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Factors influencing fill-out of a closed die during cold forging
Int. J. Mach. Tool Des. Rcs. Vol. 26. No, 4. pp. 385-401. 1986 Printed in Great Britain
{)020-7375/86; $3.(104.1111 Pergamon Journals [ J d
FACTORS INFLUENCING FILL-OUT OF A CLOSED DIE DURING COLD FORGING J. M . MONAGHAN* a n d M . O'REILLY*
(Received 13 March 1985; in final fi)rm 16 Janua O, 1986)
Abstract--Closed die cold forging is an important industrial metal ff)rming process used extensively in the manufacture of headed fasteners. In this paper an upper bound solution is presented based on observed velocity fields resulting from the deformation of initially cylindrical workpieces within hexagonal and square dies. The influence of workpiece aspect ratio, forging loads and friction conditions on the fill-out of the hexagonal and square dies is examined. It is shown that at high die fill-out, friction conditions and workpiece aspect ratio have little influence on the forging pressure ratio. The surface stress state, produced by relative movement between workpiece and punch/die, is examined with the aid of microhardness measurements.
NOMENCLATURE
E.,: k T
I?~vl Sv S
r, U U, U, U: U, U, W R Y r lql t
0
-y q, d~ e(i
L m ITo
Rf
total rate of internal energy dissipation rate of internal energy dissipation due to internal deformation. rate of internal energy dissipation due to interracial friction yield stress in shear interfacial shear shear stress magnitude of velocity discontinuity surface over which velocity discontinuity occurs within the deforming zone length of the side wall of the die component of stress vector prescribed on surface S, within the deformation zone punch velocity exit velocity from triangular deforming region velocity of flow of material entering the section region vertical velocity component velocity of material within sector radical velocity component within sector length of flat portion of the workpiece in contact with the die wall half the "'across flats" distance of the hexagon or square die distance of a material element within the triangular region when measured for the centre of the workpiece radius of a material element within sector measured from workpiece centre undeformed height of workpiece deformed height of workpiece angle of triangle region at workpieces centre angle of sector region at workpiece centre position of element within sector relative to the boundary of the sector angle subtended by an element within sector region sector angle generalised strain components radius of sector region effective stress friction factor mean forging pressure initial yield stress of the workpiece material effective strain Current cross-sectional area of workpiecc Cross-sectional area of die cavity 1.
INTRODUCTION
THE PROBLEMS a s s o c i a t e d w i t h t h e e v a l u a t i o n o f t h e f o r c e s r e q u i r e d t o a c h i e v e m a x i m u m die fill-out during closed-die cold forging operations have been examined by a number
*Department of Mechanical and Manufacturing Engineering, University of Dublin, Trinity College, Republic of Ireland 385
386
J . M . MONAGHANand M. O'REILLY
of investigators, such as, Kudo [1], Thomsen, Yang and Kobayashi [2] and Bocharov, Kobayashi and Thomsen [3]. Each of these investigators showed that die fill-out is a function of several variables, i.e. material properties, workpiece and die geometry, workpiece aspect ratio (height to diameter ratio, H/D) and lubrication conditions. Because of the interaction of these variables exact mathematical solutions to these problems are not available and use has been made of empirical and numerical techniques to achieve workable solutions. Some of the proposed solutions are based on empirical rules derived from established practice and experience, for example the investigations of Altan [4], Chang and Choi [5] while others are based on observed deformation patterns during forging such as those prepared by Sajar and Juneja [6], Onga and Kondo [7] and Nediani and Dean [8]. For the case of closed die forging of cylindrical workpieces within hexagonal and square dies an upper bound solution has recently been proposed by Monaghan and Torrance [9] which provided good agreement between theoretical and experimental results. The result achieved with this solution indicated that it could be used with some confidence to determine the forging pressure ratio at various stages during the deformation of cylindrical workpieces within hexagonal and square dies. In this paper the solution proposed in reference [9] is used in conjunction with a series of forging tests to establish the influence of workpiece aspects ratio and friction state on the forging pressure ratio at a number of forging loads. In addition the influence of specimen height and friction on die fill-out is examined. The movement of the workpiece relative to the punch and die during deformation produces strainhardening of varying intensity over the contact surfaces of the workpiece. This effect is examined with the aid of a series of microhardness measurements made over the surfaces of the deformed workpieces. 2.
VELOCITY FIELD AND DEFORMATION ZONES
The pattern of metal flow occurring in both the hexagonal and square dies was ascertained by reference to the distortion of a rectangular grid scribed on the top face of a series of originally cylindrical billets. For both the hexagon and square die two cylinders, each having a grid marked on its top face, were compressed within each die. The resulting distorted grid patterns are shown in Fig. 1. It can be seen from Fig. ! that the general pattern of deformation is similar for both the hexagon and square. Based on this evidence, the analysis which follows concentrates on the velocity pattern obtained for the hexagon. However, it will be shown that the resulting expression can be extended very simply to cover the case of the square or indeed any polygonal shape. It can be seen from Fig. 1 that the deformation zone can be considered to be composed of two distinct regions, one region is triangular whilst the other is shaped as a sector of a circle. The triangle occupies an area bounded by AB the flattened side of the originally cylindrical billet in contact with the die wall, and the centre of the billet at 0. The second region consists of the sector of a circle OBC. The line OB being a line of velocity discontinuity. For the hexagon the entire billet will consist of twelve triangles such as OAB and twelve sectors OBC. In the case of the square there will be a total of eight triangles and eight sectors. Further details of the two deformation regions used in the analysis are shown in Fig. 2. 3.
ANALYSIS OF DEFORMATION ZONES
3.1. Upper bound solution The upper bound formulation originally proposed by Prager and Hodge [10] and extended by Drucker [11] can be expressed as
E=2k f (k,j.e,i) dv+ '
T,av,ds- f T,.V,ds ~
"t
(1)
Factors Influencing Fill-Out of a Closed Die
A
387
BC'
(a)
A
B
C' C
FI¢~. 1. Deformed grid patterns used to determine velocity fiekts for (a) hexagon and (b) square.
where /~ represents the total rate of energy dissipation for the workpiece. The first term of equation (1) represents the rate of energy dissipation due to plastic deformation. This term is used to evaluate E~ and E,, the rates of energy dissipation within the triangular and sector region, due to plastic deformation. Fig. 1. The second term of equation (1) represents the rate of energy dissipation due to friction on the workpiece tool interfaces and energy dissipated on the surfaces of velocity discontinuity separating the triangular and sector regions. The rate of energy dissipation due to friction over the triangular and sector regions on the top and bottom surfaces of the workpieces are designated as /~FT and EFS respectively. Similarly the energy dissipated due to friction on the sides of the specimen
388
J.M. MONAGEIANand M. O'R~n,Lv W
i
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a:
0 B
C
!0r
V
I- ~/(ii.dUi) ~/'1 IIu~,-~u~
FJ~;. 2. Triangle and sector deforming regions for the hexagonal square shaped forgings.
in contact with the die walls is designated as EFR. This is due to the resultant effect of the horizontal and vertical velocity of the workpiece relative to the die walls. Lines shown as OB in Fig. 2 are lines of velocity discontinuity due to the difference in radial velocity components within the triangular and sector regions. The rate of energy dissipation over these surfaces is given by E v , . 3.2.
Total energy dissipation due to forging
The total energy dissipation for the deforming specimen is given by the summation of the energy dissipated due to internal deformation, internal velocity discontinuities and friction. =
Er
+
E,s
+
Ev,
+
~TFr +
E~:s" +
L'FR,
(2)
The total rate of energy dissipation E given by equation (2) must also be equal to the rate at which energy is delivered by the punch to the deforming billet .'. E must also = /5 × area × velocity of punch = P.A.U.
(3)
Where A is the contact area between the punch and specimen at a given stage of compression, U is the punch velocity, and /~ is the mean forging pressure.
Factors Influencing Fill-Out of a Closed Die
389
Substitution of the relevant terms into equation (2) and simplification of the resulting expression gives f i = 1 / ~ 2 [ 1 5 ( sin20 ) 6" area(cos20[ " \ 2~ + cos20 + 1.5 [(sin20) 2 + 122t2]~ + + [(3sin20) + I
(4R,sin20.m/t)] +
[Rm
] 3rosin20 i.cos0" (sin20 + 2"y) + 2R -
(4)
(t 2 + 4R2tan20)~H ... for the HEXAGON. J)
E
1
6" -- area cos20 \ 2~ + cos20 + [(sin20) 2 + 12~/2]~ +
(8m Rsin20]
+(2sin20) + \ + -msin20 R -.[t2
3t
( 2Rm ].
/ + \3tcos0/
(sin20 + 2",/) +
(5)
+4R2tan20] ~1/ ...fortheSQUARE.
