1996 Huseyin Slideway Pressure

8/4/2019 1996 Huseyin Slideway Pressure

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~ Pergamon I n t. J . M a c h . T o o l s M a n u f a c l . V o l . 3 7 , N o. 3 . I ~ ' - 0 9 - 3 1 8 . 1 9 9 71 9 9 7 P u b l i s h e d b y E l t e v i e r S c i c a c e D dPrinted in ~ Britain. Al l ~ rcsc,.rv~0 ~ ) O - - 6 9 5 5 / 9 7 $ 1 7 . ~ + .GOPII: S0890--69a3~96)00067-3

D E F O R M A T I O N S A N D P R E S S U R E D I S T R I B U T I O N O N M A C H I N ET O O L S L I D E W A Y S

| . H O S E Y I N F i L i Z , t , A B D U L L A H A K P O L A T t a n d |B R A H I M H . G IS IZ E LB E Yt(Received 12 March 1996)

A l ~ t r a e t - - A f in i te e l e m e n t an a l y s is o f m a c h i n e t o o l s l id e w a y s h a s b e e n c a r ri e d o u t b y u s i n g t w o - d i m e n s io n a ls l i de wa y m o de l s . M o de l s a r e c o ns i de r e d t o c o ns i s t o f c o n t a c t e l e m e n t s a t t h e i n t e r f a c e o f s l i d i ng s u r f a c e s . F l a ta nd do v e t a i l t y p e s o f s l i de wa y s a r e m o de l l e d , a nd p r e s s u r e d i s t r i b u t i o ns a nd de f o r m a t i o ns a r e de t e r m i ne d wi t ht h e u s e o f A N S Y S R e v . 5 . 0 A no n- l i ne a r c o n t a c t e l e m e n t s . C l o s e c o r r e l a t io n o f t h e r e s u l t s o b t a i ne d f r o m A N SY Swi t h t h e e x p e r i m e n t a l r e s u l t s g i v e n i n t h e l i t e r a t u r e de m o ns t r a t e s t h e v a l i d i t y o f t h e m o de l s u s e d . E a s e o fc o ns t r u c t i o n o f t h e m o de l s a nd f a s t e r s o l u t i o n t i m e s s e e m e d t o b e t h e a dv a n t a g e s o f t h i s m e t h o d . T h e e x i s t i ngde s i g ns c a n e a s i l y b e m o d i f i e d i f t h e r e q u i r e m e n t s o n t h e a l l o wa b l e p r e s s u r e d i s t r i b u t i o n a nd de f o r m a t i o ns o nt h e c o n t a c t s u r f a c e s a r e s p e c if i ed . 1 9 9 7 Pu b l i s h e d b y E l s e v i e r Sc i e nc e L t d . A l l r i g h t s r e s e r v e d

CdfFk .ImPA

N O M E N C L A T U R Ec o ns t a n t r e l a t i ng no r m a l c o n t a c t de f o r m a t i o n a nd p r e s s u r ed e p t h o f t h e m o d e lcoef f i c ient of f r i c t iona p p l i e d l o a dc o n t a c t s t i f fne s sl e n g t h o f a c o n t a c t e l e m e n tc o ns t a n t r e l a t i ng no r m a l c o n t a c t de f o r m a t i o n a nd p r e s s u r emean i n t e r f a c e p r e s s u r eno r m a l c o n t a c t de f o r m a t i o n

