Derivation of Analytical Expressions for Fast Calculation of Resistance Spot Welding System Currents

Abstract

The paper deals with the dynamics of a resistance spot welding system. At the core of this system is a transformer, which is powered on the primary side by a pulse-width modulated inverter and has a full-wave output rectifier on the secondary side that provides a direct welding current. The entire system is nonlinear, due to magnetic hysteresis and electronics. The electronics prevent the current from flowing in all parts of the welding transformer at separate time intervals during the voltage supply period; therefore, not all the parameters affect the dynamic of currents and voltages all the time so the system is also time-variant. To design a high-performance welding system and to predict the maximum possible welding current at a specific load, it is necessary to know the welding and primary currents. The leakage inductances of the system can reduce the maximum welding current significantly at higher frequencies and the same load. There are several methods to determine these currents, each with its drawbacks. Measurements are time-consuming, using professional software is expensive and requires time to learn and free open-source software has many limitations and does not guarantee the correctness of the results. The article presents a new, fourth option—a theoretical derivation of analytical expressions that facilitate straightforward and rapid calculation of the welding and primary currents of the resistance spot welding system with symmetrical secondary branches. The derivation of the mathematical expressions is based on the equivalent circuits that describe the system in different operating states. The results of the numerical simulations confirmed the derived expressions completely.