While the above expressions may appear unweildy they do not require the use of any numerical techniques for their solution. Consequently they are very suitable for use on a programmable calculator or small desk top computer. Furthermore it can be seen that the value of P/6. or/~/2k at a given stage of compression can be obtained by substitution of the current values of 0, -/, t and "area" along with an appropriate value for the friction factor, m into the relevant equation. The derivation of the above equations is described in detail in ref. [9]. 4. EXPERIMENTAL PROCEDURE
4.1. Workpiece materials Two materials were used in the experimental forging tests. A high conductivity copper (BS.2874.C101.1974) and a 1.0% nickel chrome 0,4% carbon alloy heading steel produced by SPS Technologies for the manufacture of socket head cap screws. This material is similar in both composition and properties to AISI 8740 alloy steel. In each case the material was supplied as round drawn rod and was used in the Asreceived conditions. In the case of the copper two varieties of the material were used, one moderately workhardened having an initial compressive yield stress of approximately 310.0 N/mm 2 and a second variety more severely workhardened having an initial compressive yield stress of approximately 430 N/mm 2. The heading steel was supplied as spheroidised annealed slightly cold drawn rod coated with lime stearate, The initial yield stress of this material was found to be approximately 600.0 N/ram 2. The dimensions of the punch and die units used for the forging tests are shown in Fig. 3. In the case of the hexagonal forgings the initial workpiece shape was cylindrical, and cylinders 13.5 mm diameter and machined to a series of heights ranging from 2.5 mm to 13.5 mm were produced from each material. For the square forgings the initial workpiece diameter was 13.0 mm and the cylinder heights ranged from 2.7 mm to 13.00 mm.
4.2. Stress-strain curve To determine the stress/strain characteristics of each material a compression test was performed on small cylinders of the materials using the method of Cook and Larke [12]. The stress/strain relationship obtained from the stress-strain curves of each material was found to be represented closely by the following expression 6- = ~o + 135(#) ... for the copper 6" = ~{~ + 919.92(~) ... for the heading steel
(6)
391)
J . M . MONAGtlAN and M. O'REILLY
SO.A/F 3ram
I ~HEX A/F ~ 13.86mm
Fic;. 3. Details of the punch and dic units used to produce the hexagonal and square components.
where (e;) represents the strain within the plastic range, 6", represents the yield stress at the strain (e~), 135.0 and 919.92 represent the slopes of the stress-strain curves of the copper and heading steel respectively within the plastic range. ~ro represents the initial yield strength of the material. The main strain component sustained by the workpieces during deformation was due to the change in height resulting from the downward movement of the punch. The radial strain component in a direction from the workpiece centre, o, towards the die corner, c, Fig. 2, was considerably less than the height strain, particularly in the case of the hexagonal forgings. Consequently, the effective strain ~ was taken to be equal to the compressive height strain of the deformed workpiece. d = ln(t,/t).
(7)
The value of the effective strain at any given forging load, equation (7), was used in conjunction with equation (6) to establish a value for the effective stress 6" at that particular forging load. 4.3.
Lubrication conditions
The forging tests were performed under two lubrication states. To simulate low friction conditions the surfaces of the workpieces and the walls of the die cavities, were sprayed with molybdenum disulfide prior to each test. To investigate the influence of high friction conditions, a second series of tests were performed on workpieces which were initially degreased in alcohol and then further cleaned in an ultrasonic bath containing toluene for a period of ten minutes. Prior to each test on the unlubricated workpieces the die cavity was washed with alcohol. 4.4.
Forging tests
The tooling shown in Fig. 3 was fitted to a die set and the whole assembly was then attached to an Avery Denison T42/C universal testing press. All of the tests were performed at room temperature. To examine the extent of die fill-out with increased forging load under lubricated and non-lubricated conditions the following tests were performed. Cylinders of one height, 13.5 mm in the case of the hexagon and 13.00 mm for the square where each forged to a load within the load range outlined below. The results from these tests were compared with those given by the theoretical expression, equation (4) and (5), and the results are shown plotted in Fig. (4). In the case of the lubricated hexagon and square, the loads used ranged from 60 to 220 kN. In the case of the unlubricated specimens there was no definite contact between specimen and the wall of the either the hexagonal or square die until a load of
4(a)
IO-
I
15 O (deg)
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20
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25 30
4(b)
5
I
10
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5
H E X A G O N - DRY
/2"
d
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20
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15 e (deg)
25
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EXPERIMENTAL VALUES COPPER, O'y =310N/mm 2 D COPPER, cry =430N/mm 2 x STEEL. cry =600N/mm 2 o
,x/
/
m=0.5
/
THEORETICAL CURVES EQUATION (4) m =10 4
FIG. 4. Comparison between theoretical and experimental results for both hexagon and square when forging copper and heading steel.
I
10
I
5
(y
/l
/
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/
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e C O P P E R , ~y =43ON/rum 2 x STEEL, Cry =60ON/rum 2
HEXAGON - LUBRICATED
30
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STEEL , Cry =600N/mm 2
SOUARE - LUBRICATED
50
FIo. 4(c)
%
/.,
5
9
~,,,~ x
I
lo
o1° x,~ "x
l
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20
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30 8 (deg)
I
~0
EXPERIMENTAL VALUES o COPPER, cry =310N/ram 2 [] COPPER, Cry =430 N/mm 2 x STEEL, O'y =600N/ram 2
m:o.sI/I
THEORETICAL CURVES/I; EQUATION (5) m = l . 0 / / ~
SQUARE- DRY
50
FI(;. 4(d)
N :<
©
N
e~
> z
Z
©
z"
[.,-,
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Factors Influencing Fill-Out of a Closed Die
393
approximately 80 kN was applied. Consequently, for the unlubricated tests the loads used ranged from 80 to 220 kN. To establish the influence of height to diameter ratio on the forging pressure ratio, P/6, and die fill-out, under lubricated and non-lubricated conditions, sets of cylinders of various heights were each forged to loads of 100, 150 and 250 kN. The material used for this series of tests was the low yield strength copper.
4.5.
Measurement of dimensional changes
After each test the deformed workpiece was removed from the die and its dimensions were measured with the aid of a Vickers M17 industrial microscope. In particular, measurements were taken of the change in height, t, the length of the contact surface, AB, and the distance OC, Fig. 2. These measurements were then used to find values
HEXAGON
Experimental
o lubricated
Theoretical 9..
x lubricated []dry
dr
n~ ~ X ~ ~ _ _
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X
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to {mm) 4 SQUARE Experimental
o lubricated dry x lubricated o dry
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~ n
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x
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150kN
~ ~ ~ ~ ~o
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~n
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0
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to (ram) FIG. 5. Change in forging pressure ratio PIG with change in workpiece initial height, to for (a) the hexagon and (b) the square.
394
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MON,~,(;liAN and M. O'RE]LLV
for the angles 0 and y. Figure 2 and in turn the area of contact on the top and bottom of each workpiece at each forging load was established. The fill-out of the die at a given forging load can be expressed in a number of ways. When comparing the theoretical and experimental results Fig. 4, fill-out was expressed in terms of the angle 0 of the triangular deforming regions, Fig. 2. The value of 0 will vary from zero at the start of each test to a maximum value of 30 ° for the hexagon and 45 ° for the square if the workpiece should completely fill the die cavity. In the case of the tests performed to establish the relationship between the initial aspect ratio of the workpiece and the forging pressure ratio P/(r the die fill out can be more conveniently expressed as the ratio W/S (Fig. 8).
I
250kN
HEX SO.
"a ~
1
--!
,I
'-~-~
•
I I I I
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Hex o [] Sq x 150kN ..,,
HEX ,,~
100kN
HEX.
dry [ub. dry lub
SO
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SO
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1
2
3
4
5
6
s/t
F](;. 6. Influence of initial workpiece height, t,,, and dic geometr,v on forging pressure ratio /:'/&.
I I
250kN
i~--~#
HEX
~
-8
.8
I I
He× ~ dry o lub.
I
Sq
I
Ib
,& 3
I
150kN
HEX
[] x
dry lub.
SQ
/
I "6.,.
100kN
i:~m----A
HEX.
®
6
SO
..
I I I
I
i
I
l
1
2
3 s/b~
4
5
FIG. 7. Influence of the deformed workpiece height, t, and the die geometry on the forging pressure ratio,
P/c~.
Factors Influencing Fill-Out of a Closed Die
395 X
0.g
0.9 .,,~o.>~
250 k N $
~a
o . . ~ . ~ ~~
0.~
0.8
/ °~o..... o
150kN
SQUARE 0.7
0.7
/ ~/
S
-I 0-6
0.6
HEXAGON
a/'a',,~a°~ 0-5
~ # ~ _ ~ . ~ . . . , . 100kN .... ~ ~ ..~...---_
100 kN 0.5
/
[] x
a dry o 0d,
I 5
0
I 10
lub. 0.z, 15
to (rnm)
I 5
I 10
dry lub
15
to (mm}
FIG. 8. Influence of the initial workpiece height t,,, on die fill-out, W / S , at various forging loads, for (a) the hexagon, and (b) the square.
4.6.
Hardness tests
Microhardness tests were performed on the surfaces of the deformed copper workpieces using a Shimadzu Microhardness tester. The microhardness tester was fitted with a Vickers diamond pyramid and hardness numbers were obtained from the expression MHV -
1854.P de
(8)
where P is the applied load on the indenter (500 g) and d is the mean length of the diagonals of the indentation. It has been shown [13] that hardness can be related to yield stress through the semiempirical expression Hardness H = C Y where H is the hardness number, C is a constant and Y is the approximate yield stress of the material. Earlier tests performed by the authors on torsion test pieces of the commercially pure copper established the relationship between hardness and yield stress as
= 2.96 x microhardness number (N/mm2).
(9)
This relationship was used to express the variation in hardness over the deformed surfaces of the copper workpieces in terms of surface yield stress (Figs. 9 and 10). 5.