I . I N T R O D U C T I O NM a chine t oo l s t ruc tu res genera l ly con s is t o f f ixed o r bo l t ed j o in t s and s l id ing j o in t s . Fo rcesare t ransm i t ted ac ross t he j o in t in t e r faces and the overa l l s t a t ic and dy nam ic charae t e r i s tic so f t he mach ine t oo l a re in f luenced by the compl iance a t t hese ind iv idua l connec t ions . Themain requ i rem ent s o f t hese j o in t s a re t he s t i f fness and the s t ab i l i t y bu t , fo r s l id ing j o in t s ,t he f r ic t ion and wear p roper t ie s mus t a l so be cons ide red by the des igner , s ince these cani n f lu e n c e b o t h t h e s h o r t- a n d l o n g - t e rm a c c u r a c y o f t h e m a c h in e . W e l d e d a n d b o l t e d j o i n t shave rece ived cons ide rab le a t t en t ion f rom researchers . In addi t ion t o ana ly t ica l and exper -i m e n t a l m e t h o d s , t h e r e a r e m a n y w o r k s u s i n g f i n i t e e l e m e n t m e t h o d s ( F E M s ) . S l i d e w a y s ,h o w e v e r , h a v e n o t r e c e i v e d s i m i l a r a t t e n t i o n . S t u d i e s o n c o n t a c t d e f o r m a t i o n s c o u l d b eseen in the ear ly 1960s . There were some s tud ies on s l ideways in the 1970s . W ith thea d v e n t o f h i g h s p e e d a n d h i g h s t o r ag e c a p a c i t y c o m p u t e r s , t h e a n a l y s is a n d d e s i g n s t u d ie sw i t h F E M s w e r e m a d e e a s i e r a f t e r t h e 1 9 8 0 s . B u t , t h e r e a r e o n l y a f e w s t u d i e s w h i c hused the f in i t e e l ement t echnique fo r t he de t e rmina t ion o f p ressu re d is t r ibu t ion and de fo r -m a t i o n o f s l i d e w a y s .Sur face compl iance fo r a range o f mean in t e r face p ressu res and su r face f in ish used int h e m a c h i n e t o o l s l i d e w a y s h a s b e e n a n a l y s e d b y L e v i n a [ 1, 2 ], T e n n e r [ 3 ] a n d O s t ro v s k i i[4]. The y su gges t ed an equat ion tha t is based on ex per imen ta l da t a t o desc r ibe the re la t ion-s h i p b e t w e e n t h e n o r m a l p r e s s u r e a n d t h e a p p r o a c h o f t h e s u r f a c e s a s

h = c / ' ~ (1 )

tUniversity o f G - a z ia n te p , M e c h a n i c a l E ng i ne e r i ng D e p a r t m e n t , G a z i a n t e p , T u r k e y: ~A u t h o r t o wh o m c o r r e s p o nde nc e s h o u l d b e a ddr e s s e d .30 9


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310 i. Hiise yin Filiz et al.w h e r e ~ i s t h e d e f o r m a t i o n o r n o r m a l a p p r o a c h o f t h e s u r f a c e s i n ~ m , P i s t h e i n t e r f a c ep r e s s u r e i n k g f / c m 2, a n d c a n d m a r e c o n s t a n t s d e t e r m i n e d b y t h e m o d u l u s o f e l a s t i c i t ya n d t h e s u r f a c e f i n i s h o f t h e a p p r o a c h i n g s u r f a c e s .

T h e f a c t o r s a f f e c t i n g t h e r e l a t i o n s h i p b e t w e e n t h e n o r m a l o r i n t e r f a c e p r e s s u r e a n d t h ea p p r o a c h e s o f th e s u r f a c e s a r e : m a t e r i a l o f t h e s l i d e w a y e l e m e n t s , m a c h i n i n g p r o c e s s ,a s p e r i t ie s h e i g h t , o r i e n t a t io n o f m a c h i n e d l a y s , h a r d n e s s , f l a tn e s s d e v i a t io n a n d s i z e o f t h ec o n t a c t a r e a .

