Computation of a model milling machine

Computation of a model milling machine

Citation for published version (APA):

Janssen, J. D., Touwen, N. A. L., Veldpaus, F. E., & van der Wolf, A. C. H. (1970). Computation of a model milling machine. (TH Eindhoven. Afd. Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0244). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1970

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Cod l ' q ,; ... (

.

C~"t"c?~l

COHPUTATLON OF A ~10m~L 1:1ILLING HACHINE

C.LR.P,

Computer s of

Tool Structure •

by

J.D,

Janssen,

A.C.H. van de1: vblL

of

1. INTRODUCT ION

Tllis deals the results of the

U maehin8 at the vle started frOlil a matheJnut

proposed

The

CO';;rLEY [1] *

1 mode

all

,vi.th program A~4112. The program

• J an EL--X8 of a modf~l Te::chnology. 1) H;;:' tal 1--60.

2. THE CONPUTEP_ F ROGIUil·l

2.1. Introduction

The prograrn is based on results obta::Jj2d uith the aid clf the

finil.e·-elen:ents-~metb()d, It is useful fO)~ the C01TIpu.tatio.n of th.e

static and. dynamic behiJv-iour of a:cbitxa:cy framed structures.

Lumped maSE! '3 as well as uni distributed mass can be taken

into aCCOUD t, Every elem.cmt if) Sl:PPOS;~d. to 112\18 cO:l.stant

cross--section and material properties.

2.2. The statlc b

The displacement quantities (defI,"c and slopes) are chosen ties in ,h8 nod,)l PO:i .. 1_it'S of the frame. After the

elimination of tll(;; a prlOI'I, 1{110Vl[i s (for

a fixed en.Cl , of thc structure) and 1:.112 displacem0nts which d on each other for

connected by an 1

unkno"m placen1c:nt quml.tii~i2[: of the. frflTIJed structure "Till

a~~ the of

a colurrm v2ctor u.

Tl1E·~ ex::terr181. forces lJ.l the 110(1 J 1.s of the s true ture are the

f

Q

u (2. 1 )

,'!hen:. Q is t'Lc stiffm:ss of th2 structure.

Q

,:"in

be

1 ik O,k

z lJ :

the vee.tor of element k,

Ik

u ~s the e of 1..1 k •

1.S the s s of el er;:,",'1t k.

If the frm,ic; sts of n clE:rilc,uts ~ the total 1:4

¥

~ ~k

Qk }: '""

~ ~l.

Q u k""l

The en~rgy of the external forces

! - u £ Th.:'rcfore s the I uQu·-t!f 6V "" 0 for aU of (J Y In our cal

re:movsd the DC futt.lrc: ,

of stf.. >

Q

The bUIUl structure Q J.S to

to Q alI npl' file

If

u foll 1 (2.2) energy (2,3) be:

(2.4)

as; ( ? ~.::> I") 1 be tten thi

!,

(2.6)

0118 t1:1e

vector of eleru~nt k (state var ten as:

(2.7)

2.3.

N8tura!.

The forecs at the frame EJrc forces. Therefore,

we can te:

f - 1-1 u

..

(2.8)

where M is the mass of the structure,

Now, Eqs. (2.1) yield:

Qu

+

o

(2.9)

The co1l1nm v(;:ctor U can be tten

U :::: U cos (>.jt (2.10)

",rhere w the ar ve t natural

\vith tli(, aid of the Eqs. (2.10), it is poss to te the

(2.9) .- ₂

-Qu

-

w

Nu

.- 0 (2.11) clolved {.j~ (L~l _1"1 .~ -1 I) 0 L

_.

(2.12) to I L L

--

Q (2,13) I V L u (2. 1 L a 1m".:., tr

2,.5.

ma CDn h·e t ized. trf~ th.e to

use a direct method lU order to 22tennine the and l'fl an

, the ban.d form of H ·2.n Q cannot be used.

is

di results

in

the casc~ of

The energy of the forces 1.8 found by

the contribution of each elelPent,

quan[.iti i:~8 a function of thE.

made

a s

c;:d.culation, the

contribu

of elen,,::;nt k i £01.1Jld by 11<: - u is the ra:lss tten as: of elcIr.cn k. of the the element. (2 .. 15)

For the ent 8Y of all forces

1.8 :

