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Analysis and Optimization of the Tensioning Effect on a Wood-Cutting Circular Saw Blade Tensioned by Multispot Pressure.

Presently, there is a shortage of wood resources in the world, especially in China. Wood processing enterprises all over the world have placed greater demands on the cutting precision and material-saving ability of circular saw blades. Presently, circular saw blades are becoming thinner and thinner in order to reduce kerf loss.

Wood cutting requires a circular saw blade to maintain optimal working condition for a long period of time. Thermal stress is produced, because the temperature at the edge of the blade is higher than that in other regions. High tangential compressive stress is produced in the edge of a circular saw blade because of thermal stress, causing a buckling deformation that reduces cutting precision, increases kerf loss, and shortens the saw's life. The above-mentioned phenomenon can easily occur in the case of a thin circular saw blade. In the field of wood sawing, a circular saw blade is expected to be thinner and better because of the shortage of wood resources and enhancement of environmental protection. Therefore, improved stability performance of wood-cutting circular saw blades is very important.

During the manufacturing of circular saw blades, tensioning is the most important and advanced technological process in order to avoid the phenomenon mentioned above. The natural frequency and the residual stress field of a circular saw blade are changed after the tensioning process, which is called the tensioning effect. The tensioning effect has a strong influence on cutting quality, noise, vibration, material waste, and lifetime of a circular saw blade (Li et al. 2016).

In recent years, a multispot pressure tensioning process appeared in the field of circular saw blade manufacturing. Based on a hydraulic control system, many local areas of a circular saw blade are pressed by a spherical surface, and plastic deformation is produced during this process. The feasibility and effectiveness of this process were confirmed based on a theoretical analysis and tensioning stress test (Li et al. 2015a). The multispot pressure tensioning process is effective for any circular saw blade, especially a wood-cutting circular saw blade, because the phenomenon of cutting heat is more obvious on a wood-cutting circular saw blade.

Roll tensioning and hammering were the main tensioning methods for circular saw blades before the emergence of the multispot pressure tensioning process. Many scientists have studied the tensioning effect of circular saw blades tensioned by these two methods, as discussed below.

The dynamic characteristics of a roll-tensioned circular saw blade with a tensioning stress field were determined by Carlin et al. (1975) based on energy methods. The light gap between the blade surface and edge of a curved ruler was tested by Schajer (1992) for characterizing tensioning effect indirectly. Lateral stiffness of a circular saw blade in coordination of tensioning effect with rotation speed was studied by Stakhiev (2004). A modal filter was used by Kuratani and Oda (2010) for measuring the natural frequency of a roll-tensioned saw blade. An experimental platform was built by Schajer et al. (2012) for examining the vibration mode and controlling tensioning effect. An analysis model for the dynamic characteristics of a circular saw blade under a thermal load was built (Ishihara et al. 2012, 2014). Effects of roll-tensioning process parameters on the natural frequency of a circular saw blade were studied by Cristovao et al. (2012) based on ABAQUS software. The influence of the tangential roll-tensioning process on the natural frequency of a circular saw blade was studied by Zhang et al. (2014). An active electromagnetic system for weakening the vibrations of a circular saw blade was proposed by Gospodaric et al. (2015).

The tensioning stress field of a roll-tensioned circular saw blade was tested by Szymani and Mote (1974). The tensioning stress field of a roll-tensioned circular saw blade was obtained by Szymani and Mote (1979) based on experimental measurement and theoretical analysis. A theoretical model was presented by Schajer and Mote (1983) that could accurately describe the tensioning stress field in a roll-tensioned circular saw blade. A mathematical model that could predict the optimal roll-tensioning parameters for a saw blade was built by Schajer and Mote (1984). The X-ray stress test method for measuring the tensioning stress field of a roll-tensioned circular saw blade was studied by Umetsu et al. (1989). Umetsu et al. (1994) measured the tensioning stress field in a hammering-tensioned circular saw blade using the X-ray stress meter. Nicoletti et al. (1996) built a finite element model for the roll-tensioning process and examined the tensioning stress field. The effects of roll-tensioning parameters on the tensioning stress field were examined by Heisel et al. (2014) through ABAQUS software. The effect of yield strength on the tensioning stress field of a roll-tensioned circular saw blade was studied by Li and Zhang (2017) through ABAQUS software.

