Screw air compressors have been widely used for a long time due to its advantages such as compactness, high performance, and stability. There are many studies on these machines, but there are still many problems, especially about the screw pairs machining based on the envelope theory, to study. This paper focuses on the method for disc tool profiling and selecting the position of the disc tool to avoid undercutting phenomena, assessing the influence of the angle formed by the disc tool axis and the workpiece axis on machining errors. Research results can be used to design, locate the disc tool, and select machines to meet the required accuracy of the air compressor screw pair