RESULTS AND DISCUSSION
5.1. Variation in die fill-out with forging load The theoretical curves for P/6 against die fill-out, expressed as a change in 0 for various m values, are shown in Fig. 4 for the hexagon and the square. It can be seen
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420
380}.-
~
340F
..~._.,j.~,~"
~ 380a~-----¢--.-~.____~
= 340 ~-°".~
i
o/
,
I
\~3
380, ~Nfi ~ 340 z i /~1 300 ~' ° ' - - ' ~ e~' i'
KeY o 100 kN x 150kN o 250kN
F[o. 9. Stress distribution resulting from microhardness tests on the surface of the hexagonal component.
38o~
3 8 o ~ ~
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V
/" , ~ "
0
/
/f
~-J
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=b ~"°Y A
~A
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-~
~ ~mi "~'_ ~L_ 1 I 1 ~ I
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IL , W
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,
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o 100kN x 150kN m 250kN
Fi(L 10. Stress distribution resulting from microhardness tests on the surface of the square component.
Factors Influencing Fill-Out of a Closed Die
397
from Fig. 4 that the theoretical curves compare very favourably with the experimental values over most of the forging range. The experimental results obtained from tests performed on workpieces having different values of initial yield stress ¢ro, are shown. In each case the experimental results and the theoretical predictions are in good agreement. At any given forging load, and hence forging pressure P, the value of the flow stress 6" will depend on both the value of the initial yield stress ¢ro and the strain experienced by the workpiece. Consequently values for the forging pressure ratio/5/6" for the high yield strength workpieces will tend to be lower than those obtained with specimens machined from the lower yield strength material. The results do show that because the solutions proposed in equations (4) and (5) are based only on geometrical changes and friction conditions, the initial yield strength of the workpiece material does not significantly influence the theoretical solution. Consequently curves based on equation (4) and (5) can be used to obtain an estimate of forging pressure ratio irrespective of the initial yield stress of the workpiece material.
5.2.
Influence on workpiece height on forging pressure ratio (15/6.)
The experimental and theoretical values for/5/6" at the three test loads are shown in Fig. 5 for workpieces of various initial heights. The experimental results indicate that for the tests described here workpiece height and friction conditions had only marginal influence on/5/6r at any given forging load. The theoretical analysis based on equations (14) and (5) shows that the largest elements of/~ are contributed by terms associated with internal deformation, rather than the friction terms containing, (t). Typicall internal deformation accounts for more than 80% of the calculated energy dissipated (see Tables 1 and 2), These results would suggest that for the geometry and dimensions used for the workpieces of these tests the specimen height only influences frictional energy and as this accounts for a small proportion of the total energy dissipated it has little influence on the forging process. Further evidence to support this suggestion can be seen by reference to Fig. 5 where it is shown that there is little difference between the results obtained using lubricated and non-lubricated workpieces. This may also be explained by the fact that for both lubricated and non-lubricated workpieces the die fill-out is large, even at the lower forging loads. Reference to Fig. 4 indicates that at high die fill-out friction conditions play a small part in determining the forging pressure ratio. The theoretical values for/5/6, predicted by equations (4) and (5) are also shown in Fig. 5. It can be seen that the proposed upper bound expression gives results which increase progressively as the workpiece initial height t, decreases. This is due to the presence of t in the denominator of the friction terms of equations (4) and (5). It can be seen from Fig. 5 that if the initial height of the workpiece, to, is less than approximately 5-6 mm the resulting values of the compressed height, t, have an increasingly significant influence on the values of/5/6, calculated from equations (4) and (5).
5.3.
Influence of workpiece and die geometry on 15/6"
The influence of die dimensions and workpiece height on the mean forging pressure ratio is shown in Fig. 6 for a series of forging loads. The expression s/to represents the ratio of the length of the side wall of the die to the initial height of the specimen. For a given die, S, will be a constant. In the case of the experiments discussed here, S -8 mm for the hexagonal die and 13.1 mm for the square die. The ratio S/to can be considered as an aspect ratio for the undeformed workpiece. It can be seen from Fig. 6 that the data for the hexagonal and square workpieces produce two distinct curves. In the case of the square the tallest workpiece was 13.0 mm, hence S/to was always greater than 1.0. With hexagonal workpieces of similar heights, S/to values less than 1.0 were possible. Figure 6 shows that for the hexagonal workpieces, at any of the forging loads, a minimum value for the forging pressure ratio is obtained at S/to approximately equal to 1.0. For all other values of S/to the magnitude of P/6. is greater than this minimum. In the case of the square workpiece the minimum value of/5/6, is again obtained at S/to equal to 1.0 and for higher S/tn ratios, i.e. with shorter workpieces, there is a linear increase in the value of P/gr at each load.
398
J . M . MONAGHAN and M. O'REILLY
In Fig. 7 the experimental values of i/6" are also shown plotted against the ratio S/t where (t) is the compressed or finished height of the deformed workpiece at a given forging load. The curves shown in Fig. 7 are similar to those of Fig. 6. However, due to the effect of the compression of the workpiece the S/t ratio of each deformed component will be greater than its initial Sit. value. The difference between S/t and S/to being greatest with the shortest workpieces. It can be seen from Fig. 7 that in the case of the hexagonal components the minimum value of {'/6" occurs at an Sit ratio of between 1.0-1.35. These results are in close agreement with the design codes set down in BS3692:1967 and 1SO/DR947, a supplement to ISO/R272, for the dimensions of hexagonal nuts and bolts. The hexagonal and square forging produced during the experiments described here have dimensions corresponding approximately to those of the head of an MS-M10 bolt. The BS and ISO standards for this size of hexagon component recommend an Sit value of approximately 1.311. It can be seen, therefore, that values of Sit. in the region of 1.(I result in S/t values which not only comply with the various standards but also require the minimum forging pressure for their production. Figures 6 and 7 also show that for any given forging load, and S/t~, or Sit ratio, the value of P/6. for the square is always less than that of the hexagon. This result would appear to be related to the nature of the velocity fields arising during forming of the hexagon and square. In the case of the hexagon there is a total of twelve surfaces of internal velocity discontinuity such as OB, Fig. 2, compared with eight such surfaces for the square. Consequently, the forging of a square component from an initially cylindrical workpiece requires less internal shearing. Therefore, it would be expected that the values of ]'/6" in the case of square components would be lower than those of hexagonal components having similar Sit w~lues. These points are further emphasised by reference to Tables 1 and 2 which show the contribution of the internal energy and friction terms of equations (4) and (5) to the final value of the mean forging pressure ratio P/(T. The results shown in Fig. 6 and in Tables 1 and 2, further confirm that lubrication conditions do not appear to have a significant influence on the values of P/6". They further reinforce the suggestion that the nature of the material flow is of greater significance than lubrication condition in determining the magnitude of the forging pressure required for closed die cold forging.
5.4. Influence of workpiece height to on die fill-out As the initially cylindrical workpieces deform to fill the die cavity contact is first made with the side walls of the die. The ratio of the length of the side of the deformed workpiece in contact with the die wall W, to the length of the die wall, S, can be used as a measure of die fill-out. The results presented in Figs 8(a) and 8(b) show the change in fill-out, expressed as W/S, with change in initial workpiece height, t,~. Both of these figures indicate that the values of W/S when plotted against initial specimen height, to, produce curves having two distinct regions. In the case of the hexagon, W/S increase as t. increases and reaches a maximum for values of to between 5.5-8 mm. With workpieces having initial heights greater than 8 mm the values for W/S tend to decrease. Therefore in the case of the hexagonal die maximum values for W/S at any given forging load are achieved when t. is approximately equal to the length of the side wall of the die, i.e. at S/t, approximately equal to 1.0. This was shown earlier to correspond to the geometry of a hexagonal forging requiring the minimum value for P/6.. The results for the square workpieces are shown in Fig. 8(b). The trends in this case are similar to those of the hexagon with a maximum value of fill-out, characterised by W/S, being achieved for workpieces with initial heights between 5.5 and 7.5 mm. It can be seen from Tables 1 and 2 that for those values of t~j at which W/S is a maximum the proportion of the supplied energy utilised to perform internal deformation is also a maximum. It can also be seen from the tables that the value of the mean forging pressure ratio P/6. is a minimum when W/S is a maximum. Again, these results
Factors Influencing Fill-Out of a Closed Die
399
TABLE 1. EXPERIMENTALAND THEORETICALRESULTSOF DIMENSIONALCHANGESAND ENERGYDISSIPATIONFORTHE HEXAGONALWORKPIECES
S/t,~
Height
W/S
R~
0
Ed
Er
P/~r (theor)
['/6 (expt)
13.511 10.50 7.75 6.51t 5.50 3.75
0.5926 0.7619 1.0323 1.2308 1.4545 2.1333
0.7100 0.7313 0.7350 0.7413 0.7475 0.7100
Friction factor m = 0.3 I).9814 0 . 3 8 5 4 2.8144 0.9838 0.3958 2.9715 0.9841 0.3976 3.0017 0.9848 11.4007 3 . 0 5 3 8 0.9854 0.41/37 3 . 1 0 8 2 0.9814 0.3854 2.8144
0.2980 0.3014 0.3188 0.3468 0.3790 11.4592
3.1124 3.2729 3.3205 3.4006 3.4872 3.2736
2.7178 2.7130 2.7305 2.7043 2.7122 2.731/0
13.50 10.51/ 7.75 6.511 5.50 3.75
0.5926 0.7619 1.0323 1.2308 1.4545 2.1333
0.7313 0.7038 0.6975 0.7225 0.68511 0.67511
Friction factor m = 0.5 0.9838 0.3958 2.9715 11.9807 0 . 3 8 2 4 2.7722 0.9800 0.3793 2.7316 0.9828 0.3915 2.904l 1/.9786 0 . 3 7 3 1 2.6551 11.9774 0 . 3 6 8 1 2.5978
11.5129 0.4830 11.5050 0.5610 11.5724 11.7198
3.4844 3.2552 3.2367 3.4651 3.2275 3.3176
2.7261 2.7255 2.7319 2.7178 2.7523 2.7627
Load = 150 kN, initial yield stress = 310 N/mm.
