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首页> 外文期刊>Electronic Journal Technical Acoustics >Design and modeling of bar ultrasonic horns by means of harmonic balance method
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Design and modeling of bar ultrasonic horns by means of harmonic balance method

机译：棒式超声变幅杆的谐波平衡法设计与建模

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The article considers application of harmonic balance method for solving problems of design and modeling of bar ultrasonic horns. For application of harmonic balance method function describing distribution of vibration parameters along the horn length and function describing shape of horn longitudinal section are continued in even way onto the interval [-L; +L], where L is horn length, and represented as Fourier polynomials. Equation of horn longitudinal vibration is represented as non-uniform integral-differential equation which is reduced to non-uniform system of linear algebraic equations by means of harmonic balance method. Solution of this system with minimal norm is determined by means of pseudoinverse Moore-Penrose matrix and gives coefficients of Fourier polynomial for the function describing distribution of vibration parameters along the horn length. Application of the proposed method is illustrated with numerical examples of design and modeling of conical horn and composite horn for ultrasonic welding of electrical connections of microelectronic devices. Obtained results are in good agreement with parameters calculated for conical horn using formulae known from the literature and parameters calculated for composite horn using transfer matrix method (relative error of calculated vibratory displacement amplitude is 0,2 % for conical horn for the number of harmonics N = 4 and 0,8 % for composite horn for the number of harmonics N = 7).Key words: bar ultrasonic horn, ultrasound oscillations, harmonic balance method, Fourier polynomials.
机译：本文考虑了谐波平衡法在解决棒形超声喇叭的设计和建模问题中的应用。为了应用谐波平衡法，沿振幅长度分布振动参数分布的函数和描述振幅纵截面形状的函数以均匀的方式延续到间隔[-L; + L]，其中L是喇叭长度，用傅立叶多项式表示。喇叭纵向振动方程表示为非均匀积分微分方程，通过谐波平衡法将其简化为线性代数方程的非均匀系统。用伪逆Moore-Penrose矩阵确定具有最小范数的该系统的解，并给出傅里叶多项式的系数，用于描述沿喇叭角方向振动参数分布的函数。通过数值举例说明了用于超声焊接微电子设备电连接的圆锥形变幅杆和复合变幅杆的设计和建模数值实例，说明了该方法的应用。获得的结果与使用文献中已知的公式计算出的圆锥形喇叭的参数和使用传递矩阵法计算出的复合喇叭的参数非常吻合（对于谐波次数N，圆锥形喇叭的振动位移幅度的相对误差为0.2％谐波数量N = 7时，复合喇叭角= 4和0.8％）关键词：棒形超声波喇叭，超声振荡，谐波平衡法，傅立叶多项式。

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