基于分形理论的旋转超声磨削Si<sub>3</sub>N<sub>4</sub>陶瓷表面微观形貌

孙永国; 王伟; 李文知; 魏恒举; 魏士亮

doi:10.13394/j.cnki.jgszz.2023.0103

基于分形理论的旋转超声磨削Si₃N₄陶瓷表面微观形貌

doi: 10.13394/j.cnki.jgszz.2023.0103

哈尔滨理工大学, 高效切削及刀具国家地方联合工程实验室, 哈尔滨 150080

基金项目: 黑龙江省普通本科高等学校青年创新人才培养计划“石英陶瓷超声磨-抛复合加工表面形貌收敛关键技术研究”(UNPYSCT-2020195)。

详细信息

作者简介:
孙永国，男，1964年生，硕士、教授。主要研究方向：石油开采用机械设备等。E-mail：sygedu@163.com

通讯作者:
魏士亮，男，1987年生，博士、副教授。主要研究方向：难加工材料的精密加工。E-mail：weishiliang@hrbeu.edu.cn

中图分类号: TG58; TG74
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- PDF下载量: 26
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-06
- 修回日期: 2023-08-25
- 录用日期: 2023-09-08
- 网络出版日期: 2024-06-28
- 刊出日期: 2024-06-28

Surface micromorphology of Si₃N₄ ceramic by rotating ultrasonic grinding based on fractal theory

National and Local Joint Engineering Laboratory of High Efficiency Cutting and Tool, Harbin University of Science and Technology, Harbin 150080, China

摘要

摘要:
为了研究旋转超声磨削Si₃N₄陶瓷表面的微观形貌，基于分形理论研究不同加工参数下Si₃N₄陶瓷表面微观形貌的变化。设计旋转超声磨削Si₃N₄陶瓷正交试验，对比分析不同加工参数对Si₃N₄陶瓷表面分形维数和多重分形谱的影响，并设计单因素试验研究不同加工参数下Si₃N₄陶瓷表面的粗糙度、分形维数和多重分形谱。结果表明：旋转超声磨削Si₃N₄陶瓷表面时，分形维数能更好地表征其加工表面的缺陷状态，多重分形谱则能更好地表征其加工表面缺陷的起伏程度变化。
- 旋转超声磨削 /
- Si₃N₄陶瓷 /
- 分形维数 /
- 多重分形谱 /
- 微观形貌
Abstract:
To study the surface morphology of Si₃N₄ ceramics using rotary ultrasonic grinding, changes in the surface morphology under different machining parameters were analyzed based on fractal theory. Orthogonal experiments were designed to compare and analyze the effects of various processing parameters on the fractal dimensions and multifractal spectra of the Si₃N₄ ceramic surface. Additionally, single-factor experiments were conducted to study the roughness, fractal dimensions, and multifractal spectra of the Si₃N₄ ceramic surface under different processing parameters. The results show that fractal dimensions can effectively characterize the defect state of the processed surface of Si₃N₄ ceramics during rotary ultrasonic grinding, while multifractal spectra can better represent the degree of fluctuation in surface defects.
- rotary ultrasonic grinding /
- Si₃N₄ ceramics /
- fractal dimension /
- multifractal spectrum /
- microstructure

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图 1 试验设备

Figure 1. Test equipments

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图 2 轮廓算数平均偏差

Figure 2. Contour arithmetic mean deviation

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图 3 旋转超声磨削Si₃N₄陶瓷的表面轮廓线

Figure 3. Surface profile of Si₃N₄ Ceramic machined by rotating ultrasonic grinding

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图 4 网格划分示意图

Figure 4. Schematic diagram of grid division

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图 5 分形维数计算过程

Figure 5. Calculation process of fractal dimension

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图 6 多重分形谱计算过程

Figure 6. Calculation process of multifractal spectrum

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图 7 加工表面形貌图

Figure 7. Machined surface morphology diagram

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图 8 主轴转速对加工表面粗糙度和分形维数的影响

Figure 8. Influences of spindle speeds on machined surface roughness and fractal dimension

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图 9 进给速度对表面粗糙度和分形维数影响

Figure 9. Influence of feed speed on surface roughness and fractal dimension

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图 10 切削深度对表面粗糙度和分形维数影响

Figure 10. Influence of cutting depth on surface roughness and fractal dimension

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图 11 振动功率对表面粗糙度和分形维数影响

Figure 11. Influence of vibration power on surface roughness and fractal dimension

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图 12 加工参数对表面粗糙度与多重分形谱的影响

Figure 12. Influence of machining parameters on surface roughness and multifractal spectrum

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表 1 热压烧结Si₃N₄陶瓷机械性能

Table 1. Mechanical properties of hot-pressing sintered Si₃N₄ ceramics

参数	取值
密度 ρ / (g·cm⁻³)	3.21
硬度 H / GPa	16.5
断裂韧性 K_IC / (MPa·cm^−1/2)	7.8
抗压强度 σ / MPa	1 200
弹性模量 E / GPa	305

