55f1b47d-0f23-49d3-b6a3-42330b317f08 590 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

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^* :

a 7.2263 105 -^*

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

x q 898098463499385289154126317269 nthroot 643030148529388^* x 89154126317269 nthroot 643030148529388^* 539473741699661000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (2^- 539473741699661000000000000000000000000000000000000000000000000 / sqrt * 1153179030448140000012072 / - 5000000000065359477124183 / - x + 22888183593752 x * (361993792163119001015^* 50189311257624301015^* /^* 3726288699608000000000 / + (* /

3.29 x.c_max 100 / + P.c_hor 0.0302

x Φ x q (x diff :

Maple symbolic is = Smath symbolic ... Maple a bit shorter x δ x Φ maple : 4624705437601289154126317269 nthroot 643030148529388^* x 3828571741460160 nthroot 23785260138912200^* 1677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* 6034846099755880000000000000000000000000000006710886453406723142510500458429818380445 x * + (* 1209393273012150289154126317269 nthroot 108105390625774^* x 89154126317269 nthroot 643030148529388^* + (* 5052104425341480000000000000000000000000000001339138525218340000000000000000000000000000000000000000000000001572090356101251677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* - (* 26488953535285300000000000000000000000000000000000000000000799333283177978000000453275851422025289154126317269 nthroot 18951264308505^* x 89154126317269 nthroot 553876022212119^* + (* 2361454032799682 nthroot 722908065599365^* 1677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (* x 564771926249503 nthroot 564771926249506^* - (* 65643186680834400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000255546098865343000000000000000000000000000000000031677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* - (* 1038168791935820000000588711683834285 x 297180421057563 nthroot 1846253407373740^* 289154126317269 nthroot 18951264308507^* + (* x 188866598615062 nthroot 188866598615059^* - (* 9365863571174670 sqrt * 119020645342248000000000000000000000000000000000000000000000000000000000000000000000000000000000000185086761892239761432908496730065359477124183 x * + (* 9511055704814950000002137959328294567 nthroot 29325661103226^* x 137959328294567 nthroot 995040959165195^* + (4^* 211106232532992 sqrt * 255546098865343000000000000000000000000000000000031677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* - sqrt * /

"Le format de la chaîne d'entrée est incorrect" 2.123 Φ #

Smath symbolic expansion is OK, hyperpowerful, dozens pages long !!! x Φ 7071442017511289154126317269 nthroot 643030148529388^* x 3828571741460160 nthroot 23785260138912200^* 232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (2^* 325019568515425000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (* 206386816121806000000000000000000000000000000539473741699661000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (2^- (* 6928960362536440000000000000000000000000000000000000799333283177978000000453275851422025289154126317269 nthroot 18951264308505^* x 89154126317269 nthroot 553876022212119^* + (* 232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (* x 564771926249503 nthroot 564771926249506^* - (* 1733953767177580000000000000000000000000000000000000000000000000000000000000000000000000000000000539473741699661000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (2^- (* 1038168791935820000000588711683834285 x 297180421057563 nthroot 1846253407373740^* 289154126317269 nthroot 18951264308507^* + (* x 188866598615062 nthroot 188866598615059^* - (* 4362931881321270000000000000000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (4^* 539473741699661000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot 553876022212119^* x 89154126317269 nthroot 643030148529388^* + (* + (2^- sqrt * 9365863571174670000000000000000000000000000000000000000000 sqrt * 57600 sqrt * /

x Deriv 7071442017511289154126317269 nthroot (643030148529388^* x 3828571741460160 nthroot (23785260138912200^* 232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot (553876022212119^* x 89154126317269 nthroot (643030148529388^* + (* + (2^* 325019568515425000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot (553876022212119^* x 89154126317269 nthroot (643030148529388^* + (* + (* 206386816121806000000000000000000000000000000539473741699661000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot (553876022212119^* x 89154126317269 nthroot (643030148529388^* + (* + (2^- (* 6928960362536440000000000000000000000000000000000000799333283177978000000453275851422025289154126317269 nthroot (18951264308505^* x 89154126317269 nthroot (553876022212119^* + (* 232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot (553876022212119^* x 89154126317269 nthroot (643030148529388^* + (* + (* x 564771926249503 nthroot (564771926249506^* - (* 1733953767177580000000000000000000000000000000000000000000000000000000000000000000000000000000000539473741699661000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot (553876022212119^* x 89154126317269 nthroot (643030148529388^* + (* + (2^- (* 1038168791935820000000588711683834285 x 297180421057563 nthroot (1846253407373740^* 289154126317269 nthroot (18951264308507^* + (* x 188866598615062 nthroot (188866598615059^* - (* 4362931881321270000000000000000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot (553876022212119^* x 89154126317269 nthroot (643030148529388^* + (* + (4^* 539473741699661000000000000000000000000000000000000000000000000232265740413790000000000000000003493564698379305100000000000 - 653594771241837 - 2 x * + (* + (* 79258797540124300000289154126317269 nthroot (553876022212119^* x 89154126317269 nthroot (643030148529388^* + (* + (2^- sqrt * 9365863571174670000000000000000000000000000000000000000000 sqrt * 57600 sqrt * / :

