Simulation and experiment of ultrasonic-assisted grinding process for natural diamond
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摘要:
为提高天然金刚石研磨的表面质量，引入超声振动进行复合研磨加工，建立非弹性碰撞理论模型，计算超声振动幅值。以表面粗糙度为指标，研究超声振幅、研磨转速、磨粒粒度相关工艺参数对天然金刚石（100）晶面材料去除的影响，并寻求最优工艺参数。结果表明：（110）晶面易磨方向的振幅取值范围为3.1～8.7 μm，（100）晶面易磨方向的振幅取值范围为2.9～9.1 μm。通过正交实验获取的（110）晶面研磨最优工艺组合参数是超声振幅为6.0 μm，研磨盘转速为2 800 r/min，金刚石磨粒粒度代号为M3/6。与传统机械研磨相比，超声辅助研磨后的金刚石（100）晶面表面粗糙度Ra为16.21 nm，同比下降了63.83%。超声辅助研磨天然金刚石可以获得比传统机械研磨更好的表面质量。
Abstract:[OBJECTIVES] Diamond is the hardest known naturally occurring single crystal mineral in nature, and due to its high hardness and brittleness, it has become a typical difficult-to-process material. With the development of ultrasonic composite processing technology and the updating of diamond grinding technology, ultrasonic vibration-assisted grinding shows advantages such as high surface integrity and low damage for hard brittle materials. In order to improve the surface quality of natural diamonds, ultrasonic vibration was introduced to conduct composite grinding on natural diamonds.
[METHODS] Utilizing the composite action of abrasives on the surface of diamonds during ultrasonic-assisted grinding, as well as the characteristics of natural diamonds, a non-elastic collision theory model was established to calculate the amplitude of ultrasonic vibration. Due to the anisotropy of natural diamonds, two-dimensional planar unidirectional cutting was used to avoid its influence. Mathematical limit approach was employed to simulate and analyze circular motion as linear motion. Using surface roughness as an indicator, an orthogonal experiment was established to study the effects of ultrasonic amplitude, grinding speed, and abrasive particle size on the removal of natural diamond (100) crystal surface material, and to seek the optimal process parameters. To improve grinding efficiency, diamond micro-powder with a basic particle size greater than 1.0 μm was typically selected. Coarse-grained diamond grinding powder can improve grinding efficiency. Therefore, diamond micro-powder with particle size designations of M1/2 (basic particle size of 1.0~2.5 μm), M2/4 (basic particle size of 1.5~3.5 μm), and M3/6 (basic particle size of 2.5~5.0 μm) was selected. An L34 (9) orthogonal experiment was conducted on the easy grinding direction of the natural diamond (100) crystal surface at ultrasonic amplitudes of 3.0, 6.0, and 9.0 μm.
[RESULTS] The primary and secondary relationships affecting diamond surface roughness were ultrasonic amplitude (B) > abrasive particle size designation (D) > grinding disc speed (C). The optimal process parameter combination for achieving the lowest diamond surface roughness was identified as B2C2D3, with an ultrasonic amplitude of 6.0 μm, a grinding disc speed of 2,800 r/min, and an abrasive particle size designation of M3/6. Under the optimal process parameter combination, good surface quality could be achieved after 30 minutes of grinding: the surface roughness Ra of diamond after traditional grinding was 44.81 nm, whereas after ultrasonic-assisted grinding, the surface roughness Ra was 16.21 nm, representing a decrease of 63.83%. SEM inspection of the natural diamond surface revealed cracks and scratches after traditional mechanical grinding, whereas the surface quality of diamonds ground using the optimal process parameters was good, without defects such as cracks or fractures. It can be concluded that using the optimal grinding process parameters can significantly reduce the surface roughness of natural diamonds and improve their surface quality.
[CONCLUSION] Theoretical calculations revealed that the range of ultrasonic amplitude values for the easy grinding direction of natural diamond (110) crystal surfaces was 3.1~8.7 μm, and for the easy grinding direction of (100) crystal surfaces was 2.9~9.1 μm. Simulation and analysis of cutting on (100) crystal surfaces showed that the stress experienced by the workpiece and abrasive particles increased with increasing amplitude, while the temperature decreased, indicating that ultrasonic processing could effectively reduce cutting temperature and chip accumulation. Ultrasonic vibration grinding experiments showed that the overall surface quality of materials was superior to that of traditional mechanical grinding. Among the three elements of grinding, the degree of influence was in the order of ultrasonic amplitude > abrasive particle size designation > grinding disc speed. The optimal process parameter combination obtained through orthogonal experiments was an ultrasonic amplitude of 6.0 μm, a grinding disc speed of 2,800 r/min, and an abrasive particle size designation of M3/6. Under these optimal conditions, the surface roughness of ground diamonds was as low as 16.21 nm, representing a decrease of 63.83% compared to traditional mechanical grinding.
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图 3 （100）晶面不同超声振动幅度下的应力与温度变化
Figure 3. Stress and temperature changes of (100) crystal plane under different ultrasonic vibration amplitudes
图 5 1～9条件下超声辅助研磨的天然金刚石表面粗糙度
Figure 5. Surface roughness of natural diamond after ultrasonic assisted grinding under 1 to 9 conditions
图 6 传统和超声研磨的天然金刚石表面粗糙度
Figure 6. Surface roughness of natural diamond by traditional and ultrasonic grinding
表 1 动态脆塑转变临界研磨深度值[12]
Table 1. Critical grinding depth values of dynamic brittle plastic transition[12]
易难研磨
方向数值晶面 （110） （100） 易磨值 acp1 / nm 12.3 7.7 难磨值 acp2 / nm 3.5 3.1 
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表 2 超声振幅理论计算值
Table 2. Ultrasonic amplitude theoretical calculation values
振幅 晶面 （110） （100） 最小值 Amin / μm 3.1 2.9 最大值 Amax / μm 8.7 9.1
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表 3 （100）晶面的JH-2本构模型参数
Table 3. JH-2 constitutive model parameters of (100) crystal plane
参数 取值 ρ / (ton/mm3) 2.50×10−9 E / MPa 1.05×10−6 D1 / MPa 0.35 D2 / MPa 0.35 K1 / MPa 4.42×105 K2 / MPa 5.62×105 K3 / MPa 0.00 HEL / MPa 1.5×104 PHEL / MPa 6.0×103 A 0.95 B 0.40 C 0.00 M 1.00 N 0.70 β 1.00 Fs 0.50
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表 4 超声研磨因素及水平
Table 4. Factors and levels of ultrasonic grinding
水平 因素 超声振幅
A / μm
B研磨盘转速
n / (r·rmin−1)
C磨料粒度代号
W
D1 3.0 2 600 M1/2 2 6.0 2 800 M2/4 3 9.0 3 000 M3/6
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表 5 正交实验结果
Table 5. Orthogonal test results
条件编号 B C D 表面粗糙度 Ra / nm 1 1 1 1 28.02 2 1 2 2 32.24 3 1 3 3 25.73 4 2 1 2 19.44 5 2 2 3 22.03 6 2 3 1 24.46 7 3 1 3 28.25 8 3 2 1 18.04 9 3 3 2 32.76
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表 6 极差分析结果
Table 6. Analysis results of extreme differences
水平 B C D 1 28.663 25.237 23.507 2 21.977 24.103 28.147 3 26.350 27.650 21.070 极差 6.686 3.547 4.640
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