Determination and control of the lumber stressed-strained state in the process of drying Текст научной статьи по специальности «Физика»

Украшський державний лшотехшчний унiверситет

rie з абразиву гранату збшьшувалася в 1,3... 1,5 рази, в той час коли стшмсть аб-разивних крупв з карб1ду кремнмо досягала 3 тис. nor. м. прошшфованоУ повсрхш берези i бшя 2 тис. пог. м повсрхш бука.

Рис. 1. Схема процесу шл1фуванпя

Пояснити такс явище можна тим, що завдяки зниженню температури абра-зивних зерен робочоУ noeepxHi круга значно зменшуеться ймов4ршсть налипания на них зр!заноТ стружки. BUomo, що налипания стружки на р1зальний ¡нструмент викликано наявшстю структур! деревини цукристих та смолянистих речовин. Завдяки змочуванню зерен водою цей процес значно затрудняеться. KpiM цього змо-чеш абразивш зерна мають нижчий коефщкнт тертя до оброблюваного матер1алу, що теж сприяе зниженню температури в зош р1зання та зменшуе швидюсть затупления зерен, що приймають участь в poöoTi.

Проведен! попередш дослщження показали, що запропонований cnociö шгпфування деревини жорсткими абразивними кругами е ефективним i заслуговуе на його б1льш глибоке теоретичне та практичне вивчення.

Л1тература

1.А.И. Яцюк. Ноный способ механической обработки лрсвесины. - Львйв: Вища школа,

1975

2.1.M. Гончар, O.A. Кшко. Передумови сгвореиня Jiinii для чистово! обробки деталей i леревини// Науковий вюник: Зб1рник наукових прань. Льшв: УкрДЛТУ - 1999, вин. 9.13. - С. 304.

YJJK674.815 Dr. J a. Sokolovskyy - USUFWT; Dr. J. Welling'; Dr. B. Pobcrejko

USUFWT; R. Filiniouk — Lycee Technic in Lviv

DETERMINATION AND CONTROL OF THE LUMBER STRESSED-STRAINED STATE IN THE PROCESS OF DRYING

The problem of identification and control of the stress-strain state of wood in the process of drying taking into account its viscoelastic properties in this article is considered.

1 Bundesforschungsanstalt fiir Forst und Holzwirtschaft___

134 Збфннк науково-техшчннх праць

Науковий liicinik, 2001, вип. 11.4

Доц. ЯЛ. Соколовський, к.ф.-м.н. - УкрДЛТУ; доктор Й. Вел'шг'; асист. Б. П. Поберейко, к.т.н. - УкрДЛТ; шж. Р. В. ФШнюк — Техшчний л'щей, Л bet в

Визначення та контроль напружено-дефорьнвного стану пиломатер1ал!в у

Розглядаеться проблема ¡дентифжацп та контролю, лапружено-дефоркнвного стану деревини у nponeci сушшня з врахуванням пружнов'язкопластичних fi властивостей

In this paper the calculating methods of the lumber stressed-strained state in the process of drying are worked out. On its basis the numeric experiment is carried out. This experiment finds out wood rheological behaviour peculiarities in the conditions of heat-mass exchange. The way of non-destructive current control, offered in [8], of the moisture and moisture-residual stresses on the surface and in the mean of the lumber in the process of drying, is substantiated in this paper.

1. The calculating methods of the stressed-strained state include: a) physical and mathematical model showing the interrelation of the moisture and moisture-residual stresses in the wood and its moisture state [4-7]; b) dependence of the local and mean moisture content difference in the material on drying agent paramétrés [6]; с) determining methods of the lumber rheological properties |3, 4|.

1.1. Interrelation of stressed-strained and moisture states of the wood in the process of drying can be described by the system of equations [3, 4, 6]

where i'(r, y) = E(r, y)P(x, y)/fl + yj/if,; y - coordinates of the material boundaries according to its central plane; the initial moisture content; E(t, y), (5(t, y), R(t-t, y) physical and mechanical characteristics of the wood (modulus of elasticity, coefficient of drying, kernel of relaxation), u(r,y), ucep(T) - characteristics of the wood moisture state (function of the moisture content distribution along the plate thickness and mean moisture content); crb(T,y), cr/r.y) a(r,y) - moisture, moisture and residual and full stresses correspondingly.

