This, in turn, will reduce the tendency for wall instability during deformation and decrease the severity of the surface strains during tooth formation. Also, maximum outer diameter will minimize the amount of free ring deformation and its associated surface strains, further helping to reduce the likelihood of surface cracking.

2. Pinion gears Pinion gears are simulated by ring forgings of high H/Do ratio and involute

tooth forgings having a high RT/TD ratio. The large preform-aspect-ratio can lead to wall instability and severe surface strains during ring upsetting. The high RT/TD ratio gear teeth result in low strains during tooth formation. However, if the surface is brought to incipient failure during ring deforma- tion, cracking may occur during tooth formation.

The chance of both defects occurring can be minimized through proper preform design. Maximum outer diameter and minimum inner diameter will minimize the tendency for wall instability, as previously described. Increased wall stability will reduce the severity of the ring forging strains. Maximum outer diameter will also decrease the amount of free ring deformation, further decreasing the chance of surface cracking.

3. Spur gears with a beveled face Spur gears with a beveled face are simulated by conical-bevel-die ring

forgings and involute tooth forgings made with a beveled punch. Preforms for this type of gear will be of two general types: flat or beveled to match the punch angle. Each type of preform has different defect possibilities and design guidelines.

227

Flat-preform forgings have exhibited low surface strain paths during ring deformat ion and gear-tooth formation. Therefore, use of a flat preform will minimize surface cracking at the too th tips during deformation. However, the top surface is not initially in contact with the upper punch over its entire length. Due to the combinat ion of punch angle and friction, deformat ion will be of the type that results in a state of biaxial tension on the top free surface which can lead to cracking at low levels of deformation [14].

Beveled preforms have no top free surface and cracking on top is not a problem. However, beveled preforms exhibit more severe surface strains in both stages of gear forging. Therefore, the possibility of cracking at the too th tips is higher for beveled preform forgings than for flat preform forgings.

Flat or beveled preforms are chosen by which type of cracking is to be minimized. Cracking at the too th tips can be minimized by using flat preforms. Cracking on top can be eliminated by using beveled preforms. Cracking at the too th tips of beveled preform forgings can be minimized by designing the preform to have the maximum outer diameter and a clearance between the bore and the tooling. The maximum outer diameter minimizes the amount of free ring deformation and associated surface strains. The bore clearance will help moderate the gear too th forming strains by allowing flow away from the too th tip during deformation. Bore diameters are limited in size by wall stability. Consideration of ring geometry and a maximum wail-slender- ness ratio of 3 leads to an expression for the maximum permissible bore diameter

2 H D b ~ < D o ( 1 3 Do ) (1)

where Db is the bore diameter, Do is the outer diameter and H is the height of the ring preform.

4. Spur gears with a hub Spur gears with a hub are a combinat ion of hubbed die ring forgings and

involute too th forgings made with a hubbed upper punch. During ring deformation, no strain occurs on the surface in the region of the hub. How- ever, when the die fills and hub extrusion starts to occur, the hub free surface will exhibit a tensile strain in the radial direction [15]. If no com- pressive circumferential strain, resulting from inward flow or a tapered hub recess, accompanies the tensile strain, cracking may occur.

Cracking at the too th tips and cracking on the hub free surface can be minimized through proper preform design. Maximum outer diameter and a clearance on the inner diameter will result in the most favorable surface strains at the too th tips. A clearance on the bore will also allow inward flow and a compressive circumferential strain to occur during hub extrusion.

228

Assessment of workability for gear forging

This study has revealed the nature of the surface strains for both stages of gear forging. The strains for small amounts of ring upsetting and for gear- tooth formation are not severe. Therefore, it is anticipated that, except for very low ductili ty materials, surface cracking on the tooth tips during gear forging is not a major limiting factor.

To illustrate, consider two examples: forging a ring gear from a flat pre- form, and forging a beveled faced gear from a beveled preform. The preform- design guidelines for these two gears indicate a minimum clearance should exist between the tooling and the preform outer surface. For the ring gear, consider a clearance of 5% of the preform outer diameter. The surface strain path for forging the ring gear will consist of surface strains for 5% radial expansion of a low H/Do, thin-walled ring (Ring No. 3) added to the strains for forging a 1/2 RT/TD ratio gear tooth. This composite strain path, shown in Fig. 14, remains below the forming limit of a material of limited ductility (forming line intercept of 0.1, typical of a sintered powder material), indicating no severe formability problems.

