超声微磨削生物骨非均匀热源传导机理与三维有限差分模型及验证

doi:10.3901/JME.2025.19.363

摘要/Abstract

摘要： 磨削广泛用于骨外科手术实现对骨组织材料的去除，但机械应力引发的裂纹损伤和磨削温度过高导致的热损伤是临床操作的技术瓶颈。针对以上需求和技术瓶颈，提出了一种超声微磨削生物骨新工艺，但超声作用下的非均匀热源传导机理尚不明确，亟需建立生物骨的三维热传导模型。基于此，首先，分析了磨削过程中几何学、运动学和动力学的动态演变规律，建立了超声作用下任意时间点的未变形切屑厚度模型，研究了磨削热通量在周向和径向的分布规律，建立了三维非均匀热源分布模型。其次，综合考虑材料去除机理、磨削力的动态演化机理、界面条件及材料结构性能，建立了基于热流密度、对流换热及绝热条件的三维非均匀有限差分热传导模型，揭示了超声微磨削过程中骨材料内部温度的动态传导规律。进一步，设计了一种适用于半球冠圆弧面的热电偶阵列，并通过多参数正交实验测量工件不同位置的温度。最后，创新性地提出区域数值模拟与实验测温对比的方法，结果表明，当振幅为6 μm，磨削深度为25 μm，磨头基体半径为2 mm，进给速度为3 mm/s时，实验测量值与数值计算结果的最小误差可达6.4%，误差小于10%的区域占比达到70%，实现了骨微磨削温度的有效控制，为临床骨外科手术提供了理论指导与技术支持。

关键词: 超声振动, 微磨削, 非均匀热源传导机理, 三维有限差分模型, 热电偶阵列

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

中图分类号:

TG580
R318

孙金刚, 刘纪新, 杨敏, 杨玉莹, 李润泽, 张彦彬, 刘明政, 李长河. 超声微磨削生物骨非均匀热源传导机理与三维有限差分模型及验证[J]. 机械工程学报, 2025, 61(19): 363-385.

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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