"Le format de la chaîne d'entrée est incorrect" 2.123 Deriv abs #

Maple separation [numden] is OK, very long as well x Deriv numden maple 35357210087555289154126317269 nthroot 643030148529388^* x 3828571741460160 nthroot 23785260138912200^* 3204940387920256710886453406723142510500458429818380445 x * + (* 1209393273012150289154126317269 nthroot 108105390625774^* x 89154126317269 nthroot 643030148529388^* + (* 862408378587527400000000000000000000000000000000000000000000000732647207661891677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* - (* 195478890317595799333283177978000000453275851422025289154126317269 nthroot 18951264308505^* x 89154126317269 nthroot 553876022212119^* + (* 2361454032799682 nthroot 722908065599365^* 1677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (* x 564771926249503 nthroot 564771926249506^* - (* 257263679128908000000000000000255546098865343000000000000000000000000000000000031677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* - (* 1038168791935820000000588711683834285 x 297180421057563 nthroot 1846253407373740^* 289154126317269 nthroot 18951264308507^* + (* x 188866598615062 nthroot 188866598615059^* - (* 9365863571174670 sqrt * 218257774751552000000000000000000000000000000000001677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* 211106232532992 sqrt * 255546098865343000000000000000000000000000000000031677721653406723142510500458429818380445 x * + (* 604696636506075 x 89154126317269 nthroot 643030148529388^* 289154126317269 nthroot 18951264308505^* + (2^* - sqrt * 21 mat

evaluation is OK x NUMDEN x Deriv numden maple :

x myderiv x NUMDEN 1 el x NUMDEN 2 el / :

"Le format de la chaîne d'entrée est incorrect" 2.123 myderiv #

x f x q :

h 0.0001 :

Infinitesimal Derivative x h f deriv x h - f - x f + x f + x h - f - 2 h * / :

an infinitesimal function x h f infinitesimal x h - f - x f + h / :

x D x h f deriv :

root of derivative X x D x 34 solve : 3.2726

intersection q(x)<=> D(x) I x q x D - 0 ≡ x 3 3.5 solve : 3.1177

The deviation from "Infinitesimal Derivative" wrt the true derivative is ~ in the order of 'h', for any function. The NON-plot and the NON-evaluation is from Windows ... click on the red to see message in french.

x q x D X 0 . 15 black 1 5 mat I I q + 20 green 1 5 mat 4 1 sys

3 q 3 D 3.5 q 31 mat 0.0244 0.0341 031 mat

x g 0.0001 :

root of function XX x q x g - 0 ≡ x 3.45 3.55 solve : 3.5

Integral accuracy 10000 ...higher accuracy 
expected from Romberg algo [Smath auxilliary] x q x 0 3.5 int 0.0579

2 δ #

Integrand fails ... integrator fails
solution via other methods 
"u_not defined " means=> can't compute u δ u 1012 -^3.2726 int #

There is a scaling problem ???
must be checked  again. x h f h_cumul 2 h x h + f x f - (* 2 x f * + (x 2^* (* 12 / :

x cumul x h f h_cumul 0 x ≤ (x X ≤ (& cases :

X 3.2726

residual imaginary @ X X h f h_cumul abs 0.1097

There is residual imaginary
@ '0' ... thus |babsolute| data x 0 X 0.01 range : i 1 x rows range y i el x i el D eval abs : for x y augment 31 line :

data data :

The rate of "cumul(x) decreases at max of derivative [data]

data x cumul X 1 X 1 - 2 2 mat 2.94 1 2.94 1 - 2 2 mat 4 1 sys

data rows 328

The guilty elements

is the Power function [X^Y], borrowed from Windows.
Does not support too high coefficients x 3828571741460160 nthroot (2378526013891220^

x 3828571741460160 nthroot ( 2378526013891220 ^ x 3.8286 nthroot ( 2.3785 ^ x 89154126317269 nthroot ( 643030148529388 ^

2378526013891220 2.3785 1015^*

3828571741460160 3.8286 1015^*

x 1.23456789 :

Windows: "le format de la chaîne d'entée est icorrect" x 3828571741460160 nthroot (2378526013891220^#

x 3.8286 nthroot (2.3785^1.1399

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 *