E L A S T I C P R O P E R T I E S O F O I L E D B E E C H W O O D

Y u . V . G o r b a c h e v a n d V . N. K u z n e t s o v UDC 539.3/5:678

T imber is used extensively in machine construction. However, in the l i te ra ture [1-3, etc.] there is only r a r e mention about the use of t imber for making pol i shers (abrasion ca r r i e r s ) for metal working in o rde r to achieve a high quality finish. In ins t rument design, and especial ly in the manufacture of clocks and watches, beech wood has until now remained an unreplaceable mater ia l for polishing the profi le of gear teeth.* The feature of p rocess ing gear teeth in clock mechanisms is the fact that, together with the high quality of finish on the surface of the profi le of the teeth, high to lerance p rocess ing is an essential r e - quirement .

The p roces s ing of the profi le of gear teeth is based on the use of the elast ic proper t ies of the pol isher . Consequently, in o rde r to ensure p roce s s accuracy it is neces sa ry not only to have information about the "technical elast ic constants" of the pol isher mater ia l , but also to use them proper ly in designing the p rocess . This question is complicated by other technical fea tures involved in the making of the pol i shers . The discs of the pol i shers a r e made f rom a board of a longitudinal sect ion of the trunk of a beech t ree (Fig. 1), which leads to di f ferences in the elastic p roper t i e s a c r o s s the per iphery of the polishing disc. Fur the rmore , the fea tures of the polishing p roce s s for the gear teeth requi re oiling of the t imber used for the polishing discs in o rde r to inc rease its elast ici ty.

The technical p roce s s for the po l i shers is i l lustrated in Fig. 2.

Low-v i scos i tyo i l of the industr ia l -20 type (spindle oil) is used for the t reatment . The t imber of the po l i shers is subjected to a soaking in the oil at a t empera tu re of t = 110-120~ for 5-6 h. This t ime is suf- ficient to completely remove the mois tu re f rom the wood and fill it with oil. The specific gravity of the wood of the beech t ree is stabil ized, and has a value of d = 0.76-0.77 g / c m 3 (Fig. 2a).

"* The gears a re made at the same t ime as the axle.

Fig. 1

Fig. 1.

d, g/cm z i,o:

~g /// -r qc / I /

Po l i she r for teeth process ing .

i ~ . . . . o %5 Fig. 2

///

15 22.5 T, h

Fig. 2. Rate of oil sa turat ion by beech-wood pol isher during impregna- tion and compres s ion of the oil in the polishing cycle with v = 10 m / s e c (I, II, H I - spec imen Nos.).

T rans la t ed f rom P r o b l e m y Prochnos t i , No. 12, pp. 14-16, December , 1971. Original a r t ic le sub-

mit ted F e b r u a r y 1, 1971.

�9 1972 Consultants Bureau, a division o[ Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced [or any purpose whatsoever without permission o[ the publisher. A copy o[ this article is available [rom the publisher [or $15.00.

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D i r e c t i o n o f

Fig. 3. A r r a n g e m e n t of the axes of s y m m e t r y in the wood.

I I I I l l IV V W

Fig. 4. View of spec imens for c o m - p r e s s i v e tes t ing.

During the subsequent cooling of the t i m be r in oil to 20~ the concent ra t ion of oil in the spec imens i n c r e a s e s , which c o r r e s p o n d s to a specif ic g rav i ty of d = 0.89-0.91 g / c m 3 (Fig. 2b). During the working of the po l i she r , that i s , when it is rota t ing, the oil is centr i fuged f r o m the wood, and the p r o c e s s of c o m - p r e s s i n g the oil occu r s rap id ly in the f i r s t 1.5-2 h. Then the content of oil a l t e r s sl ightly (Fig. 2c), so that in p r a c t i c e i t is poss ib l e to cons ider that s tab i l iza t ion o c c u r s with a spec i f ic g rav i ty value of d = 0.85-0.86 g / c m ~. This s ta te in the wood of the po l i she r is the s t a r t ing point for the t r e a t m e n t of the gear teeth p r o - file.

