Abstract: The program principle and debugging analysis of gear hobbing back taper teeth with flat roots using unequal pitch hobbing cutters. The aim is to achieve rapid production changeovers, reduce scrap workpieces, and enhance production efficiency.
Keywords: flat root; back taper teeth; unequal pitch hobbing cutter; gear hobbing program; debugging analysis
1. Introduction
Back taper teeth structural components are currently widely utilized in automotive transmission systems. They are generally divided into two types: helical root back taper teeth and flat root back taper teeth. The design and programming debugging requirements for helical root back taper teeth are relatively straightforward, whereas those for flat root back taper teeth necessitate the use of unequal pitch hobbing cutters. The gear hobbing program for these teeth is more complex during the debugging process. This article analyzes the precautions and countermeasures for program debugging when using unequal pitch hobbing cutters to machine flat root back taper teeth, thereby improving on-site production changeover speeds, reducing scrap, and lowering costs.
2. Structure and Machining Program Analysis of Helical Root Back Taper Teeth
The B represents tooth width, ah is the root taper angle, dH is the tooth root radius depth difference (tooth root height difference), as is the tooth side taper angle, and dS is the unilateral tooth thickness difference (tooth thickness difference between the large and small ends). Among these, dH = B tan(ah), and dS = B tan(as) = dH tan(ah/tan(an)), where an is the pressure angle. To process back taper teeth, it is essential to achieve the tooth thickness difference dS, which necessitates satisfying the root taper angle ah.
The structural characteristic of helical root back taper teeth is that the tooth thickness varies uniformly from the large end to the small end, with the tooth root circle being a sloping conical surface. Helical root back taper teeth are typically processed using methods such as gear hobbing, gear shaping, gear挤压, and rotary cutting, but external teeth are mostly processed by gear hobbing. Using a conventional hobbing cutter and a numerically controlled hobbing machine with simultaneous X-axis and Z-axis motion can achieve the processing of helical root back taper teeth structures.
3. Structure and Machining Program Analysis of Flat Root Back Taper Teeth
3.1 Principle of Gear Hobbing Flat Root Back Taper Teeth
Compared to helical root back taper teeth structures, the tooth root circle of flat root back taper teeth structures is a flat cylindrical surface with a constant tooth root circle value. This results in the inability to feed in the radial direction. Therefore, to ensure a uniform variation in tooth thickness across different cross-sections, a variable tooth thickness unequal pitch hobbing cutter is employed, achieving simultaneous proportional linkage feed in the Y-axis and Z-axis. Specifically, the hobbing cutter feeds from top to bottom in the Z-direction, while in the Y-direction, the cutter first feeds inwardly to machine the upper end back taper teeth, then reverses direction to the starting position to machine the lower end back taper teeth, ultimately achieving the processing of double-jointed flat root back taper teeth.
Taking a clutch sleeve as an example, conventional gear hobbing programs typically adopt two tool path methods: one is the centerline splitting method, mainly used for simultaneous adjustment of the upper and lower end back taper teeth, with simple program modifications ; the other is the symmetrical splitting method, primarily used for separate adjustment of the upper and lower ends, with more complex programming. This article focuses on studying related program debugging issues using the first tool path method.
(a) Centerline Splitting Method (b) Symmetrical Splitting Method
Based on the above machining program analysis, a Y-axis reducer was added to increase the synchronous linkage function of the Y-axis and Z-axis, and a customized processing plan and program interface were jointly developed with the machine tool manufacturer for processing flat root back taper teeth structures.
3.2 Example Analysis of Gear Hobbing Program Debugging for Flat Root Back Taper Teeth
3.2.1 Analysis of the Influence of Coordinate Changes on Span Measurement for Flat Root Back Taper Teeth
The following is the analysis of the influence of any variable on the span measurement of the component based on the part parameter information in Table 1.
