Abstract: The radial dressing method with a single variable center distance can lead to gradual changes in the tooth profile of the worked piece after honing with an internal gear honing tool. Based on the conjugate meshing relationship between the internal gear honing tool and the workpiece during processing, this paper analyzes the reasons for changes in the contact state between tooth surfaces caused by single radial dressing and investigates the dressing method with a floating axis angle. By introducing an axis angle correction to maintain a stable contact state between the honing tool and the tooth surface of the workpiece, models of tooth surface contact lines before and after dressing are established. The results show that the dressing method with a floating axis angle can effectively improve the problem of tooth surface contact changes caused by dressing feed. Gear processing tests conducted on an internal gear power honing machine verify the effectiveness of this method.
Keywords: power gear honing; internal gear honing tool; tool dressing; floating axis angle
1. Introduction
Internal gear honing is one of the precision gear finishing methods. It can not only effectively correct gear processing errors from previous processes but also improve the surface topography of the workpiece [1-2]. It is a high-precision and efficient gear processing technology . Internal gear honing controls the generation of the tool to the workpiece synchronously with a determined transmission ratio. It is formally equivalent to the meshing motion between two helical gears, one internal and one external. The tool used in processing is the internal gear honing wheel, a special gear honing tool resembling an internal gear and a type of grinding wheel. During processing, the tooth surface of gear honing wheel is in conjugate contact with the tooth surface of the workpiece. The abrasive grains on the surface of gear honing wheel press into the surface of the workpiece and material removal occurs through relative sliding between the tooth surfaces.
Similar to ordinary grinding wheels, after a period of gear honing, the processing capability of the internal gear honing wheel 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 the internal gear honing wheel is a gear-type diamond roller, 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 roller [6].
During single radial dressing, the dressing roller is clamped in the position of the workpiece, and the internal gear honing wheel feeds along the processing direction. Without changing other parameters, the dressing roller is used to “process” the internal gear honing wheel. Since the essence of dressing and processing of the internal gear honing wheel is the secondary enveloping of involutes, the first enveloping uses the involute tooth surface of the dressing roller as the parent surface to envelop the tooth surface of gear honing wheel; the second enveloping uses the tooth surface of gear honing wheel to envelop the tooth surface of the workpiece during processing. Therefore, when the parameters of the workpiece and dressing roller are the same, theoretically, the workpiece processed after single radial dressing should still be a mapping of the tooth shape of the dressing roller. However, in actual processing, using the single radial dressing method can cause continuous changes in the tooth shapes of gear honing wheel and the workpiece, leading to unstable processing quality of the workpiece and insufficient utilization of the internal gear honing wheel.
2. Derivation of the Meshing Equation Between the Internal Gear Honing Wheel and the Workpiece
During processing, the tooth surface of the internal gear honing wheel and the tooth surface of the workpiece satisfy a conjugate contact relationship. Below, the mathematical relationship during conjugate contact between the internal gear honing wheel and the workpiece is derived by establishing their spatial coordinate systems and the tooth surface equation of the workpiece.
2.1 Establishing Spatial Coordinate Systems for the Internal Gear Honing Wheel and the Workpiece
The spatial coordinate systems for the internal gear honing wheel and the workpiece are established. the fixed coordinate systems S(Oxyz) and Sp(Opxpypzp) for the workpiece and the internal gear honing wheel, respectively, as well as the moving coordinate systems S1(O1x1y1z1) and S2(O2x2y2z2). The origin distances of the workpiece and internal gear honing wheel coordinate systems are the center distance a; the z-axis angles are the axis angles Σ; and the rotational speeds and angles of the workpiece and internal gear honing wheel are ω1, ω2, and φ1, φ2, respectively.
