大型金刚石薄壁钻头行波振动分析及优化

刘兴东; 张德臣; 王育博; 高先一; 马国清

doi:10.13394/j.cnki.jgszz.2023.0137

大型金刚石薄壁钻头行波振动分析及优化

doi: 10.13394/j.cnki.jgszz.2023.0137

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: TG713+.1 ；TG74；TQ164
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出版历程
- 收稿日期: 2023-07-06
- 修回日期: 2023-09-20
- 录用日期: 2023-10-26
- 网络出版日期: 2023-11-06
- 刊出日期: 2024-08-20

Analysis and optimization of traveling wave vibration of large diamond thin-wall drill bits

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

摘要

摘要: 针对大型金刚石薄壁钻头在钻切中出现的振动和噪声问题，用Ansys Workbench有限元软件对无开孔、开孔、开孔且夹层和安装定位轮的薄壁钻头进行模态分析，进一步用行波振动理论计算薄壁钻头共振裕度δ，分析避开行波共振的效果，研究开孔、夹层对行波振动的影响。结果表明：钻切转速为187.32 r/min时，无开孔薄壁钻头的共振裕度δ为0，出现后行波共振；在无开孔薄壁钻头出现后行波共振固有模态变形大的区域开8组圆孔（每组3个）和8个S形孔，薄壁钻头的共振裕度δ为5.18%，避开行波共振效果良好；开孔且夹层的薄壁钻头的共振裕度δ为6.11%，避开行波共振效果最好。为提高孔的加工精度，在薄壁钻头周围安装定位轮，分析定位轮数对行波振动的影响，发现安装6个和12个定位轮的薄壁钻头的共振裕度δ分别为4.59%和4.79%，避开行波共振效果好。比较2~12个定位轮薄壁钻头的共振裕度δ，而且考虑安装方便，最后确定最佳安装定位轮数为6个。
- 金刚石薄壁钻头 /
- 开孔夹层 /
- 定位轮 /
- 行波振动
Abstract: Objectives: To reduce the vibration and noise generated by thin-walled drill bits during the drilling and cutting process, various designs of thin-walled drill bits were studied, including conventional thin-walled drill bits, open-hole thin-walled drill bits, open-hole and interlayer thin-walled drill bits, and thin-walled drill bits with positioning wheel. The reasons for vibration and noise reduction of thin-walled drill bits in different schemes were analyzed at a theoretical level. A new scheme for thin-walled drill bits was proposed, which exhibited good vibration reduction effects, protected the hearing of thin-walled drill bit operators, and complied with China's environmental indicators for workers. Methods: Modal analysis and traveling wave vibration analysis of thin-walled drill bits were performed using Workbench software to study the effects of different thin-walled drill bit designs on traveling wave vibration. First, a solid work model of the thin-walled drill bit was imported into Workbench software and meshed. The inner hole of the thin-walled drill bit was constrained (cantilever type), and the first 30-order modes of the thin-walled drill bit were calculated under standard earth gravity. Using traveling wave vibration theory, the δ value of the resonance margin of the thin-walled drill bit in different schemes was calculated to determine the effectiveness of avoiding traveling wave resonance. Results: At a drilling speed of 187.32 r/min, the conventional thin-walled drill bit had a δ value of 0, leading to rear traveling wave resonance. The opening of 8 groups of round holes and 8 S-hole thin-walled drill bits had a δ value of 5.18%, which was the best opening design scheme. Further interlayering the thin-walled drill bit resulted in a δ value of 6.11%, showing the best effect in avoiding traveling wave resonance. In the δ where 2 to 12 positioning wheels thin-walled drill bits were installed, the δ of 2, 3 and 11 positioning wheels thin-walled drill bits was less than 1.00%, effectively avoiding traveling wave resonance. Conclusions: Thin-walled drill bits with traveling wave resonance will produce strong vibration and noise. Reducing the deformation of the thin-walled drill bit increases the δ value, leading to better vibration and noise reduction. To ensure the precision of the drilled hole, the positioning theory was applied to the thin-walled drill bit. When comparing δ values for drill bits with 2 to 12 positioning wheels, the designs with 6 and 12 positioning wheels had larger δ values and better vibration damping effects. Considering installation convenience, 6 positioning wheels were determined to be the optimal number, providing a theoretical basis for reasonable determination of the number of positioning wheels.
- diamond thin-wall drill bits /
- opening and interlayer /
- positioning wheel /
- traveling wave vibration

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图 1 钻头结构

Figure 1. Structure of drill bit

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图 2 方案一钻头结构

Figure 2. Scheme 1 drill bit structure

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图 3 方案一钻头的网格划分

Figure 3. Mesh division of Scheme 1 drill bit

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图 4 方案一钻头的235.54 Hz（2，4）模态图

Figure 4. 235.54 Hz (2, 4) modal diagram of Scheme 1 drill bit

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图 5 方案一钻头坎贝尔图

Figure 5. Campbell diagram of Scheme 1 drill bits

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图 6 方案二钻头结构

Figure 6. Structure of Scheme 2 drill bit

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图 7 方案二钻头的233.25 Hz（2，4）模态图

Figure 7. 233.25 Hz (2, 4) modal diagram of Scheme 2 drill bit

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图 8 方案三钻头结构

Figure 8. Structure of Scheme 3 drill bit

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图 9 方案三钻头的201.82 Hz（2，4）模态图

Figure 9. 201.82 Hz（2，4）modal diagram of Scheme 3 drill bit

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图 10 方案四钻头结构

Figure 10. Structure of Scheme 4 drill bit

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图 11 4种方案钻头固有频率分布图

Figure 11. Distribution diagram of four schemes natural frequencies

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图 12 方案四钻头的234.01 Hz（2，8）模态图

