Analysis and optimization of traveling wave vibration of five kinds of diamond circular saw blades
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摘要: 为降低金刚石圆锯片在石材切割时产生的锯切噪声,选取常规锯片、打孔锯片、切缝锯片以及在基体上开鼻型径向槽、开孔与夹层的5种典型金刚石圆锯片,利用Workbench软件对其模态、行波振动进行分析,研究其对行波振动的影响。结果表明:直径为180和230 mm的常规锯片出现行波共振,产生强烈噪声;直径为105、115和350 mm的常规锯片不出现行波共振。直径为180和230 mm的切缝锯片δ值偏大,有效避开了行波共振;直径为115和350 mm的切缝锯片δ值偏小,其降噪效果差;而直径为105 mm的夹层锯片δ值偏大,降噪效果好。5种直径锯片采用开鼻形径向槽、雨滴孔和阻尼夹层的设计方案,其δ值分别为8.13%、7.21%、6.01%、6.39%和7.00%,可进一步避开行波共振,其降噪效果更好。Abstract: In order to reduce the sawing noise generated by diamond circular saw blades during stone processing, five typical diamond circular saw blades were selected for modal analysis and traveling wave vibration analysis by using Workbench software. The study explored the impact of various saw blade designs, including conventional saw blades, perforated saw blades, slit saw blades, and saw blades with nose-shaped radial grooves, holes, and interlayers, on traveling wave vibrations. The results show that the traveling wave resonance occurs in the conventional saw blades with diameters of 180 mm and 230 mm, causing strong noise. Conventional saw blades with diameters of 115 mm, 350 mm and 105 mm do not show traveling wave resonance. The δ value for the 180 mm and 230 mm saw blades is too large, which effectively presents traveling wave resonance. The δ value for the 115 mm and 350 mm saw blade is too small, which does not reduce noise very well. The δ value for the 105 mm sandwich saw blade is too large and has a significant effect on noise reduction. To avoid traveling wave resonance and enhance noise reduction, five design schemes incorporating radial grooves, raindrop holes, and damping interlayers are proposed for various blade diameters. The resulting δ values are 8.13 %, 7.21 %, 6.01 %, 6.39 %, and 7.00 %, respectively.
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Key words:
- diamond circular saw blade /
- interlayer /
- modal analysis /
- traveling wave vibration
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图 9 105 mm锯片模型[12]
Figure 9. 105 mm saw blade model
表 1 圆锯片尺寸和物理参数
Table 1. Dimensions and physical parameters of circular saw blade
参数 取值 直径 D / mm 115 内径 d1 / mm 22.30 法兰盘内径 d2 / mm 44.46 基体厚度 t1 / mm 1.2 刀头厚度 t2 / mm 2.0 齿数 Z / 个 10 基体杨氏模量 E1 / Pa 2.1$ \times $1011 基体泊松比 ε1 0.30 基体密度 ρ1 / (kg·m−3) 7 800 刀头杨氏模量 E2 / Pa 5.6$ \times $1011 刀头泊松比 ε2 0.47 刀头密度 ρ2 / (kg·m−3) 2100 表 2 5种方案中金刚石圆锯片的部分典型固有频率
Table 2. Partial typical natural frequencies of diamond circular saw blades in five schemes
阶
数
n固有频率 f / Hz 方案
一方案
二方案
三方案
四方案