C o n n o l l y e t a l . [ 5 ] i n v e s t i g a t e d t h e e f f e c t o f m a t e r i a l h a r d n e s s o n t h e i n i t i a l a p p r o a c ha n d s t a ti c s t i ff n e s s o f j o i n t s f o r m e d b y s u r f a c e s m a c h i n e d w i t h s i n g l e p o i n t t o o l s , a n dT h o m l e y e t a l . [ 6 ] a n a l y s e d t h e e f f e c t o f s u r f a c e t o p o g r a p h y u p o n t h e s t a t i c s t i f f n e s s o fm a c h i n e t o o l j o i n t s . T h e e f f e c t s o f th e s e f a c t o r s o n c a n d m w e r e e v a l u a t e d i n d e t a il b yB a c k [ 7 ] , a n d h e r e c o m m e n d e d t h a t i t i s a d e q u a t e t o h a v e a n a p p r o x i m a t e k n o w l e d g e o ft h e s u r f a c e c o m p l i a n c e p a r a m e t e r s o b t a i n e d f r o m a t e s t , a n d c o n c e n t r a t i o n m u s t b e g i v e nm o r e t o t h e c o m p l i a n c e o f t h e c o m p o n e n t s o f m a c h i n e t o o l jo i n t s , b e c a u s e t h e s t at ic s t i ff -n e s s o f j o i n t s i s m o r e d e p e n d e n t u p o n t h e e l as t ic i ty o f t h e c o m p o n e n t s s u r r o u n d i n g t h es u r f a c e s i n c o n t a c t r a t h e r t h a n t h e c o m p l i a n c e o f t h e c o n t a c t i n g s u r f a c e s . T h i s d o e s n o tm e a n t h a t a l l t h e w o r k o n t h e s u r f a c e c o n t a c t c o m p l i a n c e i s u n n e c e s s a r y . I n s t e a d , s u c hs u r f a c e c h a r a c t e r i s t i c s a r e n e c e s s a r y t o f o r m u l a t e t h e s o l u t i o n o f t h e c o m p l e t e j o i n t s .

M a s u k o a n d I t o [8 ] a n a l y s e d c o n t a c t p r e s s u r e d i s tr i b u t i o n o n t h e s l i d e w a y s u n d e r m i x e dl u b r i c a t e d c o n d i t i o n w i t h t h e u s e o f t h e u l t r a s o n i c w a v e m e t h o d . T h e s l i d e w a y d e s i g nm e t h o d s w h i c h h a d b e e n u s e d c o m m o n l y a m o n g m a c h i n e to o l d e si g n e rs w e r e r e - e x a m i n e dt h r o u g h t h e e x p e r i m e n t a l r e s u l t s o f c o n t a c t p r e s s u r e d i s t r ib u t i o n , a n d i t w a s c o n f i r m e d t h a tt h e d e s i g n m e t h o d i s c o r r e c t f o r m o s t c a s e s e x c e p t f o r a h e a v y c u t t i n g m a c h i n e t o o l .H i n d u j a [ 9 ] a n d B a c k [ 7 ] h a v e i n v e s t i g a t e d t h e d e f o r m a t i o n a n d p r e s s u r e d i s t r i b u t i o n i nt h e j o i n t s b y F E M . T h e y h a v e d e v e l o p e d h y d r o s t a ti c , p l a te a n d s p r in g m e t h o d s f o r m o d e l -l i n g th e c o n t a c t b e t w e e n f i x e d a n d s l i d in g j o i n t s . O n c o m p a r i s o n w i t h t h e e x p e r i m e n t a lr e s u l t s , i t w a s s h o w n t h a t t h e f i n i t e e l e m e n t t e c h n i q u e i s a p o w e r f u l e n g i n e e r i n g t o o l t h a tc a n b e a p p l i e d t o j o i n t s w i t h f ix e d a n d s l i d i n g c o m p o n e n t s .F u r u k a w a a n d M o r o n u k i [1 0 ] a n a l y s e d c o n t a c t d e f o r m a t i o n o f a m a c h i n e t o o l sl i d e w a ya n d i t s e f f e c t o n m a c h i n i n g a c c u ra c y . T h e y p r o p o s e d a d e s i g n p o l i c y to m i n i m i z e th em a c h i n i n g e r r o r b y o b t a i n i n g t h r e e - d i m e n s i o n a l d i s p l a c e m e n t s o f t h e s l i d e r c a u s e d b yc o n t a c t d e f o r m a t i o n . H a s h i m o t o e t a l . [ 11 ] d e v e l o p e d a m e t h o d f o r c o n t a c t s t i ff n e s s e s t i -m a t i o n . T h e y e s t i m a t e d c o n t a c t s t i f f n e s s b y a b e a m m o d e l v i b r a t i n g o n a n e l a s t i c f o u n -d a t i o n , a n d c o n s t r u c t e d a n e x p e r i m e n t a l e q u a t i o n a s a f u n c t i o n o f t h e c l a m p i n g l o a d a n ds u r f a c e t o p o g r a p h y .I n t h i s s t u d y , b y u s i n g A N S Y S R e v . 5 . 0 A ' s n o n - l i n e a r c o n t a c t e l e m e n t s , c o n t a c te l e m e n t s a r e d e f i n e d b e t w e e n c o m p o n e n t s o f t h e m a c h i n e t o o l s l i d e w a y s t o d e t e r m i n ed e f o r m a t i o n s a n d p r e s s u r e d i s t r i b u t i o n u n d e r s t a t i c l o a d i n g c o n d i t i o n s .

