5种规格金刚石圆锯片的行波振动分析及优化

高先一; 张德臣; 马国清; 刘兴东; 王育博

doi:10.13394/j.cnki.jgszz.2023.0008

5种规格金刚石圆锯片的行波振动分析及优化

doi: 10.13394/j.cnki.jgszz.2023.0008

辽宁科技大学机械工程与自动化学院, 辽宁鞍山 114051

详细信息

通讯作者:
张德臣，男，1964年生，教授。主要研究方向：机械动力学及其结构优化。E-mail：zhang1964ab@163.com

中图分类号: TQ164; TG74
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- 被引次数: 0
出版历程
- 收稿日期: 2023-01-13
- 修回日期: 2023-05-18
- 网络出版日期: 2023-11-06
- 刊出日期: 2024-02-20

Analysis and optimization of traveling wave vibration of five kinds of diamond circular saw blades

School of Mechanical Engineering and Automation, University of Science and Technology, Anshan 114051, Liaoning, China

摘要

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。
- 金刚石圆锯片 /
- 夹层 /
- 模态分析 /
- 行波振动
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.
- diamond circular saw blade /
- interlayer /
- modal analysis /
- traveling wave vibration

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图 1 金刚石圆锯片结构

Figure 1. Diamond circular saw blade structure

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图 2 方案一中金刚石圆锯片网格划分图

Figure 2. Grid division diagram of diamond circular saw blade in scheme 1

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图 3 方案五的金刚石圆锯片外观

Figure 3. Appearance of diamond circular saw blade in scheme 5

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图 4 5种方案的典型模态图

Figure 4. Typical modal diagrams of five schemes

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图 5 方案六的金刚石圆锯片

Figure 5. Diamond circular saw blade for scheme 6

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图 6 方案六和方案五的部分固有频率对比

Figure 6. Comparison of partial natural frequencies between scheme 6 and scheme 5

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图 7 方案六的典型固有模态图

K=5时方案六的9 344.20 Hz（2，2）模态

Figure 7. Typical intrinsic modal diagram of scheme 6

9 344.20 Hz（2，2）mode of scheme 6 at K=5

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图 8 3种规格锯片的方案五模型图

Figure 8. Scheme 5 model diagram for three sizes of saw blades

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图 9 105 mm锯片模型^[12]

Figure 9. 105 mm saw blade model

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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

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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
阶数 n	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

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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
方案	$ {P}_{\mathrm{f}} $ / Hz	$ {P}_{\mathrm{b}} $ / Hz	$ p $ / Hz	噪声 L_PN / dB	Δ_min / Hz	δ_min / %
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

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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

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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 / Hz
1	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

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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
P_f / Hz	7 591.07
P_b / Hz	9 010.86
$ p $ / Hz	8333.50
Δ_min / Hz	677.36
δ_min / %	8.13

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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
直径 D / mm	外径 D₂ / mm	内径 d₄ / mm
350	114.0	25.40
230	80.0	22.23
180	56.5	22.23

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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 L_PN1 / dB	方案二噪声 L_PN2 / dB	方案三噪声 L_PN3 / dB	方案四噪声 L_PN4 / dB	方案一与方案四比较降噪 L_PN5 / dB
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

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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 L_PN1 / dB	方案二噪声 L_PN2 / dB	方案三噪声 L_PN3/ dB	方案四噪声 L_PN4/ dB	方案七噪声 L_PN6 / dB	方案八噪声 L_PN7 / dB	降噪 L_PN5 / dB
115	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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