Mathematical modeling to predict drying deformation and stress due to the differential shrinkage within a tree disk

Although many mathematical models for wood drying have been developed to predict the drying behavior of lumber, there were limited results on drying models dealing with tree disks. This study attempted to try to develop mathematical models to predict the drying stresses and crack formation in a tree disk assumed as a cylindrically orthotropic material with radial variations of properties. The results showed that the drying stress changes nonlinearly with decreasing moisture content (MC) due to mechano-sorptive effects. The higher the orthotropic properties of tree disks are, the larger the drying stress occurs. The developed mathematical model showed that the pattern of cracks such as V-crack or heart check significantly depended on the MC distribution along the radial direction. The model also indicated that a dominant factor controlling the drying behavior of tree disk was the differences in MC between heartwood and sapwood within a tree disk of a given species without any chemical or mechanical treatments. Received 8 September 2000 The authors wish to thank Prof. H.S. Jung, Seoul National University, Korea, for his valuable advice. This work was supported by the grant of Post-Doc. Program, Chonbuk National University in Korea (2000).     

Cooling and steam conditioning after high-temperature drying of Pinus radiata board: experimental investigation and mathematical modelling

 Steam conditioning of softwood boards after kiln drying is of critical importance for relief of residual drying stresses and to improve distribution of final moisture content. The conditioning practice in New Zealand includes two steps: immediately after high temperature (HT) drying the load is cooled until the core wood temperature is 75 to 90°C, and then the stack is steam conditioned for a period of 1 to 4 hours depending on the lumber thickness and moisture content after drying. In this work, experimental and theoretical studies were performed to better understand the conditioning process and to investigate factors which influence its effectiveness. In the experiment, 50 mm thick Pinus radiata sapwood boards were first dried at 120/70°C for 11, 12, 13, 16 and 18 hours, respectively, to varying moisture contents, and then cooled and steam conditioned for 1 hour. To assess the effectiveness of conditioning, moisture pick-up, moisture gradient, and transverse residual drying stress (indicated by cup and strain) were measured. It was found that drying wood to a low moisture content (below 6%) increased the conditioning effectiveness. A separate matched stack was conditioned for 4 hours after 13 hours drying which showed better results than 1 hour conditioning. A mathematical model for wood drying was extended to include both the cooling and conditioning phases. The model was numerically solved to examine the wood temperature and moisture content changes during the whole process of drying, cooling and final steam conditioning. Increase in wood temperature, moisture pickup and moisture gradient during steam conditioning were predicted and validated by the experimental data. This information is currently being used at the New Zealand Forest Research Institute in simulation of stress development and relief for drying of Pinus radiata lumber. Received 6 July 1998     

Moisture content target optimization in lumber drying

Abstract

A Lumber Quality Model developed to predict lumber grade after drying was applied and validated in industry. The model was calibrated with a 198-piece lumber package that was dried at a local sawmill in British Columbia, Canada, and 30 sawmill grade reports were recorded from 2008 to 2010. The calibrated model was then used to predict the target moisture content that would result in the maximum lumber value. It was predicted that lumber value should increase by approximately 17 CAD (Canadian dollars) m^?3 if the target moisture content were reduced from the historic 17% to an optimum of approximate 13%. The sawmill implemented the recommendations and the predictions were validated with another seven industrial drying runs.     

Analysis of moisture diffusivity of larch timber during convective drying condition by using Crank＇s method and Dincer＇s method

Two analytical procedures （Crank＇s method and Dincer＇s method） for porous solid materials were reevaluated and used to determine moisture diffusion coefficients and moisture transfer coefficients for larch lumber subjected to drying. A diffusion-like equation was used to describe drying process data. The lumber was idealized in the modeling as infinite plates. The moisture transport process inside the board was assumed to be one-dimensional. The macroscopic drying kinetics curves of larch timber at particular conditions were determined experimentally. Based on these data, calculation for both the moisture diffusion coefficients and moisture transfer coefficients by the Dincer＇s analytical procedure were made. The dynamic moisture diffusion coefficients by the traditional Crank＇s method were calculated. In general, diffusion coefficients calculated by the Dincer＇s method were all higher than those by Crank＇s method. These results could be due to the differences between two analytical methods and also different characteristics between solid moisture diffusion process and heat transfer process. Therefore the analysis and solution procedures of moisture diffusion differential equations need to be adapted in the future. With drying temperature＇s increasing moisture diffusion coefficient （D） and moisture transfer coefficient （k） increases accordingly. Also the relationships between diffusion coefficients and temperature as well as material moisture contents were analyzed by using Arrhenius equation and bound water transport theory.     

赤桉半干材的窑干与调湿处理工艺

针对移行材和早材皱缩等主要气干缺陷,拟定出赤桉半干材的干燥工艺,窑干前进行回复皱缩和减小表面硬化的汽蒸处理,窑干至目标含水率时进行终了调湿处理.结果表明:汽蒸预处理可以有效地回复皱缩材和显著地减小表面硬化;5 d内将试材的平均含水率25.61%下降到11.72%;3 h的汽蒸处理和24 h的湿空气处理均可有效地减小含水率梯度和残余塑性变定,但后者效果更佳;板材干燥质量达到国家标准二级质量的要求.     