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表 2 因素和水平表

Table 2. Factor and level table

水平	因素
水平	主轴转速 n / (r·min⁻¹)	进给速度 V / (mm·min⁻¹)	切削深度 a_p / μm	振动功率 P / %
1	3 000	50	30	30
2	4 000	80	45	50
3	5 000	110	60	70
4	6 000	130	75	90

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表 3 试验方案

Table 3. Test scheme

试验组号	主轴转速 n / (r·min⁻¹)	进给速度 V / (mm·min⁻¹)	切削深度 a_p / μm	振动功率 P / %
1	3 000	50	30	30
2	5 000	80	30	70
3	6 000	130	30	90
4	4 000	80	30	50
5	4 000	130	60	30
6	6 000	110	45	30
7	5 000	80	75	30
8	3 000	130	75	70
9	6 000	50	75	50
10	3 000	110	60	50
11	4 000	110	75	90
12	4 000	50	45	70
13	5 000	50	60	90
14	5 000	130	45	50
15	6 000	80	60	70
16	3 000	80	45	90

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表 4 表面粗糙度、分形维数和多重分形谱的方差分析表

Table 4. Table of variance analysis of surface roughness, fractal dimension and multifractal spectrum

影响因素	因变量	均方值	F值	显著性
主轴转速 n / (r·min⁻¹)	R_a	0.032	103.648	0.002
	D	8.506	20.296	0.017
	Δa	0.001	10.007	0.045
	Δf(a)	0.000	2.548	0.231
进给速度 V / (mm·min⁻¹)	R_a	0.005	16.457	0.023
	D	0.001	146.496	0.001
	Δa	0.006	102.333	0.002
	Δf(a)	0.001	22.197	0.015
切削深度 a_p / μm	R_a	0.003	9.946	0.046
	D	3.456	8.246	0.058
	Δa	0.000	3.607	0.160
	Δf(a)	0.000	5.063	0.108
振动功率 P / %	R_a	0.000	1.023	0.493
	D	0.000	68.564	0.003
	Δa	0.001	18.185	0.020
	Δf(a)	7.743	1.784	0.323

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参考文献(23)

