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Секция 7. Технические науки
Utgof Svetlana Sergeevna, Belarusian State Technological University, postgraduate student, the Forestry Engineering and Wood Technology Faculty
E-mail: Utgof.Svetlana@yandex.by Ignatovich Lyudmila Vladimirovna, Belarusian State Technological University, associate professor, the Forestry Engineering and Wood Technology Faculty
E-mail: lignatovich6@gmail.com
Mathematical modeling application to determine the effect of technological factors on physical and mechanical properties of densified low density deciduous wood
Abstract: The article describes the modeling of deciduous wood compaction process, thereby reducing the cost of finding rational technological regimes of wood with improved physical and mechanical properties. The material is based on a statistical analysis of the experimental results on deciduous wood compaction process. The study determined the physical and mechanical characteristics of compacted wood hardness, wear resistance and degree of compaction and these characteristics are obtained depending on technological factors.
Keywords: densified wood, low density deciduous wood, physical and mechanical properties, compaction regimes, mathematical modeling, activation energy of lignin thermal oxidative degradation.
Introduction. Numerous studies show that the most advanced method for predicting the properties of the obtained materials is the mathematical modeling process. The main advantages of this approach are the reduction in the possibility of multiple complex and time-consuming experimental studies and simply varying the values of technological factors. The resulting simulation data on the effect of technological factors on the properties of the densified wood are the basis for the development of the technological process of the densified wood with the desired properties.
Main part. Durability of all wood species can be improved by densification that is by increasing the amount of wood substance per unit volume, if the densification will not be associated with the destruction of the wood cells. Wood of any kind is capable of deformation under the action of forces.
Consequently, the main technological factor in the densification process is the force — pressure. The highest wood pliability for compaction is to be expected at a temperature of 90-100 "C and humidity 25-30% [1].
Wood in this state has the least resistance to pressure, resulting in a significant softening of the filler the densification of wood cellulose skeleton occurs with minimal micro destruction. But wood high humidity complicates the technological process, as requires additional energy for drying the densified wood to exploitation humidity 10 ± 2%, resulting in significant increase in the duration of the process. In the previous studies [2], it was found that the plastification ofwood takes place due to transition more thermostable
lignin state, primary condensation of lignin bonds after softening occurs at a temperature of 90-100 "C. The presence of moisture effect on the lignins softening. Water has a plasticizing effect on the lignin and reduces the softening temperature (up to 80-130 °C). However, this effect is caused by only a small amount of water. Thus, at a moisture content of about 2% natural lignin softening temperature decreases to 115 °C. Further increase of the moisture content does not reduce the softening temperature [3]. Given the above, take moisture content equal exploitation humidity 10 ± 2%.
Wood is a complex component of polymeric nature, the main ofwhich are cellulose (35-50%) and lignin (1835%). The physical properties of cellulose and lignin vary greatly cellulose is characterized by high elasticity and tensile strength, lignin, conversely, brittleness and high resistance to compression. Natural lignin in the wood softens when heated and passes from the glassy state of relaxation into high (and sometimes the viscous). With decreasing temperature, lignin becomes more thermally stable state is to provide dimensional stability of densified wood.
As a criterion for assessing the degree of wood plasticization can take the activation energy of thermal oxidative degradation. The activation energy for thermal oxidative degradation — the excess energy required to break chemical bonds forming the main chain of the polymer, under the influence of heat, oxygen and ambient air.
Thermogravimetric analysis was conducted [2]. TG curves allow us to determine the activation energy of
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Section 7. Technical sciences
thermal oxidative degradation (Ed), which is calculated using the method Broido applied to the pyrolysis of cellulose and based on double logarithms [4, 5]. This calculation method has been improved in [6] and is now widely used to study the dependence of the mechanical properties ofpolymers from their chemical composition and structure.
Parameter Ed increases with partial crosslinking of the polymer macromolecules. Parameter Ed, ceteris paribus, is a measure of the stability of the polymer oxidative degradation. Therefore, the greater the degree of crosslinking, the higher the value of Ed. Calculation Ed based on the mathematical treatment of the TG curve using a sufficiently accurate for polymers of the double logarithm Broido, performed by the formula 1 [5]:
ln(ln
100
100 -Am
—------+ const
R T
(1)
where Am — mass loss of the sample% at each of the temperatures within the range of degradation; R — universal gas constant, equal to 8,31 • 103 kJ/mol • K.