The l i t e r a t u r e on t i m be r p r o c e s s i n g [4-6 etc.] does not contain comple te in format ion on the " technical e las t ic cons tants" for a i r - d r y (10-15% mois tu re ) beech wood, and contains no data a t al l for oiled t i m b e r .

I t is known that t i m be r is an or thot ropic m a t e r i a l in whose s t r u c t u r e the re a r e th ree p lanes of s y m - m e t r y (Fig. 3). These p lanes a r e taken to be the coord ina te p lanes of the or thogonal s y s t e m s of coord ina tes . The axes a r e denoted: ax is I - d i rec t ion of the f ibe r s , ax is H - the t r a n s v e r s e sec t ion of the f ibe r s ( ac ross the rad ius of the trunk), and axis HI - the t r a n s v e r s e d i rec t ion of the f ibe r s (adjacent to the yea r r ings) .

The connect ion between the s t r e s s e s and de fo rmat ions of an or tho t rop ic e las t ic body is de sc r ibed by Hooke ' s law [7].

Between the constants (El, ~ij - the e las t ic i ty moduli and the P o i s s o n ra t ios) used in the Hooke ' s law, the re is a re la t ionsh ip

E~I~ p = E ip.~i, (1)

following f rom the s y m m e t r y of the m a t r i x of the e las t ic cons tan t s .

The shea r modulus Gij for each p lane of s y m m e t r y can be e x p r e s s e d through the e las t ic i ty modulus o 450

~i~ and the P o i s s o n ra t io ~ i j ' obtained in c o m p r e s s i n g the s p e c i m e n s whose axis l ies in one of the p lanes

of s y m m e t r y , and with one of the se lec ted d i rec t ions , (I, II, III) m a k e s an angle of 45 ~ accord ing to the equation

a = (2)

Exper imen ta l ly , dur ing tes t ing for monoaxia l c o m p r e s s i o n , va lues w e r e de t e rmined for El, E2, E3, o 45 ~ _ _ 5 o o o E~ , El3 , E~23 , and also ~12, 4s p4s p45 ~ P21' PI3' P31' D23' ~33' PI2 ' 13 ' 23 "

The values of Gi2, Gi3, and C~3 were calculated from Eq. (2).

EXPERIMENTAL METHOD AND RESULTS

The s p e c i m e n s w e r e pa ra l l e l ep ipeds m e a s u r i n g 30 x 30 x 40 m m which w e r e cut f r o m one beech block. Depending on the d i rec t ion of the f i be r s , s ix types of spec imens w e r e p r e p a r e d (Fig. 4), with eight i t ems in each. Four spec imens of each type w e r e t r ea t ed with oil us ing the cyc le d e s c r i b e d above.

Befo re the c o m p r e s s i o n t e s t s , de te rmina t ions w e r e made of the spec i f ic g rav i ty of d ry and oiled s p e c i m e n s : ddry = 0.63-0.66 g / c m 3 (which c o r r e s p o n d s to 10-15% m o i s t u r e in the wood); doi 1 = 0.85-0.86 g / c m 3 (using the impregna t ion cycle for the po l i she r s ) .

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500 ,.

#00 ~///~! / 300

200 //

0 200 riO0 600 000 e "i0 "s mm

Fig. 5

o, kg/cm 2 , / ~ ~,~11

12L , >, -"

, y / / r V/ . ~ , . - - - - - - ,

200 z/O0 600 000 e �9 i0 "s mm

Fig. 6

Fig. 5. Relationship a - e during compress ion of d ry (d = 0.63-0.66 g / c m a) and oiled (striated lines) beech (d = 0.85-0.86 g / c m 3) in the axial (I), radial (II), and tangential (III) di rect ions of the axis of symmet ry .

Fig. 6. Relationship a - e during compress ion of d ry (d = 0.63-0.66 g / c m 3) and oiled (striated lines) beech (d = 0.85-0.86 g / c m 3) in the di rect ion at an angle of 45 ~ between the axial and tangential (IV), the axial and radial (V), and radial and tangential (VI).