TABLE 2. EXPERIMENTAL AND THEORETICAL RESULTS OF DIMENSIONAL CHANGES AND ENERGY DISSIPATION FOR THE SQUARE WORKP1ECES
S/t,
Height
W/S
R~
0
Ed
El
P/e (theor)
P/# (expt)
13.00 10.50 8.25 5.25 3.75
1.0154 1.2571 1.6000 2.5143 3.5200
I).6485 0.6712 0.6864 11.6917 0.6591
Friction factor rn = 0.3 0.93411 0 . 5 7 8 8 2.1112 0.9399 0.5947 2.2148 0.9437 0.6051 2.2925 0.9450 0.6087 2.3215 0.9368 0.5862 2.1577
0.3449 0.3680 0.4065 (I.5182 0.6178
2.4561 2.5827 2.6989 2.8397 2.7756
2.6706 2.6801 2.6723 2.6682 2.6876
13.00 10.50 8.25 5.25 3.75
1.0154 1.2571 1.6000 2.5143 3.5200
0.6432 0.6523 0.6818 0.6742 0.6652
Friction factor m 0.9325 11.5750 0.9350 0.5815 0.9426 0.6020 0.9407 0.5968 0 . 9 3 8 3 0.59115
0.5691 11.5927 0.6757 0.8364 1.0336
2.6581 2.7202 /2.9440 3.0661 3.2193
2.7048 2.6982 2.6608 2.6830 2.6927
=
0.5 2.0890 2.1275 2.2683 2.2297 2.1857
Load = 15(I kN, initial yield stress = 310 N/ram. i
co n fi rm that i n t e r n a l d e f o r m a t i o n r a t h e r t h a n friction has the g r e a t e s t influence on die fill-out. In o t h e r w o r d s m a x i m u m die fill-out is a c h i e v e d w h e n the w o r k p i e c e g e o m e t r y is such that the s u p p l i e d e n e r g y is m o s t efficiently used in g e n e r a t i n g m a x i m u m e n e r g y dissipation within th e d e f o r m i n g r e g i o n s an d al o n g lines of v e l o c i t y d i s c o n t i n u i t y .
5.5.
Surface yield stress values based on microhardness tests
A s the p u n c h d e s c e n d s into the die the d e f o r m i n g m e t a l m o v e s r e l a t i v e to the die walls an d the face of the p u n c h . This relative m o v e m e n t is a f u n c t i o n o f distance m e a s u r e d f r o m the w o r k p i e c e c e n t r e at 0, b e i n g z e r o at t h e c e n t r e an d m a x i m u m at the e x t r e m i t i e s o f the w o r k p i e c e t o p surface. T h e effect o f this r e l a t i v e m o v e m e n t b e t w e e n the w o r k p i e c e and the punch/die is to bring about a strain h a r d e n i n g of the surface layers of the m a t e r i a l which varies with distance m e a s u r e d f r o m t h e c e n t r e of the w o r k p i e c e . T h e p r e s e n c e of d i f f e r e n t i a l s t r a i n h a r d e n i n g o v e r t h e c o n t a c t surfaces o f cold f o r g e d c o m p o n e n t s can influence d i m e n s i o n a l accuracy an d i n t e r n a l stress d i s t r i b u t i o n d u e to the c o m b i n e d effects of elastic r e c o v e r y and r e s i d u a l stresses w h e n t h e c o m p o n e n t is r e m o v e d f r o m t h e die. T h e results f r o m a series of m i c r o h a r d n e s s tests p e r f o r m e d o n n o n - l u b r i c a t e d s q u a r e and h e x a g o n a l f o r g e d c o m p o n e n t s are sh o w n in Figs 9 and 10. T h e m i c r o h a r d n e s s n u m b e r s w e r e c o n v e r t e d into v a l u e s of surface yield stress using e q u a t i o n (9).
400
J . M . MONAGHANand M. O'REILLY
Top surface OAC. It can be seen in both Figs 9 and 10 that there is a gradual increase in the magnitude of the surface yield stress from the centre of the workpiece at O to the extremities at A and C. At the high levels of die fill-out achieved in the tests, there was a tendency to produce a small "flash" of metal as a result of backward extrusion through the clearance between the punch and die. The formation of this "flash" at the side walls caused additional strainhardening at this location and evidence of this is seen by reference to the high levels of stress found along a line AC parallel to the die wall. Side surface WXYZ. The stress distribution on the side surface of the components is shown for the region WXYZ. This distribution is produced by a combination of vertical displacement, due to the punch, and horizontal displacement, as metal flows towards the die corners. Along the vertical axis WX there is a gradual increase in stress magnitude from the top surface at W, to the mid-height of the workpiece at X. The distribution in a horizontal direction at the workpiece mid-height is shown as a variation along X-Y. It can be seen that for both the hexagon and square the largest stress values occur at points X and Y. The value at X is influenced by the barrelling of the side wall of the workpiece during the downward movement of the punch. The material at Y has been subjected to high relative movement between workpiece and die wall. The results show similar trends for both the hexagon and square. However the hexagon does show more variation in the stress values for changes in forging load compared with the results for the square, particularly on the top surface OAC. This effect is probably due to the influence of the velocity field of the hexagon and the greater number of lines of velocity discontinuity compared with the square. 6.
CONCLUSIONS
(i) It has been shown that the results predicted by the upper bound equations (4) and (5) are in good agreement with the experimental results and that the initial yield strength of the material is not a limiting factor in the use of these equations. (ii) The values for the forging pressure ratio P/6. predicted by equations (4) and (5) are influenced by the initial height of the workpiece. It was found that agreement between theoretical and experimental results improved as the initial workpiece height increased. Good agreement was obtained when the diameter to height ratio of the workpiece was initially greater than 2.0. (iii) The friction conditions appear to have little influence on the die fill-out at high forging loads. The fill-out is related to the amount of the available energy utilized in causing internal deformation within the workpiece. (iv) The aspect S/t at which /5/6" is a minimum corresponds closely to the values suggested in both BS and ISO standards for the finished dimensions of a hexagonal headed M8-M10 bolt. (v) Fill-out characterised by W/S is a function of the initial workpiece height to. It was shown that for any given forging load the maximum fill-out was achieved in the workpiece utilizing the maximum proportion of the energy available to produce internal deformation. For all other workpiece heights this amount of energy was lower. (vi) Microhardness test showed considerable variation in the surface stress distribution. This is due to the effects of deformation and relative movement between the workpiece and the punch/die. Such stress distribution on cold forged components may give rise to loss of dimentional accuracy and localized distortion due to the effects of residual stresses on the surface of the formed part. Acknowledgements--The authors wish to express their thanks to the technical staff of the Department of Mechanical and Manufacturing Engineering of TCD for assistance with the machining of the workpieces. The assistance of Mr. Alan Reid, Senior Experimental Officer, in the preparation of the drawings is acknowledged.
Factors Influencing Fill-Out of a Closed Die
4(11
REFERENCES [1] H. KUDO, Int. J. Mech. Sci. 1, 229 (1960). [2] E. G. TnOMSEN, C. T. YAi~ and S. KOBAYASm,Mechanics of Plastic Deformation in Metal Processing, Macmillan, New York (1965). [3] Y. Bocharov, S. Kobayashi and E. G. TnOMSEN, Trans. A S M E J. Engng. lnd, 84, 491 (1962). [4] T. AL~AN, Metallurgia Metal Forming 83, 83-88 (1972). [5] K. T. CHANG and I. J. Cnol, Ann. CIRP 20, 63 (1975). [6] R. SAJARand B. L. JUNEJA, Int. J. Mech. Tool Des. Res. 20, 68 (1980). [7] K. OnCA and K. KoNoo, J. SME 25, 1828 (1982). [8] G. NEDIANI and T. A. DEAN, Int. J. Mech. Sci. 25, 347 (1983). [9] J. M. MONAGUANand A. A. TORRANCE,Int. J. Mach. Tool Des. Res. 24, 225 (1984). [10] W. PRA~ER and P. G. HODGE, Theory of Perfectly Plastic Solids, Chapman and Hall, London (1951). [11] D. C. DRUCKER,Appl. Mech. Rev. 7, 421 (1954). [12] M. Cook and E. C. LARKE,J. Inst. Metal. 71, 371 (1946). [13] D. TABOR, The Hardness of Metal, Oxford University Press, New York (1951).