2. FINITE ELEMENT ANALYSISI n m o d e l l i n g t h e s l i d e w a y s , t h e f i r s t t h i n g t o c o n s i d e r i s t h e b e h a v i o u r o f t h e s u r f a c e si n c o n t a c t a f t e r a f o r c e i s a p p l i e d t o t h e e l e m e n t s . T h e m o d e l m u s t b e c o n s t r u c t e d s u c ht h a t d e f o r m a t i o n s a t e a c h p o i n t i n t h e j o i n t a n d t h e p r e s s u r e d i s t r i b u t i o n a t t h e s u r f a c e si n c o n t a c t c a n b e e a s i l y e v a l u a t e d . T h e m o d e l m u s t b e s i m p l e , b u t a d e q u a t e t o g i v e a c c u r -a te r esu l t s .I n t h e m o d e l s , i t i s a l w a y s n e c e s s a r y t o c o n s i d e r t h a t t h e c o n t a c t b e t w e e n t h e s u r f a c e si s e la s t ic . I f it w e r e a s s u m e d t o b e r i g id , t h e n t h e c a l c u l a t e d d e f l e c t i o n o f t h e s l i d e w a y sw o u l d b e s m a l l e r t h a n t h e a c t u a l v a l u e s . T h i s e r r o r c a n n o t b e n e g l e c t e d . F o r p r e c i s e c a l c u -l a t i o n s o f t h e d e f o r m a t i o n s a n d p r e s s u r e d i s t r i b u t i o n s , i t i s n e c e s s a r y t o c o n s i d e r t h e c o m -p l i a n c e o f th e s t r u c t u ra l c o m p o n e n t s s u r r o u n d i n g t h e c o n t a c t i n g s u r f a c e s . I n g e n e ra l , q u a l i-t a t i v e i n f l u e n c e s o f a l l f a c t o r s o n t h e b e h a v i o u r o f t h e j o i n t s a r e k n o w n f r o m e x p e r i m e n t sa n d f r o m s i m p l e t h e o r e t i c a l m o d e l s . A m e t h o d o f s o l u t i o n t a k i n g in t o a c c o u n t q u a n t i t a t-i v e l y a l l t h e f a c t o r s t h a t p e r m i t t h e c a l c u l a t i o n o f t h e p r e s s u r e d i s t r i b u t i o n a n d d e f l e c t i o n si s s t i l l n o t a v a i l a b l e . F o r t h i s p u r p o s e , t h e A N S Y S F i n i t e E l e m e n t p a c k a g e , w h i c h c a nh a n d l e m o d e l s c o n s i s ti n g o f n o n - l i n ea r c o n t a c t e l e m e n t s , i s u se d .


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Deforma tions and Pressur e Distribution on Machine Tool Slideways 311In the ANSYS non-linear contact elements, analysis of surface-to-surface contact with

large deformations, contact and separation, and sliding with friction is possible. Generalcontact is represented by following the positions of points on one surface (the contactsurface) relative to lines or areas of another surface (the target surface). The contactelements are used to track the relative positions of the two surfaces. The point-to-pointcontact element in two dimensions is Contactl2, planar and axisymmetric. These contactelements are finite elements that apply appropriate forces to nodes on two surfaces toaccount for contact and friction [ 12].The solution accuracy depends on a number of factors such as mesh density, usedelement boundary conditions, analysis type and contact stiffness. Among them the contactstiffness of a surface is a procedure variable which should be improved during the loadingprocess. The contact stiffness of a surface is the function of surface finish, pair of contactmaterial and interface pressure distribution. It is obvious that the interface pressure is theonly important factor for the contact stiffness. The contact stiffness is large for large meaninterface pressures [11]. A new contact stiffness value must be calculated according tothe new interface pressure for each element along the contacting surface during the load-ing steps.For an isotropic material the following relationship is valid [7]:

