基于磨削机理的表面形貌和粗糙度预测模型研究进展

doi:10.3901/JME.2025.13.327

摘要/Abstract

摘要： 工件表面形貌和粗糙度是磨削加工的重要衡量指标，实现其精准预测对于精密制造的智能化转型升级尤为重要。然而，磨削工件表面创成是一个具有随机性的复杂物理过程，目前基于物理机制的模型预测精度亟待提升。基于此，通过考虑磨削过程的几何学和运动学，详细综述了工件表面形貌的预测模型与方法。首先，综述了包括随机平面方法在内的6种磨粒几何建模方法，探索了磨粒表征参数对拟真性的影响规律。其次，总结磨粒在砂轮表面位姿随机分布的数学模型，探索模型参数对磨粒的突出高度等参数的影响规律，并关联总结磨粒可控排布的砂轮的制备与修整方法。随后，分析了平面磨削、超声辅助磨削等不同磨削工艺的磨粒运动学模型，讨论在不同接触形式下磨粒与工件表面之间的相互作用机理，结合动态有效磨粒模型归纳了表面粗糙度的预测模型。最后，统计分析现有粗糙度模型预测误差，误差范围4.47%～37.65%、平均误差11.59%。为磨削表面形貌和粗糙度的精准预测提供新思路，能够为磨削机理与数据分析相融合的智能预测方法提供借鉴。

关键词: 磨削, 砂轮建模, 运动轨迹, 接触模型, 工件形貌, 表面粗糙度预测

Abstract: The surface topography and roughness of workpieces are critical metrics in grinding processes, with accurate prediction considered essential for advancing intelligent manufacturing. The generation of workpiece surfaces during grinding is recognized as a complex, stochastic process, and the accuracy of existing physics-based predictive models is deemed insufficient. A comprehensive review of predictive models and methodologies for workpiece surface topography is presented, with emphasis placed on geometric and kinematic aspects of grinding. Six geometric modeling approaches for abrasive grains, including the random plane method, are summarized, and the influence of abrasive grain parameters on model fidelity is examined. Mathematical models for the random distribution of abrasive grain positions and orientations on grinding wheel surfaces are reviewed, and the effects of model parameters on features such as protrusion height are analyzed. Methods for the fabrication and conditioning of grinding wheels with controlled abrasive grain arrangements are also discussed. Kinematic models of abrasive grains for various grinding processes, including plane and ultrasonic-assisted grinding, are analyzed. The interaction mechanisms between abrasive grains and the workpiece surface under different conditions are explored, and predictive models for surface roughness are generalized based on dynamic abrasive grain models. Finally, prediction errors of existing roughness models are statistically analyzed, with error ranges identified from 4.47% to 37.65%, and an average error of 11.59% determined. New perspectives for improving the prediction of grinding surface topography and roughness are proposed, offering references for the development of intelligent predictive methods integrating grinding mechanisms with data analysis.

Key words: grinding, wheel modelling, motion trajectory, contact model, workpiece morphology, surface roughness prediction

中图分类号:

TG580

彭飞, 张彦彬, 崔歆, 刘明政, 梁晓亮, 徐培明, 周宗明, 李长河. 基于磨削机理的表面形貌和粗糙度预测模型研究进展[J]. 机械工程学报, 2025, 61(13): 327-359.

PENG Fei, ZHANG Yanbin, CUI Xin, LIU Mingzheng, LIANG Xiaoliang, XU Peiming, ZHOU Zongming, LI Changhe. Research Progress in Modelling of Surface Topography and Roughness Based on Grinding Mechanism[J]. Journal of Mechanical Engineering, 2025, 61(13): 327-359.

参考文献

[1] LI L Y，ZHANG Y B，CUI X，et al. Mechanical behavior and modeling of grinding force：A comparative analysis[J]. Journal of Manufacturing Processes，2023，102：921-954.
[2] HU S G，LI C H，ZHOU Z M，et al. Nanoparticle enhanced coolants in machining：Mechanism，application，and prospects[J]. Frontiers of Mechanical Engineering，2023，18(4)：47.
[3] KIM J H，KIM E J，LEE C M. A study on the heat affected zone and machining characteristics of difficult-to-cut materials in laser and induction assisted machining[J]. Journal of Manufacturing Processes，2020，57：499-508.
[4] GAO T，LI C H，WANG Y Q，et al. Carbon fiber reinforced polymer in drilling：From damage mechanisms to suppression[J]. Composite Structures，2022，286：26.
[5] ZHANG B，WU S，WANG D，et al. A review of surface quality control technology for robotic abrasive belt grinding of aero-engine blades[J]. Measurement，2023，220：113381.
[6] CUI X，LI C H，ZHANG Y B，et al. Comparative assessment of force，temperature，and wheel wear in sustainable grinding aerospace alloy using biolubricant[J]. Frontiers of Mechanical Engineering，2023，18(1)：33.
[7] DUAN Z J，LI C H，DING W F，et al. Milling force model for aviation aluminum alloy：Academic insight and perspective analysis[J]. Chinese Journal of Mechanical Engineering，2021，34(1)：35.