The multispot pressure tensioning process has its own advantages of automatic control and tensioning effect optimization (Li et al. 2015b, 2015c). However, there is no related research on the regulation mechanism of the tensioning effect and optimized process parameters for this process. The lack of theoretical basis restricts the development of a multispot pressure tensioning process.

The natural frequency and tensioning stress field of a circular saw blade are two of the most important indicators for the tensioning effect. The optimal tensioning effect and process parameters for multispot pressure tensioning could be obtained only by considering these two indicators synthetically. Therefore, analysis and optimization of the tensioning effect for a circular saw blade tensioned by multispot pressure were carried out in this article.

Materials and Methods

Process parameters for a multispot pressure tensioning process

According to the characteristics of a multispot pressure tensioning process, representative process parameters are summarized in this article. The representative process parameters for a multispot pressure tensioning process include the following: loading force (F), radial spot number (M), circumferential spot number (N), radius of spots in the outermost ring ([R.sub.w]), and radial distance (d), as shown in Figure 1. These process parameters have effects on the natural frequency and tensioning stress field of a circular saw blade. The spot distribution is cyclic axisymmetric. In Figure 1, [alpha] = 360/N([degrees]).

The circular saw blade chosen in this study is from a sliding table saw. It needs to maintain durable and stable cutting performance and cutting accuracy. The radius and thickness of the circular saw blade were 178 and 2.2 mm, respectively, which were unchanged. The radius of the hole in the center of the circular saw blade was 15 mm and unchanged. The number of teeth was 36 with carbide tips. There was no expansion slot. F was changed from 40 to 80 kN, M was changed from 2 to 4, N was changed from 12 to 16, [R.sub.w.] was changed from 130 to 150 mm, and d was changed from 20 to 30 mm in the research process described in this article. Factors and their levels for the orthogonal simulation experiment in this article are shown in Table 1.

Tensioning effect analysis of circular saw blade based on finite element method

The Dynamic/Explicit module of ABAQUS software was chosen to simulate the elastic-plastic loading process of multispot pressure tensioning. One simulation for verification of the finite element model is shown in Figure 2, where F was set to 40 kN, M was set to 3, A' was set to 16, [R.sub.w] was set to 140 mm, and d was set to 30 mm.

Radius and thickness of the circular saw blade were 178 and 2.2 mm, respectively, which were unchanged. The radius of the hole in the center of circular saw blade was 15 mm and unchanged. Radius of spherical pressure head was 70 mm and unchanged.

The hardness of spherical pressure head was HRC60. Elastic deformation of the spherical pressure head was ignored, and it was built as an analytical rigid body. The main part of the circular saw blade was made of 65Mn, with hardness HRC42. The constitutive model of this material was set as a linear strengthening elastic-plastic model. Its elastic modulus, poisson ratio, and density were set as 210 GPa, 0.3, and 7.8 g/[cm.sup.3], respectively. Its yield strength and strain hardening rate were set as 430 and 1,000 MPa, respectively.

All the translational degrees of freedom at the inner wall of the center hole of the circular saw blade were restricted. Loading force was applied to the spherical head. Two planes of the circular saw blade were pressed by spherical pressure heads simultaneously. Kinetic friction was applied between the spherical pressure head and the circular saw blade; the friction coefficient was set to 0.12.

The spherical pressure head was not meshed. The three-dimensional eight-node reduced integral element C3D8R was chosen for the circular saw blade. There were 80 elements in radial direction, 384 elements in circumferential direction, and 2 elements in thickness direction of saw blade.

The tensioning stress field of the circular saw blade was calculated by the Static/General module of ABAQUS software using the stress field of loading process calculated by the Dynamic/Explicit module as initial conditions.

Natural frequencies of the circular saw blade were calculated by the Frequency module of ABAQUS software using the tensioning stress field calculated by the Static/General module as initial conditions.

Verification for the finite element model

The tensioning stress field is the most important link for the model, which can also determine the precision of the natural frequency. Therefore, the tensioning stress test was carried out to confirm the accuracy of the model. The tensioning stress field of the circular saw blade tensioned by multispot pressure was tested by the X-ray stress meter.

The spot distribution is shown in Figure 2, and F was set as 40 kN. The tensioning stress test path and numerical extraction path for tensioning stress calculation results were the same, as shown by the center line in Figure 2. The simulation results and stress measurement results are shown in Figure 3. The simulated tensioning stress field was in agreement with the measurement results, which confirmed the accuracy of the model.

