• 论文与研究报告 •

### SPF规格材弹性模量的动态测试及其概率分布

1. 1. 南京林业大学材料科学与工程学院 南京 210037;
2. 南京林业大学机械电子工程学院 南京 210037
• 收稿日期:2014-04-11 修回日期:2014-09-13 出版日期:2015-02-25 发布日期:2015-03-11

### Dynamic Testing and Probability Distribution of Elastic Modulus of SPF Dimension Lumbers

Wang Zheng1, Gu Lingling2, Gao Zizhen1, Liu Bin2

1. 1. College of Materials Science and Engineering, Nanjing Forestry University Nanjing 210037;
2. College of Mechanical and Electronic Engineering, Nanjing Forestry University Nanjing 210037
• Received:2014-04-11 Revised:2014-09-13 Online:2015-02-25 Published:2015-03-11

【目的】 应用频率法精确测量SPF规格材的弹性模量,探讨应用威布尔分布分析其弹性模量数据的可行性。【方法】从南京北美木屋有限公司一批SPF规格材中随机抽取容量为300的样本作为试件,采用弹性绳垂直自由悬挂方式的支承结构对试件实现自由梁,模态试验验证自由梁的精度。在瞬态激励下,通过测试试件一阶弯曲频率,得其弹性模量值;应用应力波法验证频率法测试结果的正确性。对其测试数据采用Weibull分布拟合检验、威布尔分布和正态分布的K-S检验、SPF规格材总体弹性模量在给定值下的概率计算和SPF规格材质量评价的概率分布方法进行研究。【结果】频率法和波速法测得的弹性模量具有较好的相关性;从威布尔分布和正态分布在参数未知时的K-S检验结果可知,SPF规格材弹性模量不服从两参数威布尔分布(Eu=0),但服从于位置参数Eu大于最小测试值一半的三参数威布尔分布和正态分布;从SPF规格材总体弹性模量在给定值下的概率数据分析可得:以3 500,4 000,4 500 MPa为Eu的设定值时,计算的概率值稳定且基本相同,这时Eu设定值分别是弹性模量测试的最小值5 526 MPa的63%,72%和81%,因此推荐采用根据实测数据最小值的60%~80%作为位置参数Eu设定值的三参数威布尔分布进行概率计算;三参数威布尔分布和正态分布计算的SPF规格材弹性模量在给定值下的概率相等;从SPF规格材弹性模量的概率分布曲线和概率密度曲线可知,威布尔概率密度相对于它的均值(9 997 MPa)略显不对称性,弹性模量不超过7 000 MPa时,正态概率分布曲线略高于威布尔概率分布曲线,超过7 000 MPa后,则正好相反。【结论】模态试验验证了文中的试验装置实现了试件自由悬挂的支承条件,提出了频率法的测试方案,保证了一阶弯曲振动固有频率测试精度,可靠地推算出SPF规格材的弹性模量;瞬态激励频率法测试SPF规格材的弹性模量具有简便、快速、重复性好和精度高的优点;频率法和波速法测出的弹性模量具有较好的相关性,验证了频率法测试弹性模量的正确性;SPF规格材总体弹性模量服从三参数的威布尔分布和正态分布, 并不服从于两参数的威布尔分布;正态分布计算的弹性模量不超过7 000 MPa的概率高于威布尔分布的计算值,在其他范围,2种分布计算的概率值是相同的;SPF规格材总体弹性模量的三参数威布尔概率密度曲线相对于均值略显非对称性;在确定威布尔分布参数时,推荐按最小试验数据的60%~80%设定位置参数Eu值;计算SPF规格材总体弹性模量均值、标准离差和弹性模量在给定值下的概率,除弹性模量在低端范围内、正态分布计算的概率高于威布尔分布外, 其他范围计算的概率值相同;应用三参数威布尔分布和正态分布计算SPF二级规格材总体的弹性模量不超过8 000 MPa的概率分别为13.8%和13.6%。

Abstract:

