Abstract: This paper introduces the experimental exponential formula of gear shaving radial force into the theoretical formula of metal cutting force, establishes a gear shaving cutting force model, quantitatively analyzes the influence rule of cutting parameters on gear shaving cutting force based on the principle of single variable, and elaborates the formation mechanism of tooth profile concave error based on cutting parameters. The validity of the model is verified through the finite element method and experiments. The results show that the gear shaving cutting force is positively correlated with the radial feed and axial feed, and negatively correlated with the spindle speed, among which the radial feed has the greatest influence on the gear shaving cutting force; the gear shaving cutting force near the pitch circle reaches a peak, indicating that overcutting occurs at this position, and the tooth profile concave error of gear shaving is easy to form with the reproduction of errors.
Keywords: gear shaving; cutting parameters; gear shaving cutting force; tooth profile concave error
1. Introduction
Gear shaving processing has the characteristics of high productivity and low cost, but the gear after shaving will have a tooth profile concave error, which seriously affects the performance of the gear. At present, the research on the tooth profile concave error of gear shaving mainly focuses on the internal excitation of shaving parameters such as contact ratio and the structure and modification of shaving cutters , and seldom from the perspective of cutting mechanism. The gear shaving cutting force (hereinafter referred to as “shaving force”) is an important factor in studying the cutting mechanism.
Cutting parameters of gear shaving are important factors to systematically reveal the formation mechanism of tooth profile concave errors of gear shaving, and researchers have conducted research on them earlier. Lv Ming et al. obtained an empirical formula between cutting usage and gear shaving radial force through gear shaving experiments. LITVIN conducted contact and transmission analysis on workpiece gears. MORIWAKI et al. calculated the cutting amount based on the gear shaving model, and established the relationship between the back feed and the tooth surface load distribution through indentation tests using an empirical formula. Most of the above literature is based on empirical formulas, which is not conducive to analyzing the internal relationship between cutting parameters and shaving force. In other forms of processing, Zhang Jin et al. adopted an indirect measurement test method for the characteristics of multi-cutting edges and non-free cutting in gear milling, and calculated the theoretical cutting force of gear milling based on the cutting theoretical model, and analyzed and studied the cutting mechanism of gear milling. HEIKKALA studied the determination method of milling force components in milling processing based on simplified cutting force theory under known cutting conditions. ANTONIADIS et al. established a cutting force model for straight tooth gear hobbing based on an algorithm simulating gear hobbing.
Although the cutting models established in the above literature mainly focus on milling and hobbing, they provide research ideas for establishing a theoretical model of shaving force and analyzing the internal relationship between cutting parameters and shaving force. This paper establishes a theoretical model of shaving force based on metal cutting theory. Based on the principle of single variable, it quantitatively analyzes the influence rule of spindle speed, radial feed of shaving cutter, and axial feed of workpiece gear on the shaving force, and expounds the formation mechanism of tooth profile concave error of gear shaving from the perspective of cutting parameters.
2. Influence of Gear Shaving Cutting Parameters on Shaving Force
According to the gear handbook, the selected gear shaving cutting parameters are as follows: spindle speeds n of 140 r/min, 170 r/min, 200 r/min, and 230 r/min; axial feeds f of 30 mm/min, 36 mm/min, 51 mm/min, and 60 mm/min; radial feeds fr of 0.033 mm, 0.039 mm, 0.045 mm, and 0.058 mm. The parameters of the shaving cutter and workpiece gear selected are shown in Table 1.
| Table 1: Parameters of shaving cutter and workpiece gear |
|---|
| Parameter |
| Shaving cutter material |
| Shaving cutter module |
| Number of teeth on shaving cutter |
| Helix angle of shaving cutter |
| Workpiece gear material |
| Module of workpiece gear |
| Number of teeth on workpiece gear |
When the cutting temperature is too high during gear shaving, it will cause the strength and hardness of the tooth surface of the workpiece gear to decrease, and the meshing stiffness of the gear to decrease, resulting in a decrease in the forming quality of the tooth surface.
2.1 Influence of Radial Feed Motion
The radial feed fr and axial feed f of gear shaving jointly determine the size of the shaving volume, so the axial feed motion parameters have an important influence on the shaving force. When the spindle speed n = 170 r/min and the radial feed fr = 0.045 mm remain unchanged, change the axial feed f, and determine the shaving force Fc using Equation (6). The influence curve of different axial feeds f on the shaving force Fc. The change in the shaving force at the pitch circle (development angle of 22.307°) .
2.2 Influence of Radial Feed Motion
Increasing the radial feed fr during gear shaving will increase Fc, as the increase in radial feed fr results in an increase in the shaving volume per unit time, an increase in the elastoplastic deformation resistance of the chip and the internal material of the tooth surface of the workpiece gear, and an expansion of the plastic deformation area. Since segments CD and DE are near the pitch circle of the workpiece gear, the shaving force Fc at this location is greater than the force in other areas of the tooth profile, causing the cutting edge to deeply press into the tooth surface of the workpiece gear, resulting in overcutting, and ultimately manifesting as a tooth profile concave error near the tooth profile.
2.3 Influence of Spindle Speed
Increasing the spindle speed n reduces the shaving force Fc, as the increase in spindle speed n shortens the cutting time per unit tooth profile, reducing the amount of material removed per unit time and the deformation resistance of the tooth surface material, thereby reducing the shaving force Fc.
2.4 Relationship between Gear Shaving Cutting Parameters and Tooth Profile Concave Error
To improve the shaving effect of the workpiece gear, it is necessary to study the influence degree of different gear shaving cutting parameters on the shaving force Fc, and obtain the primary and secondary order of the influence of different gear shaving cutting parameters on the change in shaving force. Generally, for the function g = f(x, y, z), the degree of influence of different independent variables x, y, z on the dependent variable g can be obtained by taking partial derivatives of the dependent variable g with respect to the independent variables x, y, z. when the spindle speed increases from 125.581 r/min to 234.419 r/min, the shaving force decreases from 34.764 N to 26.460 N; when the axial feed increases from 30 mm/min to 60 mm/min, the shaving force increases from 14.523 N to 30.319 N; when the radial feed increases from 0.02 mm to 0.06 mm, the shaving force increases from 18.565 N to 36.609 N.
According to references, the magnitude of the gear shaving cutting force can reflect the tooth profile concave error to a certain extent. When the shaving force is large, errors are prone to form on the tooth profile. Among the gear shaving cutting parameters, the radial feed motion has the greatest influence on the shaving force, and an excessively large radial feed can easily cause tooth profile concave errors of gear shaving. Therefore, in gear shaving processing, after selecting the geometric parameters of the shaving cutter, first determine the radial feed of the shaving cutter according to the tooth surface allowance of the workpiece gear, and select the range of axial feed and spindle speed through the gear handbook. When the range of gear shaving cutting parameters is determined, the variation range of the shaving force during the gear shaving process can be obtained. Under the premise of meeting the technical requirements of the workpiece, try to select a smaller shaving force, and then optimize the gear shaving cutting parameters based on the variation law of the shaving force at the pitch circle of the workpiece gear.