SOLVING HEAT TRANSFER PROBLEM IN ULTRASONIC WELDING BASED ON HYBRID SPLINE DIFFERENCE METHOD
A Hybrid Spline Difference Method is developed to solve a nonlinear equation of welding problem in ultrasonic welding. It is shown that the method has a computational procedure as simply as the finite difference method. In addition, the proposed method can simplify complexity of the traditional spline method calculation, and increase accuracy of the first and second derivatives of space from O(〖∆x〗2) of finite difference method to O(〖∆x〗4). According to the calculated temperature distribution in the work pieces, during the ultrasonic welding process, the proposed method illustrated that not only its precision is greatly enhanced, but also its concept is very similar to that of the finite difference method. Based on analysis results, it was concluded that the simple and high-accuracy hybrid spline difference method has a strong potential to substitute the traditional finite difference method.
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