【Objective】 SPF dimension lumber is a principal material for light-frame timber structures. In this paper, modulus of elasticity (MOE) of SPF dimension lumbers was accurately measured by frequency method. The feasibility of the measured data was studied by Weibull distribution. Then, the data was fitted linearly and verified by K-S method. Meanwhile, a series of possible Weibull parameters was obtained by linear fitting of MOE data in Weibull coordinate. 【Method】 We randomly extract SPF dimension lumbers with capacity of 300 from Nanjing Cogent Home Manufactory Ltd. We realize free beam of test samples by supporting structure hung vertically and freely with elastic rope. The accuracy of free beam realization is proved by the result of modal test. Under transient excitation, the elastic modulus value of the samples is obtained by testing their first transverse bending frequency. The correctness of the test results of frequency method is proved by stress wave method. To exactly evaluate the quality of SPF dimensional lumbers, the testing data was deeply studied by using methods such as Weibull distribution, K-S method in normal distribution, calculation of probability data of MOE value under given values and probability distribution method. 【Result】 A good correlation was found between elastic modulus tested with frequency method and that tested with wave-speed method. As can be seen from the K-S testing results of Weibull distribution and normal distribution, the elastic modulus of SPF dimension lumbers is not subjected to two-parameter Weibull distribution (Eu=0), but it is subjected to three-parameter Weibull distribution, in which location parameter Eu is larger than half of the minimum test value. By analyzing the probability data of MOE value under given values for the total SPF dimension lumbers, the calculated probability values are stable and similar when using 3 500, 4 000 and 4 500 MPa as the given value of Eu. In this case, the given values of Eu are 63%, 72% and 81% of the minimum value of elastic modulus (5 526 MPa), respectively. Therefore, it is recommended to use the value that is 60%-80% of the minimum actual data as the given value of location parameter Eu in three-parameter Weibull distribution. Probabilities for elastic modulus of SPF dimension lumbers calculated with given value in three-parameter Weibull distribution and normal distribution are equal. According to the probability distribution curve and density curve, probability density in Weibull is slightly asymmetric to its mean value (9 997 MPa), which is different from probability density curve in normal distribution; Probability curve in normal distribution is a little higher than that in Weibull distribution when elastic modulus is less than 7 000 MPa. However, the results would opposite when the elastic modulus is more than 7 000 MPa. 【Conclusion】 Modal test verifies testing unit in the work and realizes the supporting conditions for free hanging of test lumbers. Test schemes of frequency method are put forward to ensure the testing precision of natural frequency of the first bending mode and reliably calculate elastic modulus of SPF dimension lumbers; Testing elastic modulus of SPF dimension lumbers by instantaneous aroused frequency method has virtues of convenience, fast, repeatability and accurate; A good correlation was found between elastic modulus tested with frequency method and that tested with wave-speed method. Such a correlation verifies correctness of elastic modulus tested with frequency method. Results tested by the K-S test method showed that general elastic modulus of SPF dimension lumbers obeyed three-parameter Weibull distribution and normal distribution, but not obeyed two-parameter Weibull distribution. Probability of elastic modulus calculated in normal distribution, which is less than 7 000 MPa, is higher than that calculated in Weibull distribution. In other scope, however, probabilities calculated in these two distribution ways are identical; Probability density curve for overall elastic modulus of SPF dimension lumbers in three-parameter Weibull distribution is slightly asymmetric; It is recommended to use 60%-80% of the minimum test data as location parameter Eu when the parameters of Weibull distribution is determined. The overall average and standard deviation of MOE values of total SPF dimension lumbers were calculated. The probabilities of MOE values under given values were also calculated. As a result, the calculated probabilities were same, except the fact that probabilities calculated by normal distribution were higher than those calculated by Weibull distribution when the MOE values were within the scope of low end. To evaluate the quality of these SPF dimension lumbers, the methods of three-parameters Weibull distribution and normal distribution were particularly used to calculate the probability that general MOE value was less than 8 000 MPa (the minimum standard value for Canadian No.2 lumbers), and the probability values were 13.8% and 13.6% respectively.