Table 1: Relevant Parameters of Flat Root Back Taper Teeth Components (mm)
| Workpiece Parameter | Large End | Small End | Span Measurement (Mop) | Tooth Width (Z) | Remarks |
|---|---|---|---|---|---|
| Tooth Thickness (Sn) | 5.000 | 4.472 | 140.263 | 138.954 | 13.88 |
| Z-axis Tool Design | – | – | – | Ratio of Y-axis Speed to Z-axis Speed: 0.3:1 | – |
Based on the difference in Mop values between the large and small ends relative to the tooth width ratio, we calculate:
(140.263 – 138.954) / 13.88 = 0.094mm
This indicates that when only the coordinate difference ΔZ shifts as a whole, the change in span measurement ΔMop follows the rule:
ΔZ + 1mm → ΔMop ± 0.094mm (1)
Where, when ΔZ shifts positively by 1mm, the Mop of the upper end back taper teeth decreases by 0.094mm, and the Mop of the lower end increases by 0.094mm.
From Table 1, the feed length of the Y-axis is calculated as:
13.88 / 0.3 = 46.267mm
The ratio of the difference in Mop values between the large and small ends relative to the feed length of the Y-axis yields:
(140.263 – 138.954) / 46.267 = 0.028mm
This shows that when only the coordinate difference ΔY shifts as a whole, the change in span measurement ΔMop is:
ΔY + 1mm → ΔMop – 0.028mm (2)
Where, when ΔY shifts positively by 1mm, the Mop values of both the upper and lower ends decrease by 0.028mm simultaneously.
3.2.2 Debugging Analysis of Span Measurement for Flat Root Back Taper Teeth
During the debugging process of the hobbing program for flat root back taper teeth, the adjustment of span measurement is a crucial step. The following is a detailed analysis of this debugging step:
(1) Inputting Preliminary Tooling Coordinates
Based on the speed ratio of 0.3:1 between the Z-direction and Y-direction of the unequal pitch hobbing cutter, input the preliminary tooling coordinates X, Y, and Z into the program interface. During this process, special attention should be paid to maintaining a constant ratio of ΔZ/ΔY = 0.3 (see Figure 7). This step is fundamental to ensuring uniform tooth thickness variation during subsequent processing.
(2) Adjusting the Tooth Root Circle
Next, adjust the tooth root circle to meet the product drawing requirements. This is typically achieved by inputting a compensation difference for the X-axis in the program interface. After the first trial cut, measure the diameter of the tooth root circle and adjust the X-axis compensation value based on the measurement results until the diameter of the tooth root circle falls within the tolerance specified in the drawing.
(3) Adjusting Span Measurement Differences
Once the tooth root circle is processed to within tolerance, the next step is to adjust the differences in span measurement (M_op). Span measurement refers to the distance between the centers of spheres on both sides of the gear, which is an important indicator for assessing gear processing accuracy.
Detecting Span Measurement Values: First, detect the span measurement M_op values at the upper and lower ends, denoted as M0 + ΔM1 and M0 + ΔM2, respectively, where M0 is the target value, and ΔM1 and ΔM2 are the differences between the span measurements at the upper and lower ends and the target value.
Adjusting Upper and Lower M_op Values to Be Consistent: Calculate the overall shift in the Z-axis (ΔZ) using Equation (1): ΔZ = 0.5(ΔM1 – ΔM2) / 0.094. Then, shift the tool entry and exit coordinates for the Z-axis up by ΔZ, i.e., Z’1 = Z1 + ΔZ, Z’2 = Z2 + ΔZ, Z’3 = Z3 + ΔZ. After adjustment, the M_op values at the upper and lower ends are equal, both being M0 + 0.5(ΔM1 + ΔM2).
Adjusting Upper and Lower M_op to the Target Value M0: Next, calculate the overall shift in the Y-axis (ΔY) using Equation (2): ΔY = 0.5(ΔM1 + ΔM2) / 0.028. Then, adjust the hobbing cutter’s lateral shifting coordinates by shifting them overall by ΔY, i.e., Y’1 = Y1 + ΔY, Y’2 = Y2 + ΔY. After adjustment, the M_op values at both the upper and lower ends are simultaneously equal to the target value M0.
By following these steps, the span measurement can be quickly adjusted to ensure that the processed gears meet the drawing requirements. This debugging method not only improves processing efficiency but also reduces scrap rates, which is significant for achieving rapid product changeovers and batch production.