[8] YI H A，FANG R J，WANG S A，et al. Research on the applicability of color vision-based roughness inspection method[J]. Surface Topography：Metrology and Properties，2022，10(2)：17.
[9] BENARDOS P G，VOSNIAKOS G C. Predicting surface roughness in machining：A review[J]. International Journal of Machine Tools and Manufacture，2003，43(8)：833-844.
[10] 潘宇航. 考虑时变特性的磨削表面粗糙度预测方法研究[D]. 大连：大连理工大学，2021. PANG Yuhang. Research on the prediction method of grinding surface roughness considering time-varying characteristics[D]. Dalian：Dalian University of Technology，2021.
[11] TÖNSHOFF H K，PETERS J，INASAKI I，et al. Modelling and simulation of grinding processes[J]. CIRP Annals，1992，41(2)：677-688.
[12] AGARWAL S，RAO P V. Modeling and prediction of surface roughness in ceramic grinding[J]. International Journal of Machine Tools and Manufacture，2010，50(12)：1065-1076.
[13] KACALAK W，SZAFRANIEC F，LIPINSKI D，et al. Modeling and analysis of micro-grinding processes with the use of grinding wheels with a conical and hyperboloid active surface[J]. Materials，2022，15(16)：5751.
[14] LIU Y M，WARKENTIN A，BAUER R，et al. Investigation of different grain shapes and dressing to predict surface roughness in grinding using kinematic simulations[J]. Precision Engineering，2013，37(3)：758-764.
[15] SAKAKURA M，TSUKAMOTO S，FUJIWARA T，et al. Visual simulation of the grinding process[J]. Proceedings of the Institution of Mechanical Engineers，Part B：Journal of Engineering Manufacture，2008，222(10)：1233-1239.
[16] TAO H F，LIU Y H，ZHAO D W，et al. Undeformed chip width non-uniformity modeling and surface roughness prediction in wafer self-rotational grinding process[J]. Tribology International，2022，171：20.
[17] WU C J，LI B Z，LIU Y，et al. Surface roughness modeling for grinding of silicon carbide ceramics considering co-existence of brittleness and ductility[J]. International Journal of Mechanical Sciences，2017，133：167-177.
[18] YAN Y Y，ZHANG Z Q，ZHAO B，et al. Study on prediction of three-dimensional surface roughness of nano-ZrO₂ ceramics under two-dimensional ultrasonic assisted grinding[J]. The International Journal of Advanced Manufacturing Technology，2021，112(9-10)：2623-2638.
[19] ZHOU W H，TANG J Y，CHEN H F，et al. A comprehensive investigation of plowing and grain-workpiece micro interactions on 3D ground surface topography[J]. International Journal of Mechanical Sciences，2018，144：639-653.
[20] 方从富，李弘扬，沈剑云，等. 融合磨粒特征和工艺参数的粗糙度智能预测研究[J]. 机械工程学报，2024，60(7)：224-235. FANG Congfu，LI Hongyang，SHEN Jianyun，et al. Study on intelligent prediction of surface roughness based on integration of abrasive characteristics and process parameters[J]. Journal of Mechanical Engineering，2024，60(7)：224-235.
[21] ASILTÜRK I，ÇELIK L，CANLI E，et al. Regression modeling of surface roughness in grinding[J]. Advanced Materials Research，2011，271-273：34-39.
[22] CHEN C C A，LIU C H，CHEN A. Grinding force control in an automatic surface finishing system[J]. Journal of Materials Processing Technology，2005，170(1-2)：367-73.
[23] KOKLU U. Optimisation of machining parameters in interrupted cylindrical grinding using the grey-based Taguchi method[J]. International Journal of Computer Integrated Manufacturing，2013，26(8)：696-702.
[24] MOHANASUNDARARAJU N，SIVASUBRAMANIAN R，ALAGUMURTHI N. Optimisation of work roll grinding using response surface methodology and evolutionary algorithm[J]. International Journal of Manufacturing Research，2008，3(2)：236-251.
[25] NEŞELI S，ASILTÜRK I，ÇELIK L. Determining the optimum process parameter for grinding operations using robust process[J]. Journal of Mechanical Science and Technology，2012，26(11)：3587-3595.
[26] ROUTARA B C，MOHANTY S D，DATTA S，et al. Combined quality loss (CQL) concept in WPCA-based Taguchi philosophy for optimization of multiple surface quality characteristics of UNS C34000 brass in cylindrical grinding[J]. The International Journal of Advanced Manufacturing Technology，2010，51(1-4)：135-143.
[27] SAGLAM H，UNSACAR F，YALDIZ S. An experimental investigation as to the effect of cutting parameters on roundness error and surface roughness in cylindrical grinding[J]. International Journal of Production Research，2005，43(11)：2309-2322.
[28] SHAJI S，RADHAKRISHNAN V M N E S H C. Analysis of process parameters in surface grinding with graphite as lubricant based on the Taguchi method[J]. Journal of Materials Processing Technology，2003，141(1)：51-59.
[29] TSAI F C，YAN B H，KUAN C Y，et al. A Taguchi and experimental investigation into the optimal processing conditions for the abrasive jet polishing of SKD61 mold steel[J]. International Journal of Machine Tools and Manufacture，2008，48(7-8)：932-945.
[30] ZHAO T，SHI Y，LIN X，et al. Surface roughness prediction and parameters optimization in grinding and polishing process for IBR of aero-engine[J]. International Journal of Advanced Manufacturing Technology，2014，74(5-8)：653-663.
[31] DENG Z H，ZHANG X H，LIU W. A hybrid model using genetic algorithm and neural network for process parameters optimization in NC camshaft grinding[J]. International Journal of Advanced Manufacturing Technology，2009，45(43718)：859-866.
[32] LIAO T W，CHEN L J. A neural network approach for grinding processes：Modelling and optimization[J]. International Journal of Machine Tools and Manufacture，1994，34(7)：919-937.
[33] MUKHERJEE I，RAY P K. A case-based and practical approach for multivariate modeling of grinding process[J]. The International Journal of Advanced Manufacturing Technology，2009，45(3-4)：245-260.
[34] NAGASAKA K，ICHIHASHI H，LEONARD R. Neuro-fuzzy GMDH and its application to modelling grinding characteristics[J]. International Journal of Production Research，1995，33(5)：1229.
[35] NAKAI M E，JUNIOR H G，AGUIAR P，et al. Neural tool condition estimation in the grinding of advanced ceramics[J]. IEEE Latin America Transactions，2015，13(1)：62-68.
[36] PRABHU S，UMA M，VINAYAGAM B. Surface roughness prediction using Taguchi-fuzzy logic-neural network analysis for CNT nanofluids based grinding process[J]. Neural Computing & Applications，2015，26(1)：41-55.
[37] WANG L X，MENDEL J M. Fuzzy basis functions，universal approximation，and orthogonal least-squares learning[J]. IEEE transactions on neural networks/a publication of the IEEE Neural Networks Council，1992，3(5)：807-814.
[38] ZHAO B，ZHANG S，LI J F. Evaluation and ANN-based prediction on functional parameters of surface roughness in precision grinding of cast iron[J]. Advanced Materials Research，2014，1017：166-171.
[39] 易怀安，刘坚，路恩会. 基于图像清晰度评价的磨削表面粗糙度检测方法[J]. 机械工程学报，2016，52(16)：15-21. YI Huaian，LIU Jian，LU Enhui. Detection method of grinding surface roughness based on image[J]. Journal of Mechanical Engineering，2016，52(16)：15-21.
[40] 孙林，杨世元. 基于最小二乘支持矢量机的成形磨削表面粗糙度预测及磨削用量优化设[J]. 机械工程学报，2009，45(10)：254-260. SUN Lin，YANG Shiyuan. Prediction for surface roughness of profile grinding and optimization of grinding parameters based on least squares support vector machine[J]. Journal of Mechanical Engineering，2009，45(10)：254-260.
[41] 王宏丽. 叶片机器人砂带磨削材料去除微观建模及实验研究[D]. 武汉：华中科技大学，2023. WANG Hongli，Microscopic modeling and experimental study of blade robot belt grinding materials[D]. Wuhan：Huazhong University of Science and Technology，2023.
[42] 吕黎曙，邓朝晖，岳文辉，等. 单颗磨粒磨削机理与数据融合驱动的磨削过程建模分析[J]. 机械工程学报，2023，59(7)：200-215. LÜ Lishu，DENG Zhaohui，YUE Wenhui，et al. Modeling analysis of grinding process driven by single grain grinding mechanism and data fusion[J]. Journal of Mechanical Engineering，2023，59(7)：200-215.
[43] AURICH J C，KIRSCH B. Kinematic simulation of high-performance grinding for analysis of chip parameters of single grains[J]. CIRP Journal of Manufacturing Science and Technology，2012，5(3)：164-74.
[44] 张勇强，汪久根，陈芳华，等. 磨粒磨损的磨粒接触热分析[J]. 润滑与密封，2018，43(10)：1-5. ZHANG Yongqiang，WANG Jiugen，CHEN Fanghua，et al. Thermal analysis of debris contact in abrasive wear[J]. Lubrication Engineering，2018，43(10)：1-5.
[45] 邓玮. 基于磨粒特性的发动机滚动轴承磨损机理研究[D].南昌：南昌航空大学，2022. DENG Wei. The particle characteristics based wear mechanism analysis of engine rolling bearings[D]. Nanchang：Nanchang Hangkong University，2022.
[46] GONG Y，WANG B，WANG W. The simulation of grinding wheels and ground surface roughness based on virtual reality technology[J]. Journal of Materials Processing Technology，2002，129(1-3)：123-126.
[47] 王君明，叶人珍，汤漾平，等. 单颗磨粒的平面磨削三维动态有限元仿真[J]. 金刚石与磨料磨具工程，2009(5)：41-5. WANG Junming，YE Renzhen，TANG Yangping，et al. 3D dynamic finite element simulation analysis of single abrasive grain during surface grinding[J]. Diamond & Abrasives Engineering，2009(5)：41-45.
[48] 李巾锭，任成祖，吕哲，等. 单颗粒金刚石平面磨削C/SiC复合材料的有限元仿真[J]. 材料科学与工程学报，2014，32(5)：686-689，715. LI Jinding，REN Chengzu，LÜ Zhe，et al. Finite element simulation of single diamond abrasive surface grinding C/SiC[J]. Journal of Materials Science & Engineering，2014，32(5)：686-689，715.
