金刚石圆锯片行波共振分析及优化

赵雷; 张德臣; 闫春宝; 雷忠兴; 程黎斌

doi:10.13394/j.cnki.jgszz.2021.0112

金刚石圆锯片行波共振分析及优化

doi: 10.13394/j.cnki.jgszz.2021.0112

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: TG74;TQ164
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- 被引次数: 0
出版历程
- 收稿日期: 2021-09-06
- 修回日期: 2022-01-04
- 刊出日期: 2022-05-27

Analysis and optimization of traveling wave resonance of diamond circular saw blade

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

摘要

摘要: 针对金刚石圆锯片工作时出现的共振和噪声问题，利用Workbench软件对直径600 mm空转的圆锯片进行行波共振和静力分析，研究圆锯片基体中的开孔和夹层对其行波共振的影响。结果表明：圆锯片基体上合理开孔可以规避行波共振，其中开雨滴型孔的圆锯片减振效果最好，其δ最大值为4.36%，远大于未开孔与开圆形流线型孔的0.09%和0.91%。进一步对开雨滴型孔的圆锯片的夹层进行优化，其δ值为7.58%，达到夹层前的近2倍，更不容易引起行波共振。同时，优化后的圆锯片变形和应力值变大，但远小于其许用应力值，表明其强度和刚度满足使用要求，不会造成疲劳失效。
- 金刚石圆锯片 /
- 模态分析 /
- 行波共振 /
- 静力分析
Abstract: To solve the resonance and the noise problems of diamond circular saw blades during operation, the workbench software was used to analyze the traveling wave resonance and the static force of the idling circular saw blade with the diameter of 600 mm, and the effects of openings and interlayers in the circular saw blade matrix on its traveling wave resonance were studied. The results show that the reasonable openings in the matrix of circular saw blade can avoid traveling wave resonance, and the circular saw blade with raindrop holes has the best vibration reduction effect, the maximum value of δ is 4.36%, which is much larger than 0.09% and 0.91% of non-perforated and circular streamlined holes. The interlayer of circular saw blade with raindrop holes is further optimized, its δ value is 7.58%, which is nearly twice that before the interlayer, and it is not easy to cause traveling wave resonance. At the same time, the deformation and stress of the optimized circular saw blade become larger, but far less than its allowable stress value, indicating that its strength and stiffness meet the service requirements and will not cause fatigue failure.
- diamond circular saw blade /
- modal analysis /
- traveling wave resonance /
- static analysis

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图 1 金刚石圆锯片结构模型

Figure 1. Structural model of diamond circular saw blade

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图 2 金刚石圆锯片网格划分图

Figure 2. Grid division diagram of diamond circular saw blade

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图 3 基体不同开孔方案的金刚石圆锯片模型图

Figure 3. Model diagram of diamond circular saw blade with different opening schemes of matrix

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图 4 3种方案的典型模态图

Figure 4. Typical modal diagrams of three methods

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图 5 δ值分布图

Figure 5. δ value distribution diagram

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图 6 方案四中基体有开孔夹层的金刚石圆锯片

Figure 6. Diamond circular saw blade with matrix slotted interlayer in forth scheme

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图 7 方案对比图

Figure 7. Scheme comparison chart

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图 8 方案四的典型模态图

Figure 8. Typical modal diagram of fourth scheme

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图 9 金刚石圆锯片总体变形和应力分布图

Figure 9. Overall deformation and stress distribution of diamond circular saw blade

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表 1 ϕ600 mm金刚石圆锯片基本参数

Table 1. Basic parameters of ϕ600 mm diamond circular saw blade

参数	取值
外径 D₁ / mm	600
内径 d₁ / mm	50
厚度 t₁ / mm	2.8
齿数 Z / 个	40
弹性模量 E₁ / Pa	2.1$ \times $10¹¹
泊松比 ε₁	0.30
密度 ρ₁ / (kg·m⁻³)	7 800

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表 2 ϕ600 mm基体开孔金刚石圆锯片固有频率表

Table 2. Natural frequency table of ϕ600 mm matrix slotted diamond circular saw blade

阶数	固有频率 P / Hz
阶数	方案一	方案二	方案三
1	24.5	24.3	23.1
10	181.8	162.0	161.9
20	378.1	249.3	250.4
30	561.6	450.5	443.3
40	766.4	528.5	533.7
50	1 049.7	677.7	687.4
60	1 220.8	841.2	836.6
70	1 365.2	1 153.4	1 148.2
80	1 539.2	1 423.1	1 432.2
90	1 902.9	1 692.6	1 694.4
100	2 101.6	1 814.8	1 827.3
110	2 371.9	1 879.3	1 913.9
120	2 432.4	2 089.3	2 078.6
124	2 549.8	2 135.5	2135.4
130	2 720.8	2 267.7	2 294.0
140	3 061.3	2 402.3	2 471.4
150	3 433.9	2 606.5	2 625.8
153	3 522.7	2 679.6	2 655.3
154	3 533.2	2 739.8	2 714.3
157	3 639.5	2 772.1	2745.7
160	3 733.8	2 964.4	2 913.5
170	3 946.2	3 284.0	3 288.6
180	4 148.2	3 589.1	3 578.3
190	4 336.0	3 780.6	3 737.7
200	4 547.0	3 977.7	3 959.3

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表 3 金刚石圆锯片的行波振动分析数据表

Table 3. Data sheet of traveling wave vibration analysis of diamond circular saw blade

方案	数据
方案	$ {P}_{{\rm{f}}} $ / Hz	$ {P}_{{\rm{b}}} $ / Hz	p / Hz	Δ/ Hz	δ / %
一	2 683.0	2 661.7	2 664.0	2.3	0.09
二	2 639.8	2 605.6	2 664.0	24.2	0.91
三	3 021.6	2 547.8	2 664.0	116.2	4.36

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表 4 阻尼夹层基本参数

Table 4. Basic parameters of damping interlayer

参数	取值
外径 D₂ / mm	450
内径 d₂ / mm	50
厚度 t₂ / mm	1.0
弹性模量 E₂ / Pa	7.8×10⁶
泊松比 ε₂	0.47
密度 ρ₂ / (kg·m⁻³)	1 300

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表 5 方案四中100阶的固有频率

Table 5. 100 order natural frequencies in method 4

阶数	固有频率 P / Hz	阶数	固有频率 P / Hz
1	13.8	80	724.6
5	32.2	85	741.6
10	106.5	90	829.2
15	154.0	95	868.3
20	201.1	100	982.7
25	242.9	105	1 073.9
30	279.3	110	1 094.0
35	320.9	115	1 133.5
40	391.3	120	1 241.2
45	418.1	125	1 284.6
50	460.7	130	1 392.4
55	474.2	135	1 464.2
60	530.9	140	1 525.9
65	605.0	145	1 558.8
70	685.8	150	1 608.8
75	703.1

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表 6 方案四的行波振动分析数据

Table 6. Traveling wave vibration analysis data of fourth scheme

项目	取值
P_f / Hz	1 184.8
P_b / Hz	1 231.1
p / Hz	1 332.0
Δ / Hz	100.9
δ / %	7.58

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