Dynamic Analysis of Tools for High Speed Metalworking

Dynamic Analysis of Tools for High Speed Metalworking P. Hum1 (2). KTH, Stockholm

- Submitted by P. 0. Strandell (1). KTH, Stockholm

Application of high speed in metalworking processes often lower the tool l i f e . The failure of those tools due to dynamic loading differs from t h a t under static or prolonged loading. This failure limits very often the employment of high speed in processes in which the high speed i s favourable with respect to the plastic deformation during the forming process. In this paper are presented results concerning dynamic analysis of tools for h i g h speed bar cropping and blanking. The stress state was calculated by help of available computer prwrams. The obtained stress state resulting from impact on tools, particularly local tensile stresses of short duration (which are generated by diffraction of elastic waves) was used in order t o estimate the tool l i f e of different tools made in different tool materials. The predicted tool l i f e was compared with experimental observations. Conclusion concerning the design of tools for high speed working can be drawn from this analysis which can also be used in the course of material-selection for tooling in high speed working.

1. Description of the problem The development of high speed bar cropping and blanking passed through three stages and reached the fourth one: 1.

2.

I t has been discovered’) t h a t the fracture-surface finish produced by cropping and blanking a t high sped i s superior t o the conventional methods. I t has been shown t h a t thedepth of material strain hardened by the deformation previous to the fracture i s less in specimens cropped and blanked a t high ~ p e e d ~ ’ ~ ) . These facts initiated developments of equipments and presses operating a t high speed suitable for high speed bar cropping and blanking (1-30 m / ~ ) ~ ’ ~ ) . During this second stage has been showed, t h a t far not all materials can be blanked or cropped favourably a t high speed6). Advantages concerning the superior surface finish failed t o appear in high-speed cropping of e.g. stainless steels and soft metals (pure Cu, ELC-steels etc). This circumstance was almost certainly one of the reasons for the hesitancy in industrial acceptance of high speed blanking and cropping. Therefore, during the next stage of development of this technique,

3.

4.

the mechanism of the deformation and fracture processes during high speed cropping and blanking has been studied in order t o find o u t how the fracture can be controlled and guided in the high speed cropping process3). The final goal for investigations in this third stage of the development process was to select materials and process parameters suitable for application of this technique. Now, when we know, for which materials, by help of which machines and w i t h which process parameters the high speed should be used in blanking and cropping, the economics become the controlling factor in the development process and i n this connection, tool l i f e arose as one of the most import a n t factors, especially in developing of machines and tools for cropping and blanking of large sections.

The higher kinetic energy necessary for cropping and blanking of larger sections i s usually achieved by a higher ram or piston velocity resulting in a higher impact velocity on the tool. I n this way, mechanical fatigue due t o the stress pulses in the tool i s increased: remember only the stress acting in a one-dimensional elastic bar when the wave propagates only in one direction7 ) :

This stress can be raised (or lowered) by superposition of reflected waves. However, the duration of such stress pulses is very short. In the course of the development of high speed cropping and blanking processes, both punches in blanking tools and moving blades in cropping tools often failed as a result of propagation and superposition of stress pulses in the dynamic loaded tools. The failure of punches corresponds to the failure occuring i n bars due to longitudinal impact on one end of a bar of f i n i t e length, see Fig.l! Also the fracture in the cropping tool (Fig. 2) can be explained in terms of intersection of two stress waves which tend t o tear the tool apart7). I n the course of tool design for high speed blanking and cropping, the knowledge of the stress state in dynamic loaded tools i s desirable as well as a suitable criterion for selection o f proper tool materials. 2. Analysis of the problem In order t o obtain the stress state in such tools and to formulate criteria for the selection of tool materials, one must both determine the level and the duration of stress pulses due t o the propagation and interaction of elastic waves and study the mechanical fatigue processes influenced by the occurence of such stress pulses. 2.1. The stress state in dynamic loaded tools The process of energy transfer in sol ids under impact conditions i s very difficult t o analyse mathematically. unless either the physical system i s idealized t o simple g e m t r i c a l configurations (bars, plates) when a complete solution should be obtained or the solution of the system of governing equations for a particular problem i s carried o u t numerically.