[49] LI L，REN X，FENG H，et al. A novel material removal rate model based on single grain force for robotic belt grinding[J]. Journal of Manufacturing Processes，2021，68：1-12.
[50] HUANG Y，LIU G，XIAO G，et al. Abrasive belt grinding force and its influence on surface integrity[J]. Mater Manuf Process，2022，38(7)：888-897.
[51] PAN Y H，ZHOU P，YAN Y，et al. New insights into the methods for predicting ground surface roughness in the age of digitalisation[J] Precision Engineering，2021，67：393-418.
[52] QUAN J K，FANG Q H，CHEN J B，et al. Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding[J]. The International Journal of Advanced Manufacturing Technology，2017，90：2461-2476.
[53] 张彦彬. 植物油基纳米粒子射流微量润滑磨削机理与磨削力预测模型及实验验证[D]. 青岛：青岛理工大学，2018. ZHANG Yanbin. Grinding mechanism，force prediction model and experimental validation of vegetable oil based nanofluids minimum quantity lubrication[D]. Qingdao：Qingdao University of Technology，2018.
[54] 言兰，融亦鸣，姜峰. 氧化铝砂轮地貌的量化评价及数学建模[J]. 机械工程学报，2011，47(17)：179-186. YAN Lan，RONG Yiming，JIANG Feng. Quantities evaluation and modeling of alumina grinding wheel surface topography[J]. Journal of Mechanical Engineering，2011，47(17)：179-186.
[55] 宿崇，许立，刘元伟，等. 基于SPH法的CBN磨粒切削过程数值模拟[J]. 中国机械工程，2013，24(5)：667- 671. SU Chong，XU Li，LIU Yuanwei，et al. Numerical simulation of cutting process of CBN grit based on SPH method[J]. China Mechanical Engineering，2013，24(5)：667-671.
[56] MINGZHENG L I U，CHANGHE L I，ZHANG Y，et al. Analysis of grinding mechanics and improved grinding force model based on randomized grain geometric characteristics[J]. Chinese Journal of Aeronautics，2023，36(7)：160-193.
[57] LI H N，YU T B，WANG Z X，et al. Detailed modeling of cutting forces in grinding process considering variable stages of grain workpiece micro interactions[J]. International Journal of Mechanical Sciences，2017，126：319-339.
[58] 李超，霍文国. 基于ABAQUS的单颗磨粒磨削GH4169高温合金有限元分析[J]. 工具技术，2023，57(8)：86-92. LI Chao，HUO Wenguo. Finite element analysis of single abrasive grinding GH4169 superalloy[J]. Tool Engineering，2023，57(8)：86-92.
[59] LIU W，ZHANG L，FANG Q，et al. A predictive model of subsurface damage and material removal volume for grinding of brittle materials considering single grit micro-geometry[J]. The International Journal of Advanced Manufacturing Technology，2019，102(5-8)：2231-2243.
[60] ZHANG P，ZHAO H W，SHI C L，et al. Influence of double-tip scratch and single-tip scratch on nano- scratching process via molecular dynamics simulation[J]. Applied Surface Science，2013，280：751-756.
[61] 范梓良. 单颗磨粒高速磨削AISI 1045钢磨削机理的仿真与实验研究[D]. 太原：太原理工大学，2018. FAN Ziliang. Simulation and experimental study on grinding mechanism of high-speed grinding AISI 1045 steel with single abrasive grain[D]. Taiyuan：Taiyuan University of Technology，2018.
[62] RüTTIMANN N，ROETHLIN M，BUHL S，et al. Simulation of hexa-octahedral diamond grain cutting tests using the SPH method[J]. Procedia CIRP，2013，8：322- 327.
[63] 刘瑞虎，郭磊，刘永胜，等. 基于SPH方法的碳化硅材料单颗磨粒磨削仿真[J]. 组合机床与自动化加工技术，2022(5)：55-58. LIU Ruihu，GUO Lei，LIU Yongsheng，et al. Simulation of single abrasive grinding of silicon carbide material based on SPH method[J]. Modular Machine Tool & Automatic Manufacturing Technique，2022(5)：55-58.
[64] 刘伟，邓朝辉，万林林，等. 单金刚石晶粒切割氮化硅的模拟与实验研究[J]. 机械工程学报，2015，21(51)：191-198. LIU Wei，DENG Zhaohui，WAN Linlin，et al. Simulation and experiment study for silicon nitride cutting with single diamond grain[J]. Journal of Mechanical Engineering，2015，21(51)：191-198.
[65] DE PELLEGRIN D V，CORBIN N D，BALDONI G，et al. Diamond particle shape：Its measurement and influence in abrasive wear[J]. Tribology International，2009，42(1)：160-168.
[66] 余剑武，刘智康，吴耀，等. 合金钢20CrMo的单颗磨粒高速磨削仿真研究[J]. 制造技术与机床，2015(12)：97-102. YU Jianwu，LIU Zhikang，WU Yao，et al. Simulation of high-speed grinding of 20CrMo based on single grain cutting[J]. Manufacturing Technology & Machine Tool，2015(12)：97-102.
