基于CFD的高速电主轴气隙风摩损耗研究

赵海宁; 王同海; 赵川; 徐方超; 杨文华; 李博; 梁忠伟; 孙凤

doi:10.3969/j.issn.0258-2724.20250548

基于CFD的高速电主轴气隙风摩损耗研究

doi: 10.3969/j.issn.0258-2724.20250548

1.
沈阳工业大学机械工程学院，辽宁沈阳 110870
2.
沈阳机床股份有限公司，辽宁沈阳 110142
3.
广州大学机械与电气工程学院，广东广州 510006

详细信息

作者简介:
赵海宁（1981—），男，高级工程师，研究方向为磁力驱动技术及数控装备技术，E-mail：zhaohaining@sut.edu.cn

通讯作者:
孙凤（1978—），男，教授，研究方向为机械系统多元驱动及其控制技术，E-mail：sunfeng@sut.edu.cn

中图分类号: TK01.1
计量
- 文章访问数: 4
- HTML全文浏览量: 3
- PDF下载量: 0
- 被引次数: 0
出版历程
- 收稿日期: 2025-10-25
- 录用日期: 2026-03-11
- 修回日期: 2026-03-01
- 网络出版日期: 2026-03-14

Research on Air-Gap Windage Loss in High-Speed Motorized Spindles Based on Computational Fluid Dynamics

1.
School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China
2.
Shenyang Mechine Tool Co., Ltd., Shenyang 110142, China
3.
School of Mechanical and Electring Engineering, Guangzhou University, Guangzhou 510006, China

摘要

摘要:
针对高速永磁电主轴因气隙内空气摩擦损耗引发的散热与能效设计难题，揭示定子槽口与轴向通风冷却的耦合作用下风摩损耗的形成机理及涡流演变规律. 首先，分别建立光滑壁面的理想气隙模型与包含18个定子槽口的实际气隙模型；其次，通过对比2种气隙模型在无轴向通风条件下的能量耗散差异，定量评估定子槽口的独立影响；最后，通过施加不同流速的轴向冷却气流，系统评估通风强度对气隙内部流场结构及能量耗散特性的非线性调控作用. 结果表明：定子槽口是导致风摩损耗激增的决定性因素，与光滑壁面理想气隙相比，定子槽口引起的附加损耗增幅近80%；在含定子槽口气隙中，轴向通风对损耗的调控呈现显著的非单调、分阶段特性：在引入微弱轴向通风后，损耗在2.00 m/s时降至最低，降幅超过19%；当流速进入6.00～10.00 m/s的临界区间，流场失稳导致能量耗散急剧跃升超过26%；而当流速超过10.00 m/s后，涡系压制效应主导流场恢复稳定，能量耗散在骤降后呈稳定单调增长趋势.
- 永磁电主轴 /
- 定子槽口 /
- 风摩损耗 /
- 轴向流 /
- 涡流 /
- 计算流体动力学
Abstract:
To address the design challenges of heat dissipation and energy efficiency caused by air friction loss in the air gap of high-speed permanent magnet motorized spindles, the formation mechanism of windage loss and the evolution laws of vortex flow under the coupled effect of stator slots and axial ventilation cooling were revealed. First, an ideal air-gap model with smooth walls and a realistic air-gap model containing 18 stator slots were established, respectively. Second, the independent impact of stator slots was quantitatively evaluated by comparing the energy dissipation differences between the two air-gap models under the condition of no axial ventilation. Finally, the nonlinear regulation effect of ventilation intensity on the internal flow field structure and energy dissipation characteristics of the air gap was systematically evaluated by applying axial cooling airflows at different velocities. The results indicate that stator slots are the decisive factor leading to the surge of windage loss. Compared with the ideal air gap with smooth walls, the increase in additional loss caused by stator slots is nearly 80%. In the air gap containing stator slots, the regulation of loss by axial ventilation exhibits significant non-monotonic and multi-stage characteristics: After weak axial ventilation is introduced, the loss decreases to the minimum at 2 m/s, with a decrease of more than 19%; when the flow velocity enters the critical range of 6–10 m/s, the flow field instability leads to a sharp surge in energy dissipation by over 26%; when the flow velocity exceeds 10 m/s, the vortex suppression effect dominates the flow field to restore stability, and the energy dissipation shows a steady and monotonic increasing trend after a sudden drop.
- permanent magnet motorized spindle /
- stator slot /
- windage loss /
- axial flow /
- vortex flow /
- Computational fluid dynamics (CFD)