While complete solutions have been achieved only for the most simple geometries (like bars and plates) and the obtainedresults have been analysed and applied t o practical problems allowing such simplifications as reviewed by e.g. W. Johnson 19727),the numerical solutions of more complicated geometries have not been available until recently. However, the developments of f i n i t e elemnt analysis and the availibility of computer programs based on FEM makes i t possible today t o utilize this method in order to analyse the stress state in metalworking tools with complicated geometrical shape. also when the loading occurs dynamically. Equations of equilibrium for a f i n i t e element system in motion can be written:

E: modulus of elasticity v: impact velocity co: sound velocity

MU

t

Cu‘+ KU

= R

where M, C and K are the mass. damping and stiffness matrices. R I s the external load vector and U. U and are the displace-

ment, velocity and acceleration vectors of the f i n i t e element assemblage.

Annals of the ClRP Vol. 30/1/1981

21 1

Mathematically, the above equation represents a system o f l i n e a r d i f f e r e n t i a l equations o f second order. The procedures available f o r the numerical s o l u t i o n o f such system can become very expensive. These procedures can be divided i n t o two methods o f solut i o n : d i r e c t i n t e g r a t i o n and mode superposition. Both methods are available i n the most finite-element computer programs.

size o f the l a r g e s t defect, i n tool steels equal t o the s i z e o f the l a r g e s t carbide size. This size i s l e s s than 0.01 mn i n powder-metallurgy high-speed tool steels and l a r g e r than 0.1 mn i n conventional t o o l steels. The above expression f o r the f a t i g u e crack growth can be i n t e grated and we obtain

U t i l i z i n g such programs, the user nust choose a suitable solving procedure f o r i n t e g r a t i o n i n the time. I n course o f t h i s work, a comparation between d i f f e r e n t solut i o n techniques and between d i f f e r e n t computer programs (MARCCDC, STARDYNE. WAVE, DYNFEM) regarding t h e i r s u i t a b i l i t y f o r

dynamic analysis o f metalworking t o o l s has been c a r r i e d out’). The use o f d i r e c t i n t e g r a t i o n methods has many advantages when studying the wave propagation, while the mode superposition analysis i s more suitable when only a few modes must be considered.

where a i s the t e n s i l e stress a c t i n g during one stress-pulse, 2a0 the preexisting crack s i z e and 2ac the c r i t i c a l crack length corresponding t o the KIC-value o f the t o o l material.

-

Because of ac >> a. we can as the f i r s t approximation - leave the c r i t i c a l length o f the crack 2ac - out o f consideration and w r i t e

N =

There are more d i r e c t i n t e g r a t i o n methods available i n the FEM computer programs. These methods can be divided i n t o two groups too: e x p l i c i t i n t e g r a t i o n method (the central difrerence method) and the imp1 i c i t i n t e g r a t i o n method (e.9. N e m r k methods).

the Houbolt, Wilson,

c-’.T-*

-

(l/ao)

In t h i s way, we do not need t o consider KIC f o r dynamic loading, which i s an important advantage. Otherwise KIC mtst be considered as independent o f the loading rate.which would c e r t a i n l y r e s u l t i n a l a r g e r e r r o r than the neglected term l/ac i n the expression above

.

Due t o the f a c t t h a t r e l a t i v e l y large-order system of equations can be analysed i n e x p l i c i t time i n t e g r a t i o n using r e l a t i v e l y

3. Results o f the analysis The finite-element computer program WAVE has been employed f o r

small high-speed core-storage, the e x p l i c i t t i m e i n t e g r a t i o n analysis would p r i m a r i l y be performed t o p r e d i c t wave propagat i o n phenomena”).

analysis o f stress s t a t e i n high speed metalworking tools. The obtained r e s u l t s f o r the cropping t o o l are i l l u s t r a t e d i n Fig.

The central difference method i s available i n e.g. MARC-COC. NONSAP and WAVE.

The highest t e n s i l e stress i n the high-speed cropping t o o l

ADINA, OYNFEM,

lmoving blade 165 x 165 x 60 mn) f o r cropping o f carbon-steel-

According t o the performed comparison o t these programs regarding computer costs’). the a p p l i c a t i o n of the program WAVE i s most effective’), though t h i s program i s y e t lacking service procedures as automatic mesh generator, mesh display, post processor etc. The boundary conditions i n the dynamic analysis o f blanking punches and cropping blades has been modelled p a r t l y by an impact of a piston (given geometry, mss and v e l o c i t y ) on the t o o l . p a r t l y by a tine-dependent force acting on the tool. The t r i a n g u l a r force-time h i s t o r y a t the impact has been calculated assuming t h a t the k i n e t i c energy o f the p i s t o n i s completely transmitted t o the t o o l .