[67] 赵小雨. 金刚石砂轮三维形貌建模及磨削工程陶瓷的数值仿真与实验研究[D]. 湘潭：湖南科技大学，2016. ZHAO Xiaoyu. Simulation and experimental research of diamond grinding wheel 3D shape modeling and cutting engineering ceramics[D]. Xiangtan：Hunan University of Science and Technology ，2016.
[68] 宿崇，施志辉，刘元伟. 陶瓷CBN砂轮地貌建模与磨削仿真[J]. 中国机械工程，2012，23(14)：1742-1745. SU Chong，SHI Zhihui，LIU Yuanwei. Topography modeling and grinding simulation of vitrified bonded CBN wheel[J]. China Mechanical Engineering，2012，23(14)：1742-1745.
[69] HUANG B T，LI C H，ZHANG Y B，et al. Advances in fabrication of ceramic corundum abrasives based on sol-gel process[J]. Chinese Journal of Aeronautics，2021，34(6)：1-17.
[70] 唐立志. 磨削区微通道几何模型及微液滴浸润机制与实验验证[D]. 青岛：青岛理工大学，2022. TANG Lizhi. Geometric model of microchannel in grinding area and microdroplet infiltration mechanism and experimental verification[D]. Qingdao：Qingdao University of Technology，2022.
[71] 卢跃. 基于磨粒运动轨迹的端面磨削热力耦合过程分析[D]. 沈阳：东北大学，2022. LU Yue. Analysis of thermal mechanical coupling process of face grinding based on the movement trajectory of abrasive grains[D]. Shenyang：Northeastern University，2022.
[72] 孙旺. 磨粒规则排布砂轮快速制造关键技术研究[D]. 焦作：河南理工大学，2022. SUN Wang. Research on key technology of fast manufacturing of regular grain arrangement grinding wheel[D]. Jiaozuo：Henan University of Technology，2022.
[73] 刘月明. 磨削过程建模与点磨削工艺的若干研究[D]. 沈阳：东北大学，2015. LIU Yueming. Research on the model of grinding process and the technology of point grinding[D]. Shenyang：Northeastern University，2015.
[74] CHEN Z L，XIAO B，WANG B. Optimum and arrangement technology of abrasive topography for brazed diamond grinding disc[J]. International Journal of Refractory Metals & Hard Materials，2021，95：105455.
[75] 王俊博，吕玉山，慕丽，等. 磨粒有序化砂轮磨削微沟槽减阻表面的研究[J]. 金刚石与磨料磨具工程，2022，42(6)：738-744. WANG Junbo，LÜ Yushan，MU Li，et al. Study of microgroove dampening surfaces for grinding with grain-ordered grinding wheels[J]. Diamond & Abrasives Engineering，2022，42(6)：738-744.
[76] 吕玉山，王军，赵成义，等. 一种磨粒族叶序排布的端面砂轮及其铣磨实验[J]. 兵工学报，2013，34(12)：1569-1574. LÜ Yushan，WANG Jun，ZHAO Chengyi，et al. An end-grinding wheel with the phyllotactic pattern of abrasive grain clusters and its mill-grinding experiments[J]. Acta Armamentarii，2013，34(12)：1569-1574.
[77] 车东泽，吕玉山，陈天宇，等. 用磨粒叶序排布砂轮磨削外圆生成的凹坑表面仿真[J]. 金刚石与磨料磨具工程，2019，39(1)：47-53. CHE Dongze，LÜ Yushan，CHEN Tianyu，et al. Simulation of the dimpled surface generated by grinding outer circle with abrasive phyllotactic arrangement wheel[J]. Diamond & Abrasives Engineering，2019，39(1)：47-53.
[78] YU H，WANG J，LU Y. Simulation of grinding surface roughness using the grinding wheel with an abrasive phyllotactic pattern[J]. The International Journal of Advanced Manufacturing Technology，2015，84(5-8)：861-71.
[79] 陈海锋，唐进元，邓朝晖，等. 考虑耕犁的超声磨削表面微观形貌建模与预测[J]. 机械工程学报，2018，54(21)：231-240. CHEN Haifeng，TANG Jinyuan，DENG Zhaohu，et al. Modeling and predicting surface topography of the ultrasonic assisted grinding process considering ploughing action[J]. Journal of Mechanical Engineering，2018，54(21)：231-240.
[80] 雷小飞. GCr15SiMn轴承钢超声振动辅助磨削机理及试验研究[D]. 湘潭：湖南科技大学，2022. LEI Xiaofei. Mechanism and experimental research on ultrasonic vibration-assisted grinding of GCr15SiMn bearing steel[D]. Xiangtan：Henan University of Science and Technology，2022.
[81] HOU Z B，KOMANDURI R. On the mechanics of the grinding process，Part II—thermal analysis of fine grinding[J]. International Journal of Machine Tools and Manufacture，2004，44(2-3)：247-270.
[82] 王艳，李德蔺，刘建国，等. 基于动态轮廓采样法的轴向超声振动辅助磨削工件表面形貌预测与试验验证[J]. 机械工程学报，2018，54(21)：221-230. WANG Yan，LI Delin，LIU Jianguo，et al. Prediction and experimental verification of workpiece surface topology in axial ultrasonic vibration assisted grinding based on dynamic profile sampling method[J]. Journal of Mechanical Engineering，2018，54(21)：221-230.
