5-axis double-flank CNC machining of spiral bevel gears via custom-shaped tools—Part II: physical validations and experiments

To physically validate the results of the modeling algorithm, the machining path of the custom-shaped tool in the manufacturing of a spiral bevel gear was applied. More specifically, the custom-shaped tool was used in the semifinishing operation, which is the place where Super Abrasive Machining technology has its potential niche of work. In Fig. 7, the valley between spiral bevel gear teeth is shown during roughing and semifinishing operations with milling and SAM operations. Observe a clearly visible difference in the quality of surface smoothness in Fig. 7(a) and (c).

Spiral bevel gear semifinishing operation. (a) Manufacturing with SAM. (b) