Face gear has great development prospects because of its compact structure, high transmission efficiency, and high load-bearing capacity. The use of skiving for face gear processing has advantages such as high efficiency and low cost compared to tooth shaping, hobbing, and grinding. This paper takes orthogonal spur face gears as the research object, analyzes the principle of face gear skiving, and performs tooth contact analysis (TCA) on face gear teeth under different installation errors. The numerical simulation method is used to analyze the influence of offset errors, shaft angle errors, and installation distance errors on the contact trajectory of face gears. Skiving processing is carried out using a YK2260MC CNC skiving machine, and gear tooth surface errors are detected using a Gleason 650GMS gear inspection machine. The results show that the maximum error on the left tooth surface is 13.9 micrometers, and the maximum error on the right tooth surface is 11.7 micrometers. This result verifies the correctness of the skiving processing mathematical model, improves the processing accuracy and efficiency of face gears, and provides a reference for further improving the face gear skiving process.
1. Introduction
Gear transmission is one of the most commonly used forms of power and motion transmission in modern mechanical equipment, playing a crucial role in the machinery manufacturing industry. Gears are considered a symbol of the development level of basic industries and have received much attention in the development of China’s industry. In recent years, emerging transmission types, especially face gears, are gradually emerging. Face gear can be regarded as a special transmission type of bevel gears. When the axis angles (i.e., shaft angle) of the two gears are 90 degrees, and the teeth are distributed on a plane, the bevel gear becomes a face gear. Face gears have advantages such as compact transmission structure, low mass, no axial positioning requirements, large transmission ratio, large contact ratio, high carrying capacity, and low noise, making them suitable for high-speed and heavy-load applications.
However, there are issues such as low processing efficiency and high tool manufacturing costs in traditional processing methods such as tooth shaping, hobbing, and grinding, which have become bottlenecks for the industrial application of face gears. Therefore, there is an urgent need to study and develop new processing technologies for face gears to improve processing efficiency and accuracy. In this paper, the skiving technology of face gears is taken as the research object, and the processing principle and tooth contact performance of face gears are analyzed in detail.
2. Literature Review
Many scholars have conducted extensive research on face gear processing technologies. Zhu Rupeng et al. designed and developed the first domestic face gear tooth-shaping machine in China and conducted a large amount of research on the geometric design, basic processing principles, and simulation analysis of face gear transmission. Tang Jinyuan et al. proposed a method of processing face gears using a combination of milling and interpolation, and proved the feasibility of this method through VERICUT simulation and experiments. Guo Hui et al. proposed a face gear hobbing method, designed spherical hobs, and verified it through experiments. In addition, they conducted extensive research on face gear grinding. Wang Yanzhong et al. analyzed the mechanism of face gear processing using a five-axis CNC milling machine, derived the hob equation, studied the influence of installation errors on processing accuracy, and proposed a compensation method for face gear processing parameters. Mao Shimin established a gear tooth surface calculation model based on the relative position and relative motion between the skiving cutter and the workpiece, and completed case analysis of skiving processing for spur gears and helical gears. Guo Erkuo studied the skiving processing mechanism based on the principle of meshing of spatial staggered-axis gears and designed a helical skiving cutter for processing spur gears. Peng Xianlong et al. proposed a method for processing face gears using a dish-shaped grinding wheel, calculated the parabolic transmission error of the face gear, and avoided edge contact while improving transmission stability. Guo Hui et al. derived the tooth surface equation for a worm grinding wheel used for face gear grinding based on the meshing principle, converted the five-coordinate dressing motion of the grinding wheel surface into a series of continuous three-coordinate motions, thereby reducing the requirements for the numerical control accuracy of the machine tool. Wang Yanzhong et al. proposed a method for grinding face gears using an involute dish-shaped grinding wheel and verified it using VERICUT software simulation. Jia Chao et al. used tooth contact analysis (TCA) to study the geometric and loaded contact characteristics of internally meshing S-shaped gears under different modification amounts and errors, and provided calculation examples. Zhou Ruchuan et al. applied topologically modified cylindrical gears derived from worms to small shaft angle face gear pairs and performed tooth contact analysis. Cao Xuemei proposed a decomposition algorithm for tooth contact analysis for conventional TCAs, which simplifies the calculation of traditional tooth contact analysis and reduces the difficulty of finding meshing points. Gao Hongying established a finite element model using a pair of spiral bevel gears as an example, performed tooth contact analysis, and obtained finite element calculation results of the gears under different installation errors, providing a reference for the design of spiral bevel gears. Han Peng et al. studied the influence of installation errors on the position changes in the meshing zone, output gear rotation angles based on finite element software, and evaluated the degree of influence of installation errors on gear meshing characteristics using transmission errors.