[83] NGUYEN T A，BUTLER D L. Simulation of precision grinding process，part 1：Generation of the grinding wheel surface[J]. International Journal of Machine Tools and Manufacture，2005，45(11)：1321-8.
[84] 吕长飞，李郝林. 外圆磨削砂轮形貌仿真与工件表面粗糙度预测[J]. 中国机械工程，2012，23(6)：666-671. LÜ Changfei，LI Haolin. Simulation of wheel topography and forecasting of roughness in cylindrical grinding[J]. China Mechanical Engineering，2012，23(6)：666-671.
[85] 王胜. 纳米粒子射流微量润滑磨削表面形貌创成机理与实验研究[D]. 青岛：青岛理工大学，2013. WANG Sheng. Generating mechanism and experimental investigation on surface topography in the grinding process using MQL by nanoparticles jet[D]. Qingdao：Qingdao University of Technology，2013.
[86] 黄荣杰，吴希让. 磨削表面粗糙度的建模和预断[J]. 精密制造与自动化，2003(3)：33-37. HUANG Rongjie，WU Xirang. Modelling and pre-breaking of grinding surface roughness[J]. Precise Manufacturing & Automation，2003(3)：33-37.
[87] 宋文韬，周里群，李玉平，等. 砂轮离散元建模的镍基合金磨削加工数值模拟[J]. 机械科学与技术，2021，40(5)：755-761. SONG Wentao，ZHOU Liqun，LI Yuping，et al. Grinding wheel modeling and numerical simulation in grinding of nickel-based alloy via discrete element method[J]. Mechanical Science and Technology for Aerospace Engineering，2021，40(5)：755-761.
[88] 程淦. 砂轮动态有效磨粒检测及对工程陶瓷加工表面的影响研究[D]. 泉州：华侨大学，2022. CHENG Gan. Research on dynamic active cutting point of grinding wheel and its effect on the ground surface of engineering ceramics[D]. Quanzhou：Huaqiao University，2022.
[89] 张园，徐念伟，鲍岩，等. 轴向超声辅助端面磨削金属表面形貌及粗糙度预测[J]. 机械工程学报，2023，59(5)：307-316. ZHANG Yuan，XU Nianwei，BAO Yan，et al. Surface topography and roughness prediction of axial ultrasonic assisted facing grinding metal[J]. Journal of Mechanical Engineering，2023，59(5)：307-316.
[90] 胡小龙，齐俊德. 基于未变形切屑厚度的砂带磨削表面粗糙度预测模型[J]. 科技创新与应用，2023，13(5)：59-63，67. HU Xiaolong，QI Junde. A model for predicting surface roughness in belt grinding based on the thickness of undeformed chips[J]. Technology Innovation and Application，2023，13(5)：59-63，67.
[91] 楚帅震，牛赢，王壮飞，等. GCr15轴套纵扭超声磨削表面形貌预测及试验研究[J]. 表面技术，2023，52(9)：294-305. CHU Shuaizhen，NIU Ying，WANG Zhuangfei，et al. Prediction and experiment on surface morphology of longitudinal torsional ultrasonic grinding of GCr15 shaft sleeve[J]. Surface Technology，2023，52(9)：294-305.
[92] 杨晓辉，周凌宇，刘宁，等. 光学玻璃磨削亚表面损伤预测模型及DOE实验设计[J]. 机械科学与技术，2022，43(3)：520-525. YANG Xiaohui，ZHOU Lingyu，LIU Ning，et al. Prediction model for subsurface damage in grinding of optical glass and doe experiment design[J]. Mechanical Science and Technology for Aerospace Engineering，2022，43(3)：520-525.
[93] CHEN X，BRIAN ROWE W. Analysis and simulation of the grinding process. Part II：Mechanics of grinding[J]. International Journal of Machine Tools and Manufacture，1996，36(8)：883-96.
[94] HOU Z B，KOMANDURI R. On the mechanics of the grinding process–Part I. Stochastic nature of the grinding process[J]. International Journal of Machine Tools and Manufacture，2003，43(15)：1579-1593.
[95] TAO H F，LIU Y H，ZHAO D W，et al. Undeformed chip width non-uniformity modeling and surface roughness prediction in wafer self-rotational grinding process[J]. Tribology International，2022，171：107547.
[96] KOSHY P，JAIN V K，LAL G K. A model for the topography of diamond grinding wheels[J]. Wear，1993，169(2)：237-242.
[97] 王双喜，刘雪敬，耿彪，等. 金属结合剂金刚石磨具的研究进展[J]. 金刚石与磨料磨具工程，2006(4)：71-75. WANG Shuangxi，LIU Xuejing，GENG Biao，et al. Development of metal bonded diamond abrasive tool[J]. Diamond & Abrasives Engineering，2006(4)：71-75.
[98] 张於亮，汪振华，姜志嵩，等. 微波烧结陶瓷结合剂金刚石砂轮研究[J]. 硅酸盐通报，2022，41(10)：3675-3679. ZHANG Yuliang，WANG Zhenhua，JIANG Zhisong，et al. Study on microwave sintering of ceramic bonded diamond grinding wheels[J]. Bulletin of the Chinese Ceramic Society，2022，41(10)：3675-3679.