HTML全文

图 1 永磁电主轴结构图

Figure 1. Structure diagram of permanent magnet motorized spindle spindle

下载: 全尺寸图片幻灯片

图 2 电主轴气隙模型三维视图

Figure 2. Three-dimensional view of motorized spindle air-gap model

下载: 全尺寸图片幻灯片

图 3 基于经验公式的风摩损耗预测

Figure 3. Windage loss prediction based on empirical formula

下载: 全尺寸图片幻灯片

图 4 电主轴气隙模型网格划分

Figure 4. Mesh independence verification of ideal air gap

下载: 全尺寸图片幻灯片

图 5 理想气隙网格无关性验证

Figure 5. Mesh generation of motorized spindle air-gap model

下载: 全尺寸图片幻灯片

图 6 凹槽气隙网格无关性验证

Figure 6. Quantitative result of mesh independence for grooved air gap

下载: 全尺寸图片幻灯片

图 7 理想光壁气隙风摩损耗数值模拟验证

Figure 7. Numerical simulation validation of windage loss in ideal smooth-walled air gap

下载: 全尺寸图片幻灯片

图 8 理想光壁气隙切向速度分布

Figure 8. Tangential velocity distribution in ideal smooth-walled air gap

下载: 全尺寸图片幻灯片

图 9 基于CFD模拟的风摩损耗对比

Figure 9. Comparison of windage loss between ideal smooth-walled and stator-grooved air-gap models based on CFD simulation

下载: 全尺寸图片幻灯片

图 10 凹槽气隙压力场与流线图

Figure 10. Pressure field and streamlines of grooved air gap

下载: 全尺寸图片幻灯片

图 11 气隙涡流与速度云图

Figure 11. Vortex flow and velocity contour of air gap

下载: 全尺寸图片幻灯片

图 12 不同轴向流速与转速条件下风摩损耗变化规律

Figure 12. Comparison of windage loss of ideal smooth-walled air gap under different conditions

下载: 全尺寸图片幻灯片

图 13 不同轴向流态区间下的风摩损耗特性

Figure 13. Windage loss characteristics under different axial flow regimes

下载: 全尺寸图片幻灯片

图 14 不同轴向流速下凹槽气隙子午面速度分布云图

Figure 14. Velocity distribution contour on meridional plane of grooved air gap under different axial flow velocities

下载: 全尺寸图片幻灯片

图 15 气隙流场涡核结构（Q准则）

Figure 15. Vortex-core structure of air-gap flow field （Q-criterion）

下载: 全尺寸图片幻灯片

表 1 电主轴主要参数

Table 1. Main parameters of motorized spindle

参数	取值
额定功率/kW	25
额定转速/r•min^–1	30 000
转子护套内外径/mm	76/80
转子护套长度/mm	158
电磁气隙长度/mm	1
槽数/极数/相数	18/4/3
永磁体材料	N35SH

下载: 导出CSV

表 2 网格收敛指数（GCI）估算结果

Table 2. Estimation result of grid convergence index （GCI）

参数	数值
N₁/N₂/N₃	2 107 860/3 647 184/4 641 151
r₂₁/r₃₂	1.200 5/1.083 7
P₁/W	135.23
P₂/W	163.15
P₃/W	163.38
p	36.121
e_a21	0.206 463
e_a32	0.001 41
P_ext/W	163.14
GCI₂₁	0.035 1%
GCI₃₂	0.010 2%