2.2.

3 and 4. These r e s u l t s allow following estimation o f t o o l l i f e :

The f a t i g u e process i n high speed blanking and cropping tools

-

sec). This value bar 0 35 m reaches 340 N/mnZ (duration has been obtained by extrapolation o f t e n s i l e stresses towards t o the v e r t i c a l central 1 ine o f the t o o l . According t o the mentioned c r i t e r i o n t/(2a/co) > 1.5 and the obtained duration o f the tensile-stress pulse we can assume KIdSKI and t r e a t the growth o f f a t i g u e cracks i n considered dynamic loaded t o o l s as a q u a s i s t a t i c f a t i g u e process. The

time-duration of the stress pulses i s enough f o r t h i s s i m p l i f i c at ion. The number o f stress pulses r e s u l t i n g i n f a i l u r e o f the considered cropping blade i s 65 000 ( t o o l steel) o r 650 000 (powdermetallurgy high-speed t o o l steel ), when applied impact v e l o c i t y 15 m/s a usual value i n the developed equipment6).

-

Due t o the f a c t t h a t one crop r e s u l t s i n more such stress pulses

The f a t i g u e process i n high speed blanking and cropping t o o l s

( a t l e a s t 5-7) we can estimate the t o o l l i f e o f the considered

can be analysed by help o f the dependence o f the f a t i g u e crack growth r a t e on stress i n t e n s i t y v a r i a t i o n AK

cropping blade t o l e s s than approximately 10 000 (tool steel) and more than 100 000 (powder-metallurgy high-speed s t e e l ) crops. The crack shown i n Fig. 2 occured a f t e r some hundreds

$ = C(AKP where da/dN i s the crack growth r a t e (change i n crack length f o r one loading cycle). C and m are constants f o r a p a r t i c u l a r material (Cdl.10-12 I~’.MN-~ and m P 4 f o r s t e e l s ) . However. before applying t h i s expression. one must check, i f the duration o f the stress pulse allows the use o f t h i s approach.

In addition, we must use the stress i n t e n s i t y f a c t o r v a l i d f o r dynamic loading and we mist know the crack length “2a” pree x i s t i n g i n the analysed t o o l made i n a p a r t i c u l a r material. According t o Thau and Lul‘) and Vardar and Finnie”) KIdQ KI for t/(2a/co) > 1.5 , where KI = o(na)’, KId

the

stress i n t e n s i t y f a c t o r under dynamic loading (corresponding t t o the s t a t i c value KI). and co the sound velocity.

the

duration o f the stress pulse

It remains t o estimate the size o f crack e x i s t i n g i n the tools.

This preexisting crack-size can be assumed t o be equal t o the

212

crops (tool steel), while a ASP-insert-tool (powder metallurgy high-speed steel) held more than 100 000 crops. The repeated r e f l e c t i o n o f stress waves i n the c y l i n d r i c a l blanking punch (Fig. 5 and 6) i s more serious than i n the cropping blade. The r e s u l t s y i e l d following estimations: Based on s i m i l a r assumption about the size o f preexisting crack, the t o o l l i f e o f the blanking punch used f o r high speed blanking o f fi 30 mn i n a 30 mn t h i c k p l a t e can be estimated t o 50 ( t o o l s t e e l ) o r 500 (powder metallurgy high-speed s t e e l ) stress pulses. With regard t o the f a c t t h a t the stress pulses are repeated a t l e a s t 10 times during the loading o f these blanking t o o l s (Fig. 6). we can estimate the tool l i f e t o 5 ( t o o l s t e e l ) o r 50 (powder metallurgy high-speed steel) blanks. Observed t o o l l i f e : non ( f a i l u r e occured during the f i r s t t r y i n blanking

fl 30 mn i n a 30 mn plate, when t o o l steel punch was used).

The essential r e s u l t o f t h i s analysis i s the estimation o f the s u i t a b i l i t y o f high speed a p p l i c a t i o n i n tFe p a r t i c u l a r process. Conclusions 1. The f i n i t e element computer programs providing the option central dffference method ( d i r e c t e x p l i c i t i n t e g r a t i o n method) are suitable f o r dynamic analysis o f metalworking tools, both f o r analysis o f tool l i f e and f o r estimation i f a p a r t i c u l a r operation i s suitable t o be carried o u t

12. S.A.

Thau. T.H.

Lu: Transient stress i n t e n s i t y factors

f o r a f i n i t e crack i n an e l a s t i c s o l i d caused by a d i l a t a t i o n a l wave I n t . J. Solids Structures.

