Abstract:
The issue of gradual tooth profile changes in workpieces after honing using a single variable center distance radial dressing method for internal gear honing tools. Based on the conjugate engagement relationship between the internal gear honing tool and the workpiece during processing, the reasons for the change in contact state between tooth surfaces caused by single radial dressing are analyzed. A dressing method with a fluctuating axis angle is studied, which introduces an axis angle correction amount to maintain the stability of the contact state between the honing tool and the workpiece tooth surface. Models of the tooth surface contact lines before and after dressing are established, and the results show that the dressing method with a fluctuating axis angle can effectively improve the problem of tooth surface contact changes caused by dressing feed. Gear processing experiments conducted on an internal gear power honing machine verify the effectiveness of this method.
1. Introduction
Internal gear power honing technology is one of the precision finishing methods for gears. It can not only effectively correct the gear processing errors from previous processes but also improve the surface morphology of the workpiece [1-2]. It is a high-precision and efficient gear processing technology [3]. In internal gear power honing, the tool and the workpiece are synchronously controlled at a determined transmission ratio for generating processing, which is similar to the meshing motion between two interleaved helical gears, one internal and one external. The tool used in processing is the internal gear honing tool, a special gear honing implement resembling an internal gear and belonging to the category of grinding wheels. During processing, the tooth surface of the honing tool is in conjugate contact with the tooth surface of the workpiece, and material removal occurs through relative sliding between the tooth surfaces after the abrasive grains on the honing tool surface are pressed into the surface of the workpiece [4].
Similar to ordinary grinding wheels, after a period of gear honing, the processing capability of the internal gear honing tool gradually decreases due to surface wear and clogging, resulting in poorer workpiece quality. At this point, it needs to be dressed. The tool used for dressing internal gear honing tools is a gear-type diamond roll, a high-precision grinding wheel dressing tool [5]. Its parameters are basically the same as those of the workpiece, and the accuracy and shape of the workpiece are largely a reproduction of the dressing roll [6].
2. Derivation of the Engagement Equation Between the Internal Gear Honing Tool and the Workpiece
During processing, the tooth surface of the internal gear honing tool and the tooth surface of the workpiece satisfy a conjugate contact relationship. Below, the mathematical relationship of the conjugate contact between the internal gear honing tool and the workpiece is derived by establishing their spatial coordinate systems and the tooth surface equation of the workpiece.
2.1. Establishment of Spatial Coordinate Systems for the Internal Gear Honing Tool and the Workpiece
The spatial coordinate systems for the internal gear honing tool and the workpiece are established. The fixed coordinate systems S(Oxyz) and Sp(Opxpypzp) for the workpiece and the internal gear honing tool, respectively, as well as the moving coordinate systems S1(O1x1y1z1) and S2(O2x2y2z2). The distance between the coordinate system origins of the workpiece and the internal gear honing tool is the center distance a; the angle between the z-axes is the axis angle Σ; the rotational speeds and angles of the workpiece and the internal gear honing tool are ω1, ω2, and φ1, φ2, respectively.
2.2. Tooth Surface Equation of the Workpiece
The tooth surface of the workpiece is a standard helical involute.
3. Changes in Tooth Surface Contact Caused by Single Radial Dressing
Whether during dressing or processing, the tooth profile is enveloped by continuous contact lines, where each instantaneous contact line represents the tooth surface contact state at that moment. The gradual change in the tooth profile of the workpiece after single radial dressing is inevitably due to a change in the contact state between the tooth surfaces of the workpiece and the internal gear honing tool. Based on Equations (1) and (5), the contact line models under any rotational angle on the tooth surface of the workpiece can be established in MATLAB. The parameters of a transmission gear and the internal gear honing tool used for processing are listed in Table 1.
Table 1. Parameters of the transmission gear and internal gear honing tool
| Parameter | Symbol | Transmission Gear Value | Honing Tool Value |
|---|---|---|---|
| Module | mn | – | – |
| Normal Pressure Angle | αn | – | – |
| Number of Teeth | z1, z2 | Specific value | Specific value |
| Helix Angle | β1, β2 | Specific value | Specific value |
| Tooth Width | b1, b2 | Specific value | Specific value |
With the parameters in Table 1, the adjacent tooth surfaces of the two gears of the transmission gear with an initial angle σ0 = ±0.298° are established, and the tooth surface contact lines are established for the workpiece rotation angle φ1 equal to -3°, 0°, and 3° when the cumulative dressing amount Δa is 0 and 2 mm.
The internal gear honing tool, being the softer party when in contact with the workpiece, undergoes easier deformation. The movement of the equivalent force position results in insufficient pressure from the tooth tip of the honing tool on the tooth root of the workpiece at the same position, leading to changes in the tooth profile of the workpiece. Each single radial dressing causes a slight change in the tooth surface contact state and maps to changes in the tooth profile of the workpiece. When the tooth profile changes accumulate to a certain extent beyond the allowable range, the processed workpiece no longer meets the requirements, and the internal gear honing tool cannot be used any further.
4. Dressing Method with a Fluctuating Axis Angle
To maintain the stability of the contact state between the tooth surfaces, a change in the axis angle amount is introduced during the dressing process, i.e., the dressing method with a fluctuating axis angle. This ensures consistent contact at selected points on the tooth surfaces before and after dressing to approximately stabilize the contact state of the entire tooth surface. Simulations reveal that after introducing the change in the axis angle, the movement of the tooth surface contact lines caused by dressing is significantly improved.
5. Gear Processing Experiments with a Fluctuating Axis Angle
5.1. Processing Equipment and Test Plan
To verify the effectiveness of the fluctuating axis angle method in actual processing, a set of processing experiments was designed for workpieces of the same specification under different axis angles. The processing equipment was the HMX-400 Fassler CNC internal gear power honing machine, and the detection equipment was the Klingelnberg P40 gear measuring center. The processing and detection setups. The parameters of the workpiece and the internal gear honing tool are the same as those listed in Table 1.
The specific test plan is as follows:
- Initially, the axis angle between the internal gear honing tool and the workpiece was less than 9°.
- After processing 20 gears, the internal gear honing tool was dressed, with each dressing amount set to 0.1 mm, and the axis angle change was calculated according to Equation (6). After calculation, for each 0.1 mm of dressing, the change in the axis angle was approximately 0.0006 rad.
- Nine sets of experiments (A1, A2, …, A9) were conducted, with the corresponding axis angle for Group A9 being 13°.
- The detection results were analyzed to observe and compare the tooth profile shapes of the workpieces processed under different axis angles.
5.2. Test Results and Analysis
The tooth profile detection results of some workpiece gears. Comparing the processing and detection results under different axis angles, it can be seen that after dressing with the fluctuating axis angle method, the tooth profile shape of the workpiece was well maintained, without the occurrence of a trend of tooth profile changes. Additionally, the processing quality of the workpiece improved due to the dressing of the tool.
6. Conclusion
Using a single variable center distance radial dressing method results in gradual changes in the tooth profile of the workpiece during processing due to changes in the contact state between the tooth surfaces of the internal gear honing tool and the workpiece before and after dressing. To maintain the stability of the contact state between the tooth surfaces, this paper introduces a change in the axis angle during the dressing process, i.e., the dressing method with a fluctuating axis angle.