Modelling and design of ultrasonic bone cutting blades

Ultrasonic cutting technology has been introduced for surgical applications since the 1950s. Ultrasonic bone cutting applies high frequency mechanical vibration of a blade tuned at a specific frequency to make incision on human hard tissues. It offers advantages such as improved safety, smooth and precise cutting. To facilitate the design of high performance surgical ultrasonic bone cutting blades, this thesis is devoted to the modelling and designing of ultrasonic blades with an attempt to better understand the dynamic characteristics of blade and improve the conventional design method. A non-coupled vibration analytical model which deals with four modes of vibration, including longitudinal oscillation, flexural bending, lateral bending, and torsional vibration of ultrasonic blades, was proposed based on one-dimensional theories. The model allows the estimation of the modal parameters of a blade without establishing a 3D model. The experimental study of this model using a uniform beam and a sectional ultrasonic blade showed that the model predicted the modal frequencies of these structures with satisfactory accuracy. This suggested that the analytical model can be used as an alternative method to FEA in the characterisation of ultrasonic blades. Two coupled models, a parametric vibration model and a longitudinal-bending coupled vibration model, were proposed to study the coupled vibration of ultrasonic blades. The parametric vibration model formulated the coupled vibration using a lumped mass beam. This enabled the investigation of interaction between the vibration modes based on a simple one-dimensional structure. However, this model resulted in governing equations of considerable complexity, which were considered to be more suitable for the purpose of theoretical study instead of performance prediction. In addition, a longitudinal-bending coupled model was proposed in this study with an attempt to understand a type of coupled vibration that is commonly observed in ultrasonic blades of beam-like profile. The model was established by introducing an extra rotation moment in the one-dimensional bending equation. Two numerical iteration approaches, with their implementation and error analysis detailed, were proposed to solve this model. An optimal design method was proposed in this study with an aim to improve the conventional design process of ultrasonic blades by applying mathematical algorithms instead of the designers' experience and intuition to optimise the design. The method was introduced based on the concept of performance indicators that measure specific physical characteristics of a blade using mathematical functions. Four kinds of indicators, the frequency based, gain based, displacement based and stress based indicators, which evaluate the main dynamic characteristics of ultrasonic blades, were detailed in this study. The process of the optimal design method consists of three major stages: formulation, optimisation and verification. The concept of the proposed method is to maximise the blade performance through the optimisation of the performance indicators. This can improve the quality of design by making sure the most desired characteristics are achieved in the blade. A software toolkit was developed using the Abaqus script interface and Python language in order to apply this method in the design of ultrasonic blades. Five ultrasonic bone cutting blades with different types of cutting edges were designed using either the conventional or the optimal design method. These blades were subjected to ultrasonic cutting tests under various cutting conditions. Ultrasonic cutting performed on biomechanical samples, ovine femur and rat bones showed that the blades were capable of making incisions on bones without the requirement of large applied force. Positive linear correlation between the applied force and the cutting speed was found in the ultrasonic cutting carried out under static applied force, and positive linear relationship between the applied force and the surface temperature was observed in the ultrasonic cutting carried out under sliding motion. The presence of elevated temperatures in the cutting tests suggested that the blades require the application of cooling in ultrasonic bone cutting. The study confirmed that the proposed optimal design method was an effective design approach. The blades were designed with expected vibration characteristics and satisfactory cutting performance