h k , ,P- 106ld (2)where P is mean interface pressure, A is the contact deformation, l is the length of acontact element, d is the depth of the model, and k, is the contact stiffness for a contactelement. From Equation (1) the following identity can be established:

I

c 1 0 6 l d (3)

or] - - mld(X) ,, -

k, = (10 l) cl/ ," (4)

At the initial stage of the process, a constant value is assigned to the contact stiffnessfor every contact element. By assuming that the interface pressure is uniform along thecontacting surface, the surface compression can be calculated from Equation (1). By usingEquation (4), the new contact stiffness values for each element along the surface in contactcan be calculated. For the next iteration, contact stiffness values are calculated from pre-vious deformation values. This procedure is fol lowed until the difference in the successivedeformation values is less than an allowed error.

3. EXAMPLESExamples for fiat and dovetail types of slideway models are prepared to illustrate the

determination of the deformation and the pressure distribution at the contacting surfacesof machine tool slideways.

Dimensions and finite element division of a first flat joint slideway model is shown inFig. 1. Contact elements are defined between contacting surfaces along lines AB, BC, DEand EF. The lengths of AB and DE are 30 mm and of BC and EF 20 mm, and the depthof the joint is 60 mm. The load was applied at the centre and plane stress was assumedin the analysis. The surface compliance parameters are c=0.69 and m=0.5, as defined in[7]. The coefficient of friction, f, for contact elements is taken as 0.1. The materials forboth fixed and sliding elements are cast iron with the modulus of elasticity of 95 GPa


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312 i . H / l s e y i n F i l i z e t a l .F /4

Fig. 1. Finite elemen t division of the joint and load applicatio n poin ts. F is the total external load.a n d P o i s s o n s ' s r a t i o o f 0 .2 1 I . M e a n i n t e r fa c e p r e s s u r e i s o b t a i n e d b y d i v i d i n g t h e t o t ala p p l i e d e x t e r n a l l o a d t o t o t al c o n t a c t a r e a o f t h e j o i n t. T h e d e f o r m e d s h a p e o f t h e m o d e lf o r 1 . 6 M P a m e a n i n t e r f a c e p r e s s u r e i s s h o w n i n F i g . 2 .

D e f o r m a t i o n s o f t h e e l e m e n t s a re o b t a i n e d a n d p r e s s u r e s a re ca l c u l a t e d f r o m E q u a t i o n( l ) a t e a c h p a i r o f n o d e s a l o n g t h e c o n t a c t i n g s u r f a c e s . F i g . 3 ( a ) a n d ( b ) s h o w t h e c a l c u l a t e dp r e s s u r e d i s t r i b u ti o n f o r s e v e r a l m e a n i n t e r fa c e p r e s s u r e s . T h e t r e n ds o f p r e s s u r e d i st r i-b u t i o n a r e s i m i l a r , b u t fo r h i g h p r e s s u r e s , t h e d is t r ib u t i o n b e c o m e l e s s u n i f o r m , b e c a u s eo f th e in f l u e n ce o f b o d y d e t b r m a t i o n . A t lo w m e a n i n t e r f a c e p r e s s u r e s , m a x i m u m i n t e r fa c ep r e s s u r e i s a b o u t t h e s a m e a s t h e m e a n i n t e r f a c e p r e s s u r e . T h e r a t i o o f m a x i m u m i n t e r f a c e

Fig. 2. Deform ed shape of the joint for 1.6 MPa interface pressure.


