Fig. 1 In gear machining, the hobbing profile error has a great influence on the precision and tool life of subsequent machining (especially shaving gear machining). There are many types of hobbing tooth profile errors and their causes. The tooth profile error may be caused by the tooth angle error of the hob, the index error of the machine tool, and the tool mounting error. This paper only analyzes the tooth profile error caused by the hob hobbing. The hobbing process can be regarded as the process of the backlash-free engagement of the cut gear and the virtual rack. When gear hobbing, the involute tooth profile of the end face of the gear is enveloped by some non-continuous fold lines (as shown in Fig. 1). An angle is formed between the fold line and the fold line. The apex of the angle and the theoretical involute The distance formed along the direction of the involute normal is called the degree of divergence (ie, DH in Figure 1, where DS is the distance between the folds of the envelope forming the involute), and DH is necessarily generated when hobbing. Principle error. The vertices of the included angles formed by the ridges are connected by a straight line, that is, an involute on the end surface is formed. Each vertex corresponds to a tooth angle on the end face and forms a straight line in the direction of the tooth width. Hob neutrality refers to the degree of coincidence between the axis of symmetry of any tooth (or slot) of the hob and the centerline of the tooth blank when the hob is mounted on the shank. In the following, the effects of hobbing centering and misalignment on the tooth profile error are separately analyzed. In the case of hob alignment (as shown in Fig. 2), the center line of the hob coincides with the centerline of the gear blank, and the tangent points M1 and M2 of the blade on the right and left sides of the hob tooth groove and the tooth blank are symmetrical, and their meshing lines are The intersection point P1 is on the centerline of the hob and tooth blank. At this time, the tangent points forming the ridges are symmetrically distributed on the left and right side tooth profiles of the gear teeth. The corresponding ridge value DH on the right and left side of the tooth profile is completely equal and symmetrical, and the right and left sides of the tooth profile (including the formation of the tooth profile curve). The polyline is also completely symmetrical and the corresponding DS values are exactly the same and symmetrically distributed. It can be seen that the tooth form error formed at this time is also symmetrically distributed. Fig. 3 shows the tooth profile curve formed by the simulation of the hobbing state envelope and the broken lines of each segment in the case of hob alignment (the intersection of each horizontal line and the tooth profile curve in the figure is the fold line and fold line constituting the tooth profile curve. The vertex between the vertices).
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Fig. 5 In the case of misalignment of the reel (as shown in Fig. 4), the position of the reel on the tool shank is difficult to determine. The centerline of the reel will be offset by a certain angle with respect to the centerline of the gear blank. The tangent points M3 and M4 of the blade on both sides and the tooth blank are no longer symmetrically distributed, but are offset by a certain distance. The intersection P2 of the meshing line is on the center line of the tooth blank instead of the centerline of the hob, that is, the cutting edge and the meshing line. The point of intersection (ie, cutting point) is asymmetric with respect to the line connecting the node and the gear centerline. At this time, the tangential points forming the ridges are asymmetrically distributed on the left and right sides of the face tooth profile, and the corresponding ridge value is neither equal nor asymmetric. Obviously, the left and right sides of the end tooth profile (including the fold lines constituting the tooth profile curve) are asymmetrical. Figure 5 shows the broken lines formed by the simulation of hobbing under the condition of misalignment of the hob. Although the entire involute curve finally enveloped is symmetrical, each segment of the envelope and each vertex enveloping the involute curve is asymmetrical. At this time, the tooth angles of the corresponding points on the right and left side tooth forms where the kurtosis is located are not equal, and the kurtosis values corresponding to the tooth angles of each corresponding point and the corresponding DS values are also different. It can be seen from this that the tooth form error formed at this time is not only asymmetrical but also not identical. From the above analysis, it can be seen that the hob has a great influence on the symmetry of the tooth profile. Asymmetric tooth shape after gear hobbing will lead to uneven force on the left and right sides of the shaving cutter teeth during shaving, which will directly affect the shaving tooth shape error and the service life of the shaving cutter. It will also reduce the accuracy of the machine tool. Therefore, in the hobbing of gears (especially gears with few teeth), the hob alignment should be ensured as much as possible.
July 18, 2022
