Iron Core Model of a Resistance Spot Welding Transformer

Disertacija obravnava model železnega C jedra transformatorja za uporovno točkasto varjenje. Predstavljen je nov model C jedra, ki upošteva vplive vrtinčnih tokov na razporeditev magnetnega polja v jedru ter nelinearno magnetilno karakteristiko pločevine s histerezo. Model izhaja iz predpostavke, da se domensko strukturo magnetno usmerjene pločevine v jedru transformatorja lahko obravnava s klasičnim modelom pločevine, ki predvideva homogeno magnetno strukturo pločevine brez domen. Vpliv vrtinčnega toka na razporeditev magnetnega polja v pločevini smo upoštevali z navidezno razdelitvijo pločevine na tanke rezine, znotraj katerih je vpliv lastnega vrtinčnega toka rezine na razporeditev magnetnega polja v rezini tako majhen, da je upravičena predpostavka o homogenem magnetnem polju znotraj rezine. Za homogeno magnetno polje smo s pomočjo Amperovega in Faradayevega zakona za vsako rezino v pločevini dobili magnetno napetostno ravnotežno enačbo. V magnetni napetostni ravnotežni enačbi nastopa tudi nelinearna magnetilna karakteristika magnetnega materiala s histerezo, ki smo jo modelirali s skalarnim modelom histereze. Skupne izgube v jedru smo izračunali kot vsoto histereznih izgub in joulskih izgub zaradi vrtinčnih tokov v jedru. Preizkus je pokazal, da je zaradi upoštevanja vpliva vrtinčnih tokov v jedru transformatorja na razporeditev magnetnega polja v jedru razlika med izmerjenimi izgubami in z modelom izračunanimi izgubami tako majhna, da tako imenovanih presežnih izgub v jedru ni potrebno upoštevati. Razviti model železnega jedra transformatorja je enostavno vključiti v vezni model transformatorja. Model je uporaben za numerično analizo vodenja sistema za uporovno točkasto varjenje, ker pa so v modelu dimenzije jedra in pločevine ter električne in magnetne lastnosti pločevine podane parametrično, je model primeren tudi za optimizacijo dimenzij jedra transformatorja, debeline pločevine in izbiro materiala, iz katerega je narejena pločevina.The thesis describes iron core model of a resistance spot welding transformer. The proposed model considers eddy currents, hysteresis, and the saturation effect of a magnetic field in a laminated iron core. The model is based on the presumption that the domain magnetic structure of the grain oriented electrical steel sheet can be neglected and modelled with the classical model, which presume homogeneous magnetic structure of the steel sheet. In order to consider the influence of the eddy currents on the magnetic field in the iron core, the cross-section of lamellas is divided into slices so that the presumption of the homogeneous magnetic field in the virtual slice is adequately fulfilled. From Amperes law and Faraday\u27s Law of induction, the equation of magnetic field for each slice in the lamella is obtained. Hysteresis properties of the magnetic steel sheet in the equation of magnetic field are modelled by simple scalar hysteresis model. Iron core losses are calculated by separation losses into hysteresis losses and eddy current losses. Since the iron core model proposed in this work considers the influence of eddy currents on the distribution of the magnetic flux density, the excess losses are neglected. A good agreement of calculated and measured results confirms that excess losses can be ignored in this case. The proposed iron core model of the resistance spot welding transformer is simple, computationally effective, and based on parameters that can be easily obtained from data sheet. Since the iron core model is easy to integrate into the circuit model of the transformer, it is applicable for the design of control algorithms as well as a rough optimisation of blade thickness, air gap width, and the dimensions of the transformer\u27s core