Results and Discussion

For the circular saw blade after the tensioning process, natural frequencies for the nodal circle (Nc) = 0 and nodal diameter (Nd) < 2 generally are decreased slightly. Natural frequencies for Nc = 0 and Nd [greater than or equal to] 2 are increased to different extents. The critical speed of the circular saw blade is primarily affected by the natural frequencies for Nc = 0 and Nd [greater than or equal to] 2. In general, the increase of natural frequencies for Nc = 0 and Nd [greater than or equal to] 2 is beneficial for a circular saw blade under the premise that the natural frequencies for Nc = 0 and Nd < 2 are unchanged or decreased slightly.

Tangential tensile stress is produced in the edge of a circular saw blade after the tensioning process. Tangential tensile stress in the edge of circular saw blade can compensate the tangential compressive thermal stress and improve the stability of circular saw blade under working conditions. In general, the increase of tangential tensile stress in the edge of a circular saw blade is beneficial for the circular saw blade under the premise that the natural frequencies of the circular saw blade are reasonable.

To summarize, the natural frequency and tangential tensile stress in the edge of a circular saw blade are two important indicators for tensioning effect, and are also the basis for the optimization of a multispot pressure tensioning process.

The natural frequency of the circular saw blade in its initial state is shown in Table 2. The natural frequency for Nc = 0 and Nd = 0 is slightly larger than that for Nc = 0 and Nd = 1. The natural frequency is increased with nodal diameter for Nc = 0 and Nd [greater than or equal to] 1. The simulation results of the natural frequency of the circular saw blade were consistent with previous research results of other scientists (Szymani and Mote 1979, Schajer and Mote 1983), which also confirmed the accuracy of the finite element model in this study.

F, M, N, [R.sub.w], and d influence the tensioning effect. These factors also affect each other. When the influence of one factor on the tensioning effect is studied while the other factors are fixed, the degree of influence of different factors on the tensioning effect cannot be compared comprehensively. Therefore, the orthogonal experimental method was chosen for the optimization of a multispot pressure tensioning process. Because the orthogonal table has the characteristics of balanced dispersion, each test has a strong representation, thus ensuring the requirements of a comprehensive experiment.

The orthogonal table [L.sub.27]([3.sup.13]) was used for the design of the orthogonal simulation experiment, as shown in Table 3. The natural frequency of tensioned the circular saw blade is shown in Table 4. Average tangential tensile stress in the edge of the circular saw blade is also shown in Table 4. According to the principle of the orthogonal experiment, all of the following analyses were based on Tables 3 and 4. For example, if the effect of F on the natural frequency of Nc = 0 and Nd = 0 needs to be studied, the natural frequencies of Nc = 0 and Nd = 0 when F = 40, 60, or 80 kN from Table 4 are averaged separately. In the same way, the natural frequencies of Nc = 0, Nd > 0, and average tangential tensile stress in the edge of the circular saw blade when F = 40, 60, or 80 kN are extracted from Table 4 and averaged separately. Tables 5 through 9 were obtained by this method, which allows us to compare the degree of influence of these factors on tensioning effect comprehensively and find the optimized scheme for a multispot pressure tensioning process.

As shown in Table 5, the effect of F on the natural frequencies of Nc = 0 and Nd [greater than or equal to] 2 is limited. The average tangential tensile stress in the edge of the circular saw blade is increased with F. As shown in Figure 4, the natural frequency of Nc = 0 and Nd = 2 is less than that of the circular saw blade in its initial state. The natural frequency of Nc = 0 and Nd = 4 is greater than that of the circular saw blade in its initial state.

As shown in Table 6, the effect of M on the dynamic characteristics of the circular saw blade is significant. The natural frequencies of Nc = 0 and Nd < 2 have a certain degree of reduction with M. The natural frequencies of Nc = 0 and Nd [greater than or equal to] 2 are increased significantly with M. The number of local plastic deformation regions is increased with M. The average tangential tensile stress in the edge of the circular saw blade is increased with M because of the superposition of tangential residual tensile stress. As shown in Figure 5, the natural frequencies of Nc = 0 and Nd [less than or equal to] 2 gradually align with those of the circular saw blade in its initial state with the increase of M. The natural frequencies of Nc = 0 and Nd > 2 gradually exceed those of the circular saw blade in its initial state with the increase of M.

