Analytical design and optimization of ultrasonic vibrational transducers for spinal surgery

Just about every other technical publication you pick up these days makes sweeping statements concerning the pressures on scientists, engineers, and industries as a whole to get to market in less time, with an improved, less expensive product. I am reminded of a slogan used rather ubiquitously by a prior employer : Cheaper, Faster, Better. The mention of this race has become almost blase for most, but for the individuals taking the brunt of the pressure, can be disconcerting if not outright painful. Expected to live up to this ambition, the design engineer is faced with the fact that the door is closing on antiquated methods of trial and error engineering. Unfortunately, most individuals have not been equipped with the necessary skills to enact a more intelligent design process and in many cases when the skills are present, industry, a bit paradoxically, is wary of expending the time and resources needed to fit into this new streamlined paradigm. This thesis could be considered as a case study of a somewhat mature technology coming to grips with this new rushed reality. Typical design methods for ultrasonic transducers, while based on analytical models, have relied heavily on building a transducer from quarter wave segments that have somewhat known characteristics. Prototypes are built, tested and modified until the desired results are obtained. Advances have been made to this method with the introduction of finite element softwares that allow modeling without realizing a prototype. The finite element methodology also permits a limited amount of system optimization, and while this is a definite improvement, it can still take months to realize an acceptable design. In this work, we draw on the analytical models, but abandon the quarter wave approach. We also use finite elements, to a limited extent, to validate results obtained from the analytical models, but do not attempt to use the finite element analysis to perform optimizations. On the contrary, a novel optimization method is developed which uses the analytical models to calculate values for the various cost functions necessary to optimize a transducer and its drive electronics. In this way, system parameters are left free to vary in the search for a maximum or minimum solution. While some systems are not candidates for system optimization as a means to get to market faster with a better product, this is not the case for ultrasonic transducers. The design of ultrasonic transducers is an application that begs for models, for optimization, and characterization. The investment made here in understanding the mathematical models, and in the development of optimization routines and softwares has allowed for a modified method of development for ultrasonic handpieces and their drive electronics. This thesis shows that, given a set of design specifications, the design of a transducer can be done in a very short period of time, a few days, even-and furthermore, the resulting design will function as predicted by the simulations. This work presents analytical models for the transducers elements with analysis and discussion. It then introduces a new method of optimization that is well adapted to optimizing the transducers as well as the drive electronics. The control electronics and a simple method of transducer control, which allow for the operation of the system for testing purposes, are also laid out.


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