Abstract
Non-destructive evaluation methods for timber stiffness are gaining increased interest as an alternative to static testing since they can be fast, cost-effective, and transportable, as well as non-destructive. The objective of this study was to evaluate the accuracy and limitations of a newly developed smartphone application (SMART THUMPER™) for the non-destructive evaluation of timber stiffness properties. The study determined the effect of the length, density (species), and cross-section sizes of the timber samples on the stiffness results. The results were compared to beam identification by non-destructive grading (BING©), an existing commercial non-destructive testing technology for evaluating the mechanical quality of wood and other materials. It was found that the application can be used to reliably estimate the stiffness of various timber products with a resonance frequency value below 2000 Hz. Frequencies greater than 2000 Hz were found to induce errors due to the smartphone microphone, which is engineered to acquire a lower frequency range. A reliability matrix providing an indication of the accuracy of SMART THUMPER™ estimation was presented, which may also prove useful in selecting appropriate sample lengths prior to testing. The sample length or dimensions can be manipulated to lower the frequency, and hence, to improve the results.
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Assessment of the Application of a SMART THUMPER™ as a Low-cost and Portable Device Used for Stiffness Estimation of Timber Products
Chandan Kumar,a,* Adam Redman,b William Leggate,a Robert L. McGavin, a and Tony Dakin a
Non-destructive evaluation methods for timber stiffness are gaining increased interest as an alternative to static testing since they can be fast, cost-effective, and transportable, as well as non-destructive. The objective of this study was to evaluate the accuracy and limitations of a newly developed smartphone application (SMART THUMPER™) for the non-destructive evaluation of timber stiffness properties. The study determined the effect of the length, density (species), and cross-section sizes of the timber samples on the stiffness results. The results were compared to beam identification by non-destructive grading (BING©), an existing commercial non-destructive testing technology for evaluating the mechanical quality of wood and other materials. It was found that the application can be used to reliably estimate the stiffness of various timber products with a resonance frequency value below 2000 Hz. Frequencies greater than 2000 Hz were found to induce errors due to the smartphone microphone, which is engineered to acquire a lower frequency range. A reliability matrix providing an indication of the accuracy of SMART THUMPER™ estimation was presented, which may also prove useful in selecting appropriate sample lengths prior to testing. The sample length or dimensions can be manipulated to lower the frequency, and hence, to improve the results.
Keywords: Non-destructive evaluation; Dynamic MOE; Timber products; Acoustic measurement; Stiffness estimation
Contact information: a: Queensland Department of Agriculture and Fisheries, Horticulture and Forestry Science, Salisbury Research Facility, 50 Evans Rd, Salisbury Qld 4107 Australia; b: Burapha Agro-Forestry Co. Ltd. 23 Singha Rd. Ban Phonexay, Saysettha District P.O. Box 11834 Vientiane 01000 Lao PDR; *Corresponding author: chandan.kumar@daf.qld.gov.au or c.kumar.me@gmail.com
INTRODUCTION
The modulus of elasticity (MOE), i.e., stiffness, is one of the most important mechanical properties of wood. Along with governing its serviceability performance when used in a structure, the MOE is also a key parameter in determining the structural grade of timber (Kumar et al. 2021). Whilst minimum strength properties are also required for different grades of timber, these are typically accounted for during processing through established correlations with MOE for the species in question, or through visual identification and exclusion for large, discrete defects. The market value of a structural sawn board is directly linked to its structural grade.
