Abstract: This paper analyzes the causes of errors in CNC programs for screw machining using the instantaneous center envelope method, and proposes an analytical method for verifying the accuracy of CNC programs, providing a theoretical basis for improving CNC programs. Keywords: Instantaneous center envelope; Screw; Accuracy analysis 1. Overview With the development of oil and gas resource development technology in China, especially directional drilling technology, the use of screw drilling tools is constantly increasing, and the machining technology of its important component—the rotor screw—is also constantly being updated. Currently, the instantaneous center envelope method is widely used on CNC screw milling machines both domestically and internationally for milling the rotor of screw drilling tools. This efficient screw machining technology has been studied since 1994 and has gradually been promoted and applied. In actual production, compiling efficient and high-precision CNC machining programs can fully utilize the functions of machine tools and the technological advantages of the instantaneous center envelope method. This paper addresses the shortcomings of currently used programming methods and proposes a method for analyzing the machining accuracy of screws through computer simulation. This method can realize the verification and simulation of program accuracy and also provides a theoretical basis for programmers to improve program design. 2. Machining Technology 2.1 Geometric Characteristics and Machining Principle of Screws Most screw drill rotors are 3-9 head screws, and their typical cross-sectional profile is shown in Figure 1. However, the cross-sectional profiles designed by different manufacturers are not entirely the same. They are generally complex curves composed of inner and outer arcs, inner and outer cycloids, and their transition curves. [align=center] Figure 1 Screw cross-sectional profile (a) Three-head screw cross-section (b) Five-head screw cross-section[/align] The machining principle of this type of screw using the non-instantaneous center envelope method is shown in Figure 2. The cutting tool used is a disc milling cutter with a tip angle of α, with rotation (n) as the main cutting motion. Under the control of CNC, the machine tool realizes the linkage of workpiece rotation (Y-axis) and tool radial displacement (X-axis) according to a certain law, and envelops the workpiece cross-sectional profile curve; the feed motion of the tool along the helical direction is realized through the linkage of the Y-axis and Z-axis to complete the helical envelope machining. That is to say, the machining of this type of screw with any number of heads and any cross-sectional profile can be realized through the linkage of the X, Y, and Z axes. [align=center]Figure 2. Schematic diagram of machining principle without instantaneous center envelope[/align] 2.2 Programming and Accuracy Inspection Methods When machining a screw according to the above-mentioned principle without instantaneous center envelope, the accuracy of its contour curve mainly relies on the CNC machining program. Therefore, good programming is an important task in machining such curved parts. Currently, the programming methods commonly used by various manufacturers fall into two main categories: one is to calculate the coordinate values ​​of several points on the workpiece cross-section contour curve at equal intervals based on experience, and then perform linear interpolation on each point; the other is to perform curve approximation calculations using the equal accuracy method in program programming. The latter method requires relatively fewer program segments and has slightly higher accuracy. The machined screw is inspected using the template optical gap method. The above-mentioned programming methods are all performed under simplified conditions, resulting in certain errors, and the inspection methods also have relatively large errors. To further improve the machining accuracy of the workpiece and enhance the performance of the screw drill, more in-depth and careful research is necessary. 3. Machining Accuracy Analysis 3.1 Main Factors Affecting Machining Accuracy Theoretically speaking, the section envelope method is to cut out the profile point by point by the cutting edge during the mutual movement of the milling cutter and the workpiece in the X, Y, and Z directions. Since most current CNC machining programs are based on the motion relationship between the workpiece and the tool within the workpiece cross section, a series of errors are generated, mainly the following four: (1) When programming, only the planar motion relationship between the workpiece and the tool within the workpiece cross section is considered, while the error caused by the spatial meshing relationship between the tool and the workpiece is ignored; (2) The installation angle of the milling cutter is δ, which is equal to the helix angle β0 of the screw's mean diameter. Thus, at positions deviating from the mean diameter, errors are generated due to the difference between the tool installation angle δ and the actual helix angle β of the workpiece; (3) CNC machining programs are input point-to-point. When performing linear interpolation, the actual movement of the tool is the interpolation of the Archimedean spiral, which will also generate certain errors; (4) When performing tool tip arc compensation, the shape of the tool tip projection is currently simplified to an arc. However, due to the existence of the tool installation angle δ, the actual projection of the tool tip within the cross section should be an ellipse. Thus, the magnitude of the error varies with the size of the tool tip arc radius. Therefore, this paper considers the above four factors, simulates the actual motion relationship between the tool and the workpiece in a computer, calculates the actual machining profile of the workpiece in space, and then compares it with the theoretical profile to calculate the profile error of the workpiece, thereby verifying the CNC program and providing a reliable basis for the improvement of the CNC machining program. 3.2 Analysis Method of Machining Accuracy 3.2.1 Establishing a Mathematical Model In order to facilitate analysis, the following mathematical models need to be established: According to the actual machining situation, the tool is established as a composite surface model of a toroidal surface and a conical surface; according to the motion relationship between the workpiece and the tool, a model of the relative position relationship between the tool and the workpiece and a model of the motion trajectory of the tool and the workpiece according to the CNC machining program are established; a model of the relationship between the theoretical curve and the actual machining workpiece profile is established, that is, an error calculation model, etc. 3.2.2 Dynamic Simulation and Accuracy Analysis The tool and the workpiece are discretized into multiple cross sections in a given area near the cutting point, and they are discretized into multiple points in each cross section, and the coordinate values ​​of each point are calculated. According to the actual machining situation, the coordinates of the discrete points on the cutting surface of the workpiece model cut by the tool model at a certain machining position are calculated. The cutting tool is moved to a new position according to the rules given in the CNC program, and the coordinates of discrete points on the corresponding cutting surface are calculated. This process is repeated to calculate the actual machining profile of the workpiece for one cycle. The workpiece moves along the Y-axis and the cutting tool along the Z-axis, moving in a spiral direction according to the rules given in the CNC program to a new cross-section, and the actual machining profile of the workpiece for one cycle is calculated again. This simulates the actual cutting process of the workpiece and obtains the discrete point coordinates of the entire workpiece profile. The obtained data accurately reflects the actual shape, dimensional accuracy, and waviness of the workpiece profile during machining. The accuracy analysis program flowchart is shown in Figure 3. [align=center] Figure 3 Program Flowchart[/align] By comparing the above calculation results with the theoretical profile, the magnitude and direction of the profile error at various positions of the workpiece can be calculated. Analysis reveals the error variation pattern. This verifies the accuracy of the existing CNC program and provides a basis for its improvement. After one or two simulation cycles, a satisfactory CNC program can be obtained. The accuracy of the CNC program can be calculated through this simulation analysis, and the ideal machining program can be easily obtained without cutting tests. 4 Conclusion (1) Using computer simulation for accuracy analysis is an effective method to verify machining accuracy; (2) The accuracy analysis method described in this paper is an effective way to obtain an ideal CNC machining program and achieve economical and efficient machining of screws.