{)020-7375/86; $3.(104.1111 Pergamon Journals [ J d
FACTORS INFLUENCING FILL-OUT OF A CLOSED DIE DURING COLD FORGING J. M . MONAGHAN* a n d M . O'REILLY*
(Received 13 March 1985; in final fi)rm 16 Janua O, 1986)
Abstract--Closed die cold forging is an important industrial metal ff)rming process used extensively in the manufacture of headed fasteners. In this paper an upper bound solution is presented based on observed velocity fields resulting from the deformation of initially cylindrical workpieces within hexagonal and square dies. The influence of workpiece aspect ratio, forging loads and friction conditions on the fill-out of the hexagonal and square dies is examined. It is shown that at high die fill-out, friction conditions and workpiece aspect ratio have little influence on the forging pressure ratio. The surface stress state, produced by relative movement between workpiece and punch/die, is examined with the aid of microhardness measurements.
NOMENCLATURE
E.,: k T
I?~vl Sv S
r, U U, U, U: U, U, W R Y r lql t
0
-y q, d~ e(i
L m ITo
Rf
total rate of internal energy dissipation rate of internal energy dissipation due to internal deformation. rate of internal energy dissipation due to interracial friction yield stress in shear interfacial shear shear stress magnitude of velocity discontinuity surface over which velocity discontinuity occurs within the deforming zone length of the side wall of the die component of stress vector prescribed on surface S, within the deformation zone punch velocity exit velocity from triangular deforming region velocity of flow of material entering the section region vertical velocity component velocity of material within sector radical velocity component within sector length of flat portion of the workpiece in contact with the die wall half the "'across flats" distance of the hexagon or square die distance of a material element within the triangular region when measured for the centre of the workpiece radius of a material element within sector measured from workpiece centre undeformed height of workpiece deformed height of workpiece angle of triangle region at workpieces centre angle of sector region at workpiece centre position of element within sector relative to the boundary of the sector angle subtended by an element within sector region sector angle generalised strain components radius of sector region effective stress friction factor mean forging pressure initial yield stress of the workpiece material effective strain Current cross-sectional area of workpiecc Cross-sectional area of die cavity 1.
INTRODUCTION
THE PROBLEMS a s s o c i a t e d w i t h t h e e v a l u a t i o n o f t h e f o r c e s r e q u i r e d t o a c h i e v e m a x i m u m die fill-out during closed-die cold forging operations have been examined by a number
*Department of Mechanical and Manufacturing Engineering, University of Dublin, Trinity College, Republic of Ireland 385
386
J . M . MONAGHANand M. O'REILLY
of investigators, such as, Kudo [1], Thomsen, Yang and Kobayashi [2] and Bocharov, Kobayashi and Thomsen [3]. Each of these investigators showed that die fill-out is a function of several variables, i.e. material properties, workpiece and die geometry, workpiece aspect ratio (height to diameter ratio, H/D) and lubrication conditions. Because of the interaction of these variables exact mathematical solutions to these problems are not available and use has been made of empirical and numerical techniques to achieve workable solutions. Some of the proposed solutions are based on empirical rules derived from established practice and experience, for example the investigations of Altan [4], Chang and Choi [5] while others are based on observed deformation patterns during forging such as those prepared by Sajar and Juneja [6], Onga and Kondo [7] and Nediani and Dean [8]. For the case of closed die forging of cylindrical workpieces within hexagonal and square dies an upper bound solution has recently been proposed by Monaghan and Torrance [9] which provided good agreement between theoretical and experimental results. The result achieved with this solution indicated that it could be used with some confidence to determine the forging pressure ratio at various stages during the deformation of cylindrical workpieces within hexagonal and square dies. In this paper the solution proposed in reference [9] is used in conjunction with a series of forging tests to establish the influence of workpiece aspects ratio and friction state on the forging pressure ratio at a number of forging loads. In addition the influence of specimen height and friction on die fill-out is examined. The movement of the workpiece relative to the punch and die during deformation produces strainhardening of varying intensity over the contact surfaces of the workpiece. This effect is examined with the aid of a series of microhardness measurements made over the surfaces of the deformed workpieces. 2.
VELOCITY FIELD AND DEFORMATION ZONES
The pattern of metal flow occurring in both the hexagonal and square dies was ascertained by reference to the distortion of a rectangular grid scribed on the top face of a series of originally cylindrical billets. For both the hexagon and square die two cylinders, each having a grid marked on its top face, were compressed within each die. The resulting distorted grid patterns are shown in Fig. 1. It can be seen from Fig. ! that the general pattern of deformation is similar for both the hexagon and square. Based on this evidence, the analysis which follows concentrates on the velocity pattern obtained for the hexagon. However, it will be shown that the resulting expression can be extended very simply to cover the case of the square or indeed any polygonal shape. It can be seen from Fig. 1 that the deformation zone can be considered to be composed of two distinct regions, one region is triangular whilst the other is shaped as a sector of a circle. The triangle occupies an area bounded by AB the flattened side of the originally cylindrical billet in contact with the die wall, and the centre of the billet at 0. The second region consists of the sector of a circle OBC. The line OB being a line of velocity discontinuity. For the hexagon the entire billet will consist of twelve triangles such as OAB and twelve sectors OBC. In the case of the square there will be a total of eight triangles and eight sectors. Further details of the two deformation regions used in the analysis are shown in Fig. 2. 3.
ANALYSIS OF DEFORMATION ZONES
3.1. Upper bound solution The upper bound formulation originally proposed by Prager and Hodge [10] and extended by Drucker [11] can be expressed as
E=2k f (k,j.e,i) dv+ '
T,av,ds- f T,.V,ds ~
"t
(1)
Factors Influencing Fill-Out of a Closed Die
A
387
BC'
(a)
A
B
C' C
FI¢~. 1. Deformed grid patterns used to determine velocity fiekts for (a) hexagon and (b) square.
where /~ represents the total rate of energy dissipation for the workpiece. The first term of equation (1) represents the rate of energy dissipation due to plastic deformation. This term is used to evaluate E~ and E,, the rates of energy dissipation within the triangular and sector region, due to plastic deformation. Fig. 1. The second term of equation (1) represents the rate of energy dissipation due to friction on the workpiece tool interfaces and energy dissipated on the surfaces of velocity discontinuity separating the triangular and sector regions. The rate of energy dissipation due to friction over the triangular and sector regions on the top and bottom surfaces of the workpieces are designated as /~FT and EFS respectively. Similarly the energy dissipated due to friction on the sides of the specimen
388
J.M. MONAGEIANand M. O'R~n,Lv W
i
UJ
a:
0 B
C
!0r
V
I- ~/(ii.dUi) ~/'1 IIu~,-~u~
FJ~;. 2. Triangle and sector deforming regions for the hexagonal square shaped forgings.
in contact with the die walls is designated as EFR. This is due to the resultant effect of the horizontal and vertical velocity of the workpiece relative to the die walls. Lines shown as OB in Fig. 2 are lines of velocity discontinuity due to the difference in radial velocity components within the triangular and sector regions. The rate of energy dissipation over these surfaces is given by E v , . 3.2.
Total energy dissipation due to forging
The total energy dissipation for the deforming specimen is given by the summation of the energy dissipated due to internal deformation, internal velocity discontinuities and friction. =
Er
+
E,s
+
Ev,
+
~TFr +
E~:s" +
L'FR,
(2)
The total rate of energy dissipation E given by equation (2) must also be equal to the rate at which energy is delivered by the punch to the deforming billet .'. E must also = /5 × area × velocity of punch = P.A.U.
(3)
Where A is the contact area between the punch and specimen at a given stage of compression, U is the punch velocity, and /~ is the mean forging pressure.
Factors Influencing Fill-Out of a Closed Die
389
Substitution of the relevant terms into equation (2) and simplification of the resulting expression gives f i = 1 / ~ 2 [ 1 5 ( sin20 ) 6" area(cos20[ " \ 2~ + cos20 + 1.5 [(sin20) 2 + 122t2]~ + + [(3sin20) + I
(4R,sin20.m/t)] +
[Rm
] 3rosin20 i.cos0" (sin20 + 2"y) + 2R -
(4)
(t 2 + 4R2tan20)~H ... for the HEXAGON. J)
E
1
6" -- area cos20 \ 2~ + cos20 + [(sin20) 2 + 12~/2]~ +
(8m Rsin20]
+(2sin20) + \ + -msin20 R -.[t2
3t
( 2Rm ].
/ + \3tcos0/
(sin20 + 2",/) +
(5)
+4R2tan20] ~1/ ...fortheSQUARE.
While the above expressions may appear unweildy they do not require the use of any numerical techniques for their solution. Consequently they are very suitable for use on a programmable calculator or small desk top computer. Furthermore it can be seen that the value of P/6. or/~/2k at a given stage of compression can be obtained by substitution of the current values of 0, -/, t and "area" along with an appropriate value for the friction factor, m into the relevant equation. The derivation of the above equations is described in detail in ref. [9]. 4. EXPERIMENTAL PROCEDURE
4.1. Workpiece materials Two materials were used in the experimental forging tests. A high conductivity copper (BS.2874.C101.1974) and a 1.0% nickel chrome 0,4% carbon alloy heading steel produced by SPS Technologies for the manufacture of socket head cap screws. This material is similar in both composition and properties to AISI 8740 alloy steel. In each case the material was supplied as round drawn rod and was used in the Asreceived conditions. In the case of the copper two varieties of the material were used, one moderately workhardened having an initial compressive yield stress of approximately 310.0 N/mm 2 and a second variety more severely workhardened having an initial compressive yield stress of approximately 430 N/mm 2. The heading steel was supplied as spheroidised annealed slightly cold drawn rod coated with lime stearate, The initial yield stress of this material was found to be approximately 600.0 N/ram 2. The dimensions of the punch and die units used for the forging tests are shown in Fig. 3. In the case of the hexagonal forgings the initial workpiece shape was cylindrical, and cylinders 13.5 mm diameter and machined to a series of heights ranging from 2.5 mm to 13.5 mm were produced from each material. For the square forgings the initial workpiece diameter was 13.0 mm and the cylinder heights ranged from 2.7 mm to 13.00 mm.