The condition of applicability of the first order is Broido decomposition reaction, which is true for many polymers [4]. Losing weight is a process substance 1st order (n = 1), if the following linear dependence ln100/100 — Am from T, K. Knowing the mass loss (Am) of the sample at temperature T, graphically build the line, which expressed Unit a slope of the logarithmic Am T [5, 6]. Then, the value of activation energy degradation in kJ/mol found by the formula (2):
E = %Ф- R (2)
Processing of the results of the experiment is to perform a mathematical transformation TG weight loss curve (DTG) was performed in Excel. Below is a graph of the logarithmic dependence Am T (Fig. 1).
Fig. 1. Am logarithmic dependence of T for the thermal degradation of Row 1 — densified alder wood; Row 2 — natural alder wood
The activation energy of thermal oxidative degradation of densified wood lignin exceeds the activation energy of natural wood lignin by 12.5%, indicating an increase in stability after processing wood lignin and the appropriateness of the activation energy as a criterion for assessing the degree of densified wood plasticization.
During the analysis of the main factors affecting the process of the wood densification were identified features that reduce the number of major factors studied to three: densification pressure, temperature and time of the densification. Accepts the following values of variables factors: pressure 9.8-19.6 MPa, the temperature of the press platens 70-110 °C and densification time 1-3 min.
To assess changes in the physico-mechanical properties of densified wood accept the following controlled output parameters: the densification degree, hardness and wear resistance of the wood.
Densified wood has better physical and mechanical properties than the original, while in the process of compaction do not apply chemical compositions, and improvement of properties occurs only at high temperatures and pressures.
The purpose of the experimental study was to obtain the dependency of physical and mechanical properties of densified wood on technological factors and the development of regimes produce material with properties equivalent hardwood.
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For testing were selected the most common in the territory of the Republic of Belarus low density deciduous wood: birch (22.6%) and alder (8.4%).
The main types of birch species are medium density. Their average density (at 12% moisture content) — 640 kg/m 3 Birch responds well to bending and other kinds of processing, easily simulate a valuable species. Application for birch construction parts is limited because of its tendency to warp.
Alder refers to low-density species. Average density alder wood at standard moisture (12%) — 525 kg/m 3 Alder wood is soft, light, well-cut, a little warped by drying, has good dimensional stability. For compaction were manufactured samples of 100 x 100 mm and a thickness of 6 mm, the density of samples corresponds to the average indicator. For planning the experiment used Box plan. Planning matrix in natural terms, and the results of the experiment are shown in Table 1
Table 1 - Planning matrix in natural terms, experimental results of compwood
№ regime Matrix experiment in physical terms The experimental results for birch The experimental results for alder wood
P, MPa T, °C t, min Y.,% Y2, MPa Y„ g Y.,% Y2, MPa Y„ g
1. 19,6 110 3 39,8 54,5 0,147 48,9 59,1 0,116
2. 9,8 110 3 31,8 46,8 0,185 43,3 43,6 0,136
3. 19,6 70 3 35,9 45,3 0,163 42,6 52,9 0,157
4. 9,8 70 3 22,5 38,8 0,211 40,1 32,9 0,177
5. 19,6 110 1 34,9 45,9 0,207 45,8 48,8 0,156
6. 9,8 110 1 27,2 40,4 0,222 42,0 38,3 0,166
7. 19,6 70 1 34,6 45,8 0,226 38,1 36,5 0,200
8. 9,8 70 1 20,4 39,6 0,251 36,4 32,5 0,202
9. 19,6 90 2 35,6 45,1 0,175 44,9 59,4 0,155
10. 9,8 90 2 22,8 38,7 0,212 41,2 50,7 0,168
11. 14,7 110 2 30,7 42,7 0,189 44,5 58,7 0,128
12. 14,7 70 2 25,8 39,7 0,211 39,9 52,3 0,173
13. 14,7 90 3 30,0 43,4 0,212 43,8 56,1 0,153
14. 14,7 90 1 26,3 40,8 0,276 40,1 47,6 0,195
The table shows the mean value of parallel experiments. The experimental data were determined according to the regression of the response functions of the dependent and independent factors. The calculations of regression equations of second order natural notation, taking into account the impact of each technological factor on the value of hardness, the densification degree and wear resistanse.
Checking the regression equation using Fisher’s exact test confirmed the adequacy of the data models [7]. The resulting mathematical models allowyou to choose a rational technological regime depending on the requirements made to obtain materials and predict the properties of densified wood with different combinations ofvariables.