The standard test method to determine the MOE of timber in Australia is the static bending test, according to AS/NZS standard 4063.1 (2010). Predicting the MOE of timber has become a crucial issue in the operational value chain and received considerable attention in recent years in terms of grading and presorting (Brashaw et al. 2009; Aro et al. 2016; Nistal França et al. 2019). However, non-destructive techniques (NDT) to characterise wood and other materials are gaining popularity due to being non-destructive, comparatively faster, and not necessarily confined to a laboratory (Faircloth et al. 2021). Assessment of mechnical properties using vibration and other NDTs have a long history in the wood products industry (Hearmon 1946, 1958; James 1961; Falk et al. 1990; Halabe et al. 1997). Ross et al. (1998) described a wide range of non-destructive assessment technologies and their use for evaluating various wood products. Of the available technologies, ultrasound, transverse vibration, longitudinal vibration, X-ray, and stress wave have been well investigated and have been adopted by industries in various scales (Simpson and Wang 2001; Yang et al. 2002; Brashaw et al. 2009; Nistal França et al. 2019). Some other methods involve radiography, impulse excitation technique, electromagnetic testing, near infrared, and magnetic resonance (Baillères et al. 2009). Schimleck et al. (2002) calibrated near-infrared (NIR) to characterise a number of physical properties including density, MOE, micro fibril angle, and modulus of rupture (MOR) on small clear samples of Eucalyptus delegatensis and Pinus radiata. The MOE and density are the main parameters that describe the wave propagation in materials. Therefore, the MOE can be calculated by using the stress wave velocity measurement (Steiger 1996; Bucur 2003; Baillères et al. 2009). Some commercial NTD methods such as Hitman ST300 (Fibre-gen, Christchurch, New Zealand), Metriguard 7200 High Capacity Lumber Tester (HCLT, Metriguard Inc., Pullman, WA), E-computer Model 340 (Metriguard Inc.), portable Timber Grader MTG (Brookhuis Micro-Electronics), portable Lumber Grader PLG (Fakopp, Sopron, Hungary), and STIG grading machine (Slovenia) are already available for measuring mechanical properties of timber (Baltrušaitis et al. 2009; Baillères et al. 2012; Paradis et al. 2013; Yang et al. 2015; Fortuna et al. 2018; Llana et al. 2020). However, the most convenient method for measuring MOE non-destructively with high precision is the vibration method by measuring natural frequencies in different modes (longitudinal, flexion, or torsional) and the geometry and boundary conditions (Brancheriau and Baillères 2002; Arriaga et al. 2014).
Beam identification by non-destructive grading (BING©) is one such commercial, non-destructive testing technology developed by the agricultural research for development, France (CIRAD) for evaluating the mechanical quality of wood and other materials (Paradis et al. 2017). In addition, BING© allows for the determination of bending (transverse) and compression (longitudinal) MOE of a timber beam via analysis of the natural vibration spectrum. This technique is also known as the resonance method, as it allows the determination of the resonance frequencies of a beam from its response to an impact (Baillères et al. 2009). Furthermore, BING© can provide a good estimation (R2 = 0.91) of the mechanical properties of a timber when compared with the standard static bending test (Baillères et al. 2019). However, the BING© system requires relatively expensive and complicated hardware and software, and a computer, thus limiting is portability.
A newly developed smartphone application called SMART THUMPER™ aims to provide a low-cost and effective alternative for the dynamic measurement of the stiffness of timber. The application was developed by Mississippi State University’s Department of Sustainable Bioproducts (Timberbiz 2019). Since it is a smartphone application, this approach has the potential to be an easy-to-use, low-cost, and portable means of obtaining indicative stiffness properties of timber, which will make it readily available to a wider community (Timberbiz 2019).
The SMART THUMPER™ application uses a well-established and published relationship to calculate the MOE in the longitudinal direction from natural frequencies of soundwave, density, and dimension of the sample expressed as Eq. 1,
(1)
where ρ is the density (kg/m3), L is the length (m), fL,n is the nth longitudinal mode frequency, and n refers to the mode number (1, 2, 3, etc.). The application uses the first mode, i.e., n = 1. The application calculates density based on the mass and dimension input by user.
However, the feasibility, accuracy, and limitations of the SMART THUMPER™ application in terms of measuring the indicative stiffness of timber needs to be identified and understood for different timber species and sample conditions to support wider adoption. The objective of this study was to conduct a detailed analysis of the accuracy and limitations of the SMART THUMPER™ application, which included the effects of the sample length, density (species), and cross-section size on the results.
EXPERIMENTAL
The experimental plan is summarized in Table 1. Prior to testing, all samples were stored in a conditioning chamber set to a temperature of 20 °C and a relative humidity of 65% until the equilibrium moisture content was reached. The samples were then tested using the SMART THUMPER™ and the BING© system, respectively. The test results were compared using the data analysis method described below. The stiffness results estimated for the same samples of wood using BING© were adopted as a baseline. The Pearson correlations and coefficients of variation (COV) between the stiffness values estimated via BING© and SMART THUMPER™ systems were presented for various species (density), board lengths, and cross-section sizes of the tested timber samples.
Trials 1 to 6 were conducted using 4 different short length sawn timber boards (4 hardwoods and 1 softwood), and a section of softwood plywood representing an engineered wood product (EWP), to investigate the effect of density (species) and sample length. The hardwoods assessed were mature native forest spotted gum (Corymbia citriodora), blackbutt (Eucalyptus pilularis Sm), jarrah (Eucalyptus marginata D. Don ex Sm.), and messmate (Eucalyptus obliqua L’Herit.). The softwood was a southern pine, which is the dominant plantation softwood growing in Queensland, which is typically Pinus elliottii (PEE), Pinus caribaea (PCH), or a hybrid between these two species (PEE) X (PCH). All samples in trial 1 to 6 were cut to a length of 1.2 m, machined to a cross-section as specified in Table 1, and numbered for identification. The MOE estimations were collected at a length of 1.2 m, with the samples then iteratively docked to 1.1 m, 1.0 m, and 0.8 m, and tested at each decrement.