4.2. Stress-strain curve To determine the stress/strain characteristics of each material a compression test was performed on small cylinders of the materials using the method of Cook and Larke [12]. The stress/strain relationship obtained from the stress-strain curves of each material was found to be represented closely by the following expression 6- = ~o + 135(#) ... for the copper 6" = ~{~ + 919.92(~) ... for the heading steel
(6)
391)
J . M . MONAGtlAN and M. O'REILLY
SO.A/F 3ram
I ~HEX A/F ~ 13.86mm
Fic;. 3. Details of the punch and dic units used to produce the hexagonal and square components.
where (e;) represents the strain within the plastic range, 6", represents the yield stress at the strain (e~), 135.0 and 919.92 represent the slopes of the stress-strain curves of the copper and heading steel respectively within the plastic range. ~ro represents the initial yield strength of the material. The main strain component sustained by the workpieces during deformation was due to the change in height resulting from the downward movement of the punch. The radial strain component in a direction from the workpiece centre, o, towards the die corner, c, Fig. 2, was considerably less than the height strain, particularly in the case of the hexagonal forgings. Consequently, the effective strain ~ was taken to be equal to the compressive height strain of the deformed workpiece. d = ln(t,/t).
(7)
The value of the effective strain at any given forging load, equation (7), was used in conjunction with equation (6) to establish a value for the effective stress 6" at that particular forging load. 4.3.
Lubrication conditions
The forging tests were performed under two lubrication states. To simulate low friction conditions the surfaces of the workpieces and the walls of the die cavities, were sprayed with molybdenum disulfide prior to each test. To investigate the influence of high friction conditions, a second series of tests were performed on workpieces which were initially degreased in alcohol and then further cleaned in an ultrasonic bath containing toluene for a period of ten minutes. Prior to each test on the unlubricated workpieces the die cavity was washed with alcohol. 4.4.
Forging tests
The tooling shown in Fig. 3 was fitted to a die set and the whole assembly was then attached to an Avery Denison T42/C universal testing press. All of the tests were performed at room temperature. To examine the extent of die fill-out with increased forging load under lubricated and non-lubricated conditions the following tests were performed. Cylinders of one height, 13.5 mm in the case of the hexagon and 13.00 mm for the square where each forged to a load within the load range outlined below. The results from these tests were compared with those given by the theoretical expression, equation (4) and (5), and the results are shown plotted in Fig. (4). In the case of the lubricated hexagon and square, the loads used ranged from 60 to 220 kN. In the case of the unlubricated specimens there was no definite contact between specimen and the wall of the either the hexagonal or square die until a load of
4(a)
IO-
I
15 O (deg)
I
20
I
25 30
4(b)
5
I
10
I
5
H E X A G O N - DRY
/2"
d
I
20
I
15 e (deg)
25
I
EXPERIMENTAL VALUES COPPER, O'y =310N/mm 2 D COPPER, cry =430N/mm 2 x STEEL. cry =600N/mm 2 o
,x/
/
m=0.5
/
THEORETICAL CURVES EQUATION (4) m =10 4
FIG. 4. Comparison between theoretical and experimental results for both hexagon and square when forging copper and heading steel.
I
10
I
5
(y
/l
/
J
/
/tJ
e C O P P E R , ~y =43ON/rum 2 x STEEL, Cry =60ON/rum 2
HEXAGON - LUBRICATED
30
e~
Z
©
o~
g
Ib
f~
,. 00
/4
5
9
I
10
I
20
x
,!It
J!, h
I
30 e (deg)
I
/-.0
STEEL , Cry =600N/mm 2
SOUARE - LUBRICATED
50
FIo. 4(c)
%
/.,
5
9
~,,,~ x
I
lo
o1° x,~ "x
l
I
20
I
30 8 (deg)
I
~0
EXPERIMENTAL VALUES o COPPER, cry =310N/ram 2 [] COPPER, Cry =430 N/mm 2 x STEEL, O'y =600N/ram 2
m:o.sI/I
THEORETICAL CURVES/I; EQUATION (5) m = l . 0 / / ~
SQUARE- DRY
50
FI(;. 4(d)
N :<
©
N
e~
> z
Z
©
z"
[.,-,
bJ
Factors Influencing Fill-Out of a Closed Die
393
approximately 80 kN was applied. Consequently, for the unlubricated tests the loads used ranged from 80 to 220 kN. To establish the influence of height to diameter ratio on the forging pressure ratio, P/6, and die fill-out, under lubricated and non-lubricated conditions, sets of cylinders of various heights were each forged to loads of 100, 150 and 250 kN. The material used for this series of tests was the low yield strength copper.
4.5.
Measurement of dimensional changes
After each test the deformed workpiece was removed from the die and its dimensions were measured with the aid of a Vickers M17 industrial microscope. In particular, measurements were taken of the change in height, t, the length of the contact surface, AB, and the distance OC, Fig. 2. These measurements were then used to find values
HEXAGON
Experimental
o lubricated
Theoretical 9..
x lubricated []dry
dr
n~ ~ X ~ ~ _ _
~'-×~
~
.~
~
150 k N
150kN []~
~Q-Ib
x ~....._ ~
lOOkN
~ ° ~--°~...o._
X
X
X
~
~
--D.
100kN
10
I
I
5
10
15
to {mm) 4 SQUARE Experimental
o lubricated dry x lubricated o dry
Theoretical
~ n
" ~ x ~
~o~
~
x
o
~
150kN
~ ~ ~ ~ ~o
100kN
~n
~x.~..~_
0
~
I
I
5
10
15
to (ram) FIG. 5. Change in forging pressure ratio PIG with change in workpiece initial height, to for (a) the hexagon and (b) the square.
394
J.M.
MON,~,(;liAN and M. O'RE]LLV
for the angles 0 and y. Figure 2 and in turn the area of contact on the top and bottom of each workpiece at each forging load was established. The fill-out of the die at a given forging load can be expressed in a number of ways. When comparing the theoretical and experimental results Fig. 4, fill-out was expressed in terms of the angle 0 of the triangular deforming regions, Fig. 2. The value of 0 will vary from zero at the start of each test to a maximum value of 30 ° for the hexagon and 45 ° for the square if the workpiece should completely fill the die cavity. In the case of the tests performed to establish the relationship between the initial aspect ratio of the workpiece and the forging pressure ratio P/(r the die fill out can be more conveniently expressed as the ratio W/S (Fig. 8).
I
250kN
HEX SO.
"a ~
1
--!
,I
'-~-~
•
I I I I
3
Hex o [] Sq x 150kN ..,,
HEX ,,~
100kN
HEX.
dry [ub. dry lub
SO
I I I I
SO
I
I
i
I
i
I
1
2
3
4
5
6
s/t
F](;. 6. Influence of initial workpiece height, t,,, and dic geometr,v on forging pressure ratio /:'/&.
I I
250kN
i~--~#
HEX
~
-8
.8
I I
He× ~ dry o lub.
I
Sq
I
Ib
,& 3
I
150kN
HEX
[] x
dry lub.
SQ
/
I "6.,.
100kN
i:~m----A
HEX.
®
6
SO
..
I I I
I
i
I
l
1
2
3 s/b~
4
5
FIG. 7. Influence of the deformed workpiece height, t, and the die geometry on the forging pressure ratio,
P/c~.
Factors Influencing Fill-Out of a Closed Die
395 X
0.g
0.9 .,,~o.>~
250 k N $
~a
o . . ~ . ~ ~~
0.~
0.8
/ °~o..... o
150kN
SQUARE 0.7
0.7
/ ~/
S
-I 0-6
0.6
HEXAGON
a/'a',,~a°~ 0-5
~ # ~ _ ~ . ~ . . . , . 100kN .... ~ ~ ..~...---_
100 kN 0.5
/
[] x
a dry o 0d,
I 5
0
I 10
lub. 0.z, 15
to (rnm)
I 5
I 10
dry lub
15
to (mm}
FIG. 8. Influence of the initial workpiece height t,,, on die fill-out, W / S , at various forging loads, for (a) the hexagon, and (b) the square.
4.6.
Hardness tests
Microhardness tests were performed on the surfaces of the deformed copper workpieces using a Shimadzu Microhardness tester. The microhardness tester was fitted with a Vickers diamond pyramid and hardness numbers were obtained from the expression MHV -
1854.P de
(8)
where P is the applied load on the indenter (500 g) and d is the mean length of the diagonals of the indentation. It has been shown [13] that hardness can be related to yield stress through the semiempirical expression Hardness H = C Y where H is the hardness number, C is a constant and Y is the approximate yield stress of the material. Earlier tests performed by the authors on torsion test pieces of the commercially pure copper established the relationship between hardness and yield stress as
= 2.96 x microhardness number (N/mm2).
(9)
This relationship was used to express the variation in hardness over the deformed surfaces of the copper workpieces in terms of surface yield stress (Figs. 9 and 10). 5.