The ah(r,y) is preconditioned by elastic properties of the wood and after drying process termination, for example at the moment of time r = rK its change in relation to time is constant, i.e./ that is ah(r,y)= =ab(rK,y)=const for r > rK preconditions the decrease of the component at,(t,y). The component o>,./i,y) is characterized by wood viscous properties and its quantity and the character of its change in relation to time depend on the "history" of moisture content change development.

Finishing the analysis of the system (1) it should be noted, that it gives the possibility for calculating (estimation) of the stressed-strained state in lumber in the case, when dynamics of the local and mean moisture contents difference and the kernel of material relaxation R(t-t) are known.

1.2. Dependence of local (u(r,y)) and average (uccp(t)) moisture contents difference according to the data from the studies |6] are as follows: for the period of constant drying rate

npoueci сушшня

o(t. у) = аь(т,у) + оЬз(т, y);

(1)

I exiiujioi ÎH та устаткувапня дереьообробмнх пщпрнгмств

185

yKpaÏHCtKHH .:K'])H;aiiiinii mcoTexrnHHHH yHÎBepcHTeT

u(x,y)-ucep(x) =

Nu

Dpb 2am P0L

îjy 3 lb

cxp

— !785Ai(x) (2J«+ic(T))2

-<p(x)

(2)

for irregular and regular regimes of the period of declining drying rate

u(x,y)-u

cepW = [(ur

-ifiiuuc-unc

+ A,h(Fo - 0,1)cos

{[h(Fo)-h(Fo-0,/)]S(x,y,Bi) exp(-|i;Fo)[ +

-Ï

(3)

cos

IV

+ {2( u.-u where

S(x, y, Bi) = 1 - /,3VfÔ exp

-Bi u

■u.M

'/ + r (u. -O 1

J

Uxp(-ji;Fo)

(/- y/b) 4Fo

2\

1j4fo + /-y/b /, jVfÔ + / - y / b + 2BiFo

Po - relative density of lumber; - coefficient of wood moisture conductivity; Dp -coefficient of wood moisture conductivity referred to pressures difference; u„c, u,,c -moisture contents at the beginning of the irregular regime period of moisture change (on the surface and in the central plane of the plate); uc constant moisture content; P„ c -pressure of saturated vapour; <p(r), tc(z). At (t) — drying agent paramétrés (relative moisture, temperature, psychometrical difference of temperatures); F0 -amr/b2, Bi=ab/am; Nu=0,6(uL/vf}563 - the criteria of Fourier, Bio and Nuselt, correspondingly; u drying agent rate; v- coefficient of drying agent viscosity; 2b - material thickness; L - characteristic linear dimension of material; h(F0) - function of Heaviside. Coefficients ni,At-are determined by the equations, presented in the studies |2|

ctgn, =n,; A, =2sin|i,/(|i, +2sinn, cos|a,)

for 0 < ft, < nj2 .

Formula (3) can be carried out in the case when Bi>iO.

1.3. The methods for determination ofphysical and mechanical characteristics of the wood, worked out in the studies |3,4| are based on the results of reological tests, carried out on the wood patterns to determine their creep nature in different stationary temperature and moisture conditions and interpolation methods of wood manufacturing. These methods give the possibility to determine the kernel of relaxation for lumber which belongs to the equation of the system (1).

Specifically, these methods have determined R(t-t') for pine and fir-tree in tangential direction of deformation

(4)

R(t-t—;-—L--r exd

I J E w,t t (w,t) ^

E(w,t)

TpeJ1(w,t) ET(w,t)

186

36ipniiK iiayKOBO-TcxiiiMHiix npau»»

Науковий вниик, 2GG1, вип. 11.4

yKpai'HCtKHH .:K'])w;aiiiiiiii mcoTexrnHHHH ymBepcHTeT

Analysis of the graphical dependence (fig. 2a) proves, that with the time increase at the irregular regime period the stretching moistures of <ji,(z,y) stress on the surface (y=b) of the material and compressing ones <Jb(^,y) in the central layer (y=0) increase. At the regular regime period (r>0,2b2/amj <Jh(r,b) and t,0) with the growth of r decrease to zero asymptotically. In the dots, which are remote from the surface of lumber at the distance y=b/2 in time range 0,1 b2/am<r<0,2b2/amthere is the change of value sign (am(r,b/2')) happens (curve 3 in the fig. 2a). This change, according to the second equation of the system (1) is preconditioned, obviously, by the change of the sign in the difference of moisture contents u(t, b/2) and ucep(r). This is the proof of that in the process of lumber drying (of lumber) the boundary of distribution of surface stretching and inner compressing stresses moves along the material thickness and in any moment of time rcan be determined by the equation

u(r.y)=ujr). (5)

