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Title: Design and analysis of ultrasonic horns operating in longitudinal and torsional vibration
Author: Al-Budairi, Hassan Dakhil
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 2012
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Combining modes of vibration, such as longitudinal and torsional vibration, is advantageous in many ultrasonic applications such as ultrasonic drilling, welding, and motors. In this work we present a novel approach to the design a longitudinal-torsional (LT) ultrasonic horn which adapts the front mass in a traditional Langevin transducer. Different approaches, such as degeneration of longitudinal vibration and coupling between longitudinal (L) and torsional (T) modes, have been used to generate the LT mode of vibration. The degeneration approach creates a non-uniform section, by cutting and twisting a number of slots along the path of the L wave such that part of the wave converts into T wave whilst the remaining part propagates unchanged through the section; these two parts are recombined near the output surface to form LT vibration. The mode coupling approach uses two set of vibration generators, usually piezoelectric elements, where one set generates L vibration whilst the second set generates T vibration. An exponential cross-sectional horn uses to combine the two modes where the area reduction factor is selected such that these modes resonate at the same frequency. However, many limitations prevent the wide usage of these methods in ultrasonic applications. These limitations are the complex design and excitation, possible coupling with surrounding modes, instability in operating at different boundaries, difficulty in securing the structure without influencing the vibrational response and the low produced torsionality, which is the ratio of torsional to longitudinal response at the output face. The new approach is based on combining the principles of these methods to overcome the previously stated limitations, the slotting technique is incorporated into the exponential cross-sectional path and the horn produced is utilised as the front mass of a Langevin transducer. A set of design and performance criteria are used to optimise the transducer and includes applicable design; methods of securing the transducer; and the excitation features of LT transducer such that it can operate without the effects of surrounding modes of vibration and can produce high response and torsionality at the output surface. A methodology which combines mathematical and experimental modelling is used to optimise LT transducer design. The mathematical modelling, which includes finite element (FE) and analytical methods, is performed to optimise the geometry and to predict electromechanical parameters, modal parameters and the dynamic behaviour of LT transducer. The experimental modelling is used to validate the mathematical results and to characterise the fabricated prototypes under different operating conditions. The dimensions of the initial design of the L mode Langevin transducer are derived from the principles of the wave equation. This transducer has a set of piezoceramic components sandwich between a cylindrical back mass and an exponential front mass connected by a pre-stressed bolt. The dimensions are used to create the FE model, using the FE software package ABAQUS, where different shapes of cut at different dimensions and at various angle of twist along the front mass are introduced and examined by a modal analysis procedure to the front mass. An optimised model is then utilised in a size scaling study to confirm the suitability of using this approach for different ultrasonic applications. The dimensions of the optimised design are also used in the analytical study, based on Mason’s electric equivalent circuit approach, to predict the electromechanical parameters where a one-dimensional equivalent circuit approach is created separately for each part whilst the combination vibrational motion in the front mass is represented by two, longitudinal and torsional, equivalent circuits. The complete equivalent network of the LT transducer is then solved using the mathematical software package MATHEMATICA. The analytical model is also extended to validate some of particular FE findings such as the distribution of the response amplitude and the location of the longitudinal nodal plane along the transducer’s structure. Two optimised models of different sizes are fabricated and characterised through different testing techniques including electrical impedance analysis, experimental modal analysis (EMA) and experimental harmonic analysis. Optimisation of the pre-stressing of the transducer is performed by applying different torques to the pre-stressed bolt and measuring the electrical impedance spectra where the results are compared to analytical findings. EMA is then used to describe the natural characteristics of the structures where the results are used to accurately extract the modal parameters and to validate the predictions of the FE and analytical model. Different levels of harmonic excitation are used to characterise the fabricated prototypes where the results are compared to the findings of the mathematical modelling. A case study of the design of the LT drill is presented to validate the design approach for real ultrasonic applications. A similar methodology is applied and the resulting LT drill is tested for both unloaded and loaded operating conditions. The results obtained show that this new approach can be easily and successfully applied to ultrasonic applications to produce a torsional to longitudinal amplitude response of 0.8 which is measured on a fabricated prototype.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: TJ Mechanical engineering and machinery