2.2 Workpiece Tooth Surface Equation
Both during dressing and processing, the tooth surface profile is formed by the enveloping of continuous contact lines, where each instantaneous contact line represents the tooth surface contact state at that moment. The gradual change in the tooth shape 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 wheel. Based on Equations (1) and (5), the contact line model at 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 wheel used for processing are listed in Table 1.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Module | mn | (specific) | mm |
| Normal pressure angle | αn | (specific) | ° |
| Number of teeth (workpiece) | z1 | (specific) | – |
| Helix angle (workpiece) | β1 | (specific) | ° |
| Face width (workpiece) | b1 | (specific) | mm |
| Number of teeth (honing wheel) | z2 | (specific) | – |
| Helix angle (honing wheel) | β2 | (specific) | ° |
| Face width (honing wheel) | b2 | (specific) | mm |
Table 1: Parameters of the transmission gear and internal gear honing wheel
Using the parameters in Table 1, the adjacent tooth surfaces of the two wheels on the tooth surface of the workpiece with an initial angle σ0 = ±0.298° are established, and the tooth surface contact lines are established at workpiece angles φ1 equal to -3°, 0°, and 3° when the cumulative dressing amount Δa is 0 and 2 mm.
Due to the softer material of gear honing wheel compared to the workpiece, it is more prone to deformation during contact. The movement of the equivalent force position results in insufficient processing pressure on the tooth top of gear honing wheel against the tooth root of the workpiece at the same position, leading to changes in the tooth shape of the workpiece. Each single radial dressing results in a slight change in the tooth surface contact state, which is mapped as a change in the tooth shape of the workpiece. When the tooth shape change accumulates to a certain extent beyond the allowed range, the processed workpiece no longer meets requirements, and the internal gear honing wheel can no longer be used.
3. Dressing Method with a Floating Axis Angle
To maintain the stability of the contact state between the tooth surfaces, a variation in the axis angle is introduced during dressing, i.e., the dressing method with a floating axis angle. This method approximately stabilizes the contact state of the entire tooth surface by ensuring that the contact at selected points on the tooth surface before and after dressing remains consistent. After simulation, it was found that adding a change in the axis angle significantly improves the movement of the tooth surface contact line caused by dressing.
4. Processing Test Equipment and Scheme
To verify the effectiveness of the variable axis angle honing method in practical applications, a series of processing tests were conducted on workpieces of the same specification but with different axis angles. The details of the processing test equipment and scheme are as follows:
Processing Equipment:
- HMX-400Fassler CNC Internal Gear Power Honing Machine: This high-precision machine was used for gear honing process. It is capable of precise control over gear honing parameters, including the axis angle, to ensure accurate and consistent processing results.
Detection Equipment:
- Klingelnberg P40 Gear Measuring Center: This advanced gear measuring center was used to detect the tooth profiles of the processed workpieces. It provides highly accurate measurements to evaluate the effectiveness of gear honing method.
Processing and Detection Setup:
The workpieces and internal gear honing wheel parameters were the same as those listed in Table 1 (refer to the original document for detailed parameters). The setup ensured that gear honing process was conducted under controlled conditions, allowing for accurate measurement and analysis of the processed workpieces.
Test Scheme:
- Initial Processing:
- The initial axis angle between the internal gear honing wheel and the workpiece was set to less than 9 degrees.
- Honing and Grinding Intervals:
- After processing 20 gear workpieces, the internal gear honing wheel was subjected to grinding.
- The grinding amount was set to 0.1mm each time.
- The axis angle was adjusted according to a predetermined formula (not explicitly shown here but implied in the original document). Each 0.1mm of grinding resulted in an approximately 0.0006 radian change in the axis angle.
- Variable Axis Angle Test Groups:
- Multiple test groups were established, with axis angles ranging from the initial angle to 13 degrees in increments.
- Specifically, the test groups were labeled A1, A2, …, A9, where group A9 corresponded to an axis angle of 13 degrees.
- Detection and Analysis:
- After processing, the tooth profiles of the workpieces were measured using the Klingelnberg P40 gear measuring center.
- The measurement results were analyzed to observe and compare the tooth profile shapes of the workpieces processed at different axis angles.
By conducting this series of processing tests, the researchers aimed to evaluate the effectiveness of the variable axis angle honing method in maintaining consistent tooth profile shapes and improving the processing quality of the workpieces. The results of these tests are crucial for validating the theoretical findings and ensuring the practical applicability of the proposed method.