[99] CHATTOPADHYAY A K，CHOLLET L，HINTERMANN H E. On performance of brazed bonded monolayer diamond grinding wheel[J]. CIRP Annals - Manufacturing Technology，1991，40(1)：347-350.
[100] MA B，YU Q. Hot-filament chemical vapor deposition of amorphous carbon film on diamond grits and induction brazing of the diamond grits[J]. Applied Surface Science，2012，258(10)：4750-4755.
[101] 陈冰，郭烨，邓朝晖. 超硬磨粒可控排布砂轮研究进展[J]. 中国机械工程，2023，34(9)：1019-1034.CHEN Bing，GUO Ye，DENG Zhaohui. Research progresses of super-hard abrasive grain controllable arrangement grinding wheel[J]. China Mechanical Engineering，2023，34(9)：1019-1034.
[102] ZHANG F L，LI M C，WANG J，et al. Effect of arraying parameters on dry grinding performance of patterned monolayer brazed CBN wheel[J]. International Journal of Advanced Manufacturing Technology，2020，107(5-6)：2081-2089.
[103] YANG Z B，XU J H，FU Y C，et al. Laser brazing of diamond grits with a Ni-based brazing alloy[J]. Key Engineering Materials，2008，359：43-47.
[104] TIAN C，LI X，ZHANG S，et al. Study on design and performance of metal-bonded diamond grinding wheels fabricated by selective laser melting (SLM)[J]. Materials & Design，2018，156：52-61.
[105] LI K W，ZHANG M J，ZHANG J，et al. Preparation and performance of grinding wheel with orderly arranged abrasive particles based on laser processing technology[J]. International Journal of Advanced Manufacturing Technology，2023，127(9-10)：4519-4532.
[106] 侯侠. 磨料三维多层可控排布电镀砂轮的若干研究[D]. 大连：大连理工大学，2006. HOU Xia. Some researches on electroplating grinding wheel with 3D controlled distributing of multi-layer abrasives[D]. Dalian：Dalian University of Technology，2006.
[107] XU Z Y，XU H J，FU Y C，et al. Induction brazing diamond grinding wheel with Ni-Cr filler alloy[J]. Materials Science Forum，2007，26(32-533)：377-380.
[108] AURICH J C，HERZENSTIEL P，SUDERMANN H，et al. High-performance dry grinding using a grinding wheel with a defined grain pattern[J]. CIRP Annals-Manufacturing Technology，2008，57(1)：357-362.
[109] 李祥瑞. 基于磨粒有序排布的钎焊金刚石工具制造工艺研究[D]. 秦皇岛：燕山大学，2018. LI Xiangrui . A study on the abrasive orderly arrayed diamond tools manufacture[D]. Qinhuangdao：Yanshan University，2018.
[110] MA B，YU Q. Performance of brazed diamond wheels fabricated in hydrogen/methane plasmas or a vacuum [J]. The International Journal of Advanced Manufacturing Technology，2012，63：555-60.
[111] 吕玉山，王军，赵成义，等. 一种磨粒族叶序排布的端面砂轮及其铣磨实验[J]. 兵工学报，2013，34(12)：1569-1574. LÜ Yushan，WANG Jun，ZHAO Chengyi，et al. An end-grinding wheel with the phyllotactic patternof abrasive grain clusters and its mill-grinding experiments[J]. Acta Armamentarii，2013，34(12)：1569-1574.
[112] 冯创举，崔仲鸣，赫青山，等. 超硬磨具磨粒有序排布技术的原理及应用[J]. 金刚石与磨料磨具工程，2018，38(1)：65-72. FENG Chuangju，CUI Zhongming，HE Qingshan，et al. Principle and application of orderly arranging grain technology of superabrasive[J]. Diamond & Abrasives Engineering，2018，38(1)：65-72.
[113] LUO S Y，YU T H，LIU C Y，et al. Grinding characteristics of micro-abrasive pellet tools fabricated by a LIGA-like process [J]. International Journal of Machine Tools and Manufacture，2009，49(3-4)：212-219.
[114] PARK H. ARIX-a major advance in diamond segment design [J]. Industrial Diamond Review，2005(2)：40-42.
[115] 牛亮. 新型金刚石多层有序排布方法及其应用研究[D]. 广州：广东工业大学，2016. NIU Liang. A new method for multilayer orderly arrangement diamond and its application[D]. Guangzhou：Guangdong University of Technology，2016.
[116] BURKHARD G，REHSTEINER F，SCHUMACHER B. High efficiency abrasive tool for honing[J]. CIRP Annals，2002，51(1)：271-274.
[117] 王昆明. 有序化砂轮磨削仿真与制备研究[D]. 湘潭：湖南科技大学，2024. WANG Kunming. Study on grinding simulation and preparationof ordered grinding wheel[D]. Xiangtan：Hunan University of Science and Technology，2024.