Trial 7 further investigated the sensitivity of the stiffness results for long length boards. Five softwood boards were used, and the lengths were progressively reduced (4.8 m, 4.5 m, 4.2 m, 3.7 m, 3.2 m, 2.7 m, 2.2 m, 1.7 m, and 1.2 m) and the MOE was estimated at each length decrement. Similar tests were completed on 5 hardwood boards for 5 different lengths (4.8 m, 4.2 m, 3.2 m, 2.2 m, 1.2 m).
Trial 8 was similar to Trial 7, i.e., longer softwood pine; however, it included 5 long length sawn hardwood (spotted gum) boards tested at various lengths (4.8 m, 4.2 m, 3.2 m, 2.2 m, and 1.2 m).
Table 1. Experimental Plan and Sample Description
Trial 9 investigated the applicability of the application on veneer. Forty southern pine rotary veneer samples measuring 3 mm thick by 100 mm wide and 1 m long were tested.
Trial 10 investigated the effect of different cross-section sizes. Southern pine sawn boards of a constant length (1.2 m) and reducing cross-section sizes (88 mm x 35 mm, 88 mm x 30 mm, 80 mm x 30 mm, 80 mm x 25 mm, and 80 mm x 20 mm) were tested.
BING© Testing
The BING© system consists of a microphone, an acquisition card (Pico Technology), two elastic supports, and a hand-held hammer (Fig. 1). The dimensions and mass of the samples were measured with digital callipers and a weight scale, respectively. The sample was placed on the two elastic supports to ensure free vibration, before an impulse was generated by hitting one end of the sample with the hammer, and the acoustic sensor (Sennheiser K6) recorded the induced vibrations at the other end. The BING© software allowed the automatic detection of resonance frequencies and the computation of the results. The samples were tested using the compression (longitudinal) mode.
Fig. 1. The BING© test configuration for measuring the stiffness of a timber board
SMART THUMPER™ Testing
As the SMART THUMPER™ uses the same principles as BING©, the test configuration was similar (Fig. 2).
Fig. 2. Test configuration for the SMART THUMPER™ application
The specimen was placed on two elastic bands, equidistance apart, and hit with a small hammer on one end. A smartphone (iPhone 5s) with the SMART THUMPER™ application was placed with its microphone directed toward the opposite end of the sample. The specimen number, species, dimensions, and weight of the sample were entered into the SMART THUMPER™ application. Once struck by the hammer, the MOE and resonance frequency of the sample were calculated and displayed by the application. The testing was performed using the soundwave test (longitudinal) option on the app.
Data Analysis Method
The correlation matrices between the MOE values collected from the SMART THUMPER™ application and the BING© system were calculated using R-studio (R-Studio, Boston, MA), an integrated development environment for R. The correlation matrices were developed using the ‘psych’ package in R-studio (Cran.R-project 2019). The correlation matrices showed the bivariate scatter plots below the diagonal, histograms on the diagonal, and the Pearson correlation above the diagonal.
Coefficient of variations (COV)
The coefficient of variation (COV), or relative standard deviation (RSD), is a dispersion of data points in a data series around the mean. It is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another. In this study, the COVs were calculated between the MOE of the same specimens for various lengths or cross-sections measured via BING© and SMART THUMPER™ systems. The coefficient of variations (COVs) were calculated by the ratio of the standard deviation to the mean using an Excel spreadsheet (version 2016, Microsoft, Redmond, WA).
Linear regression
The linear regression analyses were conducted between the variables obtained from BING© and SMART THUMPER™ using Microsoft Excel. The regression analyses were evaluated by their coefficient of determination, i.e., R2, and slope of the regression line.
RESULTS AND DISCUSSION
Effect of Density
The effect of density on MOE estimated by the SMARTTHUMPER™ app was investigated on the 1.2 m length of 4 hardwoods and 1 softwood samples (test 1 to 5) as shown in Table 1. The density of these samples varies between 539 kg/m3 to 1242 kg/m3.
Figure 3 shows a strong positive correlation (R2=0.97) between BING© and SMART THUMPER™ MOEs, indicating that the SMART THUMPER™ application can estimate the MOE of timber with various densities. The application measures frequency and then calculates the MOE from the frequency and density according to Eq. 1. The density in the app is calculated from the input data of mass and dimension input data provided by users. Therefore, the density was not expected to affect the final MOE estimation by the applications if the frequency measurement was correct. More detail of frequency measurement by the app at various timber densities is discussed in the next section.