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Deformations and Pressure Distribution on Machine Tool Slideways 313$

, - , 7e lIS .~" s.=,IS 4ht J

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o

- - C ~ - - - 0 . $ ]

3.2 I \. . . , R , , r~ I \~ , ~ .o R. , t 'n I y ~_ _ o I \ \

y ++ \. . . . : ' , ' ' : . . . . : . . . . : . . . . : . . . . : . . . . : " : " ~ ' ~ . I ~ 1 - - , - + , -- -I - - H C l

S 1 0 1 5 2 0 2 S 3 0 3 6 4 0 4 6 5 0C o n t a c t l e n g t h ( ra m )

(a )

I ko - - ~ - - l z sl : t~ ,o0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 SO

C o n t a c t L e n g t h ( m m )

( b )F i g . 3 . P r e s s u r e d i s t r i b u t i o n t t h e c o n t a c t i n g s u r f a c e s f o r s e v e r a l i n t e r f a c e p r e s s u r e s .

p r e s s m ' c t o m e ~ . n i n t e r f a c e p r e s s u r e i n c r e a se s w i t h t h e m e a n i n t e r f ac e p r e s s u r e . A n d a l s ot h e m e a n i n t e d ' ~ e p r e s s u r e i s i n c r e a s e d , t h e c o n t a c t l e n g t h o n B C a n d ~ b e c o m e s s m al l e r .

W h e n t h e d e f l e c ti o n s a t t h e c en t r e o f t h e j o i n t a r e p l o t te d a g e n t t h e i n t er f a c e p r e s s ur e ,the diagram in Fig. 4 is obtained. It allows the designers to determine the required loadfor the allowable deflection. Non-linearity between deflections and mean interface pressurecan be observed.

The structural elements which are used in the second sfideway model are shown in Fig.5. This is a typical example on closed-type sfideways. Depth of the joint, surface com-pliance parameters, other assumptions and material properties are the same as in the firstexample. In this problem, contact elements are defined along the fines AB, CD, DE andFG, HI, IJ. The lengths of AB and FG are 40 nun, CD and HI are 90 mm, and DE andIJ are 35 nun. Contact elements are not defined along the fines BC and GH, because whenthe joint is loaded due to the deformation, a separation at this surface will be developed.The deformed shape of the model is shown for 1.6 MPa mean interface pressure inFig. 6. The calculated pressure distribution for five mean interface pressures is shown in


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314 I . Htlseyin Filiz et aL

~ ' +

~ . ~ + ~ +0 2 0 4 0 6 0 8 0 l e O 1 2 0

D e f l e c t i o n ( ) u n )Fig. 4. Relat ionship between the applied interface pr essu re and the deflection at the centre of the first example.

F ~F / 4 F / 4

11111111 11111111I 1111111 11 I I I 111.11111111 I1111111I I I I I I I I I 1 1 1 1 1 1 1I l l l l l l l I l l l l l l lI I I I I I I I l l l l l l l lI 1 1 1 1 1 1 1 I I I 1 1 1 1 1I I I I I I I 1 l l l l l l l l' I Ii i i l J J J J l J t t i i i , ,

~ 1 ] 1 1 1 1 1 ' " ' " "I I l l l l lI I i l 1 1 1 1I 1 1 1 1 1 1 1 , , , , , , , ,I I 1 1 1 l l lI1111111I1111111I1111111I1111111, .4JJ.kkkkk

I ~ r X D

m m m l m m m l i

Fig. 5. Finite element division of the joint and load application points.

tO n~n

, i i l j i i [

I I I I I I II I I I 1 1 1i i i i i i. . . . . [ I~ L

. . . . 4-4"t"?", ~ L , l l i ~ -- I ! ~ ! ! I l l l ~- - i 1 . I F I - . ' : x : I i I I Ii q L : : : : [ l l l l~ l l l l

: ~ r . . . . I ' , I I I~ , i i i l

11. : : : t I1 1 ] . . . .

Fig. 6. Defo rmed shape of the join t for 1.6 MPa interface pressure.


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Deformations and Pressure Distribution on Machine Tool Slideways 315Fig. 7(a) and (b). In this example, at low mean interface pressures, the maximum interfacepressure is about 1.5 times the mean interface pressure, but at high mean interface press-ures, the maximum interface pressure is about three times the mean interface pressure.

