روشی برای بهینه سازی شکل آمپلی فایر مافوق صوت با استفاده از الگوریتم ژنتیکی و روش سیمپلکس

Designing devices for ultrasonic vibration applications is mostly done by intuitively adjusting the geometry to obtain the desired mode of vibration at a specific operating frequency. Recent studies have shown that with optimization methods, new devices with improved performance can be easily found. In this investigation, a new methodology for designing an ultrasonic amplifier through shape optimization using genetic algorithms and simplex method with specific fitness functions is presented. Displacements at specific functional areas, main functionality, and mode frequency are considered to determine the properties of an individual shape to meet the stated criteria. Length, diameter, position of mountings, and further specific geometric parameters are set up for the algorithm search for an optimized shape. Beginning with genetic algorithms, the basic shape fitting the stated requirements is found. After that the simplex method further improves the found shape to most appropriately minimize the fitness function. At the end, the fittest individual is selected as the final solution. Finally, resulting shapes are experimentally tested to show the effectiveness of the methodology.

Recent developments in ultrasonic vibration assisted machining call for new designs of tools, horns, boosters, and other components. While a wider application range of the hybrid technology of ultrasonic vibration assistance for many manufacturing technologies is of great interest, one key challenge is the design of the system in order to achieve the desired resonance vibration. The most common mode used in ultrasonic-vibration-assisted machining is the longitudinal mode of an axisymmetrical horn, which can be easily obtained when solving the Webster Horn Equation [1]. equation(1) View the MathML source∂2u∂z2+1A(z)dA(z)dz∂u∂z=1c2∂2u∂t2 where t is time, u is displacement, A(z) is the cross sectional area as function of position z, and c is the acoustic velocity. The acoustic velocity c can be obtained with equation(2) View the MathML sourcec=EYρ where EY is the material's Young's modulus, and ρ the material density. In case of a harmonic motion, Eq. (1) can be rewritten as equation(3) View the MathML source∂2u∂z2+1A(z)dA(z)dz∂u∂z=ω2c2u where ω is the angular frequency. Using Eq. (3) the length of axisymmetric horns can easily be calculated given a specific resonance frequency. The design of tool holders and horns can be obtained by solving the above equations [2], [3] and [4] for various A(z). Based on these findings, a great variety of axisymmetric horns has been found and are used in the industry today. In medical engineering, a novel ultrasonic vibration tool for surgery has been designed and tuned to the appropriate frequency for the optimal configuration [5]. A percussive drill system was designed for rock coring on planetary robotic missions using ultrasonic vibration assistance to reduce power and torque requirements [6]. More challenging are new designs for ultrasonic vibration assisted machining by combining two modes for operational purposes [7]. The longitudinal-torsional composite mode allows advanced applications for machining like drilling. Tsujino et al. designed a one-dimensional longitudinal-torsional vibration converter using diagonal slits within the resonating structure [8]. Designing transducers for ultrasonic assisted wire bonding with finite element method has been discussed in [9] with the goal of matching simulation results with experimental results. Enhancing vibration performance and matching simulation with experimental results has also been discussed in [10] for ultrasonic block horns. Properly designing a rotary ultrasonic milling tool with finite element method is introduced in [11]. For many of the mentioned designs of horns and ultrasonic vibration components, intuitive design strategies were used by evaluating the nodal displacements of modes simulated with an FEM software. A common non-automated design procedure can be found in [12], which outlines the step-by-step procedure to manually design an ultrasonic device. Automating the intuitive/manual design process can be done by shape optimization. Many optimization methods have been applied for finding shapes and structures that provide good results for ultrasonic vibration applications. Combining multi-objective decision making such as the NIMBUS method with the finite element method can provide very good designs as shown in [13]. Another very good optimization was introduced in [14] to find advanced transducer designs while satisfying conflicting optimal values in the design space. In [15], design of experiments is used to find the correct parameters for an ultrasonic linear motor and perform a sensitivity analysis for each parameter and their interactions with each other. Based on Eq. (1), a ultrasonic horn optimization method is done in [16]. Porto et al. developed a genetic algorithm to optimize the amplitude of a surgical ultrasonic transducer by changing the length of specific geometric parts at a given frequency [17]. Designing the components for ultrasonic vibration assisted machining is generally challenging, because the high frequency vibrations need to precisely occur at the tool edge or a preferred location. While the maximum amplitude is desired at the tool, minimal vibration should occur at the clamping or mounting of the ultrasonic vibration device. In this investigation, a new methodology for a shape optimization [18] of ultrasonic vibration amplifiers and reducers using generic algorithm (GA) and simplex method [19] and [20] is introduced. Since the GA is capable of searching for the optimum of the entire design space for non convex problems, it serves as a global search method. The subsequent simplex method, as a local search method, is used to further refine the found optimum. The optimized shapes are experimentally tested by conducting an FFT Analysis and measuring displacements using a laser vibrometer.

In conclusion, it has been shown that the presented optimization methodology for ultrasonic devices is capable of delivering usable results that are in accordance with the specifications of the application. The presented fitness functions allow the optimizer to appropriately find geometric shapes of ultrasonic devices. They consist of the displacements at essential areas of the ultrasonic device and position of functional parts of the device. For finding the optimal design, a GA and simplex method is used. A longitudinal mode with the appropriate amplification at the functional area and two fix points with minimal vibration was tested for the amplitude modifiers. Changing the amplification factor resulted in new shapes that meet the optimization criteria. Changing other specifications, such as frequency or resonance mode type, can also be done. For further investigations, this optimization methodology needs to be tested on various ultrasonic components as well as cutting tools. To enhance the presented optimization procedure, minimization of internal stress [25] can be included in the fitness function. This is very important for small and thin high-power ultrasonic devices. Adding further constraints to simulate the connection at the mountings might also be included. Furthermore, a topology optimization needs to be developed to enable a wider range of possible solutions for ultrasonic components.