In the sawing process, there is a serious problem of vibration and noise of the saw blade. Opening an appropriate slot on the saw blade is one of the effective ways to control the vibration and noise of the saw blade. In order to provide mathematics for the design of slotted saw blade and the re-repair use of the radial root crack saw blade, this paper considers the radial slot and the radial crack as the same thing, and analyzes them to the saw blade by the finite element method. The impact of vibration characteristics. 1 Vibration Characteristics of Common Saw Blades For comparison purposes, first analyze and understand the vibration modes of ordinary saw blades. Take a metal eager circular saw blade as the analysis object, its basic parameters are: outer diameter 2a=1.0m, thickness h=0.006m, clamping diameter ratio (ratio of chuck outer diameter to saw blade outer diameter) f=0.5, Yang Elastic modulus E = 2.058 × 1011 N/m2, Poisson's ratio v = 0.3, density r = 7.8 × 103 kg/m3. According to the axial symmetry of the saw blade, only one half piece can be used to build a finite element model. Divided into 90 quadrilateral plate elements, 114 nodes (5 radial divisions, 18 equal circumferential divisions) were calculated using the finite element method of structural analysis program SAP6. After the calculation is completed, the self-made special post-processing program is used to perform secondary processing on the output file of SAP6 to identify the vibration mode of the saw blade (m is the number of pitch circles and n is the number of node diameters), and a grid diagram and various Vibration pattern. In order to examine the effect of cell division density on the calculation results, the unit division of the half-saw blade was encrypted to 180 units, 222 nodes (radial 5 equal divisions, and circumferential 36 equal divisions) and 360 units and 407 nodes (paths) respectively. Divide to 10, divide into 36 equal parts of the week, and recalculate. The results of the finite element method for calculating the natural frequency of the saw blade for various cell densities and the exact solution are shown in Table 1. It can be seen that under the three cell division densities, the calculation results of the lower order natural frequencies are basically consistent and very accurate. Since it is generally only interested in the lower-order modes, such as 0-node circles and 0-6-node diameter modes, it is sufficient that the unit dividing density is 90 units. 2 The vibration characteristics of the saw blade with radial grooves are set as the parameters of the saw blade. One to three edge radial grooves with a groove width of no more than 1 mm are uniformly distributed on the saw blade. These grooves can also represent radial root fatigue cracks. The ordinary saw blade is divided into 180 units and 216 nodes. The unit of the slotted saw blade is divided and referenced, and the slotted unit is replaced by a blank unit. Change the slot length, calculate the vibration mode of the saw blade under various conditions and make various vibration mode diagrams. In Table 2, f'N and f"N respectively represent the two frequencies of modality (0,N). The mode shape is identified by a self-made special post-processing program. It should be noted here that when there are radial slots The pitch line of the mode shape of the saw blade is not necessarily a strict diameter, depending on the distribution of the slot, but for convenience, the diameter of the node is still used to approximate the description.From Table 2, it can be seen that the slot can make some of the original coincidence The modal frequencies are separated, and specifically which modal frequencies are separated depends on the number and distribution of the slots. When the slot type is constant, the frequency of each order slowly decreases as the slot length increases, when the slot length and the blade radius When the ratio does not exceed 0.2, the frequency does not drop by more than 10%. When the slot length is constant, the overall trend of frequency change is slowly decreasing (except in rare cases) as the number of slots increases. The section radius of the chip shape and the relative position of the saw blade are fixed, which can prevent the formation of the stationary wave at the critical speed.Table 1 The finite element method (SAP6) of ordinary saw blade and the exact solution (Hz) ) mode (m, n) (0,0) (0,1) (0,2) (0,3) (0,4) (0,5) (0,6) (0 7) (0,8) (1,0) 90 units 76.01 77.62 86.06 108.8 149.8 208.4 282.7 370.7 470.8 475.1 180 units 76.11 77.83 86.54 109.5 150.5 208.9 282.9 370.9 471.7 475.2 360 units 76.99 78.57 86.98 109.8 151.4 211.2 287.5 378.8 484.1 496.9 Exact solution 77.3 78.9 87.3 110.2 152.0 212.1 289.0 381.1 487.5 504.8 Table 2 Natural frequency of saw blade at different number of slots and slot length fN(Hz) Number of slots 0 1 2 3 Slot length/radius 0 0.1 0.2 0.4 0.1 0.2 0.4 0.1 0.2 0.4 f0 76.01 76.01 75.95 75.31 76.01 75.21 74.98 76.01 75.84 74.45 f'1 77.62 77.60 77.47 76.25 77.57 76.96 75.71 77.59 77.35 75.13 f"1 77.62 77.62 77.59 77.21 77.63 77.26 76.43 77.59 77.35 75.13 f'2 86.06 85.95 85.44 81.84 85.85 84.56 78.71 85.90 85.16 81.16 f" 2 86.06 86.05 86.04 86.00 86.04 85.50 85.94 85.90 85.16 81.16 f'3 108.8 108.5 107.3 98.67 108.3 105.4 91.28 108.1 104.4 85.66 f"3 108.8 108.7 108.2 107.5 108.6 107.3 106.4 108.4 107.1 105.4 f'4 149.8 149.4 146.9 130.2 149.0 143.6 116.0 148.6 142.8 115.4 f"4 149.8 149.5 147.8 144.7 149.1 145.7 140.4 148.6 142.8 115.4 f'5 20 8.4 207.6 203.2 176.1 206.8 197.8 152.6 206.2 195.2 161.7 f"5 208.4 207.8 204.3 197.8 207.1 200.0 188.7 206.2 195.2 161.7 f'6 282.7 281.2 273.5 235.9 279.7 264.9 200.8 278.3 257.6 174.6 3 Conclusion Some of the molds that originally overlapped after slotting the saw blade The separation of the state frequency occurs, so that the energy of the slot saw blade is more dispersed when it is excited by the pulse. The mode of vibration of the blade with radial grooves depends on the number and distribution of the grooves. The radius of the node and the relative position of the blade are fixed, and the pitch of the common blade is arbitrary. When the number and distribution of radial slots do not change, the natural frequency of each step decreases as the slot length increases, but when the ratio of the slot length to the radius of the saw blade does not exceed 0.2, the decrease in frequency is not significant, and therefore it is not necessary. Worry about the weakening of the bending stiffness of the saw blade. When the slot length is constant, the overall trend of the frequency change of each order is slowly decreasing as the number of slots increases. When the ratio of the radial root fatigue crack length to the blade radius does not exceed 0.2, the crack will not lead to a decrease in the dynamic performance of the saw blade. The saw blade can continue to be used after the crack tip has been drilled to eliminate stress and properly balanced.
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