Also shown in Fig. 14 is the composite strain path for the beveled face

~ C,~ 0.3 5

0 3 ~ t-

0 . 2 5

0 2 ~

!!i - 0 . 2 5 -0 .2 -0.15 -0.1 -0 .05 0

MINOR STRAIN

Fig. 14. Composite strain paths simulating the forging of a ring gear and a beveled-faced gear. Broken lines indicate first-stage ring-forging strains; full lines indicate second-stage tooth-forging strains. Forming limits with intercepts of 0.1 (typical sintered powder material) and 0.25 (CC and W-commercially cast and wrought material of moderate ductility) are shown for comparison.

229

gear. It is composed of the strain path for 3% radial expansion of a high H/Do beveled ring forging (Ring No. 8) added to the strain path for a 1/1 RT/TD ratio beveled gear tooth forged from a beveled preform. The resulting composite strain path remains below the forming limit of a typical commer- ciaUy cast and wrought material with moderate ductility (intercept of 0.25). Thus, materials with ductility levels commonly used in cold-forming applica- tions may be forged into gears having beveled faces without cracking of the tooth tips, but forging the same type of gear from sintered powder materials would risk cracking (see Fig. 1). These examples indicate that, if the proper preform shape is utilized, workability will not be a severe limiting factor in forging gears with integral teeth.

Analyzing gear forging by adding the two surface strain paths head-to-tail may seem simplistic. However, gear forging is truly a two-step sequential process. Initially, the surface of the preform moves radially outward under simple upsetting conditions. During gear-tooth formation, the same surface continues to move radially outward into the tooth cavity. Therefore, the total surface strains are represented by the addition of strains occurring during each stage.

Although workability does not place severe limitations on gear forging, another limiting factor is die damage in the form of cracking or excessive wear. Both of these are related to the pressure distribution in the die cavity during forging. Cracking is directly related to the pressure distribution. Pressure at a point in combination with the amount of metal flow past that point interacts with the die surface to determine die wear. An analysis of the pressure distribution and flow in a gear die cavity is currently in prepara- tion.

Acknowledgment

This project was supported by a grant from the American Iron and Steel Institute (AISI Project # 56-350).

References

1 H.A. Kuhn, P.W. Lee and T. Ertiirk, Trans. ASME, J. Eng. Mater. Technol., 95 H (1973) 213.

2 S. Kobayashi, Trans. ASME, J. Eng. Industry, 92B (1970) 391. 3 S. Biswas and F.W. Travis, Int. J. Mach. Tool Des. Res., 2 (1971) 235. 4 K.M. Kulkarni and S. Kalpakjian, Trans. ASME, J. Eng. Industry, 91B (1969) 743. 5 B. Avitzur, Metal Forming: Processes and Analysis, McGraw-Hill, New York, 1968. 6 H. Kudo, Int. J. Mech. Sci., 2 (1960) 102. 7 J.Y. Liu, Trans. ASME, J. Eng. Industry, 94B (1972) 1149. 8 J.B. Hawkyard and W. Johnson, Int. J. Mech. Sei., 9 (1967) 163. 9 M.L. Robinson, Ph.D. Thesis, Dept. Materials Engineering, Drexel University,

Philadelphia, Pennsylvania, 1976. 10 A.T. Male and M.J. Cockcroft , J. Inst. Met., 93 (1964) 38. 11 J.A. Schey and P.W. Wallace, Metal Flow in Closed Die Forging of Steel, Part II:

Speed and Lubrication Effects, AISI, New York, 1967.

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12 M. Kunogi, Sci. Res. Inst. Rep., 30 (1954) 63. 13 H. Kudo, Int. J. Mech. Sci., 1 (1960) 57. 14 S.K. Suh, H.A. Kuhn and C.L. Downey, Trans. ASME, J. Eng. Mater. Technol., 98H

(1976). 15 C.L. Downey and H.A. Kuhn, Trans. ASME, J. Eng. Mater. Technol., 97H (1975) 121