下载: 导出CSV

表 3 理想光壁气隙风摩损耗误差分析

Table 3. Error analysis of windage loss of ideal smooth-walled air gap

转速/（r•min^–1）	雷诺数	CFD模拟/W	式（1）预测值/W	绝对误差/%
20 000	5 570	28.62	32.11	10.87
22 000	6 127	37.41	40.76	8.22
25 000	6 963	53.62	56.10	4.42
28 000	7 798	73.80	74.48	0.91
30 000	8 355	89.70	88.50	1.36
35 000	9 748	138.50	130.11	6.45
40 000	11 140	202.23	187.68	7.75
45 000	12 533	277.69	261.00	6.39
50 000	13 925	366.39	350.56	4.52
55 000	15 317	470.58	457.79	2.79
60 000	16 710	592.05	584.08	1.36
65 000	18 102	734.82	730.81	0.55
70 000	19 495	900.76	899.34	0.16
75 000	20 888	1 087.09	1 090.99	0.36

下载: 导出CSV

表 4 临界失稳阶段风摩损耗波动特性统计

Table 4. Statistics of windage loss fluctuation characteristics at critical instability stage

V_axial /（m•s^–1）	P_wind/W 最小值	P_wind/W 最大值	幅值ΔP /W
6.0	171.04	182.44	11.40
7.0	174.01	184.03	10.02
8.0	175.74	185.81	10.07
9.0	177.24	188.33	11.09
10.0	181.55	189.11	7.56

下载: 导出CSV

参考文献(31)