RESULTS AND DISCUSSION
5.1. Variation in die fill-out with forging load The theoretical curves for P/6 against die fill-out, expressed as a change in 0 for various m values, are shown in Fig. 4 for the hexagon and the square. It can be seen
396
J.M. MONA(iHAN and M. O'REILL;' 420 /
420
380}.-
~
340F
..~._.,j.~,~"
~ 380a~-----¢--.-~.____~
= 340 ~-°".~
i
o/
,
I
\~3
380, ~Nfi ~ 340 z i /~1 300 ~' ° ' - - ' ~ e~' i'
KeY o 100 kN x 150kN o 250kN
F[o. 9. Stress distribution resulting from microhardness tests on the surface of the hexagonal component.
38o~
3 8 o ~ ~
I
~340t
V
/" , ~ "
0
/
/f
~-J
I
=b ~"°Y A
~A
C
380
-~
~ ~mi "~'_ ~L_ 1 I 1 ~ I
I
'~
\
34°I:.
~"-~'
300
IL , W
,
2// I ,
,
X
e~ 3 8 0 ,m,..
I
I
o'7
o 100kN x 150kN m 250kN
Fi(L 10. Stress distribution resulting from microhardness tests on the surface of the square component.
Factors Influencing Fill-Out of a Closed Die
397
from Fig. 4 that the theoretical curves compare very favourably with the experimental values over most of the forging range. The experimental results obtained from tests performed on workpieces having different values of initial yield stress ¢ro, are shown. In each case the experimental results and the theoretical predictions are in good agreement. At any given forging load, and hence forging pressure P, the value of the flow stress 6" will depend on both the value of the initial yield stress ¢ro and the strain experienced by the workpiece. Consequently values for the forging pressure ratio/5/6" for the high yield strength workpieces will tend to be lower than those obtained with specimens machined from the lower yield strength material. The results do show that because the solutions proposed in equations (4) and (5) are based only on geometrical changes and friction conditions, the initial yield strength of the workpiece material does not significantly influence the theoretical solution. Consequently curves based on equation (4) and (5) can be used to obtain an estimate of forging pressure ratio irrespective of the initial yield stress of the workpiece material.
5.2.
Influence on workpiece height on forging pressure ratio (15/6.)
The experimental and theoretical values for/5/6" at the three test loads are shown in Fig. 5 for workpieces of various initial heights. The experimental results indicate that for the tests described here workpiece height and friction conditions had only marginal influence on/5/6r at any given forging load. The theoretical analysis based on equations (14) and (5) shows that the largest elements of/~ are contributed by terms associated with internal deformation, rather than the friction terms containing, (t). Typicall internal deformation accounts for more than 80% of the calculated energy dissipated (see Tables 1 and 2), These results would suggest that for the geometry and dimensions used for the workpieces of these tests the specimen height only influences frictional energy and as this accounts for a small proportion of the total energy dissipated it has little influence on the forging process. Further evidence to support this suggestion can be seen by reference to Fig. 5 where it is shown that there is little difference between the results obtained using lubricated and non-lubricated workpieces. This may also be explained by the fact that for both lubricated and non-lubricated workpieces the die fill-out is large, even at the lower forging loads. Reference to Fig. 4 indicates that at high die fill-out friction conditions play a small part in determining the forging pressure ratio. The theoretical values for/5/6, predicted by equations (4) and (5) are also shown in Fig. 5. It can be seen that the proposed upper bound expression gives results which increase progressively as the workpiece initial height t, decreases. This is due to the presence of t in the denominator of the friction terms of equations (4) and (5). It can be seen from Fig. 5 that if the initial height of the workpiece, to, is less than approximately 5-6 mm the resulting values of the compressed height, t, have an increasingly significant influence on the values of/5/6, calculated from equations (4) and (5).
5.3.
Influence of workpiece and die geometry on 15/6"
The influence of die dimensions and workpiece height on the mean forging pressure ratio is shown in Fig. 6 for a series of forging loads. The expression s/to represents the ratio of the length of the side wall of the die to the initial height of the specimen. For a given die, S, will be a constant. In the case of the experiments discussed here, S -8 mm for the hexagonal die and 13.1 mm for the square die. The ratio S/to can be considered as an aspect ratio for the undeformed workpiece. It can be seen from Fig. 6 that the data for the hexagonal and square workpieces produce two distinct curves. In the case of the square the tallest workpiece was 13.0 mm, hence S/to was always greater than 1.0. With hexagonal workpieces of similar heights, S/to values less than 1.0 were possible. Figure 6 shows that for the hexagonal workpieces, at any of the forging loads, a minimum value for the forging pressure ratio is obtained at S/to approximately equal to 1.0. For all other values of S/to the magnitude of P/6. is greater than this minimum. In the case of the square workpiece the minimum value of/5/6, is again obtained at S/to equal to 1.0 and for higher S/tn ratios, i.e. with shorter workpieces, there is a linear increase in the value of P/gr at each load.
398
J . M . MONAGHAN and M. O'REILLY
In Fig. 7 the experimental values of i/6" are also shown plotted against the ratio S/t where (t) is the compressed or finished height of the deformed workpiece at a given forging load. The curves shown in Fig. 7 are similar to those of Fig. 6. However, due to the effect of the compression of the workpiece the S/t ratio of each deformed component will be greater than its initial Sit. value. The difference between S/t and S/to being greatest with the shortest workpieces. It can be seen from Fig. 7 that in the case of the hexagonal components the minimum value of {'/6" occurs at an Sit ratio of between 1.0-1.35. These results are in close agreement with the design codes set down in BS3692:1967 and 1SO/DR947, a supplement to ISO/R272, for the dimensions of hexagonal nuts and bolts. The hexagonal and square forging produced during the experiments described here have dimensions corresponding approximately to those of the head of an MS-M10 bolt. The BS and ISO standards for this size of hexagon component recommend an Sit value of approximately 1.311. It can be seen, therefore, that values of Sit. in the region of 1.(I result in S/t values which not only comply with the various standards but also require the minimum forging pressure for their production. Figures 6 and 7 also show that for any given forging load, and S/t~, or Sit ratio, the value of P/6. for the square is always less than that of the hexagon. This result would appear to be related to the nature of the velocity fields arising during forming of the hexagon and square. In the case of the hexagon there is a total of twelve surfaces of internal velocity discontinuity such as OB, Fig. 2, compared with eight such surfaces for the square. Consequently, the forging of a square component from an initially cylindrical workpiece requires less internal shearing. Therefore, it would be expected that the values of ]'/6" in the case of square components would be lower than those of hexagonal components having similar Sit w~lues. These points are further emphasised by reference to Tables 1 and 2 which show the contribution of the internal energy and friction terms of equations (4) and (5) to the final value of the mean forging pressure ratio P/(T. The results shown in Fig. 6 and in Tables 1 and 2, further confirm that lubrication conditions do not appear to have a significant influence on the values of P/6". They further reinforce the suggestion that the nature of the material flow is of greater significance than lubrication condition in determining the magnitude of the forging pressure required for closed die cold forging.
5.4. Influence of workpiece height to on die fill-out As the initially cylindrical workpieces deform to fill the die cavity contact is first made with the side walls of the die. The ratio of the length of the side of the deformed workpiece in contact with the die wall W, to the length of the die wall, S, can be used as a measure of die fill-out. The results presented in Figs 8(a) and 8(b) show the change in fill-out, expressed as W/S, with change in initial workpiece height, t,~. Both of these figures indicate that the values of W/S when plotted against initial specimen height, to, produce curves having two distinct regions. In the case of the hexagon, W/S increase as t. increases and reaches a maximum for values of to between 5.5-8 mm. With workpieces having initial heights greater than 8 mm the values for W/S tend to decrease. Therefore in the case of the hexagonal die maximum values for W/S at any given forging load are achieved when t. is approximately equal to the length of the side wall of the die, i.e. at S/t, approximately equal to 1.0. This was shown earlier to correspond to the geometry of a hexagonal forging requiring the minimum value for P/6.. The results for the square workpieces are shown in Fig. 8(b). The trends in this case are similar to those of the hexagon with a maximum value of fill-out, characterised by W/S, being achieved for workpieces with initial heights between 5.5 and 7.5 mm. It can be seen from Tables 1 and 2 that for those values of t~j at which W/S is a maximum the proportion of the supplied energy utilised to perform internal deformation is also a maximum. It can also be seen from the tables that the value of the mean forging pressure ratio P/6. is a minimum when W/S is a maximum. Again, these results
Factors Influencing Fill-Out of a Closed Die
399
TABLE 1. EXPERIMENTALAND THEORETICALRESULTSOF DIMENSIONALCHANGESAND ENERGYDISSIPATIONFORTHE HEXAGONALWORKPIECES
S/t,~
Height
W/S
R~
0
Ed
Er
P/~r (theor)
['/6 (expt)
13.511 10.50 7.75 6.51t 5.50 3.75
0.5926 0.7619 1.0323 1.2308 1.4545 2.1333
0.7100 0.7313 0.7350 0.7413 0.7475 0.7100
Friction factor m = 0.3 I).9814 0 . 3 8 5 4 2.8144 0.9838 0.3958 2.9715 0.9841 0.3976 3.0017 0.9848 11.4007 3 . 0 5 3 8 0.9854 0.41/37 3 . 1 0 8 2 0.9814 0.3854 2.8144
0.2980 0.3014 0.3188 0.3468 0.3790 11.4592
3.1124 3.2729 3.3205 3.4006 3.4872 3.2736
2.7178 2.7130 2.7305 2.7043 2.7122 2.731/0
13.50 10.51/ 7.75 6.511 5.50 3.75
0.5926 0.7619 1.0323 1.2308 1.4545 2.1333
0.7313 0.7038 0.6975 0.7225 0.68511 0.67511
Friction factor m = 0.5 0.9838 0.3958 2.9715 11.9807 0 . 3 8 2 4 2.7722 0.9800 0.3793 2.7316 0.9828 0.3915 2.904l 1/.9786 0 . 3 7 3 1 2.6551 11.9774 0 . 3 6 8 1 2.5978
11.5129 0.4830 11.5050 0.5610 11.5724 11.7198
3.4844 3.2552 3.2367 3.4651 3.2275 3.3176
2.7261 2.7255 2.7319 2.7178 2.7523 2.7627
Load = 150 kN, initial yield stress = 310 N/mm.
