Non-uniform Heat Source Conduction Mechanism and Three-dimensional Finite Difference Model of Ultrasonic Micro-grinding Biological Bone and Its Verification

doi:10.3901/JME.2025.19.363

Abstract

Abstract: Grinding is widely used in orthopedic surgery to remove bone tissue. However, crack damage caused by mechanical stress and thermal injury due to excessive grinding temperature remain technical challenges in clinical operations. In view of the above needs and technical bottlenecks, an ultrasonic micro-grinding technique for biological bone is proposed, while the non-uniform heat source conduction mechanism under ultrasonic excitation remains unclear, necessitating the establishment of a three-dimensional heat conduction model for biological bone. Based on this, the dynamic evolution of geometry, kinematics, and dynamics in the grinding process is analyzed, leading to the development of an undeformed chip thickness model at any given time under ultrasonic excitation. The circumferential and radial distribution of grinding heat flux is investigated, and a three-dimensional non-uniform heat source distribution model is constructed. Furthermore, considering the material removal mechanism, the dynamic evolution of grinding force, interface conditions, and material structural properties, a three-dimensional non-uniform finite difference heat conduction model is established based on heat flux density, convective heat transfer, and adiabatic conditions. This model reveals the dynamic heat conduction behavior within bone material during ultrasonic micro-grinding. Additionally, a thermocouple array suitable for hemispherical crown surfaces is designed, and multi-parameter orthogonal experiments are conducted to measure the temperature at different positions of the workpiece. Finally, an innovative method combining regional numerical simulation and experimental temperature measurement comparison is introduced. The results indicate that when the vibration amplitude is 6 μm, grinding depth is 25 μm, tool substrate radius is 2 mm, and feed rate is 3 mm/s, the minimum error between experimental measurements and numerical calculations reaches 6.4%, with 70% of the measured regions exhibiting errors below 10%. Effective temperature control during bone micro-grinding is achieved, providing theoretical guidance and technical support for clinical orthopedic surgery.

Key words: ultrasonic vibration, micro-grinding, conduction mechanism of non-uniform heat sources, three-dimensional finite difference model, thermocouple array

CLC Number:

TG580
R318

SUN Jingang, LIU Jixin, YANG Min, YANG Yuying, LI Runze, ZHANG Yanbin, LIU Mingzheng, LI Changhe. Non-uniform Heat Source Conduction Mechanism and Three-dimensional Finite Difference Model of Ultrasonic Micro-grinding Biological Bone and Its Verification[J]. Journal of Mechanical Engineering, 2025, 61(19): 363-385.

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URL: http://www.cjmenet.com.cn/EN/10.3901/JME.2025.19.363

http://www.cjmenet.com.cn/EN/Y2025/V61/I19/363

References

[1] ZHANG Yue，ROBLES-LINARES J A，CHEN Lei，et al. Advances in machining of hard tissues-From material removal mechanisms to tooling solutions[J]. International Journal of Machine Tools & Manufacture，2022，172：103838.
[2] SHU Liming，LI Shihao，TERASHIMA M，et al. A novel self-centring drill bit design for low-trauma bone drilling[J]. International Journal of Machine Tools & Manufacture，2020，154：103568.
[3] CHEN Qisen，LIU Yu，DONG Qiushi. Modeling and experimental validation on temperature diffusion mechanism in high-speed bone milling[J]. Journal of Materials Processing Technology，2020，286：116810.
[4] CHEN Qisen，DAI Li，LIU Yu，et al. A cortical bone milling force model based on orthogonal cutting distribution method[J]. Advances in Manufacturing，2020，8(2)：204-215.
[5] DUAN Zhenjing，WANG Shuaishuai，WANG Ziheng，et al. Tool wear mechanisms in cold plasma and nano- lubricant multi-energy field coupled micro-milling of Al-Li alloy[J]. Tribology International，2024，192：109337.
[6] TIAN Heqiang，DANG Xiaoqing，MENG Debao，et al. Influence of drilling parameters on bone drilling force and temperature by FE simulation and parameters optimization based Taguchi method[J]. Alexandria Engineering Journal，2023，75：115-126.
[7] 王成勇，陈志桦，陈华伟，等. 生物骨材料切除理论研究综述[J]. 机械工程学报，2021，57(11)：2-32. WANG Chengyong，CHEN Zhihua，CHEN Huawei，et al. A review on cutting mechanism for bone materia[J]. Journal of Mechanical Engineering，2021，57(11)：2-32.
[8] 邹磊，文东辉，张丽慧，等. 骨组织磨削力计算模型及实验研究[J]. 中国机械工程，2020，31(24)：3016-3023. ZOU Lei，WEN Donghui，ZHANG Lihui，et al. Computational model and experimental study for bone tissue grinding forces[J]. China Mechanical Engineering，2020，31(24)：3016-3023.
[9] ZHANG Airong，ZHANG Song，BIAN Cuirong，et al. Modified chip-evacuation force modeling and chip- clogging prediction in drilling of cortical bone[J]. IEEE Access，2019，7：180671-180683.
[10] YANG Min，LI Changhe，LUO Liang，et al. Predictive model of convective heat transfer coefficient in bone micro-grinding using nanofluid aerosol cooling[J]. International Communications in Heat and Mass Transfer，2021，125：105317.
[11] DUAN Zhenjing，WANG Shuaishaui，LI Changhe，et al. Cold plasma and different nano-lubricants multi-energy field coupling-assisted micro-milling of Al-Li alloy 2195- T8 and flow rate optimization[J]. Journal of Manufacturing Processes，2024，127：218-237.
[12] LI Xiashuang，ZHU Wei，WANG Junqiang，et al. Optimization of bone drilling process based on finite element analysis[J]. Applied Thermal Engineering，2016，108：211-220.
[13] ZHAO Biao，HUANG Qiang，CAO Yang，et al. Thermal analysis of ultrasonic vibration-assisted grinding with moment-triangle heat sources[J]. International Journal of Heat and Mass Transfer，2023，216：124552.
[14] RAN Yichuan，KANG Renke，DONG Zhigang，et al. Ultrasonic assisted grinding force model considering anisotropy of SiCf/SiC composites[J]. International Journal of Mechanical Sciences，2023，250：108311.
[15] YANG Zhichao，ZHU Lida，ZHANG Guixiang，et al. Review of ultrasonic vibration-assisted machining in advanced materials[J]. International Journal of Machine Tools & Manufacture，2020，156：103594.
[16] YANG Yuying，YANG Min，LI Changhe，et al. Machinability of ultrasonic vibration-assisted micro- grinding in biological bone using nanolubricant[J]. Frontiers of Mechanical Engineering，2023，18(1)：1.
[17] BABBAR A，JAIN V，GUPTA D. Preliminary investigations of rotary ultrasonic neurosurgical bone grinding using Grey-Taguchi optimization methodology[J]. Grey Systems-Theory and Application，2020，10(4)：479-493.
[18] GAO Teng，ZHANG Xianpeng，LI Changhe，et al. Surface morphology evaluation of multi-angle 2D ultrasonic vibration integrated with nanofluid minimum quantity lubrication grinding[J]. Journal of Manufacturing Processes，2020，51：44-61.
[19] 王晓铭，张建超，王绪平，等. 不同冷却工况下的磨削钛合金温度场模型及验证[J]. 中国机械工程，2021，32(5)：572-578，586. WANG Xiaoming，ZHANG Jianchao，WANG Xuping，et al. Temperature field model and verification of titanium alloy grinding under different cooling conditions[J]. China Mechanical Engineering，2021，32(5)：572-578，586.