[1]	张曙, 张柄生, 卫汉华. 机床的主轴单元(上)[J]. 机械设计与制造工程, 2016, 45(5): 1-10. doi: 10.3901/JME.2014.11.144 ZHANG Shu, ZHANG Bingsheng, WEI Hanhua. Machine tool spindle unit (Part1)[J]. Machine Design and Manufacturing Engineering, 2016, 45(5): 1-10. doi: 10.3901/JME.2014.11.144
[2]	高宏力, 孙弋, 郭亮, 等. 机械加工质量预测研究现状与发展趋势[J]. 西南交通大学学报, 2024, 59(1): 121-141. doi: 10.3969/j.issn.0258-2724.20220085 GAO Hongli, SUN Yi, GUO Liang, et al. Research status and development trend of machining quality prediction[J]. Journal of Southwest Jiaotong University, 2024, 59(1): 121-141. doi: 10.3969/j.issn.0258-2724.20220085
[3]	郝磊, 刘孟奇, 韩云龙, 等. 高精密机床制造热性能分析与热管理技术研究[J]. 航空精密制造技术, 2024, 60(6): 1-4, 8. HAO Lei, LIU Mengqi, HAN Yunlong, et al. Research on thermal performance analysis and thermal management technology for high precision machine tool manufacturing[J]. Aviation Precision Manufacturing Technology, 2024, 60(6): 1-4,8.
[4]	Staton D A, Cavagnino A. Convection Heat Transfer and Flow Calculations Suitable for Electric Machines Thermal Models[J]. IEEE Transactions on Industrial Electronics, 2008, 55(10): 3509-3516. doi: 10.1109/TIE.2008.922604
[5]	Zhu Z Q, Liang D. Perspective of Thermal Analysis and Management for Permanent Magnet Machines, with Particular Reference to Hotspot Temperatures[J]. Energies, 2022, 15(21): 8189. doi: 10.3390/en15218189
[6]	Wang R, Fan X, Li D, et al. Comparison of Two Hollow-Shaft Liquid Cooling Methods for High Speed Permanent Magnet Synchronous-Machines[C]//2020 IEEE Energy Conversion Congress and Exposition (ECCE). Detroit: IEEE, 2020: 3511-3517.
[7]	Gai Y, Widmer J D, Steven A, et al. Numerical and Experimental Calculation of CHTC in an Oil-Based Shaft Cooling System for a High-Speed High-Power PMSM[J]. IEEE Transactions on Industrial Electronics, 2020, 67(6): 4371-4380. doi: 10.1109/TIE.2019.2922938
[8]	Camilleri R, Beard P, Howey D A, et al. Prediction and Measurement of the Heat Transfer Coefficient in a Direct Oil-Cooled Electrical Machine With Segmented Stator[J]. IEEE Transactions on Industrial Electronics, 2018, 65(1): 94-102. doi: 10.1109/TIE.2017.2714131
[9]	Chong Y C, Goss J, Popescu M, et al. EXPERIMENTAL CHARACTERISATION OF RADIAL OIL SPRAY COOLING ON A STATOR WITH HAIRPIN WINDINGS[C]//The 10th International Conference on Power Electronics, Machines and Drives (PEMD 2020). Online Conference: IEEE, 2020: 879-884.
[10]	Liu C, Xu Z, Gerada D, et al. Experimental Investigation on Oil Spray Cooling With Hairpin Windings[J]. IEEE Transactions on Industrial Electronics, 2020, 67(9): 7343-7353. doi: 10.1109/TIE.2019.2942563
[11]	Ghahfarokhi P S, Podgornovs A, Kallaste A, et al. Oil Spray Cooling with Hairpin Windings in High-Performance Electric Vehicle Motors[C]//2021 28th International Workshop on Electric Drives: Improving Reliability of Electric Drives (IWED). Moscow: IEEE, 2021: 1-5.
[12]	Liu C, Gerada D, Xu Z, et al. Estimation of Oil Spray Cooling Heat Transfer Coefficients on Hairpin Windings With Reduced-Parameter Models[J]. IEEE Transactions on Transportation Electrification, 2021, 7(2): 793-803. doi: 10.1109/TTE.2020.3031373
[13]	Xu Z, Rocca A L, Arumugam P, et al. A semi-flooded cooling for a high speed machine: Concept, design and practice of an oil sleeve[C]//IECON 2017-43rd Annual Conference of the IEEE Industrial Electronics Society. Beijing: IEEE, 2017: 8557-8562.
[14]	Zhu T, Wang Y, Geng W, et al. Rotor air-friction loss and thermal analysis of high-speed rotor for axial flux PM motor[C]//2021 23rd European Conference on Power Electronics and Applications (EPE'21 ECCE Europe). Ghent: IEEE, 2021: 1-12.
[15]	Taras P, Nilifard R, Zhu Z Q, et al. Cooling Techniques in Direct-Drive Generators for Wind Power Application[J]. Energies, 2022, 15(16): 5986. doi: 10.3390/en15165986
[16]	Saari J. Thermal Analysis of High-Speed Induction Machines[D]. Helsink: Helsinki University of Technology, 1998.
