BFGS and Hybrid Spline Difference Method for Determining the Heat Generation and Temperature in Ultrasonic Welding Problems

• Main Authors: Ngo Thi Thao, 吳文草
• Other Authors: 黃錦煌
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/21481350164541588641

博士 === 逢甲大學 === 機械與航空工程博士學位學程 === 104 === The Hybrid Spline Difference Method is developed to solve the direct nonlinear heat transfer problem in ultrasonic welding process. Verification by welding problem finds that the presented method can simplify the complex determination process of traditional spline theory. Interestingly, its concept is very similar to that of finite difference method; however, its numerical accuracy is significantly enhanced. Thus, not only the hybrid spline difference method presented in this thesis has a simple computational process, but also it can be strongly potential replaced the conventional finite difference method and complicate spline method. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) inverse algorithm is investigated to predict the unknown time-dependent heat generation at the weld interface and convection heat transfer coefficient during a one-dimensional ultrasonic metal welding process based on the knowledge of temperature measurements taken on the horn. With known temperature data at some locations on the horn, the inverse solution was rapidly obtained through a computational procedure that involves the hybrid spline difference method for nonlinear direct problem, central finite difference, and simple step method in collaboration with BFGS method. The proposed algorithm, which did not need solving adjoint problem and sensitivity problem, reveals the characteristics of high efficiency, lower iterations, and high accuracy for estimating values even when measurement errors were considered. These results show that an accurate estimation on interfacial heat generation (or temperature) and the convection coefficient can be quickly found with arbitrary initial guesses. The BFGS combined with steepest descent method (SDM) is proposed for estimating unknown interface heat generation in a two-dimensional ultrasonic seam welding process. If the temperature within a lower workpiece is known, the interface temperature and heat generation can be determined inversely through the direct problem, adjoint problem, and simple step method. When the simple step method is used to find the search step length instead of the sensitivity problem, the computational algorithm becomes easier to calculate unknown parameters. Moreover, the convergence speed of the proposed inverse method is compared to that of the previous methods (i.e. BFGS, CGM and SDM). Special feature of proposed method is stable, accurate, and efficient for estimating moving heat sources and interface temperature even including some degree of measurement errors. In addition, the influence of the measurement location on the accuracy of estimated solutions with or without error of measurement was also discussed. These findings indicate that the estimated heat generation is more sensitive than the temperature to different measured temperatures and locations. To broaden the application of the inverse method, the BFGS method is continuously developed to estimate unknown interface heat generation during an actual ultrasonic seam welding with knowledge of experimental temperatures in a workpiece. Following the computational iteration process contains reading experimental temperature, solving adjont problem, using BFGS method, and using simple step method, the nonlinear inverse ultrasonic welding problem can be accurately solved. The estimated temperature was in very good agreement with the measurement temperature. In addition, the heat generation and its distributed range as well as interface temperature were rapidly predicted. According to understanding of the temperature distribution history at the workpieces and heat generated at the interface, the occurrence of thermal defects can be avoided during the welding process. In addition, the proposed method, which is a reliable and robust method for solving some welding applications, strongly provides valuable information for the optimization problem in the ultrasonic welding process. Therefore, the welding conditions can be appropriately adjusted, and then the weld quality will be controlled entirely.