As shown in Table 7, the effect of N on the natural frequencies is limited. The average tangential tensile stress in the edge of the circular saw blade is increased with N within a limited range. As shown in Figure 6, the natural frequencies of Nd = 0, Nd= 1, and Nd = 3 with Nc = 0 is not changed significantly, compared with those of the circular saw blade in its initial state. The natural frequency of Nc = 0, Nd = 2 is less than that of the circular saw blade in its initial state. The natural frequency of Nc = 0, Nd = 4 is greater than that of the circular saw blade in its initial state.

As shown in Table 8, the effect of [R.sub.w] on the dynamic characteristics of circular saw blade is significant. The natural frequencies of Nc = 0 and Nd < 2 have a certain degree of reduction with the decrease of [R.sub.w]. The natural frequencies of Nc = 0 and Nd [greater than or equal to] 2 are increased significantly with the decrease of [R.sub.w]. The local plastic deformation regions extend to the center of the circular saw blade with the decrease of [R.sub.w]. The average tangential tensile stress in the edge of the circular saw blade is decreased with the decrease of [R.sub.w]. in an acceptable degree. As shown in Figure 7, the natural frequencies of Nc = 0 and Nd [less than or equal to] 2 gradually align with those of the circular saw blade in its initial state with the decrease of [R.sub.w]. The natural frequencies of Nc = 0 and Nd > 2 gradually exceed those of the circular saw blade in its initial state with the decrease of [R.sub.w].

As shown in Table 9, the effect of d on the dynamic characteristics of circular saw blade is significant. The natural frequencies of Nc = 0 and Nd < 2 have a certain degree of reduction with d. The natural frequencies of Nc = 0 and Nd [greater than or equal to] 2 are increased significantly with d. The local plastic deformation regions extend to the center of the circular saw blade with d. The average tangential tensile stress in the edge of the circular saw blade is decreased with d to an acceptable degree. As shown in Figure 8, the natural frequencies of Nc = 0 and Nd [less than or equal to] 2 gradually align with those of the circular saw blade in its initial state with d. The natural frequencies of Nc = 0 and Nd > 2 gradually exceed those of the circular saw blade in its initial state with d.

The degree of influence of process parameters on the natural frequencies of the circular saw blade, as characterized by [DELTA]f, is shown below:

[mathematical expression not reproducible] (1)

where [[DELTA]f.sub.ij] represents the range of the natural frequency, i represents Nc, and j represents Nd.

According to the data in Tables 5 through 9, [DELTA]f values were calculated as shown below. For F, [DELTA]f= 13.05 Hz; for M. [DELTA]f = 29.93 Hz; for N, [DELTA]f= 11.72 Hz; for [R.sub.w], [DELTA]f= 54.34 Hz; and for d, [DELTA]f= 35.54 Hz.

According to [DELTA]f and Figures 4 through 8, [R.sub.w] has the greatest effect on the natural frequencies of the circular saw blade. The tensioning effect is enhanced with the decrease of [R.sub.w]. Dynamic characteristics can be regulated and controlled effectively by adjusting [R.sub.w] within the appropriate range.

M and d have the second greatest effects on the natural frequencies of the circular saw blade. The tensioning effect is enhanced with their increase. Dynamic characteristics can be regulated and controlled effectively by adjusting them.

F and N have the smallest effects on the natural frequencies of the circular saw blade. The tensioning effect is enhanced with their increase in a small range. In general, it is not recommended to regulate and control the dynamic characteristics of the circular saw blade by adjusting them.

According to the range of average tangential tensile stress in the edge of the circular saw blade in Tables 5 through 9, F and M have the greatest effects on the average tangential tensile stress in the edge of the circular saw blade. Average tangential tensile stress in the edge of the circular saw blade is increased with them.

[R.sub.w]. has the second greatest effect on the average tangential tensile stress in the edge of the circular saw blade. Average tangential tensile stress in the edge of the circular saw blade is increased with it.

N and d have the smallest effects on the average tangential tensile stress in the edge of the circular saw blade, and could be ignored.

From the perspective of the average tangential tensile stress in the edge of the circular saw blade, according to the above analysis, F, M, N, [R.sub.w], and d are identified for its optimization. The average tangential tensile stress in the edge of the circular saw blade is the objective function. The greater the value of the average tangential tensile stress in the edge of the circular saw blade, the better. As shown in Tables 5 through 8, the process parameter configuration with F = 80 kN, M = 4, N = 16, [R.sub.w] = 150 mm, and d = 20 mm can obtain the maximum average tangential tensile stress in the edge of the circular saw blade.

