1 Introduction
2 Materials and measurement methods
2.1 Sampling of material
Sub- sample | Origin | Dimensions (mm)a/no. of specimens | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
30 × 95 × 3700 | 30 × 120 × 4400 | 40 × 70 × 3000 | 40 × 120 × 3600 | 45 × 95 × 3600 | 45 × 145 × 3600 | 45 × 170 × 5100 | 58 × 170 × 5800 | 70 × 220 × 5800 | 70 × 245 × 5800 | Total | ||
1 | Sweden North | 48 | 56 | 104 | ||||||||
2 | Sweden Mid | 75 | 138 | 60 | 273 | |||||||
3 | Sweden South | 57 | 14 | 32 | 36 | 69 | 30 | 238 | ||||
4 | Norway | 21 | 51 | 123 | 22 | 217 | ||||||
5 | Finland | 44 | 60 | 104 | ||||||||
Total | 21 | 44 | 57 | 14 | 174 | 409 | 82 | 36 | 69 | 30 | 936 |
2.2 Measurements and equipment for IP determining data
2.2.1 Resonance frequency and mass
2.2.2 Fibre orientation on wood surfaces
2.3 Determination and requirements of grade determining properties
2.3.1 Modulus of elasticity, MOE
2.3.2 Bending strength
2.3.3 Density
3 Calculation model and definitions of indicating properties
3.1 Determination of local MOE valid for bending
-
The density (ρ) and the MOE in the fibre direction (E l) are constant within a board,
-
An initial, nominal value of the MOE in the fibre direction (E l,0) as well as nominal values of other material parameters are assumed, see Table 2,Table 2Nominal material parameters employed (Norway spruce), values originating from Dinwoodie (2000)E 1,010700MPaE r,0710MPaE t,0430MPaG lr,0500MPaG lt,0620MPaG rt,024MPav lr0.38v lt0.51v rt0.51
-
When a value of E l that should be valid for an examined board is determined, it is assumed that the relationships between the other board stiffness parameters (E r, E t, G lr, G lt, and G rt) and their corresponding nominal values (E r,0, E t,0, G lr,0, G lt,0, G rt,0) are the same as the relationship between E l and E l,0. Regarding notation of the stiffness parameters, E and G represent MOE and shear modulus, respectively, and indices l, r and t, represent longitudinal, radial and tangential direction, respectively. Poisson’s ratios, displayed in Table 2, are denoted as v.
-
Fibre directions measured on the wood surface (Fig. 5a) are located in the longitudinal-tangential plane of the wood material,×
-
The fibre direction coincides with the wood surface, i.e. the out of plane angle is set to zero, and
3.2 Definitions of indicating properties
4 Grading and regulations
4.1 Requirements and assessment of repeatability and significance of scanning speed
Optimum grade | Assigned grade | ||
---|---|---|---|
3 | 2 | 1 | |
Size matrix | |||
3 | 161 | 4 | 0 |
2 | 4 | 160 | 5 |
1 | 1 | 3 | 162 |
Elementary cost matrix | |||
3 | 0 | 1 | 2 |
2 | 1 | 0 | 1 |
1 | 2 | 1 | 0 |
Global cost matrix | |||
3 | 0 | 0.024 | 0 |
2 | 0.024 | 0 | 0.030 |
1 | 0.012 | 0.006 | 0 |
4.2 Calculation of settings for strength classes
-
When settings are calculated at least 0.5 % of the sample, and not less than five pieces, must be rejected.
-
At least 20 pieces must be assigned to each strength class being graded.
-
Requirements on the sample, where one subsample at a time is excluded, must be fulfilled.
-
Cost matrices shall be established and considered.
-
A certain country check must be performed.