人面子木材干燥特性及干燥工艺初探

采用百度试验法研究人面子木材的干燥特性,根据百度试验结果和企业的实际情况,拟定了相对偏软的24 mm和50 mm 2种厚度规格家具用材干燥工艺基准,进行了生产试验。24 mm厚人面子木材从初含水率85%干燥至12%,共用时506h,干燥质量良好,达到预期要求。针对50 mm厚毛边板材干燥速度慢,干燥不均匀,同一块板材内局部区域含水率异常偏高的现象,拟定了气干/窑干联合干燥工艺和相应的半波动窑干基准。     

小径级柞木干燥工艺的试验研究

小径级柞木干燥试验结果表明:在干燥初期干球温度为35℃、干燥末期干球温度为70℃、干燥周期中进行两次中间处理和末期终了处理、干燥周期为15 d的工艺条件下,板材干燥前总平均含水率41.6%,干燥结束后总平均含水率11.7%,板材厚度上含水率偏差<3%;干燥结束后伸长应力和压缩应力甚微,板材表面的颜色轻微变暗,除髓心材和水纹材有少数裂纹和轻微变形外,其余木材并没有发生翘曲、变形、开裂等干燥缺陷,干燥质量满足了GB6491—86《国家锯材干燥质量标准》二级以上的指标要求。本次试验确定的干燥工艺满足了小径级柞木板材的干燥工艺要求。     

The temperature and moisture content in lumber during preheating and drying

Summary The time required to thoroughly preheat/presteam green 8/4 (51 mm) thick red pine and white birch lumber was determined. Thermocouples imbedded in the centre of samples were used to determine presteaming/preheating times for experimental material. These data were then compared to time determined by analytical methods (using formulae developed by Kollmann). No significant differences were found.During the subsequent drying period data were collected on interior wood temperature, mousture content and gradient. Results of the drying tests indicated: i) interior temperature increases in direct relation to elapsed time, ii) moisture content drops exponentially with elapsed time, and iii) an exponential relationship exists between average moisture content and the core temperature of the lumber.Results indicate that monitoring of the lumber drying process through measurements of interior wood temperature may be feasible.The first author was visiting Canada under the Chinese Scholar Program established by the Council of Ministers of Education, Canada. His research work was carried out at Forintek Canada Corp., Eastern Laboratory, OttawaThe authors would like to acknowledge the assistance and support of the following: Dr. M. Y. Cech, Manager, Lumber Manufacturing Technology, Forintek Canada Corp., Eastern Forest Products Laboratory-Senior Project Supervisor, and Mr. F. Pfaff, Research Scientist, Forintek Canada Corp     

Lumber Quality Model: The theory

Abstract

A new model for predicting moisture content, distortion and shrinkage distribution after lumber drying has been designed, implemented and tested. The model was implemented using Monte Carlo simulation, and it involves three empirical equations that were developed on the basis of experimental data. The model is referred as the Lumber Quality Model, and it is designed to be calibrated by knowing the initial and final moisture content, distortion and shrinkage distribution for a reference drying run. After calibration, the model can be used to predict the same information for other hypothetical drying scenarios. The present study explains the theoretical aspects of the model and the methodology for implementation. The model was validated with experimental data measured in a laboratory kiln. A full-scale industrial validation will be reported in a future paper.     

Modelling and simulation of deformation behaviour during drying using a concept of linear difference method

This study deals with the development of a two-dimensional model to simulate the deformations in wood samples during the wood drying process for the evaluation of the drying quality. The samples cut from sapwood of beech were used to analyse the moisture content distribution of the samples at two different drying conditions. A new concept based on a linear difference method was developed to use the moisture content distribution of the samples for the simulation process to predict deformation due to casehardening. The real deformations of the prongs were compared with the simulated ones for further improvements. The results show that the model can be used to simulate the deformations independently from different drying times and drying conditions. A good comparison between real and simulated changes in deformation was found for the drying process at constant climate conditions. The results provide a useful basis for further investigations on the modelling and simulation of the deformation of the samples due to different drying processes.     

小型除湿干燥机干燥乐器用材的实践

本研究使用小型除湿干燥机对提琴用材进行了干燥工艺生产性试验。结果表明，干燥过程中试材未产生内裂和表裂；干燥后板材的含水率在材堆内分布均匀，在板材厚度方向分布有一定差异，平衡后可以使用；干燥成本在100元/m^3左右；干燥后的木材质量符合乐器制作的要求。本试验确定的干燥工艺可适用楔形不规则乐器用材，还可进行不同规格乐器用材的混合干燥。     

Method to estimate the internal stresses due to moisture in wood using transmission properties of microwaves