From the perspective of the natural frequency of the circular saw blade, according to the above analysis, F, M, N, [R.sub.w], and d are identified for its optimization. The natural frequency for Nc = 0 and Nd = 4 and natural frequency for Nc = 0 and Nd = 0 are the objective functions. The greater the natural frequency for Nc = 0 and Nd = 4, the better, under the premise that natural frequency for Nc = 0 and Nd = 0 is unchanged or decreased slightly. The process parameter configuration with F = 80 kN, M = 4, N = 16, [R.sub.w] = 130 mm, and d = 30 mm can increase the natural frequency for Nc = 0 and Nd = 4 to a maximum degree, but can also reduce the natural frequency for Nc = 0 and Nd = 0 greatly. For example, as shown in Number 7 from Tables 3 and 4, the natural frequency of Nc = 0 and Nd = 0 is decreased greatly, which is called overtensioning.

Therefore, both the average tangential tensile stress in the edge of the circular saw blade and the natural frequency of Nc = 0 and Nd = 4 should be considered for the optimization of process parameters. F= 80 kN, M=4, N= 16 can first be identified. There are two schemes for the optimization of a multispot pressure tensioning process, as shown below. If average tangential tensile stress in the edge of the circular saw blade is given priority, [R.sub.w] is set as 150 mm. and d is set as 30 mm to ensure that the natural frequency of Nc = 0 and Nd = 4 does not decrease too much. If the natural frequency of Nc = 0 and Nd = 4 is given priority, [R.sub.w] is set as 130 mm. The value of d is set as 20 mm to ensure that the average tangential tensile stress in the edge of the circular saw blade does not decrease too much.

As shown in Table 10, the two schemes for the optimization of a multispot pressure tensioning process could obtain both reasonable natural frequencies and average tangential tensile stress in the edge of the circular saw blade.

Conclusions

Elastic plastic deformation, linear elastic unloading, and modal analysis models of the circular saw blade tensioned by multispot pressure were built by ABAQUS software. The effects of process parameters on the natural frequency and tangential tensile stress in the edge of the circular saw blade were examined and compared. Considering the natural frequency and tangential tensile stress in the edge of the circular saw blade synthetically, optimal process parameters for multispot pressure tensioning were obtained based on the orthogonal method.

Simulation results show that [R.sub.w] has the greatest effect on the natural frequencies of the circular saw blade. M and d have the second greatest effects on the natural frequencies of the circular saw blade. The dynamic characteristics can be regulated and controlled effectively by adjusting them within the appropriate range. F and N have the smallest effects on the natural frequencies of the circular saw blade. Regulation and control of the dynamic characteristics of the circular saw blade by adjusting F and N is not recommended.

Simulation results show that F and M have the greatest effects on tangential tensile stress in the edge of the circular saw blade. Tangential tensile stress in the edge of the circular saw blade is increased with these factors. [R.sub.w] has the second greatest effect on tangential tensile stress in the edge of the circular saw blade. Tangential tensile stress in the edge of the circular saw blade is increased with it. Finally, d and N have the smallest effects on tangential tensile stress in the edge of the circular saw blade, and can be ignored. Tangential tensile stress in the edge of the circular saw blade can be regulated and controlled effectively by adjusting F after [R.sub.w], M, and d are determined.

Acknowledgments

We gratefully acknowledge the financial support of Fundamental Research Funds for the Central Nonprofit Research Institution of CAF (No. CAFYBB2019QB006,-CAFYBB2017SY039) and National Natural Science Foundation of China (No. 31600458).

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Bo Li

Zhankuan Zhang

The authors are, respectively, Assistant Professor and Professor, Research Inst. of Wood Industry, Chinese Academy of Forestry. Beijing, China (libohongxing@sina.com [corresponding author], zhangzk@caf.ac.cn). This paper was received for publication in October 2017. Article no. 17-00063.

[c]Forest Products Society 2019.

Forest Prod. J. 69(1):61-69.

doi: 10.13073/FPJ-D-17-00063
                  Factor (a)
Level  F (kN)  M  N   [R.sub.w] (mm)  d (mm)

I      40      2  12  150             30
2      60      3  14  140             25
3      80      4  16  130             20

(a) F = loading force; M = radial spot number; N = circumferential spot
number; [R.sub.w] = radius of spots in the outermost ring; d = radial
distance.

