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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