[118] 李长河，修世超，蔡光起. 超硬磨料砂轮修锐技术最新进展[J]. 工具技术，2005(3)：7-9. LI Changhe，XIU Shichao，CAI Guangqi. Development of truing/dressing technology on superabrasive grinding wheel[J]. Tool Engineering，2005(3)：7-9.
[119] 崔仲鸣，赫青山，冯创举，等. 超硬磨料磨具修整技术研究[J]. 金刚石与磨料磨具工程，2016，36(1)：43-49. CUI Zhongming，HE Qingshan，FENG Chuangju，et al. Study on dressing technology of super abrasive product [J]. Diamond & Abrasives Engineering，2016，36(1)：43-49.
[120] 王先逵，刘为刚，应宝阁. 超硬磨料磨具修整技术的发展[J]. 磨料磨具与磨削，1994(3)：30-32. WANG Xiankui，LUI Weigang，YING Baoge. Development of superabrasives dressing technology [J]. Diamond & Abrasives Engineering，1994(3)：30-32.
[121] DING W F，LI H N，ZHANG L C，et al.Diamond wheel dressing：A comprehensive review [J]. Journal of Manufacturing Science and Engineering，Transactions of the ASME，2017，139(12)：121006.
[122] HUANG H. Effects of truing/dressing intensity on truing/dressing efficiency and grinding performance of vitrified diamond wheels[J]. Journal of Materials Processing Technology，2001，117(1-2)：9-14.
[123] CHEN B，GUO B，ZHAO Q. On-machine precision form truing of arc-shaped diamond wheels[J] Journal of Mechanical Engineering，2015，223：65-74.
[124] MOCHIDA Y，KUBO A，TAMAKI J I，et al. Performance of newly developed single-point diamond dresser in terms of cutting-point rake angle[J]. Advanced Materials Research，2012，565：205-210.
[125] ZHANG K，SU H H，DAI F M. Study on the dullness of monolayer brazed diamond grinding wheel through plate wheel dressing[J]. Advanced Materials Research，2014，1027：159-62.
[126] TAWAKOLI T，DANESHI A. T-dress，a novel approach in dressing and structuring of grinding wheels[J]. Advanced Materials Research，2012，565：217-221.
[127] DENG H，CHEN G Y，ZHOU C，et al. Processing parameter optimization for the laser dressing of bronze-bonded diamond wheels[J]. Applied Surface Science，2014，290：475-481.
[128] SONG C，GENYU C，CONG Z，et al. The mechanism and application of bronze-bond diamond grinding wheel pulsed laser dressing based on phase explosion[J]. The International Journal of Advanced Manufacturing Technology，2015，80：1641-1453.
[129] WALTER C，RABIEY M，WARHANEK M，et al. Dressing and truing of hybrid bonded CBN grinding tools using a short-pulsed fibre laser[J]. CIRP Annals - Manufacturing Technology，2012，61(1)：279-282.
[130] WALTER C，KOMISCHKE T，KUSTER F，et al. Laser-structured grinding tools–Generation of prototype patterns and performance evaluation[J]. Journal of Materials Processing Technology，2014，214(4)：951-961.
[131] XU M M，LI D D，HU D J，et al. Laminated manufacturing and milling electrical discharge dressing of metal-bonded diamond grinding wheels[J]. Proceedings of the Institution of Mechanical Engineers，Part B：Journal of Engineering Manufacture，2012，226(1)：137-144.
[132] WEINGäRTNER E，ROTH R，KUSTER F，et al. Electrical discharge dressing and its influence on metal bonded diamond wheels[J]. CIRP Annals-Manufacturing Technology，2012，61(1)：183-186.
[133] CAI L R，LI M，YANG H，et al. Electrical discharge dressing metal-bonded diamond grinding wheels with various mediums[J]. Proceedings of the Institution of Mechanical Engineers，Part B：Journal of Engineering Manufacture，2013，227(1)：102-108.
[134] XIE J，TAMAKI J. In-process evaluation of grit protrusion feature for fine diamond grinding wheel by means of electro-contact discharge dressing[J]. Journal of Materials Processing Technology，2006，180(1-3)：83-90.
[135] WANG Y，ZHOU X J，HU D J. An experimental investigation of dry-electrical discharge assisted truing and dressing of metal bonded diamond wheel[J]. International Journal of Machine Tools and Manufacture，2006，46(3-4)：333-342.
[136] ZHANG C，SHIN Y C. A novel laser-assisted truing and dressing technique for vitrified CBN wheels[J]. International Journal of Machine Tools and Manufacture，2002，42(7)：825-835.
[137] SCHÖPF M，BELTRAMI I，BOCCADORO M，et al. ECDM (electro chemical discharge machining)，a new method for trueing and dressing of metal bonded diamond grinding tools[J]. CIRP Annals-Manufacturing Technology，2001，50(1)：125-128.
[138] 赵捷，高国富. 超硬磨料砂轮超声振动修整新进展[J]. 金刚石与磨料磨具工程，2010(2)：79-82. ZHAO Jie，GAO Guofu. Progress in ultrasonic dressing technologies of superabrasives grinding wheels[J]. Diamond & Abrasives Engineering，2010(2)：79-82.
[139] LI H N，AXINTE D. Textured grinding wheels：A review[J]. International Journal of Advanced Manufacturing Technology，2016，109：8-35.