In natural notation, the dependencies have the form: The quantity of the birch densification degree:
YN = 20,14 + 0,279 • P - 0,129 -T - 4,759 -t - 0,015 • P -T --0,013 • P-t + 0,038-T-t + 0,077 • P2 + 0,002-T2 + 0,794-t2 The quantity of the alder densification degree:
Y1N = 24,039 -1,019 - P + 0,233-T + 5,093 -t + 0,007 - P-T + +0,066-P-t-0,024-T-t + 0,022-P2 -0,001 -T2 -0,575-t2
The quantity of the birch hardness:
Y2bn = 79,341 -1,508-P - 0,521 -T -15,751 -t + 0,0006-P-T +
+0,0638-P-t + 0,102-T-t + 0,067-P2 + 0,0023-T2 +1,8188-t2
The quantity of the alder hardness:
Y/n = -141,777 + 6,254-P + 2,232-T + 31,728 -t - 0,001 -P-T +
+0,466-P-t - 0,025-T-t - 0,199-P2 - 0,011 -T2 - 7,992 -t2 The quantity of the birch wear resistance:
Y3bn =-0,105 + 0,027 - P + 0,007 - T - 0,116 -t + 0,00003-P-T -
-0,00117-P-t + 0,0000375-T-t - 0,001-P2 - 0,00005-T2 + 0,026-t2
The quantity of the alder wear resistance:
Y3N = 0,113 + 0,00056 - P + 0,00392 - T - 0,0579 -1 - 0,00001 - P-T -
-0,00071-P-t - 0,00001-T-t + 0,00002 -P2 - 0,00003-T2 + 0,013-t2 Based on these models were constructed response surface densification degree, hardness and wear resistance of birch and alder. Figure 2 shows the levels of response surfaces mathematical models of alder and birch wood densification degree, hardness and wear resistance for a fixed value of 19.6 MPa pressure.
Analyzing the surface of the response, it should be noted that in the studied range variable factors, only one receives the optimum value of dependence — the hardness of alder wood compacted technological regime.
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Fig. 2. Dependences of the densification degree; hardness and wear resistance of the densification temperature and time at a fixed pressure value P = 19.6 MPa: a, c, e — alder, b, d, f — birch.
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Function describing the dependence of the hardness compacted alder wood from pressure, time and temperature densification reaches a maximum at values: pressure P = 18.27 MPa, the temperature of the press platens t = 98.1 °C and Packing time T = 2.37 min.
To find the optimum degree of densification and hardness densified birch need to conduct additional research to extending the range variable factors that is impractical, because suggested range of temperatures and pressure densification selected based on energy consumption.
In the case of the degree of densification of the optimal value regime is a mode in which the density of the compacted wood reaches the density ofwood substance 1560 kg/m 3- Aim of this study was to develop a mode of obtaining equivalent material wood solid hardwood (oak, ash) whose density 690-750 kg/m 3, what has been achieved, further densification wood is impractical.
Conclusion. The activation energy of thermal oxidative degradation of densified wood lignin exceeds the activation energy of natural wood lignin by 12.5%, indicating an increase in stability after processing wood lignin and the appropriateness of the activation energy as a criterion for assessing the degree of densified wood plasticization.
Analysis of the results of studies showing that the densification on the wood selected mode leads to a considerable increase in the density of 36.4-48.9% for
alder wood and 22.4-39.8% for birch. Tangential hardness value alder and birch wood is 32.5-59.1 N/mm 2 and 39.6-54.5 N/mm 2 respectively.
Hardness of densified birch and alder wood for some modes reaches and exceeds the hardness of oak wood 12.6-18.6%. Relatively initial hardness value after densification has improved hardness at maximum 92-99%. As for the alder wood and birch wood durability improved by 2 times.
Analyzing the regression dependences can be seen that by increasing the values of all variable factors den-sification wood increases, therefore, improved hardness and wear resistance.
Obtained mathematical model can be used to predict the properties of the resulting densified wood and development of rational modes of densification low density deciduous wood with the desired characteristics.
These results indicate that a greater degree of densification enhances the properties ofwood alder, birch than because birch initially has a higher density than alder and accordingly less prone to densification. Thus, for the production of multilayer articles as parquet surface layer is expedient to use compacted wood soft hardwood as during densification improves the hardness and durability of the wood. The results are a basis for the development of rational modes of densification softwood hardwood parquet flooring multilayer technology with facial layer of densified wood.
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