Figure 12. 234.01 Hz (2, 8) modal diagram of Scheme 4 drill bit

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图 13 4种方案$ \mathbf{\delta } $分布图

Figure 13. Distribution diagram of four schemes of $ \mathbf{\delta } $

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图 14 方案六钻头结构

Figure 14. Structure of Scheme 6 drill bit

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图 15 安装定位轮的4种方案钻头固有频率分布图

Figure 15. Four schemes for installing positioning wheels: natural frequency distribution of drill bits

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图 16 4种方案钻头的模态图

Figure 16. Modal diagram of four schemes drill bits

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图 17 安装不同定位轮数钻头的$ \mathbf{\delta } $分布图

Figure 17. Distribution diagram of installing different number of positioning wheels $ \mathbf{\delta } $

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表 1 钻头基本参数

Table 1. Basic parameters of thin-wall drill bit

参数	数值
外径 $ D_1/\mathrm{m}\mathrm{m} $	1200
内径 $ {d}_{1}/\mathrm{m}\mathrm{m} $	300
厚度 $ {t}_{1}/\mathrm{m}\mathrm{m} $	12
齿数 $ Z\ /\mathrm{个} $	72
高度 $ {H}_{1}/\mathrm{m}\mathrm{m} $	1500
基体弹性模量 $ E_1/\ \mathrm{P}\mathrm{a} $	2.1 × 10¹¹
基体泊松比 $ {\varepsilon }_{1} $	0.30
密度 $ \rho_{1\ }/\left(\mathrm{k}\mathrm{g}\cdot\mathrm{m}^{-3}\right) $	7800

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表 2 方案一钻头前30阶固有频率

Table 2. First 30 natural frequencies of Scheme 1 drill bit

阶数	固有频率 $ P_{ }\left(\mathrm{\mathit{m}},\mathrm{\mathit{n}}\right)/\ \mathrm{H}\mathrm{z} $	阶数	固有频率 $ P_{ }\left(\mathrm{\mathit{m}},\mathrm{\mathit{n}}\right)\ /\mathrm{\ H}\mathrm{z} $
1	8.73	16	254.88
2	8.73	17	285.60
3	24.19	18	285.63
4	24.19	19	298.96
5	27.25	20	298.96
6	64.88	21	325.28
7	64.89	22	325.31
8	122.11	23	348.30
9	122.11	24	348.31
10	195.72	25	357.71
11	195.74	26	391.60
12	198.41	27	391.67
13	235.54	28	400.03
14	235.54	29	400.06
15	254.87	30	424.89

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表 3 方案四钻头夹层材料基本参数

Table 3. Basic parameters of Scheme 4 drill bit interlayer material

参数	数值
外径 $ {D}_{2} $ / mm	1192
厚度 $ {t}_{2} $/ mm	4
高度 $ {H}_{2} $/ mm	933
弹性模量 $ {E}_{2} $/ $ \mathrm{P}\mathrm{a} $	$ 7.86\times {10}^{6} $
泊松比 $ {\varepsilon }_{2} $	0.47
密度 $ {\rho }_{2} $ / ($ \mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{-3} $)	1300

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表 4 钻头行波振动计算结果

Table 4. Calculation results of drill bits traveling wave vibration

方案	前行波频率 $ \mathrm{\mathit{P}}_{\mathrm{f}}\ /\ \mathrm{H}\mathrm{z} $	后行波频率 $ \mathrm{\mathit{P}}_{\mathrm{b}}\ /\mathrm{\ H}\mathrm{z} $	$ \mathit{\Delta}_{\mathrm{m}\mathrm{i}\mathrm{n}}\ /\mathrm{\ H}\mathrm{z} $	共振裕度 $ \mathrm{\delta }/\mathrm{\%} $
一	246.82	224.78	0	0
二	244.53	222.49	2.29	1.03
三	213.14	191.10	11.64	5.18
四	259.50	211.05	13.73	6.11

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表 5 前30阶固有频率

Table 5. First 30 natural frequencies

阶数	固有频率P（m, n）/Hz
阶数	方案六	方案八	方案九	方案十一
1	26.65	26.41	26.17	25.72
2	83.71	76.77	131.21	185.39
4	99.56	95.88	134.39	200.55
6	141.06	134.03	150.19	227.90
8	143.00	191.79	177.82	258.09
10	222.42	225.04	226.95	269.46
12	223.23	228.42	240.42	271.27
13	240.44	301.30	244.29	305.67
14	280.72	303.58	286.92	308.94
16	298.43	331.48	307.79	347.72
18	330.93	341.22	347.05	362.87
20	344.19	348.57	355.73	380.93
22	347.35	355.93	390.73	383.65
24	356.13	400.48	400.47	401.33
26	399.07	406.26	404.10	411.16
28	409.79	409.80	411.10	433.30
30	439.46	448.67	456.11	471.20

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表 6 行波振动计算结果

Table 6. Calculation results of traveling wave vibration

方案	定位轮数N' / 个	前行波频率 $ P_{\mathrm{f}}\ /\ \mathrm{H}\mathrm{z} $	后行波频率 $ P_{\mathrm{b}}\ /\mathrm{\ H}\mathrm{z} $	$ \mathit{\Delta}_{\mathrm{m}\mathrm{i}\mathrm{n}}\ /\mathrm{\ H}\mathrm{z} $	共振裕度 $ \delta\ /\ \mathrm{\%} $
五	2	248.03	225.99	1.21	0.54
六	4	251.71	229.67	4.89	2.18
七	5	250.57	221.75	3.03	1.35
八	6	243.28	214.46	10.32	4.59
九	8	265.84	217.43	7.35	3.27
十	10	290.55	229.35	4.57	2.03
十一	12	242.82	214.01	10.77	4.79

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