As the third example, finite element division and position of the loads for a dovetailslideway is represented in Fig. 8. The material is cast iron and surface compliance para-meters are c--0.25 and m--0.70, and the other parameters are the same as in the previousexamples. The length of contacting lines AB and CD is 42.42 mm.The deformed shape of the model is shown for 1.6 MPa mean interface pressure inFig. 9. Fig. 10(a) and (b) show the calculated pressure distribution at contacting surfacesof the dovetail slideway model for five different mean interface pressures. As the pressureincreases, the length of contact decreases. In this example, for low mean interface press-ures, the maximum pressure is about twice the mean interface pressure, but for high meaninterface pressures, it is about four times the mean interface pressure.

e

, - ~ - - o . 8= 5 I _ + _ 1 . I

0 1 0 2 o 3 o 4 o s o s o 7 o . 0 s o lO O 1 1 0 1 2 0 1 ~ 0 1 4 0 1 s o l m 1 7 0C o n t a c t L e n g t h ( m m )

( a )

lO

0 1 0 2 0 3 0 4 0 S O I O "0 I O I1 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 8 0 I MCo n t a c t Le n g t h ( ram )

( b )Fig. 7. Pressure distribution at the contacting surfaces for several interface pressures.

1 7 0


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316 i . Htlseyin Fil iz e t a l .

Fig. 8. Finite elem ent divisio n of the jo int and load application txfints.

Fig . 9 . Defo rmed shape o f the dove ta i l s l ideway mo del for 1 .6 MP a inte rface pressure.4 . D I S C U S S I O N A N D C O N C L U S I O N S

A c c u r a c y o f s h a pe a n d d i m e n s i o n o f t h e w o r k p i e c e , a n d h ig h t e c h n i ca l p e r f o r m a n c ewi th economic e f f ic iency a re the bas ic fac to rs cons ide red in the des ign o f mach ine t oo l s .These a re mos t ly dependent upon s t a t ic and dynamic s t i f fness o f mach ine t oo l s t ruc tu res .M ach ine t oo l s have compl ica t ed s t ruc tu res and the i r ana lys is i s ex t remely d i f f icu l t byana ly t ica l me thods .T h e m o d e l s p r e s e n te d i n th i s s tu d y c o v e r s o m e c o m m o n t y p e s o f j o i n t s u s e d in m a c h i n etoo l s . As seen in F ig . 3 (a ) , t he re i s a lmos t 100% cor re l a t ion wi th the resu l t s g iven byBack [7 ] .S t i f fness and p ressu re d is t r ibu t ion in mach ine t oo l j o in t s can be ca l cu la t ed eas i ly andprec ise ly . Depending upon the de f l ec t ion requ i rement s , modi f ica t ions such as chang ingthe l eng th o f main s l id ing su r faces o r aux i l ia ry s l id ing su r faces , chang ing the l eng th andl o c a ti o n s o f n a r ro w g u i d e w a y s , a n d c h a n g i n g t h e g e o m e t r y o f th e s l i d e w a y s y s t e m s c o u l d


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D e f o r m a t i o ns a nd Pr e s s u r e D i s t r i b u t i o n o n M a c h i ne T o o l S l i de wa y s 31 7

_ o _ _ o , i- _ 3 . 2 I

g

0 7 . 0 7 1 4 . 1 4 2 1 . 2 1 2 8 . 2 8 3 8 . 3 8 4 2 . 4 2C o n t a c t L e n g t h (m m )

( a )

0 7 . 0 7 1 4 . 1 4 2 1 . 2 1 2 8 . 2 8 3 5 . 3 8 4 2 . 4 2C o n t a c t L e n g t h (m m )

( t ) )Fig . 10 . Pressure di s t r ibut ion a t the contac t ing sur faces of the doveta i l model for severa l in te r face pressures .

be done in a very short time. Ease of construction of the models and faster solution timesar e the advantage s o f th i s me thod .Car e fu l c ons i de r at i on must be g i ve n to i nc r e as i ng the me an i n te r fac e pr essur e, be c ausemaximum pressure may reach a value greater than the permiss ible value for the se lectedslideway material.

