# Analytical and Graphical Profiling of Thread-Milling Cutters for Forming Internal Threads
## 2 Literature Review
### Forming of Internal Threads by Milling  
Forming internal threads by cutting is the most common method. Internal threads can be formed with thread-turning tools, taps, disk thread-milling cutters, thread-milling cutters and thread-cutting heads [1,2]. In practice, forming internal threads is mainly realized with thread-milling cutters. Short internal threads with fine and normal pitches are made with thread-milling cutters. The method of cutting threads with thread-milling cutters is performed on special thread-milling machines or CNC machines under conditions of medium and mass production. These tools in certain cases successfully replace thread-cutting taps, especially when cutting threads in body parts, due to the fact that when the tool is destroyed, the geometric characteristics of the machined threaded surfaces remain intact. The disadvantages of this type of tool include the deviations in the profile of the formed thread due to the thread-forming scheme and the design features of the tools. These deviations are reduced by implementing a new working profile of the cutters determined by profiling. During operation, the tool axis is parallel to the workpiece axis. The working movements performed by the thread-milling cutter are shown in Figures 2 and 3. Milling of internal threads is realized by the main rotary movement 1, radial feed movement 2, circular feed movement 3 and longitudinal feed movement 4. The thread-milling cutter cuts radially into the workpiece with movement 2 until the complete profile of the thread is formed. The thread is formed by up-milling while performing a circular feed movement 3 and axial movement of the tool with a movement 4 equal to the thread pitch P.  
Figure 1: Flowchart for determining the applicability of the most common groups of thread forming methods. Figure 2: Working movements when milling an internal thread with a thread-milling cutter in a cross-section of the workpiece. The forming of internal threads by milling is performed on CNC machines, and specifically on machining centers, because of their capabilities to provide the complex combinations of main and feed-forming movements. CNC systems contain a variety of automated cycles for thread processing. Through them, high accuracy and efficiency of processing is achieved, significantly reducing machine times [3; 4; 5]. Despite the many sources of information on the process of milling internal threads with thread-milling cutters, there are many issues that have not been sufficiently addressed. For example, questions about solving the problem of determining the tool profile to compensate for deviations from the theoretical profile due to the parallelism of the axes of the tool and the workpiece, the formation of helical chip flutes or the presence of a rake angle. There are also issues related to technological and design errors when milling internal threads, etc. Figure 4 shows the methods used for profiling the working part of metal-cutting tools. The classical methods for profiling cutting tools are the grapho-analytical methods. In this type of design, part of the input data for the analytical part of the profiling is taken  
Figure 4: Profiling methods. Figure 3: Working movements when milling an internal thread in an axial section of the workpiece. from graphical schemes developed on a scale with high magnification. However, their accuracy is relatively low. Grapho-analytical methods are used to verify the results of classical analytical modeling. With the advent of modern CAD systems for three-dimensional modeling, the need for such scaling disappears because it is possible to work with the real dimensions of the products, and the accuracy with which the graphic schemes are measured, for example in the CAD system SolidWorks, is eight digits after the decimal point. The required accuracy, which is usually used when profiling the cutting tools, is high, at four digits after the decimal point.