- u H u (2.1

It has to be no tllDt s

Sec. 2.3. The method of cal

s iJle

The. InpL: <'

TIl£tE ses or

The

of nodal e of elements of

The

a corUlrlon. c:.oord

- Geow~.: ci:,l properties of every

e.ler:.ent)

- The

of the two to every

element a to te that the flexibility

of an

- The laCerne!l t quan t 1~ t:L2.S are to zero,

- The local nate system of every element:~

- The total mass of every eleffi8Dt and the

in the 1

- The

of

Further80H' ~ to take of the

fact tl~at som.c e attcl nc}dal po t:5 havoc tIle sa:m.e c1).arcl.cteristics.

2.6. cl,'?ta

1S a160 as

]?llrt~herlT:01:~e, th.f;

for all k

lU U

is

In tlt;" cast:, of s Ci::lcule CiB thE; fol t elata are

t

- DisplF.1 1. s

In the case of coJ.eula t11 pro gr anl the

des

3. RESULTS OF THE COJ,fPUTliTION

de.flect of all structural B caused

unit forees 1.'1:5 7 and 14 HI X, Y fmd Z

are calculated. Table 2 and 2, 3 and 4 show the

result,

The for stfi C was 130 sees. The

for one case was

14

sees. The

system.

The s are also out Fith the

[ 2'. The results were the s _- ~

We calculated the natural es of the lov7E:st 6 mod.~s of

an,d t IH.::. ill the case of 1

tbe , 5; 6" 7. 8 ~ 9 Bud 10 •

-9-If. DISC1JSSIO>J OF THE RESULTS

ned lndlcates very good

The m'tllral of the. l.ovles 6 rcodBl of

u~lIST And _led 'f[ltle 3.

t-Je caJcUl[lted the 10\ve.st 6 mode:; also dis butec1 milSS

and OIlC s J 5.

The rel:mlts of these v7i:re prE~ctically the same as thon8

obta.1ned with rnasses .. As fa.r as

a crep211ey" 3), but the 6th modal the case of

uniformly 1:1" fnGSS i s the SHln{~ [J tllc one \-lith

-10-8

S ta t:5 Y eli

y

+1 ~OE03 12-7 and. -1 e

·-13--y

Fi .

4.

Static d load ~I' 4 3 u 7 and 1.0E03

-]

y

lS~ \ " \

,

\ \ . 6. , 1

--j 6··

--z

v

y

,h.

( '

u

\

, 1C, 6th

\

\

-20-\

\

\

• 11. 920 d >27!~ 1: ) in sta :l.t 15,

,-, , 2 ? T"!-,t ",'" j _-~ "'""~ .. ':. ,,',_ v .. ;:I~<;.~ , -' c d. () G

o

f) 0 Cl

c:

' ... i n "-' (, 0 L08.cl ~ .. 1

at

o

\) rc ,-' (}

o

o

n "<J

o

o

c

o

o

o

o

-.

- c - 0

-.

',r ~~.

z

o

-1-. -""J:::"~ijJ".,JJ *r Q .f-i!1 ...c~ Q "'f~

.

+$ :t11. Z. d.o flection. +.1

=====J, ___ -.

-.--- ---- ... -.=-=.-= .. =.=.=--=-=--=-..

=_.-=-._--

_.

=.=-=-.= .. = .. =.-

=============='=============<]-1

i t

r-1 8L~ 1 Sf;!. 33,4 33l,

r-I

_____ ._ .J

I

==j

i i ! I

I

3/,-0

i---,~---~

L~08

LOS

l~,7g ₄₇₆ 670

₆₇₀

₆₉₂ I I

i

j ---~---r--- ---~i---l 713 ₇ 13 ₉₂₀ TIJJ3.sses

JH(- uniforr::.ly distri.buted mass and one lumped mass

(3.274 kg)

sta point

15.

Dy'narr.ic :results of T •

r

1

LIJ

Eo1'k by

A.

"ASl(A. 1

as

A Prob

0:.:1 II :; Vol, .L

VoZ.

Tn

'if; In,D

.'

De.n an.d It. COr·teEY" C, I, L. VAN IBN cT,

C.I.B.P.

1070.

De and for Structurnl ~Jork< on Too 1 S tTtlC tUJ:'E:S n 1970.