[1]	ZHANG Z, SHI K, HUANG X, et al. Development of a probabilistic algorithm of surface residual materials on Si₃N₄ ceramics under longitudinal torsional ultrasonic grinding [J]. Ceramics International,2022,48(9):12028-12037. doi: 10.1016/j.ceramint.2022.01.060
[2]	KUMAR K, KIM M J, PARK Y J, et al. Twofold increase in Weibull modulus of hot-pressed Si₃N₄ ceramic by modified pressing profile [J]. Materials Today Communications,2022(32):103979. doi: 10.1016/j.mtcomm.2022.103979
[3]	MOZAMMEL M, MORSHEDO M S, MD K, et al. Prediction and optimization of surface roughness in minimum quantity coolant lubrication applied turning of high hardness steel [J]. Measurement,2018(118):43-51.
[4]	全书海. 基于表面灰度图像的加工表面形貌分形特征研究 [D]. 武汉: 武汉理工大学, 2003. QUAN Shuhai. Research on fractal features of machined surface morphology based on surface grayscale images [D]. Wuhan: Wuhan University of Technology, 2003.
[5]	李静, 尹衍升, 马来鹏, 等. 分形理论在陶瓷材料断裂行为中的应用 [J]. 稀有金属材料与工程,2007(S1):707-710. LI Jing, YIN Yansheng, MA Laipeng, et al. Application of fractal theory in the fracture behavior of ceramic materials [J]. Rare Metal Materials and Engineering,2007(S1):707-710.
[6]	奚欣欣, 丁文锋, 傅玉灿, 等. 颗粒增强钛基复合材料高速磨削表面分形分析 [J]. 金刚石与磨料磨具工程,2014,34(6):26-29, 33. XI Xinxin, DING Wenfeng, FU Yucan, et al. Surface fractal analysis of particle reinforced titanium matrix composites during high-speed grinding [J]. Diamond and Abrasives Engineering,2014,34(6):26-29, 33.
[7]	邹明清. 分形理论的若干应用 [D]. 湖北: 华中科技大学, 2007. ZOU Mingqing. Several applications of fractal theory [D]. Hubei: Huazhong University of Science and Technology, 2007.
[8]	吴丁贵. 基于分形几何理论表面粗糙度测量系统的研究 [D]. 厦门: 厦门大学, 2014. WU Dinggui . Research on surface roughness measurement system based on fractal geometry theory [D]. Xiamen: Xiamen University, 2014.
[9]	张彦斌, 林滨, 梁小虎, 等. 基于分形理论表征工程陶瓷磨削表面 [J]. 硅酸盐学报,2013,41(11):1558-1563. ZHANG Yanbin, LIN Bin, LIANG Xiaohu, et al. Characterization of engineering ceramic grinding surface based on fractal theory [J]. Journal of Silicates,2013,41(11):1558-1563.
[10]	NI X, SUN J, MA C, et al. Wear model of a mechanical seal based on piecewise fractal theory [J]. Fractal and Fractional,2023,7(3):251. doi: 10.3390/fractalfract7030251
[11]	王洪娇, 秦襄培. 涂层表面形貌的分形表征研究 [J]. 机械,2020,47(11):71-75. doi: 10.3969/j.issn.1006-0316.2020.11.011 WANG Hongjiao, QIN Xiangpei. Fractal characterization of coating surface morphology [J]. Machinery,2020,47(11):71-75. doi: 10.3969/j.issn.1006-0316.2020.11.011
[12]	SHAO C X, GUO H, MENG S H, et al. Characterization of ceramic thermal shock cracks based on the multifractal spectrum [J]. Fractal and Fractional,2022,6(10):539. doi: 10.3390/fractalfract6100539
[13]	宋伟杰, 庞弘阳, 关山, 等. 基于多重分形谱参数的刀具磨损状态特征提取 [J]. 东北电力大学学报,2019,39(1):35-40. SONG Weijie, PANG Hongyang, GUAN Shan, et al. Feature extraction of tool wear state based on multifractal spectral parameters [J]. Journal of Northeast Electric Power University,2019,39(1):35-40.
[14]	徐善华, 夏敏. 锈蚀钢材表面的分形维数与多重分形谱 [J]. 材料导报,2020,34(16):16140-16143. doi: 10.11896/cldb.19070257 XU Shanhua, XIA Min. fractal dimension and multifractal spectrum of corroded steel surface [J]. Materials Herald,2020,34(16):16140-16143. doi: 10.11896/cldb.19070257
[15]	董中林, 汪祚远, 施毅, 等. 基于多重分形谱的粗糙模拟表面分析 [J]. 真空,2016(6):59-62. DONG Zhonglin, WANG Zuoyuan, SHI Yi, et al. Rough simulation surface analysis based on multifractal spectra [J]. Vacuum,2016(6):59-62.
[16]	王和旭. Si₃N₄ 陶瓷旋转超声磨削表面摩擦磨损特性研究 [D]. 哈尔滨: 哈尔滨工程大学, 2015. WANG Hexu. Study on the surface friction and wear characteristics of Si₃N₄ ceramic during rotary ultrasonic grinding [D]. Harbin: Harbin Engineering University, 2015.
[17]	魏士亮. Si₃N₄旋转超声磨削加工表面微观形貌创成机理及优化技术 [D]. 哈尔滨: 哈尔滨工程大学, 2016. WEI Shiliang. Mechanism and optimization technology of surface micromorphology formation in Si₃N₄ rotary ultrasonic grinding process [D]. Harbin: Harbin Engineering University, 2016.
[18]	樊福梅, 梁平, 吴庚申. 基于分形盒维数的汽轮机转子振动故障诊断的实验研究 [J]. 核动力工程,2006(1):85-89. FAN Fumei, LIANG Ping, WU Gengshen. Experimental study on fault diagnosis of steam turbine rotor vibration based on fractal box dimension [J]. Nuclear Power Engineering,2006(1):85-89.
[19]	淦犇, 黄宜坚. 铣削加工表面轮廓的几何分形特征 [J]. 华侨大学学报,2010,31(4):371-377. GAN Ben, HUANG Yijian. Geometric fractal features of surface profile in milling [J]. Journal of Huaqiao University,2010,31(4):371-377.
[20]	王雯朝. 加工表面形貌特征仿真与切削参数影响规律研究 [D]. 陕西: 西安理工大学, 2016. WANG Wenchao. Research on the simulation of surface morphology characteristics and the influence of cutting parameters in nachining [D] Shanxi: Xi’an University of Technology, 2016.
[21]	MIAO B, WANG X, Li H. Quantitative analysis of infrared thermal images in rock fractures based on multi-fractal theory [J]. Sustainability,2022,14(11):6543. doi: 10.3390/su14116543
[22]	杨红平, 傅卫平, 王雯, 等. 基于分形几何与接触力学理论的结合面法向接触刚度计算模型 [J]. 机械工程学报,2013,49(1):102-107. doi: 10.3901/JME.2013.01.102 YANG Hongping, FU Weiping, WANG Wen, et al. Calculation model of normal contact stiffness of joint surface based on fractal geometry and contact mechanics theory [J]. Journal of Mechanical Engineering,2013,49(1):102-107. doi: 10.3901/JME.2013.01.102
[23]	周兴林, 肖神清, 刘万康, 等. 沥青路面表面纹理的多重分形特征及其磨光行为 [J]. 东南大学学报(自然科学版),2018,48(1):175-180. doi: 10.3969/j.issn.1001-0505.2018.01.027 ZHOU Xinglin, XIAO Shenqing, LIU Wankang, et al. Multifractal characteristics and polishing behavior of asphalt pavement surface texture [J]. Journal of Southeast University (Natural Science Edition),2018,48(1):175-180. doi: 10.3969/j.issn.1001-0505.2018.01.027