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This research develops Friction stir welding mathematical model to predict the ideal temperature and plunging force to optimize the weld path quality, by considering only material properties. The Heat transfer and plastic deformation equations for describing the phenomena, specifically the deformation caused by friction of the metal, are revealed in this study. The Analysis considers temperature transfer and principles from fluid mechanics.聽 The model enhances precision and concentrates on crucial FSW conditions by implementing scaling and calibration techniques using literature data. The temperature at the outer limit of the shear layers is determined using a geometric method, which accounts for deformation rate, stress, and temperature. Additionally, the plunging factor is calculated by minimizing the logarithm square error of temperature and torque. The model results in crucial equations to determine key parameters for welding any material and undergoes thorough validation. This model serves as a valuable resource for estimating temperature and torque and allows the identification of the best procedure variables and the creation of comprehensive process limit maps. This study contributes to advancing FSW technologies, which are utilized in diverse industries such as rocket manufacturing. The research addresses challenges within FSW, enhancing its applicability and impact.