Fig. 3. Correlation between the BING© and SMART THUMPER™ MOEs of timber with various densities
Effect of Board Length
This section discusses the effect of length on MOE estimation by the SMART THUMPER™ as described in Table 1. The investigations included hardwood, softwood and plywood of various shorter lengths (0.8 m to 1.2 m) and longer lengths hardwoods and softwoods.
Fig. 4. Correlation matrix between the BING© and SMART THUMPER™ MOEs in MPa showing the Pearson correlation, histogram, and scatterplot with linear model for sawn blackbutt timber
Figure 4 shows the scatter plots below the diagonal along with the linear fit line, the histograms on the diagonal, and the Pearson correlation above the diagonal between the MOE estimated via BING© and the SMART THUMPER™ app at different lengths for sawn blackbutt timber. Overall, a strong correlation exists among the BING© results (r = 0.98 to 1.00), between the BING© vs the SMART THUMPER™ results (r = 0.96 to 0.98), and among the SMART THUMPER™ results (r = 0.94 to 0.96) for the various lengths tested. The scatter plots and linear regression line below the histograms show positive correlations without outliers.
The mean COVs for the 30 sawn blackbutt samples were 1.03% and 3.20% for BING© and SMART THUMPER™, respectively, which indicated that the SMART THUMPER™ had greater variation in MOE estimation of a single sample measured at different lengths (Table 2).
Table 2. COV Values of the BING© and SMART THUMPER™ MOEs for the Sawn Blackbutt Samples
The histograms for the SMART THUMPER™ app data (as shown in Fig. 4) show fewer group segregations, classes, or bins in terms of the MOE for 1.0 m and 0.8 m long boards compared to the 1.2 m and 1.1 m long boards. Further investigation revealed that the frequency obtained from the SMART THUMPER™ app for the 1.0 m and 0.8 m samples had a discrete cluster of some frequency values, i.e., had the same frequencies for a number of samples, (Fig. 5a).
Fig. 5. Frequency values for the 0.8 m Blackbutt sample obtained from a) SMART THUMPER™ and b) BING©
Fig. 6. Correlation between frequency for the 1.2 m and 0.8 m samples obtained from a) BING© and b) SMART THUMPER™
This clustering, or rounding, of the frequency values could be due to limitations of the app, or the frequency response of the smartphone and requires further investigation. However, this problem did not appear in the BING© results (Fig. 5b). This indicated that BING© measures the frequency more precisely at higher frequencies than the SMART THUMPER™ app and subsequently provided a more accurate MOE estimation. This is further evidenced by the coefficient of determination (R2) between frequencies for the 1.2 m and 0.8 m samples obtained from the BING© and SMART THUMPER™ systems (Fig. 6). The R2 values for the 1.2 m and 0.8 m samples were 0.9525 and 0.895 for the BING© and SMART THUMPER™ systems, respectively.
The correlations between BING© MOE estimation were between 0.98 and 0.99, whereas the correlations for SMART THUMPER™ were between 0.92 to 0.98 for varying lengths of sawn jarrah (Fig. 7). The correlation between BING© and SMART THUMPER™ MOE ranged from 0.94 to 0.98 for all board lengths. The minimum value (0.94) occurred in the 1.2 m and 0.8 m length samples, due to differences in the precision of the frequency measurements, as shown previously.
Similar to sawn blackbutt, the COVs for the SMART THUMPER™ system were higher than the COVs for the BING© system. The average COVs were 1.35% and 3.17% for BING© and SMART THUMPER™, respectively (as shown in Table 3).
Table 3. COV Values of the BING© and SMART THUMPER™ Systems for the Jarrah Samples
Fig. 7. Correlation matrix between the BING© and SMART THUMPER™ MOEs showing the Pearson correlation, histogram, and scatterplot with a linear model for sawn jarrah timber
Fig. 8. Frequencies obtained from various lengths (0.8 m to 1.2 m) of jarrah samples using the SMART THUMPER™ application
The frequencies for all sawn jarrah samples at various lengths are shown in Fig. 8. The clustering, or rounding, of the frequency values becomes noticeable as the frequencies increase due to the sample length decreasing.
The rounding of the frequencies to discrete values, as obtained via the SMART THUMPER™ system, can also be clearly seen in the scatter plots between the BING© and SMART THUMPER™ frequencies for the 1.2 m and 0.8 m samples (Fig. 9). Figure 9 shows that for shorter samples the frequency obtained from the SMART THUMPER™ system clustered in four major groups, whereas there were more than four groups for the 1.2 m samples. This indicated that the SMART THUMPER™ app may not provide accurate results for shorter samples that require higher frequencies, i.e., greater than approximately 2000 Hz.