The purpose of this paper is to offer a new method for detecting stress in wood due to moisture along the lines of a theory reported previously. According to the theory, the stress in wood could be estimated from the moisture content of the wood and the power voltage of a microwave moisture meter (i.e., attenuation of the projected microwave). This seems to suggest a possibility of utilizing microwaves in the field of stress detection. To develop such an idea, the stress formulas were initially modified to the form of an uni-variable function of power voltage, and the application method of the formulas to detection was tried. Finally, these results were applied to the data of sugi (Cryptomeria japonica) lumber in the previous experiment. The estimated strains showed fairly good agreement with those observed. It could be concluded from this study that the proposed method might be available for detecting stress in wood due to moisture.Part of this report was presented at the 52nd Annual Meeting of the Japan Wood Research Society, Gifu, April 2002     

高温水供热干燥速生杉木方材

运用高温水供热系统干燥速生杉木方材。生产性试验表明，6天内初含水率为55．5％的杉木方材干至始含水率5．4％，干燥质量符合细木工板生产的要求（少数高含水率木材除外）。此干燥法集中供热，具有热效率高、运行安全和经济可行等特点。     

Determination of diffusion coefficients for sub-alpine fir

Estimates of the drying rate for sub-alpine fir lumber and the effect of process variables on final moisture contents are valuable information for kiln operators. The diffusion approach offers one generalized way to estimate the drying time required and the final moisture content distribution. The diffusion coefficients of normal wood and wet wood of sub-alpine fir lumber were determined by two types of approaches in this study: the traditional method and the inverse moisture diffusion algorithm. The results from both approaches indicate that the diffusion coefficient of normal wood is greater than that of wet wood for sub-alpine fir.     

杉木人工林木材的高频真空干燥工艺

对人工林杉木25mm和50mm厚板材进行了系列高频真空干燥试验.结果表明:干燥后的板材变形小,表面平整,表芯层含水率差异较小.尽管试板的初始含水率差异较大,但根据高频真空干燥靠近正极板的木材比靠近负极板的干燥速度快的特点,试板的初始含水率由低至高在负极板至正极板之间进行顺序摆放码垛,干燥后的板材含水率可达到均匀一致.     

辐射松与杉木在高温干燥中萜烯类释放浓度研究

以40 mm厚的辐射松(Pinus radiata)和人工林杉木(Cunninghamia lanceolat)锯材为对象,研究高温干燥过程中干燥温度和锯材含水率对萜烯类产物释放浓度的影响,并与辐射松常规干燥中的萜烯类释放浓度作比较。高温和常规干燥过程中采抽气样次数均为5次,抽气速度为1.0 L/min,采样时间为30 min,采用Tenax管收集干燥过程中萜烯类产物,用气相色谱仪分析其成分及浓度。结果表明:高温干燥辐射松萜烯类释放浓度高于常规干燥辐射松与高温干燥人工林杉木,但萜烯类挥发物的组分有所差别。常规干燥辐射松锯材萜烯类释放浓度对环境是安全的,然而在高温干燥过程中,尤其在干燥中后期,当萜烯类挥发物浓度大于1.5 mg/m3时,对辐射松和人工林杉木释放萜烯类挥发物应采取回收措施,以确保对环境的安全。     

杨木太阳能干燥工艺特性

应用一种带有石蜡储热的新型太阳能干燥室干燥杨木,分析该干燥室的温、湿度变化对木材内外温度差和木材干燥速率的影响,并检测了杨木木材的干燥质量,结果表明:太阳能干燥室的温、湿度呈周期性变化规律,在一个温度变化周期内,干燥速度亦呈周期性.建议在升温段控制干燥速度,在降温段加快干燥速度.     

铁线子地板坯料的干燥工艺

采用百度试验法,进行铁线子木材干燥特性和干燥工艺的试验。结果表明,铁线子木材初期开裂较严重,为5级,内裂为2级,截面变形为3级;干燥速度较慢,为4级。按照试验拟定的干燥基准,进行22 mm厚铁线子地板坯料干燥试验。从初含水率30.7%到终含水率12.3%,干燥周期为28 d,干燥质量满足实木地板的加工要求。     

木材干燥导水系数和换水系数的研究

木材(板、方材)的导水系数和换水系数是反映木材干燥或存放过程中水分迁移的重要物性参数。然而,我国对木材导水系数和换水系数的研究和测定工作十分有限。木材干燥有关的理论计算中,常用原苏联的数据。由于这些数据本身可能存在的误差及用于我国树种的可靠程度难以估计,故使理论结果的实际运用受到限制。本文采用等厚试件系数分离法研究和测定了木材干燥过程动态导水系数和换水系数。     

金檀干燥工艺的研究

文章采用百度试验法对金檀木材进行干燥特性研究,提出金檀家具用料板材的干燥基准,并进行了工艺试验研究。结果表明,金檀木材初期开裂为5级;内裂为2级;截面变形为3级,干燥速度为4级。初期开裂较严重,干燥速度慢,故金檀为难干燥木材。采用给出的干燥工艺,42 mm厚铁线子地板坯料从初含水率30.66%干燥到12.8%的干燥周期为43d,干燥质量满足家具用料的加工要求。