[20] GRIMMERT A，PACHNEK F，WIEDERKEHR P. Temperature modeling of creep-feed grinding processes for nickel-based superalloys with variable heat flux distribution[J]. CIRP Journal of Manufacturing Science and Technology，2023，41：477-489.
[21] LI Benkai，DING Wenfeng，ZHU Yejun，et al. Thermal analysis on profile grinding of turbine disc slots of powder metallurgy superalloy FGH96[J]. International Communications in Heat and Mass Transfer，2024，159：108207.
[22] SHIH A J，TAI B L，ZHANG Lihui，et al. Prediction of bone grinding temperature in skull base neurosurgery[J]. CIRP Annals-Manufacturing Technology，2012，61(1)：307-310.
[23] ZHANG Lihui，TAI B L，WANG Guangjun，et al. Thermal model to investigate the temperature in bone grinding for skull base neurosurgery[J]. Medical Engineering & Physics，2013，35(10)：1391-1398.
[24] WANG Guangjun，ZHANG Lihui，WANG Xudong，et al. An inverse method to reconstruct the heat flux produced by bone grinding tools[J]. International Journal of Thermal Sciences，2016，101：85-92.
[25] YANG Min，LI Changhe，SAID Z，et al. Semiempirical heat flux model of hard-brittle bone material in ductile microgrinding[J]. Journal of Manufacturing Processes，2021，71：501-514.
[26] 杨敏，李长河，张彦彬，等. 神经外科颅骨磨削温度场预测新模型[J]. 机械工程学报，2018，54(23)：215-22. YANG Min，LI Changhe，ZHANG Yanbin，et al. A new model for predicting neurosurgery skull bone grinding temperature field[J]. Journal of Mechanical Engineering，2018，54(23)：215-222.
[27] SUN Jingang，LI Changhe，ZHOU Zongming，et al. Material removal mechanism and force modeling in ultrasonic vibration-assisted micro-grinding biological bone[J]. Chinese Journal of Mechanical Engineering，2023，36(1)：129.
[28] 孙金刚，杨敏，杨玉莹，等. 超声微磨削生物骨非均匀热源温度场模型与实验验证[J]. 机械工程学报，2024，1-21. SUN Jingang，YANG Min，YANG Yuying，et al. Ultrasonic micro-grinding biological bone non-uniform heat source temperature field model and experimental verification[J]. Journal of Mechanical Engineering，2024，1-21.
[29] JAEGER J C. Moving sources of heat and the temperature of sliding contacts[J]. Proceedings of the royal society of New South Wales，1942，76(3)：203-224.
[30] OUTWATER J O，SHAW M C. Surface temperature in grinding[J]ASME，1952，74：73-81.
[31] HAHN R S. On the nature of the grinding process[C]// Proceedings of the 3rd Machine Tool Design and Research Conference，1962：129-154.
[32] YANG Min，KONG Ming，LI Changhe，et al. Temperature field model in surface grinding：a comparative assessment[J]. International Journal of Extreme Manufacturing，2023，5(4)：042011.
[33] YANG Min，LI Changhe，ZHANG Yanbin，et al. Research on microscale skull grinding temperature field under different cooling conditions[J]. Applied Thermal Engineering，2017，126：525-537.
[34] WANG Xuezhi，YU Tianbiao，SUN Xue，et al. Study of 3D grinding temperature field based on finite difference method：considering machining parameters and energy partition[J]. International Journal of Advanced Manufacturing Technology，2016，84(5-8)：915-927.
[35] CHEN Hao，ZHAO Ji，DAI Yuanxing，et al. Simulation of 3D grinding temperature field by using an improved finite difference method[J]. International Journal of Advanced Manufacturing Technology，2020，108(11-12)：3871-3884.
[36] LIAO Zhirong，AXINTE D，Gao Dong. On modelling of cutting force and temperature in bone milling[J]. Journal of Materials Processing Technology，2019，266：627-638.
[37] 杨敏，李长河，张彦彬，等. 骨外科纳米粒子射流喷雾式微磨削温度场理论分析及试验[J]. 机械工程学报， 2018，54(18)：194-203. YANG Min，LI Changhe，ZHANG Yanbin，et al. Theoretical analysis and experimental research on temperature field of microscale bone grinding under nanoparticle jet mist cooling[J]. Journal of Mechanical Engineering，2018，54(18)：194-203.
[38] ROBLES-LINARES J A，AXINTE D，LIAO Zhirong，et al. Machining-induced thermal damage in cortical bone：Necrosis and micro-mechanical integrity[J]. Materials & Design，2021，197：109215.
[39] LI Haonan，AXINTE D. On a stochastically grain- discretised model for 2D/3D temperature mapping prediction in grinding[J]. International Journal of Machine Tools & Manufacture，2017，116：60-76.
[40] LIU Mingzheng，LI Changhe，ZHANG Yanbin，et al. Analysis of grain tribology and improved grinding temperature model based on discrete heat source[J]. Tribology International，2023，180：108196.