[17]	Fang H, Li D, Qu R, et al. Rotor Design and Eddy-Current Loss Suppression for High-Speed Machines With a Solid-PM Rotor[J]. IEEE Transactions on Industry Applications, 2019, 55(1): 448-457. doi: 10.1109/TIA.2018.2871095
[18]	Geng W, Zhu T, Zhang Y, et al. Rotor Air-Friction Loss and Thermal Analysis of IPM Rotors for High Speed Axial-Flux Machine[J]. IEEE Transactions on Industry Applications, 2023, 59(1): 779-788. doi: 10.1109/TIA.2022.3210896
[19]	梁腾和, 黄宏立, 马乐, 等. 涡轮机械转子在CO₂工质中风摩损耗的数值分析[J]. 厦门大学学报(自然科学版), 2020, 59(4): 547-552. doi: 10.6043/j.issn.0438-0479.201905021 LIANG Tenghe, HUANG Hongli, MA Le, et al. Numerical analysis of windage loss of turbomachinery rotor in CO₂[J]. Journal of Xiamen University (Natural Science), 2020, 59(4): 547-552. doi: 10.6043/j.issn.0438-0479.201905021
[20]	Bilgen E, Boulos R. Functional Dependence of Torque Coefficient of Coaxial Cylinders on Gap Width and Reynolds Numbers[J]. Journal of Fluids Engineering, 1973, 95(1): 122-126. doi: 10.1115/1.3446944
[21]	赵弟宏, 覃珌潭, 张文佳, 等. CO₂轴向流动对转子风摩损耗的影响[J]. 厦门大学学报(自然科学版), 2023, 62(5): 842-847. doi: 10.6043/j.issn.0438-0479.202208012 ZHAO Dihong, QIN Bitan, ZHANG Wenjia, et al. Effect of CO₂ axial flow on rotor windage loss[J]. Journal of Xiamen University (Natural Science), 2023, 62(5): 842-847. doi: 10.6043/j.issn.0438-0479.202208012
[22]	毛玉红, 陈超, 李亚蓉, 等. Taylor-Couette波状涡流场环隙波动的变化特征[J]. 西南交通大学学报, 2025, 60(2): 425-433. doi: 10.3969/j.issn.0258-2724.20230308 MAO Yuhong, CHEN Chao, LI Yarong, et al. Fluctuation characteristics of wavy vortex field within annular gap in Taylor-Couette[J]. Journal of Southwest Jiaotong University, 2025, 60(2): 425-433. doi: 10.3969/j.issn.0258-2724.20230308
[23]	Dai Y, Li W, Qu H, et al. Study on parameters of T-type cooling system for motorized spindle based on thermal characteristics[J]. The International Journal of Advanced Manufacturing Technology, 2024, 131(9): 5265-5276.
[24]	Zhao J, Ding Y, Zhang T, et al. Investigating the impact of cruciform stepped spoiler bars on floc formation and flocculation kinetics parameters[J]. Separation and Purification Technology, 2025, 358: 130371. doi: 10.1016/j.seppur.2024.130371
[25]	Zhang S, Wang F, Zhang Y, et al. A Comparative Study on Coupled Fluid–Thermal Field of a Large Nuclear Turbine Generator with Radial and Composited Radial–Axial–Radial Ventilation Systems[J]. Machines, 2024, 12(5): 326. doi: 10.3390/machines12050326
[26]	康啊真, 殷瑞涛, 祝兵, 等. 基于LES的跨海桥梁施工期围堰波流力数值模拟[J]. 西南交通大学学报, 2020, 55(3): 537-544, 589. KANG Azhen, YIN Ruitao, ZHU Bing, et al. Numerical simulation of wave-current forces acting on cofferdam for sea-crossing bridge based on large eddy simulation[J]. Journal of Southwest Jiaotong University, 2020, 55(3): 537-544,589.
[27]	郑云, 刘志祥, 余志祥, 等. 基于PIV试验的积雪平屋面风场特性研究[J]. 西南交通大学学报, 2023, 58(2): 430-437, 461. doi: 10.3969/j.issn.0258-2724.20210262 ZHENG Yun, LIU Zhixiang, YU Zhixiang, et al. Wind field characteristics of snow-covered low-rise building roof based on PIV experiments[J]. Journal of Southwest Jiaotong University, 2023, 58(2): 430-437,461. doi: 10.3969/j.issn.0258-2724.20210262
[28]	Bilde K G, Hærvig J, Sørensen K. On the design of compact hydraulic pipe flocculators using CFD-PBE[J]. Chemical Engineering Research and Design, 2023, 194(1): 151-162. doi: 10.1016/j.cherd.2023.04.045
[29]	Wang X, Cui B, Wei D, et al. CFD-PBM modelling of tailings flocculation in a lab-scale gravity thickener[J]. Powder Technology, 2022, 396(1): 139-151. doi: 10.1016/j.powtec.2021.10.054
[30]	Celik I B, Ghia U, Roache P J, et al. Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications[J]. Journal of Fluids Engineering, 2008, 130(7): 78001-78004. doi: 10.1115/1.2960953
[31]	Sedrez T A, Decker R K, Da Silva M K, et al. Experiments and CFD-based erosion modeling for gas-solids flow in cyclones[J]. Powder Technology, 2017, 311: 120-131. doi: 10.1016/j.powtec.2016.12.059