Table 2.--Natural frequency of circular saw blade in initial state.

Modal (a)       Natural frequency (Hz)

Nc = 0, Nd = 0   69.40
Nc = 0, Nd = 1   55.45
Nc = 0, Nd = 2   94.86
Nc = 0. Nd = 3  213.18
Nc = 0. Nd = 4  373.88

(a) Nc = nodal circle; Nd = nodal diameter.

Table 3.--Design of orthogonal simulation experiment.
                  Factor(a)
Number  F(kN)  M  N          [R.sub.w](mm)  d (mm)

1       40     2  12         150            30
2       40     2  12         150            25
3       40     2  12         150            20
4       40     3  14         140            30
5       40     3  14         140            25
6       40     3  14         140            20
7       40     4  16         130            30
8       40     4  16         130            25
9       40     4  16         130            20
10      60     2  14         130            30
11      60     2  14         130            25
12      60     2  14         130            20
13      60     3  16         150            30
14      60     3  16         150            25
15      60     3  16         150            20
16      60     4  12         140            30
17      60     4  12         140            25
18      60     4  12         140            20
19      80     2  16         140            30
20      80     2  16         140            25
21      80     2  16         140            20
22      80     3  12         130            30
23      80     3  12         130            25
24      so     3  12         130            20
25      80     4  14         150            30
26      80     4  14         150            25
27      80     4  14         150            20

(a) F = loading force: M = radial spot number: N = circumferential spot
number; [R.sub.w] = radius of spots in the outermost ring; d = radial
distance.

Table 4.--Results of orthogonal simulation experiment.

                        Natural frequency (Hz) (a)   Average tangential
                                                     lensile
        Ne = 0  Ne = 0  Nc = 0  Nc = 0   Nc = 0      stress in the edge
                                                     of
Number  Nd = 0  Nd = 1  Nd = 2  Nd = 3   Nd = 4      circular saw blade
                                                     (MPa)

 1       85.16  58.96    64.34   185.74  352.81       42.52
 2       88.05  59.39    52.21   173.43  340.01       44.53
 3       93.47  60.45    31.20   150.13  317.23       46.71
 4       68.94  57.79   103.68   239.44  416.91       49.45
 5       79.48  59.91    84.15   219.37  399.67       55.43
 6       93.28  62.72    31.97   177.58  363.15       56.12
 7        6.47  45.43   157.26   304.70  486.12       68.43
 8       12.93  51.59   142.68   290.48  474.83       68.69
 9       51.64  58.21   111.52   261.05  455.08       72.54
10       71.90  58.43    97.32   233.97  415.36       49.73
11       79.10  59.75    82.22   217.64  400.42       51.56
12       81.09  60.04    77.08  21 1.33  393.80       53.32
13       85.41  60.56    70.85   203.71  381.72       93.52
14       96.35  62.53    61.23   150.23  326.23       95.36
15      108.41  64.89    50.45    89.82  288.45      100.51
16       39.02  53.73   132.75   277.65  461.19       83.64
17       65.82  60.09    98.26   245.04  436.92       86.53
18       83.67  64.05    35.89   193.92  395.74       92.57
19       84.92  60.45    69.19   202.31  383.13       75.62
20       86.92  60.79    61.88   194.76  375.78       81.05
21       85.62  60.12    66.73   195.81  374.89       73.36
22       45.46  56.83   120.45   269.88  461.66       76.74
23       59.47  59.99    94.82   243.59  442.29       79.93
24       66.54  60.45    86.82   232.12  429.16       79.83
25       70.25  58.60   101.39   239.90  422.34      129.45
26       91.79  64.17    30.50   186.34  379.21      137.52
27      105.06  65.30    10.12   142.94  339.40      140.42

(a) Nc = nodal circle; Nd = nodal diameter.

Table 5.--Tensioning effect under different loading forces.

                            Natural  frequency (Hz)  Average taneential
                                                     tensile
            Nc = 0  Nc = 0           Nc = 0  Nc = 0  stress in the edge
                                                     of
F (kN) (a)  Nd = 0  Nd = 1           Nd = 2  Nd = 3  circular saw blade
                                                     (MPa)

40          64.38   57.16            86.55   222.43  56.04
60          78.97   60.45            78.45   202.59  78.52
80          77.33   60.74            71.32   211.96  97.10
Range       14.59    3.58             15.23   19.84  41.06

(a) F = loading force; Nc = nodal circle; Nd = nodal diameter.