In determining the specific gravi ty the specimens were weighed with an accuracy of up to 0.1 g.

The compr es s ive tes ts of the specimens were done on the SHOPPER machine with a capacity of 10,000 kg. Loading was done by hand (rate of deformation approximately 1 m m / m i n ) in s tages of 100-200 kg. The load was m e a s u r e d on the scale of the machine with an accu racy of up to • 1%.

The m e a s u r e m e n t of the deformat ion on the specimens was done with lever tensometers (s train gages) of the type TR with a m e a s u r e m e n t base of l = 20 =~ 0.05 ram, and a scale division of 1 • 0.1 p.

Tes t s were done at room tempera tu re (about 19~ Using the experimental data obtained we con- s t ruc ted compres s ive force d iag rams for a as the longitudinal deformation e (~ = P / F 0 : ~ = A l / l , where F 0 is the c r o s s - s e c t i o n a l a r ea of the nondeformed specimen).

In o rde r to de termine the e las t ic i ty moduli and P o i s s o n ra t ios we used values charac te r iz ing the l inear sect ions of the d iag rams . F igure 5 shows the relat ionship between the s t r e s s ~ and the deformation

during the compre s s ion of d ry and oiled specimens cut in the di rect ions I, II, and III. The direct ion of the compres s ive forces coincided with the di rect ion of cutting the specimens .

The Po i s s on rat io was calculated through the average values of the t r a n s v e r s e and longitudinal de - format ions .

F igure 6 shows s imi la r re la t ionships for a - e obtained during compres s ion of specimens cut in other d i rec t ions , indicated in the descr ip t ion of the experimental methods. The modulus values and the Po i s son rat io values of the cor responding di rec t ions a r e given in Table 1.

In the exper iments descr ibed he re the spread in the experimental values for d ry wood does not exceed 16%, and for the oiled wood 9%. Accord ing to l i t e ra tu re data [4] the spread in the elast ici ty moduli values for d ry beech wood is about 30% (E 1 = (1.3-1.8). 10 ~ kg/cm2) .

TABLE 1

Elasticity modulus Shear modulus .103 kg/cm2__ .10-s, kg/cm 2 Poisson ratios

Beech wood i E, s E, 11,,

Air-dry (d= 0.63-0.66 kg/cm s) . . . . . . . . . . . .

Oiled (d = 0.85-0.86 kg/cm s) . . . . . . . . . . . .

160 14,4 8,6

III 17,0 11,4

G. GsJ Gs.

10,I 7,2 1,9

12,8 9,5 2,6

0.038

0.054

I

0,43 0,02 0,36

0,35 0,035 0,38

0,38 0,72

0,42 0,62

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Thus, it was found that oiling somewhat reduces the spread in the values of the mechanical propert ies of beech wood.

The experimental data show that oiling reduces the elasticity modulus value in the axial direction, by about 30%, and increases the elasticity moduli values in the radial and tangential directions, respectively by 18% and 33%, that is, there is a certain levelling out in the elastic propert ies of the wood in different directions which is important for the operation of polishers. We note that the deformation curves, for beech wood both dry and oiled, consist of slightly bending curves with a clear linear section.

The results of these experiments allow determinations of the complete system of elastic constants for a i r -dr ied and oiled beech wood.

lo 2.

31 4.

5. 6. 7.

LITERATURE CITED

M. I. Garber, Decorative Grinding and Polishing [in Russian], Mashinostroenie, Moscow (1964). G. M. Lur'e, Methods of Finishing the Components of Abrasive Tools [in Russian], Trudrezervizdat (1958). S. P. Kiselev, Polishing Metals [in Russian], Mashgiz, L e ~ g r a d (1961). N. L. Leont'ev, Elastic Deformation of Timber [in Russian], Goslesbumizdat, Moscow-Leningrad (1952). L. M. Perelygin, Woodworking [in Russian], Goslesbumizdat (1963). B. I. Ugolev, Testing Timber and Timber Materials [in Russian], Lesr~ya Promyshlennost (1965). S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Body [in Russian], GTTI, Moscow (1950).

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