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AXN Performa D

1. Input parameters

machine pitch

D.p 750 :

machine stiffness

R.m 0.17 1000101^* / (1 -^: 58823.5294

compression roller diameter

D.c 240 :

number of punches

z.p 53 :

number of layers (single/double layer)

z.l 2 :

max. compression force, initial value

F.c_max 90 :

σ.c 0.2 :

F.c_ini σ.c F.c_max * : 18

max. compression roller stroke, initial value

x.c_max 3.5 :

x.c_ini 1 σ.c - (x.c_max * : 2.8

compression efficiency

η.c 0.7 :

tabletting speed

Q.m 49501 -^:

Q.m_max 0 :

n.m Q.m z.p z.l * / : 1.9059 106 -^*

total reduction

i.tot 33 :

clutch reduction

i.c 21 :

belt reduction

i.b 1 :

steel density

ρ 7850 :

external diameter of turret guides

D.ext_m 675 :

die length

L.die 90 :

moment of inertia of die

J.die 12 / π * L.die * ρ * D.ext_m 2 / (4^* : 1.4399 1016^*

2. Calculations

2.1 Dynamics

linear speed

v.lin D.p 2 / 2 π * n.m * (* : 0.0045

v.lin_max 220 :

n.max v.lin_max π D.p * / : 0.0934

centrifugal acceleration

a D.p 2 / 2 π * n.m * (2^* : 5.3774 108 -^*

distance & time between punches

L.bp π D.p * z.p / : 44.4565

t.bp L.bp v.lin / : 9900

2.2 Compression model

assume symmetric lower & upper punch penetration -> total compression stroke = 2x compression roller stroke

F a 2 x * (n^* ≡ F.2 F.1 - a 2 x.2 * (n^2 x.1 * (n^- (* ≡ F.2 F.1 / 10 log n x.2 x.1 / 10 log * ≡ F.c_max F.c_ini / 10 log n x.c_max x.c_ini / 10 log * ≡ 41 line

n F.c_max F.c_ini / 10 log x.c_max x.c_ini / 10 log / : 7.2126

a F.c_max (2 x.c_max * (n^/ : 7.2263 105 -^*

compression force

x F.c a 2 x * (n^* :

x F.c

x.c_max F.c 90

powder compression energy ("D")

x U.x x F.c x int ≡ x U.x a 2 x * (n^* 2 x * (int ≡ x U.x a n 1 + / 2 x * (n 1 +^* 103 -^* : 31 line

x.c_max U.x 0.0767

elastic machine deformation (strain) energy only deformation impact on machine by upper punch, hence factor 0.5

x U.m 12 / x F.c R.m / (* x F.c * :

x.c_max U.m 0.0689

total compression energy ("I")

x U.tot x U.x x U.m + :

x.c_max U.tot 0.1456

x.test 2.8 :

real stroke to be done, incl. machine deformation ("K", has to be zero for x=3.5mm)

x K x.c_max F.c_max 2 R.m * / + (x x F.c 2 R.m * / + (- :

0 K 3.5008

3.5 K 0

x.test K 0.7006

horizontal stroke ("L")

x x.c_hor D.c 2 / (2^D.c 2 / x K - (2^- sqrt :

x.test x.c_hor 12.9482

x.c_max x.c_hor 0

contact angle ("M")

x α.c D.c 2 / x K - D.c 2 / / acos :

x.test α.c deg 6.1944

horizontal force ("O") force present on lower and upper compression roller, acting in same direction -> factor 2

x F.c_hor x F.c x α.c tan * 2 * :

x.test F.c_hor 3.9073

instant normal force ("P")

x F.c_n x F.c x α.c cos / :

x.c_max F.c_n 90

x.test F.c_n 18.1057

instant horizontal power

x P.c_hor x F.c_hor v.lin * :

x.test P.c_hor 0.0175

x F.c a 2 x * (n^* :

x F.c x P.c_hor

actual compression power (based on time between 2 punches)

P.c_actual z.l x.c_max U.tot * t.bp η.c * / : 4.2009 105 -^*

average compression power (based on time for one downward punch movement)

P.c_avg z.l x.c_max U.tot * 0 x.c_hor v.lin / (η.c * / : 6.4906 105 -^*

x q x P.c_hor :

0 q 0

max. compression power

x q

3.29 P.c_hor 0.0307

3.29 x.c_max 100 / + P.c_hor 0.0302

x Φ x q (x diff :

2 Φ #

x f x q :

h 0.01 :

Infinitesimal Derivative x h f deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* (:

x D x h f deriv :

X x D x 34 solve : 3.2775

x h f deriv X 0 . 15 red 1 5 mat x q 3 1 sys x Φ

2 q 2 D 21 mat 0.0023 0.0073 21 mat

extr 4 mm * :

k 0 : k x.c_max mm / > k k x.c_max 100 mm * / + : k mm * P.c_hor extr > extr k mm * P.c_hor : extr 3 : if 11 line for

extr 0.004 m *