Table 6.--Tensioning effect under different radial spot numbers.

                       Natural frequency (Hz)  Average tangential
                                               tensile
       Nc = 0  Nc = 0  Nc = 0  Nc = 0  Nc = 0  stress in the edge of
M (a)  Nd = 0  Nd = 1  Nd = 2  Nd = 3  Nd = 4  circular saw blade (MPa)

2      84.02   59.82   66.90   196.12  372.60  57.60
3      78.14   60.63   78.26   202.86  389.91  76.32
4      58.51   57.90   91.15   238.00  427.87  97.75
Range  25.51    2.73   24.25    41.88   55.27  40.15

(a) M = radial spot number; Nc = nodal circle; Nd = nodal diameter.

Table 7.--Tensioning effect under different circumferential spot
numbers.

                       Natural frequency (Hz)  Average tangential
                                               tensile
       Nc = 0  Nc = 0  Nc = 0  Nc = 0  Nc =0   stress in the edge of
N (a)  Nd = 0  Nd = 1  Nd = 2  Nd = 3  Nd = 4  circular saw blade (MPa)

12     69.62   59.32   79.63   219.05  404.11  70.33
14     82.32   60.74   68.71   207.61  392.25  80.33
16     68.74   58.28   87.97   210.31  394.02  81.00
Range  13.58    2.46   19.26    11.44   11.86  10.67

(a) N = circumferential spot number; Nc = nodal circle; Nd = nodal
diameter.

Table 8.--Tensioning effect under different radii of spots in the
outermost ring.

                           Natural frequency (Hz)  Average tangential
                                                   tensile
           Nc = 0  Nc = 0  Nc = 0  Nc = 0  Nc = 0  stress in the edge of
[R.sub.w]
(mm) (a)   Nd = 0  Nd = 1  Nd = 2  Nd = 3  Nd = 4  circular saw blade
                                                   (MPa)

150        91.55   61.65   52.47   169.13  349.71  92.28
140        76.40   59.96   76.05   216.20  400.82  72.64
130        52.73   56.74   107.79  251.64  439.85  66.75
Range      38.82   4.91    55.32   82.51   90.14   25.53

(a) [R.sub.w] = radius of spots in the outermost ring; Nc = nodal
circle; Nd = nodal diameter.

Table 9.--Tensioning effect under different radial distances.

                            Natural frequency (Hz)  Average tangential
                                                    tensile
            Nc = 0  Nc = 0  Nc = 0  Nc = 0  Nc = 0  stress in the edge
                                                    of
d (mm) (a)  Nd = 0  Nd = 1  Nd = 2  Nd = 3  Nd = 4  circular saw blade
                                                    (MPa)

30          61.94   56.75   101.91  239.70  420.13  74.34
25          73.32   59.80   78.66   213.43  397.26  77.84
20          85.42   61.80   55.75   183.85  372.98  79.48
Range       23.48    5.05   46.16   55.85   47.15    5.14

(a) d = radial distance; Nc = nodal circle; Nd = nodal diameter.

Table 10.--Optimization schemes for multispot pressure tensioning
process.

            Process par rocess
            par ameters (a)                     Natural frequency (Hz)

                                        Nc = 0  Nc = 0  Nc = 0  Nc = 0
No.  F(kN)  M  N   [R.sub.w]
                   (mm)         d (mm)  Nd = 0  Nd = 1  Nd = 2  Nd = 3

1    80     4  16  150          30      62.07   56.98   113.38  252.19
2    80     4  16  130          20      46.49   57.64   123.43  278.53

             Average tangential tensile
     Nc = 0  stress in the edae of
No.  Nd = 4  circular saw blade (MPa)

1    433.36  129.14
2    480.73  110.24

(a) F = loading force; M = radial spot number; N = circumferential
spot number; [R.sub.w] = radius of spots in the outermost ring;
d = radial distance; Nc = nodal circle: Nd = nodal diameter.
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Author:Li, Bo; Zhang, Zhankuan
Publication:Forest Products Journal
Geographic Code:1USA
Date:Mar 22, 2019
Words:6223
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