Such a behaviour of moisture stresses dependence from the beginning of the process of drying in the declining rate period is natural and has physical substantiation. In fact, in the declining rate drying period two processes take place in lumber: hygroscopic moisture evaporation from the subsurface levels and transfer of moisture from the drying material mean to its surface. At the stage of irregular regime the forces of moisture transfer (capillary, osmotic, diffusive, adsorption forces etc.) are not quite powerful and thus they are not able to fulfill minimal work for overcoming potential difference of moisture transfer from central and surface layers of the material |2], This phenomenon we will call potential barrier. That is why in this case the evaporation process of bonded moisture, namely osmotic moisture is mainly observed. The energy of its bondedness is the lowest [2] in comparison with capillary-, adsorption- and chemical-bonded moisture. As the result the surface layers dry and their linear dimensions become decreased (shrinkage phenomenon), and the same phenomenon is happening with inner layers dimensions. It preconditions some increase of stretching moisture stresses in the subsurface layers and compressing moisture stresses in the mean layers at the stage of irregular regime (fig. 2a).

With the increase of drying continuity at the stage of irregular regime moisture content on the lumber surface gradually decreases, the distribution of moisture in central and surface layers increases, and thus, moisture transfer potential dimension increases as well (moisture gradient). However, the forces, preconditioned by the moisture gradient are not able to overcome the potential barrier mentioned above. Simultaneously with the surface drying the amount of lightly bonded moisture in the subsurface layers and evaporation potential decrease. Evaporation potential is the difference between partial pressures of the vapours in the water from the lumber side and drying agent on the surface, which separates them. Thus the evaporation process takes place slowly and the shrinkage phenomena race on the lumber surface in the process of drying decreases. This limits the increase of moisture stress <yh (r,y) at the stage of irregular regime. Actually, according to the figure 2a increasing race ab( r,y) at the range of time 0<r<0,lb2/am declines to zero.

At the stage of regular regime moisture evaporation race from the surface of the material is approximately the same as the race of surface moistening, which is preconditioned by moisture transfer processes in the material volume. That is why it can be con-

188 36ipiiiiK HayKOBO-TexHinuix npailfc

HayKOBHH liicniiK. 2001, Bun. 11.4

sidered that in the case of t>0,lb /am moisture content on the surface of drying lumber is the constant value. In such case, it obviously, that the character of moisture is stresses development in the process of drying will be determined by the moisture flux from the mean of the material to its surface. It will brings about the subsurface layers moistening and drying of the inner layers. Moistening will cause swelling and drying — shrinkage, which is the reason of decrease of the absolute values <Jb(r,y) on the surface and in the mean of the material at the stage of regular regime in the process of drying (fig. 2a).

The comparative analysis of the graphical dependence for moisture <Jb(T,y) (fig. 2a) and moisture-residual <Jb.,(r,y) (fig. 2b) stresses has found out that the character of the change <Tb.3 (r.y), is determined by increase crb(r,y) at the range of time 0<r<0,lb2/am from 1,8 MPa ao 2,7 MPa, moisture-residual stresses ab.3 (r,y) increase from 0,8 MPa to 1,3 MPa, and in the case when r>4 hours both components decrease. Relation of er4_, (r,y) and <ym(r,y) is substantiated by the equations of the system (1). Actually, putting the second equation of the system (1) into the third equation of this system we will get

<v>•>-)=-14 - <■'* -y)>(6>

Or

b-3

(x,y) = -E

JR^t-t .y)°b(c .y}1' U + <*b(T,y)

Hence, as according to the equations of Voltaire-Bolzmann

yh(r,y) + ]^r-r\yyh{r'.yyyenoh(r.y)

then

Jb-3(z'y> = -EEnob(T'y)+ab(T-y>

(7)

(8)

(9)

where £noh(t,y) - deformations of creep in drying lumber, preconditioned by the force of moisture stresses ab(r,y).

Since R(t-t)>0, then according to (8), the character of the development of the creep deformations £noh(T,y) can be determined by value ab(r,y). That means that under the force of stretching stresses <yb(r,y) in drying wood the stretching deformations of creep will develop em>b(t,y), and under the force of compressing stresses <Jb(T,y) - compressing deformations.