Currently, there is relatively little research on tooth contact analysis for face gears. This paper analyzes the tooth contact performance of face gears under different installation errors. Firstly, the principle of face gear skiving is analyzed, and a mathematical model for face gear skiving processing and an accurate mathematical model for tooth contact analysis of face gears and cylindrical gears are established. Then, a meshing equation considering installation errors is established, and the influence laws of installation distance, shaft angle, and offset on contact trajectories and transmission errors are analyzed. Finally, the YK2260MC CNC skiving machine is used for skiving processing, and the Gleason 650GMS gear inspection machine is used to detect tooth surface errors. The results verify the correctness of the skiving processing mathematical model, improve the processing accuracy and efficiency of face gears, and provide a reference for further improving the face gear skiving process.
3. Face Gear Skiving Principle and Mathematical Model
3.1 Theoretical Tooth Surface Design of Orthogonal Spur Face Gears
3.1.1 Analysis of Face Gear Skiving Motion
The face gear skiving process involves two degrees of freedom of motion: one is the generating motion between the skiving cutter and the workpiece, and the other is the continuous feed motion of the skiving cutter along the direction of the face gear tooth line. The skiving cutter and the workpiece to be processed rotate around their respective axes at angular velocities ω1 and ω2, respectively. Z1 and Z2 are the number of teeth of the skiving cutter and the face gear to be processed, respectively, and the ratio of ω1 to ω2 is equal to the ratio of the number of teeth of the face gear to the skiving cutter. The two rotate strictly around their respective axes during processing according to the tooth number ratio, with the relationship given by Equation (1). The reference zero point of the skiving cutter is set at its end face center N1. The direction of the perpendicular bisector of the rotational axes of the skiving cutter and the workpiece to be processed is defined as the offset adjustment direction, with E as the initial offset distance. According to geometric relationships, the offset distance E can be expressed as Equation (2).
In Figure 1, which shows the schematic diagram of the skiving process for orthogonal spur face gears, the skiving cutter reference zero point is set at its end face center N1. The skiving cutter and the workpiece blank rotate around their respective axes with angular velocities ω1 and ω2, respectively. N1 and N2 are two points in the diameter direction of the face gear, representing the two instantaneous positions when the skiving cutter starts cutting at N1 and cuts out at the inner diameter at N2. V1 and V2 are the linear velocities at the meshing points N1 and N2, respectively, and the tool linear velocity VT remains constant at the meshing points. There is a relative velocity between the corresponding meshing points of the skiving cutter and the face gear, and as the tool moves closer to the geometric center of the face gear, the linear velocity at the meshing point on the face gear becomes smaller, and thus the relative velocity also changes. The skiving process of the face gear relies on this relative velocity to achieve cutting of the workpiece.
Figure 1. Diagram of face gear skiving process
3.1.2 Skiving Cutter Tooth Surface Equation
The involute tool tooth profile and spiral motion are shown in Figure 2. The tool coordinate system Sd (Od-XdYdZd) and the involute starting point Q1 are indicated. The curves Q1 and Q2 are the cutting edge working tooth profiles that generate the working tooth surface of the face gear. Since the skiving cutter is a helical gear, the tooth surface equation of the skiving cutter can be obtained through the spiral motion shown in Figure 2-b. In the coordinate system Sd, the tool tooth profile is represented by Equation 。
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