TABLE 2. EXPERIMENTAL AND THEORETICAL RESULTS OF DIMENSIONAL CHANGES AND ENERGY DISSIPATION FOR THE SQUARE WORKP1ECES
S/t,
Height
W/S
R~
0
Ed
El
P/e (theor)
P/# (expt)
13.00 10.50 8.25 5.25 3.75
1.0154 1.2571 1.6000 2.5143 3.5200
I).6485 0.6712 0.6864 11.6917 0.6591
Friction factor rn = 0.3 0.93411 0 . 5 7 8 8 2.1112 0.9399 0.5947 2.2148 0.9437 0.6051 2.2925 0.9450 0.6087 2.3215 0.9368 0.5862 2.1577
0.3449 0.3680 0.4065 (I.5182 0.6178
2.4561 2.5827 2.6989 2.8397 2.7756
2.6706 2.6801 2.6723 2.6682 2.6876
13.00 10.50 8.25 5.25 3.75
1.0154 1.2571 1.6000 2.5143 3.5200
0.6432 0.6523 0.6818 0.6742 0.6652
Friction factor m 0.9325 11.5750 0.9350 0.5815 0.9426 0.6020 0.9407 0.5968 0 . 9 3 8 3 0.59115
0.5691 11.5927 0.6757 0.8364 1.0336
2.6581 2.7202 /2.9440 3.0661 3.2193
2.7048 2.6982 2.6608 2.6830 2.6927
=
0.5 2.0890 2.1275 2.2683 2.2297 2.1857
Load = 15(I kN, initial yield stress = 310 N/ram. i
co n fi rm that i n t e r n a l d e f o r m a t i o n r a t h e r t h a n friction has the g r e a t e s t influence on die fill-out. In o t h e r w o r d s m a x i m u m die fill-out is a c h i e v e d w h e n the w o r k p i e c e g e o m e t r y is such that the s u p p l i e d e n e r g y is m o s t efficiently used in g e n e r a t i n g m a x i m u m e n e r g y dissipation within th e d e f o r m i n g r e g i o n s an d al o n g lines of v e l o c i t y d i s c o n t i n u i t y .
5.5.
Surface yield stress values based on microhardness tests
A s the p u n c h d e s c e n d s into the die the d e f o r m i n g m e t a l m o v e s r e l a t i v e to the die walls an d the face of the p u n c h . This relative m o v e m e n t is a f u n c t i o n o f distance m e a s u r e d f r o m the w o r k p i e c e c e n t r e at 0, b e i n g z e r o at t h e c e n t r e an d m a x i m u m at the e x t r e m i t i e s o f the w o r k p i e c e t o p surface. T h e effect o f this r e l a t i v e m o v e m e n t b e t w e e n the w o r k p i e c e and the punch/die is to bring about a strain h a r d e n i n g of the surface layers of the m a t e r i a l which varies with distance m e a s u r e d f r o m t h e c e n t r e of the w o r k p i e c e . T h e p r e s e n c e of d i f f e r e n t i a l s t r a i n h a r d e n i n g o v e r t h e c o n t a c t surfaces o f cold f o r g e d c o m p o n e n t s can influence d i m e n s i o n a l accuracy an d i n t e r n a l stress d i s t r i b u t i o n d u e to the c o m b i n e d effects of elastic r e c o v e r y and r e s i d u a l stresses w h e n t h e c o m p o n e n t is r e m o v e d f r o m t h e die. T h e results f r o m a series of m i c r o h a r d n e s s tests p e r f o r m e d o n n o n - l u b r i c a t e d s q u a r e and h e x a g o n a l f o r g e d c o m p o n e n t s are sh o w n in Figs 9 and 10. T h e m i c r o h a r d n e s s n u m b e r s w e r e c o n v e r t e d into v a l u e s of surface yield stress using e q u a t i o n (9).
400
J . M . MONAGHANand M. O'REILLY
Top surface OAC. It can be seen in both Figs 9 and 10 that there is a gradual increase in the magnitude of the surface yield stress from the centre of the workpiece at O to the extremities at A and C. At the high levels of die fill-out achieved in the tests, there was a tendency to produce a small "flash" of metal as a result of backward extrusion through the clearance between the punch and die. The formation of this "flash" at the side walls caused additional strainhardening at this location and evidence of this is seen by reference to the high levels of stress found along a line AC parallel to the die wall. Side surface WXYZ. The stress distribution on the side surface of the components is shown for the region WXYZ. This distribution is produced by a combination of vertical displacement, due to the punch, and horizontal displacement, as metal flows towards the die corners. Along the vertical axis WX there is a gradual increase in stress magnitude from the top surface at W, to the mid-height of the workpiece at X. The distribution in a horizontal direction at the workpiece mid-height is shown as a variation along X-Y. It can be seen that for both the hexagon and square the largest stress values occur at points X and Y. The value at X is influenced by the barrelling of the side wall of the workpiece during the downward movement of the punch. The material at Y has been subjected to high relative movement between workpiece and die wall. The results show similar trends for both the hexagon and square. However the hexagon does show more variation in the stress values for changes in forging load compared with the results for the square, particularly on the top surface OAC. This effect is probably due to the influence of the velocity field of the hexagon and the greater number of lines of velocity discontinuity compared with the square. 6.
CONCLUSIONS
(i) It has been shown that the results predicted by the upper bound equations (4) and (5) are in good agreement with the experimental results and that the initial yield strength of the material is not a limiting factor in the use of these equations. (ii) The values for the forging pressure ratio P/6. predicted by equations (4) and (5) are influenced by the initial height of the workpiece. It was found that agreement between theoretical and experimental results improved as the initial workpiece height increased. Good agreement was obtained when the diameter to height ratio of the workpiece was initially greater than 2.0. (iii) The friction conditions appear to have little influence on the die fill-out at high forging loads. The fill-out is related to the amount of the available energy utilized in causing internal deformation within the workpiece. (iv) The aspect S/t at which /5/6" is a minimum corresponds closely to the values suggested in both BS and ISO standards for the finished dimensions of a hexagonal headed M8-M10 bolt. (v) Fill-out characterised by W/S is a function of the initial workpiece height to. It was shown that for any given forging load the maximum fill-out was achieved in the workpiece utilizing the maximum proportion of the energy available to produce internal deformation. For all other workpiece heights this amount of energy was lower. (vi) Microhardness test showed considerable variation in the surface stress distribution. This is due to the effects of deformation and relative movement between the workpiece and the punch/die. Such stress distribution on cold forged components may give rise to loss of dimentional accuracy and localized distortion due to the effects of residual stresses on the surface of the formed part. Acknowledgements--The authors wish to express their thanks to the technical staff of the Department of Mechanical and Manufacturing Engineering of TCD for assistance with the machining of the workpieces. The assistance of Mr. Alan Reid, Senior Experimental Officer, in the preparation of the drawings is acknowledged.
Factors Influencing Fill-Out of a Closed Die
4(11
REFERENCES [1] H. KUDO, Int. J. Mech. Sci. 1, 229 (1960). [2] E. G. TnOMSEN, C. T. YAi~ and S. KOBAYASm,Mechanics of Plastic Deformation in Metal Processing, Macmillan, New York (1965). [3] Y. Bocharov, S. Kobayashi and E. G. TnOMSEN, Trans. A S M E J. Engng. lnd, 84, 491 (1962). [4] T. AL~AN, Metallurgia Metal Forming 83, 83-88 (1972). [5] K. T. CHANG and I. J. Cnol, Ann. CIRP 20, 63 (1975). [6] R. SAJARand B. L. JUNEJA, Int. J. Mech. Tool Des. Res. 20, 68 (1980). [7] K. OnCA and K. KoNoo, J. SME 25, 1828 (1982). [8] G. NEDIANI and T. A. DEAN, Int. J. Mech. Sci. 25, 347 (1983). [9] J. M. MONAGUANand A. A. TORRANCE,Int. J. Mach. Tool Des. Res. 24, 225 (1984). [10] W. PRA~ER and P. G. HODGE, Theory of Perfectly Plastic Solids, Chapman and Hall, London (1951). [11] D. C. DRUCKER,Appl. Mech. Rev. 7, 421 (1954). [12] M. Cook and E. C. LARKE,J. Inst. Metal. 71, 371 (1946). [13] D. TABOR, The Hardness of Metal, Oxford University Press, New York (1951).