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AXN Performa D

1. Input parameters

1.1 Machine parameters

machine stiffness

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

turret pitch

D.t 750 mm * :

number of punches

z.t 53 :

number of layers (single/double layer)

z.l 2 :

compression roller diameter

D.c 240 mm * :

external diameter & height of upper & lower table (= turret top & bottom)

D.1t 840 mm * :

L.1t 100 mm * :

external diameter & height of die table (= turret center)

D.2t 800 mm * :

L.2t 30 mm * :

external diameter & length of central shaft (= turret shaft)

D.3t 300 mm * :

L.3t 100 mm * :

dimensions of pulley at gearbox output (connected to gearbox worm)

D.p 250 mm * :

L.p 125 mm * :

belt reduction

i.b 11250 / : 2.24

gearbox reduction (brand: ZE)

i.g 10 :

total reduction

i.tot i.b i.g * : 22.4

armature inertia of main drive motor (brand: SEW)

J.mot 0.28 kg * m 2^* :

turret acceleration time

t.t 0.5 s * :

steel density

ρ.st 7850 kg m 3^/ * :

1.2 Process parameters

max. compression force & initial value, the latter to be considered as assumption

F.c_max 90 kN * :

σ.c 0.2 :

F.c_ini σ.c F.c_max * : kN 18

max. compression roller stroke & initial value

x.c_max 3.5 mm * :

x.c_ini 1 σ.c - (x.c_max * : mm 2.8

compression efficiency

η.c 0.7 :

ejection stroke

x.e 14 mm * :

max. linear speed @ turret pitch

v.t_max 220 m min / * :

external tablet diameter

D.tab 25.4 mm * :

internal tablet diameter

d.tab 0 mm * :

tablet height

h.tab 4 mm * :

transformation factor

k.tab 0.4 :

friction coefficient

f.tab 0.1 :

tabletting speed

Q.tab 4950 min 1 -^* :

2. Calculations

2.1 Press dynamics

turret speed

n.t Q.tab z.t z.l * / : min 1 -^46.6981

n.t_max v.t_max π D.t * / : min 1 -^93.3709

linear speed at turret pitch

v.t D.t 2 / 2 π * n.t * (* : m min / 110.0298

centrifugal acceleration at turret pitch

a.t D.t 2 / 2 π * n.t * (2^* : 8.9678 m s 2^/ *

motor speed

n.mot n.t i.tot * : min 1 -^1046.0377

gearbox output speed

n.g n.t i.b * : min 1 -^104.6038

max. clutch torque (clutch? to be asked... ) http://www.atlantadrives.com/pdf/ads_servosel.pdf

P T n * 9550 η * / ≡

2 π * 60103^* / (1 -^9549.2966

T.cl_max 15 kW * 2 π * 1500 min 1 -^* i.b / (* / : N m * 213.9042

mass moment of inertia of turret https://en.wikipedia.org/wiki/List_of_moments_of_inertia

I 12 / m * r 2^* ≡ m ρ V * ≡ I 12 / ρ π D 2^* 4 / * L * (* D 2 / (2^* ≡ I 132 / ρ * π * D 4^* L * ≡ 41 line

J.1t 132 / ρ.st * π * D.1t 4^* L.1t * : 38.3695 kg * m 2^*

J.2t 132 / ρ.st * π * D.2t 4^* L.2t * : 9.47 kg * m 2^*

J.3t 132 / ρ.st * π * D.3t 4^* L.3t * : 0.6242 kg * m 2^*

J.t J.1t J.2t + J.3t + : 48.4638 kg * m 2^*

reflected turret inertia at motor shaft

J.t_mot J.t i.tot 2^/ : 0.0966 kg * m 2^*

inertial energy of turret https://en.wikipedia.org/wiki/Rotational_energy

W.rot 12 / J * ω 2^* ≡ W.rot 12 / J * 2 π * n * (2^* ≡ W.rot 2 J * π 2^* n 2^* ≡ 31 line