五1 616.91 602.23 407.67 514.89 473.46 10 966.07 950.96 759.00 841.28 902.41 20 3 074.60 3 052.90 2 712.60 2859.00 3 037.60 24 5 376.40 5 321.20 3 474.10 4 719.00 4 891.70 26 6 145.50 6 082.40 3 484.60 5 191.70 5 593.40 30 7427.00 7 333.20 3 513.80 5 682.40 6 415.40 40 12 455.00 12 173.00 4 590.10 8 392.70 10 911.00 49 13 764.00 13 648.00 5 048.60 9 990.10 13 132.00 50 13 765.00 13 648.00 5 048.80 9 994.70 13 134.00 60 16 867.00 16 810.00 6 362.60 10 994.00 15 854.00 70 23 274.00 23 121.00 9 931.20 11 332.00 19 187.00 80 25 984.00 25 901.00 11 678.00 13 530.00 22 574.00 90 29 741.00 28 971.00 12 164.00 17 256.00 23 951.00 100 32 652.00 32 505.00 12 517.00 18 262.00 26 648.00 表 3 5种方案的锯片行波振动计算值
Table 3. Calculated values of saw blade traveling wave vibration in 5 schemes
方案 数据 $ {P}_{\mathrm{f}} $ / Hz $ {P}_{\mathrm{b}} $ / Hz $ p $ / Hz 噪声 LPN / dB Δmin / Hz δmin / % 一 6645.51 6312.02 6666.80 98.0 21.29 0.32 二 12975.02 13481.33 13333.60 96.5 147.73 1.11 三 12667.35 13155.65 13333.60 96.0 177.95 1.33 四 6515.75 6400.15 6666.80 95.5 151.05 2.27 五 5225.04 5640.62 5000.10 224.94 4.50 表 4 阻尼夹层的尺寸和物理参数
Table 4. Size and physical parameters of damping interlayer
参数 取值 外径 D1 / mm 73.0 内径 d3 / mm 22.23 厚度 t3 / mm 0.4 弹性模量 E3 / Pa 7.8 × 106 泊松比 ε3 0.47 密度 ρ3 / (kg·m−3) 1 300 表 5 方案六的部分固有频率
Table 5. Partial natural frequencies of scheme 6
阶数
n固有频率
f / Hz阶数 n 固有频率
f / Hz1 378.75 45 9 732.20 5 414.13 50 10 139.00 10 848.54 65 10 704.00 15 1 817.20 70 13 669.00 20 2 117.00 75 14 665.00 25 3 693.00 80 15 601.00 30 5 459.70 85 16 469.00 35 8 388.20 90 16 661.00 40 9 290.00 95 17 244.00 42 9 344.20 100 19 262.00 表 6 方案六的行波振动计算值
Table 6. Traveling wave vibration calculate values of scheme 6
项目 取值 Pf / Hz 7 591.07 Pb / Hz 9 010.86 $ p $ / Hz 8333.50 Δmin / Hz 677.36 δmin / % 8.13 表 7 3种规格锯片阻尼夹层的尺寸
Table 7. Dimensions of three types of saw blade damping interlayer
直径
D / mm取值 外径 D2 / mm 内径 d4 / mm 350 114.0 25.40 230 80.0 22.23 180 56.5 22.23 表 8 3种方案的行波振动计算结果
Table 8. Calculation results of traveling wave vibration for three schemes
直径
D / mm是否行
波振动方案一
δ1 / %方案二
δ2 / %方案三
δ3 / %方案四
δ4 / %方案五
δ5 / %方案六
δ6 / %方案一
噪声
LPN1 / dB方案二
噪声
LPN2 / dB方案三
噪声
LPN3 / dB方案四
噪声
LPN4 / dB方案一与方案
四比较降噪
LPN5 / dB350 否 0.48 1.13 1.49 2.39 5.82 7.21 98.0 100.0 97.0 96.5 1.5 230 是 0.11 1.52 4.01 4.07 5.17 6.39 107.0 103.0 101.0 100.0 7.0 180 是 0.04 2.23 3.53 4.17 4.43 6.01 103.0 101.0 96.5 96.0 7.0 表 9 5种规格金刚石圆锯片行波振动计算结果
Table 9. Calculation results of traveling wave vibration for five kinds of diamond circular saw blades
直径
D / mm是否
行波
振动方案一
δ1 / %方案二
δ2 / %方案三
δ3 / %方案四
δ4 / %方案五
δ5 / %方案六
δ6 / %方案七
δ7 / %方案八
δ8 / %方案九
δ9 / %方案十
δ10 / %方案一
噪声
LPN1 / dB方案二
噪声
LPN2 / dB方案三
噪声
LPN3/ dB方案四
噪声
LPN4/ dB方案七
噪声
LPN6 / dB方案八
噪声
LPN7 / dB降噪
LPN5 / dB115 否 0.32 1.11 1.33 2.27 4.50 8.13 98.0 96.5 96 95.5 2.5 350 否 0.48 1.13 1.49 2.39 5.82 7.21 98.0 100.0 97.0 96.5 1.5 230 是 0.11 1.52 4.01 4.07 5.17 6.39 107.0 103.0 101.0 100.0 7.0 180 是 0.04 2.23 3.53 4.17 4.43 6.01 103.0 101.0 96.5 96.0 7.0 105 否 0.24 4.68 4.14 7.00 94.0 84.0 10.0 -
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