2

/1971), 731-750.

13. U. Vardar, 1. Finnie: The p r e d i c t i o n o f fracture i n b r i t t l e sol i d s subjected t o very short duration t e n s i l e stresses I n t . J. Fracture (1977). 115-131.

13

by help o f high speed.

2.

The f a t i g u e process i n these t o o l s during dynamic loading i s c o n t r o l l e d by the i n i t i a l (preexisting) crack length and the l e v e l o f maximum t e n s i l e stress occuring during propagation o f stress pulses due t o impact on the t o o l .

3.

I

IMPACT

I t i s more important t o use t o o l matecial containing small

preexisting cracks, e.g. powder metallurgy t o o l steels than more tough materials (tough i n terms o f KIC). 4.

High speed cropping and blanking o f l a r g e r sections may be c a r r i e d out by r a t h e r r e l a t i v e l y low speed, which means t h a t the necessary k i n e t i c energy should

not be

achieved by increasing the impact velocity, but by increasing the piston weight.

5.

failure

The presented analysis o f dynamic loaded metalworking t o o l s seems t o be a s u i t a b l e and feasible way t o produce basic data f o r design o f t o o l s and presses f o r high speed metalworking and selection o f proper t o o l materials.

Acknowledgements This work was supported by the Swedish Board f o r Technical Development, STU. The author i s grateful t o Dr. 5. Essle who c a r r i e d out numerous calculations and implemented the WAVE-FEM

Fig. 1.

Typical f a i l u r e o f a high speed blanking punch.

program a t the I n s t i t u t e computer.

1.

C. Zener. J.H. Hollomon: Effect o f S t r a i n Rate on the

P l a s t i c Flow o f Steel. J. Appl. Physice. 2.

22 (1944).

22-31.

R. Davies, E.R. Austin: Developments i n high speed metal forming, p. 124-157. The Machinery Publ., London 1970.

3.

P. Huml: Some E f f e c t s o f high speed i n Metal Cropping and Blanking. Annals o f the C I R P 3 (1974). 61.

4.

As r e f . 2, p. 41-64.

5.

P.O.Strandel1,

moving blade

P. Huml: Tronconnage de barres M t a l l i q u e s .

Formage e t Traitements des Metaux 6.

1

IMPACT

29

(1971). 43.

P. Huml : Decoupage a grande vitesse g (1977). 127.

Le T r e f i l e 7.

8.

W. Johnson: Impact Strength o f Materials Edward Arnold Publ., London 1972. K-J. Bathe, E-L.

Wilson: Numerical lnethods i n F i n i t e

element analysis Pretience-Hall Inc., 9.

1976.

S. Essle. P. Huml: Analys av s t 8 t f i j r l o p p e t i bearbetnings-

i n Fig. 2b

verktyg (76-4068),

KTH Stockholm, 1980.

10. K-J. Bathe: On the development o f solution methods f o r nonlinear analysis i n mechanics Proceedings, Conf. on Computer Aids i n Manufacturing, Nice, France, 1978 (p. 333-353).

Fig. 2a.

Appearance of f a i l u r e i n a moving blade f o r high speed bar cropping (Design as described i n 5, and ').)

11. L.G. Nilsson: Impact loading on Concrete Structures Publ. 79:1, Dep. Struct. Mech. Chalmers. Goteborg. 1978.

21 3

Fig. 5.

Fig. 2b.

30 inn (axisynmetric elements)

Mesh o f t h e analysed c y l i n d r i c a l punch (0 30 mn) f o r h i g h speed blanking o f a p l a t e w i t h thickness

1

IMPACT

D e t a i l o f t h e f a i l u r e showed i n F i g . 2a.

time

( P l a i n s t r a i n elements)

punch showed i n Fig. 5.

i n dynamic loaded

. l o 4 [5]

f o r h i g h speed cropping o f a 0 35 mm bar

Mesh of t h e analysed moving blade (165x165~60mn)

Calculated s t r e s s v a r i a t i o n (a,)

i

-

Fig. 6.

-3000

-2000

Fig. 3.

I

IMPACT

Fig. 4.

-100

. lo5

1s~

city

15 m/s.)

(Dynamic l o a d i n g corresponding t o impact velo-

V a r i a t i o n o f s t r e s s s t a t e (a ) i n element 16 YY o f t h e analysed moving blade showed i n Fig. 3

time