W.t 2 J.t * π 2^* n.t 2^* : 579.4867 J *

turret acceleration power

P.t W.t t.t / : 1158.9734 W *

turret mass

m.t π 4 / ρ.st * D.1t 2^L.1t * D.2t 2^L.2t * + D.3t 2^L.3t * + (* : 608.8925 kg *

mass moment of inertia of gearbox pulley, reflected inertia at motor shaft

J.p 132 / ρ.st * π * D.p 4^* L.p * : 0.3763 kg * m 2^*

J.p_mot J.p i.g 2^/ : 0.0038 kg * m 2^*

inertial energy of gearbox pulley and motor

W.p 2 J.p * π 2^* n.g 2^* : 22.5768 J *

W.mot 2 J.mot * π 2^* n.mot 2^* : 1679.8866 J *

total inertial energy of turret, gearbox pulley and motor

W.i W.t W.p + W.mot + : 2281.9501 J *

2.2 Ejection power

frontal tablet area

Af.tab π 4 / D.tab 2^d.tab 2^- (* : mm 2^506.7075

lateral tablet area

Al.tab π D.tab * h.tab * : mm 2^319.1858

specific pressure

p.tab F.c_max Af.tab / : N mm 2^/ 177.6173

ejection force

F.e k.tab Al.tab * p.tab * f.tab * : 2267.7165 N *

ejection work

W.e 12 / F.e * x.e * : 15.874 J *

ejection power

P.e W.e Q.tab * : 1309.6063 W *

2.3 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 N / (2 x.c_max * mm / (n^/ : 0.0723

compression force

x F.c a 2 x mm / * (n^* N * :

x.c_max F.c kN 90

powder compression energy ("D")

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

x.c_max W.x 76.7117 J *

elastic machine deformation (strain) energy triangle?

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

x.c_max W.m 68.85 J *

total compression energy ("I")

x W.c x W.x x W.m + :

x.c_max W.c 145.5617 J *

x.test 2.8 mm * :

real compression 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 mm * K mm 4.265

3.5 mm * K mm 0

x.test K mm 1.312

horizontal compression stroke ("L")

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

x.test x.c_hor mm 17.6963

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 8.4803

horizontal compression force component ("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 5367.5723 N *

instant normal compression force component ("P")

x F.c_n x F.c x α.c cos / :

x.c_max F.c_n 90000 N *

x.test F.c_n 18198.9755 N *

instant compression power

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

x.test P.c_hor 9843.2183 W *

compression force [N] vs. vertical compression roller stroke [mm]

x mm * F.c

horizontal compression force [N] vs. vertical compression roller stroke [mm]

x mm * F.c_hor

compression power [W] vs. vertical compression roller stroke [mm]

x mm * P.c_hor

determination of max. compression force and power using an infinitesimal derivative: * standard derivative doesn't seem to work in this version of SMath (forum informed) * no units are used here to facilitate the "solve" commmand

x f x mm * P.c_hor W / :

h 0.0001 :

infinitesimal derivative x h f deriv x h - f - x f + x f + x h - f - 2 h * / :

x D x h f deriv :

2 f 1145.6228

2 D 3856.4143

x.root x D x 34 solve mm * : mm 3.2937

F.c_hor_max x.root F.c_hor : 10394.0076 N *

P.c_hor_max x.root P.c_hor : 19060.8494 W *

root determination of compression power function derivative

x f x D x.root mm / x.root mm / f . 20 blue 1 5 mat x.root mm / 0 . 20 red 1 5 mat 4 1 sys

distance & time between punches (= average compression time)

L.bp π D.t * z.t / : mm 44.4565

t.bp L.bp v.t / : ms 24.2424

time required for one compression cycle = time between "punch attack" & roller center (= actual compression time)

t.c 0 x.c_hor v.t / : ms 17.2907

average compression power & torque

P.c_avg z.l x.c_max W.c * t.bp η.c * / : kW 17.1555

T.c_avg P.c_avg η.c * 2 π * n.t * / : N m * 2455.6876

actual compression power & torque

P.c_actual z.l x.c_max W.c * t.c η.c * / : kW 24.0529

T.c_actual P.c_actual η.c * 2 π * n.t * / : N m * 3442.9985

max. compression torque

T.c_max F.c_hor_max D.t 2 / * : N m * 3897.7529

P.c_max T.c_max 2 π * n.t * (* : kW 19.0608

total average power (= compression + ejection power)

P.tot P.c_avg P.e + : kW 18.4651