Accordingly, surface layers will produce the resistance to compression of inner layers, and inner layers produce thew resistance to stretching the surface layers. Thus, moisture-residual stresses in drying lumber are preconditioned by uneven distribution of creep deformations in its volume.

3. The control of stressed-strained state in drying lumber according to the difference of local and mean moisture contents [8| The essence of this way lies in continual calculating by conductive and metrical method of the difference of local u(T,y) and average u„p(t) moisture contents and the following calculating moisture ab(T,y)\ moisture and residual ab.3(r,y) and full a(x,y) stresses by the formulae (1) and (4). This way of calculating differs from known methods |1,9) (namely, differential shrinkage, according to moisture distribution and average moisture content) first of all because it

Texiiojioriu id ycTaiKyBaHim aepeBoo6pouiinx uLinpiicMcrB 1 89

Украшський державний лшотехшчний унiверситет

allows during drying time to determine: 1) the influence of viscous-elastic characteristics of lumber (£, Er, V an<^ r'r'-y)) on 'ts stressed-strained state; 2) the dynamics of moisture and residual stresses on the surface and inside the lumber.

On the basis of the describe way of control of stresses in this studies the system of automatic conducting the process of lumber drying according to the stresses values in their volume is worked out, and its functional scheme is shown on the fig. 3.

Q(n,0)r

ufry)

iWT)

A/D u(n,0) CPK

г*

Hcp(n,0

A/D

D/A

U[n,0]

eu*)

NC

Цх)

A/D

NC

Ut)

A/D *

«n,0)

Figure 3. The functional scheme of the system of automatically conducting the process of lumber drying: A/D and D/A - analogous-digital, and digital-analogous transformers; CPK -digital conducting mechanism, namely IBM PC; NC - executing mechanism.

References

1.Ecping В., Ilajek 1$. Drying Quality standards - A Statistical and Industrial Evaluation// (Proc.3 thIUFRO Wood Drying Conf.-Rotoma. - 1994. - P. 305-312.

2. Лыков Д.В. Теория сушки. - M.: Энергия, 1968.-471 с.

3. Побсрейко Б.П. Методика визначення парамстрт кривнх мовзучосп деревини// Науко-вий вюннк 36. наук.-техн. пр. - Льв!в: УкрДЛТУ. - 1998, вип. 8.1. -С. 232-237.

4. Соколовськнй Я.1., Побсрейко Ii.II. Визначення напружепь у деревиш в npoiicci су-шшня// Науковий в ¡сник. 36. наук.-техн. пр. -Лы«в: УкрДЛТУ. -1997, вип. 7. - С. 121-126

5. Соколовськнй Я.И., Побсрейко li.Il. Филинюк Р.В. Экспериментальные исследования реологических свойств древесины и древесных композитов. Мат.м1жн.конф."Рокгоку vo vyrobe a pouziti leppidcl v drevopricmysle", Словаччина, 3-5 вересня 1997 p. - С. 85-94.

6. Соколовськнй ЯЛ, Побсрейко Б.П. Досл1дження волопених i залишкових напружень дерсвики у npoueci сушшня// Науковий bichhk. 36. наук.-техн. пр. - Jlbeie: УкрДЛ'ГУ. - 1998, вип. 8.1.-С. 196-207.

7. Sokolovsky Ya.l., Pobcrcjko B.I\, Filinyuk R.V. Technological stresses and strains of wood in the process of drying. XIII konferencija Naukowa Wydziatu Tcchnologii Drcwna SGGN."Drcwno-Matcrial о wyzcchstronnym Ozeznaczeniu i zastosowaniu". Warszawa 16-18 listopada 1999.

8. Соколовский Я.II., Ноберсйко Б.П. Идентификация и способ ко!ггроля напряженно-де^юрмирусмого состояния древесины в процессе сушки. Материалы III Международною симпозиума "Строение, свойства н качество древесины-2000", - Петрозаводск 2000. - С. 284-287.

9. Welling ,1. Pre-normative (CF.N) R+D Activities Related to Drying Quality Specification and Assessment//Proc. 5Л 1UFRO Wood Drying Conf-Quehec City (Canada) - 1996. - P. 309-314.

УДК674: 621.928.93 Проф. СМ. Лютий, д.пин.; доц. П.П. Нахаев,

K.nui. - УкрДЛТУ; A.B. Ляшепик - Коломийський nosiimcxnimtuii коледзк

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190

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