# Analysis of Sheet Metal Tapping Screw Fabrication Using a Finite Element Method
## 2 Fundamental Theory
### Brief Introduction to Flat-Die Thread Rolling  
Two methods can be used for screw thread rolling. One involves cutting parallel grooves on the surface of each mold between two flat dies, where the groove shape is the reverse of the screw threads. One mold is fixed and the other undergoes reciprocation with the workpiece (blank) between them. This process is called the flat-die thread rolling process, wherein the screw thread rolling die is composed of a fixed plate and a moving plate. The fixed plate is generally shorter (short thread plate) and the moving plate is longer (long thread plate) (Figure 3).  
The other method involves a cylindrical roller mold with two or three grooves, and the rolling of the workpiece between the molds. When two roller holds are used, the workpiece between them is supported on a parallel holder and the right roller exerts pressure. When three rollers are used, three axes are parallel and synchronously rotated at appropriate speeds. The three rollers are operated by a cam while the workpiece is fed radially, and this process is called round mold thread rolling.  
Flat-die thread rolling is a chipless cold-working precision forming process for producing screws. Cold forging is primarily utilized in mass production; hot forging is used to manufacture large screws and nuts, and cutting processing is utilized only to manufacture a few products with special specifications. The underlying principle is to apply proper pressure on a round rod blank between a rotating roller mold and a reciprocating plane mold during cold processing. The threads on the mold are the reverse screw threads of the workpiece. Rolled under pressure, the metal undergoes plastic flow and the bulged wedging mold compresses the bottom of the screw thread so that the metal is extruded along both sides to form the peak of the screw thread.  
Screw thread rolling produces smoother surfaces than turning, milling, or grinding. It provides greater strength and hardness of the screw thread surface because of work hardening, high material utilization, and double the productivity of cutting processing; it is easily automated, and results in a long service life for dies. Nevertheless, the hardness of the workpiece material for rolling screw threads cannot exceed HRC40; the need for precise blank sizing is greater; the need for precise rolling and a hard die is greater; producing the dies is more difficult, and the process cannot be used to roll  
Figure 3: Flat-die thread rolling (with fixed flat die and moving flat die).  
Figure 2: Screw thread spiral diagram.  
asymmetric screw threads. More than 90% of screws with diameters less than 50 mm are produced by rolling. In metal stretching tests, a 5 cm gauge length with 12% elongation exhibits excellent rollability and is suitable for the rolling process. Numerous metal characteristics, such as hardness, ductility, internal friction that is generated during plastic deformation, yield strength, and cold hardening, affect the plastic deformation and rollability of metals.  
An automatic thread rolling machine completes a large deformation in a single operation. It provides a high production rate, but product defects and the short service life of the thread plate negatively affect productivity and production costs. As a result, a comprehensive understanding of the characteristics of process parameters through simulation would improve process design and quality evaluation. The blank material, surface quality, blank size, thread plate size, thread plate speed, thread flat-die geometry, interface lubricant, and service life of the thread plate all significantly influence the quality of the thread rolling product, its production cost, and its production efficiency.