R E F E R E N C E S[ I ] Z . M . L e v i na , C a l c u l a t i o n o f c o n t a c t de f o r m a t i o ns i n s l i de wa y s , Machines and Tool ing 36 , 8 - 1 7 ( 1 9 6 5 ) .[ 2] Z . M . L e v i na , R e s e a r c h o n t h e s t a t ic s t i f f ne s s o f j o i n t s i n m a c h i ne t o o l s . Proc. 8 th Machine Tool Designand Research Conference, M a n c h e s t e r. M a c m i l la n , p p . 7 3 7 - 7 5 8 ( 1 9 6 7 ).[ 3] D . G . T e nn e r , C o n t a c t s t i f f ne s s o f f r i c t io n s l i de wa y s , Machines and Tool ing 3 9 ( 3 ) , 3 - 6 ( 1 9 6 8 ) .[ 4] V . I . O s t r o v s k i i, T h e i n f l u e nc e o f m a c h i n i ng m e t h o ds o n s l i de wa y c o n t a c t s ti f f ne ss , Machines and Tool ing3 6 , 1 7 - 1 9 ( 1 9 6 5 ) .[ 5 ] R . C o nno l l y , R . E . Sc h o f i e l d a nd R . H . T h o m l e y , T h e a p p r o a c h o f m a c h i ne d s u r f a c e s wi t h p a r t i c u l a rr e f e r e nc e t o t h e i r h a r dne s s . Proc. 8 th In t . Machine Tool Design and Research Conference, M a nc h e s t e r .M a c m i l l a n , p p. 7 5 9 - 7 7 5 ( 1 9 6 7 ) .[ 6 ] R . H . T h o r n l e y , R . C o n no l l y , M . M . B a r a s h a nd F . K o e n i g s b e r g e r , T h e e f f e c t o f s u r f a c e to p o g r a p h y u p o nt h e s t a t i c s t if f ne s s o f m a c h i ne t o o l s j o i n t s , In ternational Journal o f Mac hine Too l Design and Resear ch 5 ,5 7 - 7 4 ( 1 96 5 ) .[ 7 ] N . B a c k , D e f o r m a t i o ns i n m a c h i ne t o o l j o i n t s . Ph . D . t h e s i s , U . M . I .S . T . , 1 9 7 2 .[ 8] M . M a s u k o a nd Y . I t o , D i s tr i b u t i o n o f c o n t a c t p r e s s u re o n m a c h i ne t o o l s l i dc wa y s . Proc. lOth In t . MachineTool Design and Research Conference, M a n c h e s t e r. M a c m i l l a n , p p . 6 4 1 - 6 5 0 ( 1 9 6 9 ) .


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318 1 . Ht lseyin Fi l i z et al.[9] S. Hind uja , Analy s i s of mac hine too l s t ruc tures by f in i te e lem ent method. Ph .D. thes i s , U.M.I .S.T ., 1971.[ I 0 ] Y . Fu r u k a wa a n d N . M o r o nu k i , C o n t a c t de f o r m a t i o n o f a m a c h i ne t o o l s l i de wa y a nd i t s e f f e c t o n m a c h i n i nga c c u r a c y , International Jour nal of Japanese Socie~. of Mechanical E ngineers, 3 0 ( 2 6 3 ) , 8 6 8 - 8 7 4 ( 1 9 8 7 ) .[ l I ] M . H a s h i m o t o , E . M a r u i a nd S . K a t o , E s t i m a t i o n o f c o n t a c t s t if f ne s s a t i n te r f a c e s in m a c h i ne s t ru c t u r e sb y a b e a m m o de l o n a n e l a s t i c f o u nda t i o n , Tribology International 2 7 ( 6 ) , 42 3 - 431 ( 1 9 9 4) .[12] AN SYS User ' s Man ual for Revision 5 .0 ,4 , V o l . I V , Theor)'. Sw anso n Analys i s Sys tem s Inc . , U.S.A. , 1992 .

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1996 Huseyin Slideway Pressure