5 Results and discussion
5.1 Properties decisive for the grade determining properties
Sub-sample |
f
m,corr (N/mm2) |
E
local,corr (N/mm2) |
E
global,corr (N/mm2) |
ρ
corr (kg/m3) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
m | s | CoV | m | s | CoV | m | s | CoV | m | s | CoV | |
1 | 46.1 | 9.7 | 0.21 | 12,500 | 2300 | 0.18 | 11,500 | 1920 | 0.17 | 451 | 43 | 0.10 |
2 | 44.1 | 11.1 | 0.25 | 11,600 | 1950 | 0.17 | 11,000 | 1620 | 0.15 | 430 | 37 | 0.09 |
3 | 38.1 | 11.2 | 0.29 | 11,300 | 2540 | 0.22 | 10,700 | 2020 | 0.19 | 445 | 39 | 0.09 |
4 | 41.3 | 11.9 | 0.29 | 11,500 | 2680 | 0.23 | 11,000 | 1890 | 0.17 | 445 | 46 | 0.10 |
5 | 41.7 | 9.3 | 0.22 | 11,800 | 2100 | 0.18 | 11,400 | 1630 | 0.14 | 442 | 38 | 0.09 |
All | 42.1 | 11.3 | 0.27 | 11,600 | 2370 | 0.20 | 11,000 | 1840 | 0.17 | 441 | 41 | 0.09 |
5.2 Repeatability check and significance of scanning speed on indicating properties
Optimum grade | Assigned grade | |||
---|---|---|---|---|
4 | 3 | 2 | 1 | |
Size matrix | ||||
4 | 142 | 3 | 0 | 0 |
3 | 8 | 141 | 1 | 0 |
2 | 0 | 6 | 144 | 5 |
1 | 0 | 0 | 5 | 145 |
Elementary cost matrix | ||||
4 | 0 | 1 | 2 | 3 |
3 | 1 | 0 | 1 | 2 |
2 | 2 | 1 | 0 | 1 |
1 | 3 | 2 | 1 | 0 |
Global cost matrix | ||||
4 | 0 | 0.020 | 0 | 0 |
3 | 0.053 | 0 | 0.067 | 0 |
2 | 0 | 0.040 | 0 | 0.033 |
1 | 0 | 0 | 0.033 | 0 |
5.3 Regression analysis
R
2
|
f
m,corr
|
E
local,corr
|
E
global,corr
|
ρ
corr
|
IP
fb
|
IP
MOE
|
IP
density
|
---|---|---|---|---|---|---|---|
f
m,corr
|
1
|
0.62 ± 0.04 |
0.64 ± 0.04 |
0.20 ± 0.05 |
0.69 ± 0.03 |
0.53 ± 0.04 |
0.16 ± 0.06 |
E
local,corr
|
0.62 ± 0.04 |
1
|
0.85 ± 0.02 |
0.32 ± 0.05 |
0.76 ± 0.03 |
0.69 ± 0.03 |
0.27 ± 0.05 |
E
global,corr
|
0.64 ± 0.04 |
0.85 ± 0.02 |
1
|
0.42 ± 0.05 |
0.82 ± 0.02 |
0.84 ± 0.02 |
0.37 ± 0.05 |
ρ
corr
|
0.20 ± 0.05 |
0.32 ± .05 |
0.42 ± 0.05 |
1
|
0.33 ± 0.04 |
0.53 ± 0.04 |
0.84 ± 0.02 |
IP
fb
|
0.69 ± 0.03 |
0.76 ± 0.03 |
0.82 ± 0.02 |
0.33 ± 0.05 |
1
|
0.84 ± 0.02 |
0.30 ± 0.05 |
IP
MOE
|
0.53 ± 0.04 |
0.69 ± 0.03 |
0.84 ± 0.02 |
0.53 ± 0.04 |
0.84 ± 0.02 |
1
|
0.53 ± 0.04 |
IP
density
|
0.16 ± 0.06 |
0.27 ± 0.05 |
0.37 ± 0.05 |
0.84 ± 0.02 |
0.30 ± 0.05 |
0.53 ± 0.04 | 1 |
5.4 Yield in strength classes
Class or class combination | IPs used for prediction of grade determining properties/yield (%) | |||
---|---|---|---|---|
IP
MOE
a
|
IP
fb
b
|
IP
fb and IP
density
c
| Perfect machined
| |
C24 | 99.5 | 99.5 | 99.5 | 100e
|
TR26f
| 99.1 | 99.5 | 99.5 | 99.5 |
C30 | 95.4 | 96.4 | 96.8 | 97.1 |
C35 | 24.3 | 45.8 | 45.8 | 69.2 |
C40 | 14.5 | 27.9 | 30.3 | 47.7 |
C35/C18 | 24.3/75.2 | 45.8/53.6 | 45.8/53.6 | 69.2/30.2 |
C40/C24 | 14.5/84.9 | 27.9/71.6 | 30.3/69.1 | 47.7/47.7 |
-
The ability to predict bending strength is governing the yield. As a matter of fact, for the classes and class combinations displayed in Table 7, and using IP MOE for prediction of strength, the requirements on density and MOE stated in the standard do not affect the yield at all, i.e. even if there were no requirements on density and MOE in the definitions of the strength classes the yield would not increase. This is, however, not always the case. For some samples requirements on density could be of great importance for settings and yield, since the properties of a few pieces of a sample may affect settings considerably. There is an element of chance.
-
When using IP fb for prediction of both strength and density (column three in Table 7) the yield is limited by requirements on density. However, if the density is accurately predicted using IP density (column four in Table 7) the yield is not significantly decreased due to requirements on density. Only in the strength class C40 the yield would increase from 30.3 to 31.6 % if the requirement on density was omitted in the definition of the class.
-
Requirements on MOE in the definitions of the strength classes do not limit the yield for any of the real grading methods or strength classes assessed.
-
For a perfect machine the requirements on density considerably limit the yield in high strength classes. For example, for the class C35 the yield would increase from 69.2 to 74.4 % if the requirement of density was omitted. If the same requirement was omitted for class C40, the yield would increase from 47.7 to 51.7 %.
-
Regarding other requirements for calculation of settings and yield, see Sect. 4.2, it is concluded that requirements on cost matrices, in a few cases, lead to slightly decreased yield. For example, when grading C30 using IP fb and IP density for prediction of strength and density, respectively, a requirement on the cost matrix brought about that the yield decreased from 97.1 to 96.8 %, i.e. three more pieces out of the 936 pieces included in the sample had to be rejected in order to fulfil requirements on the global cost matrix.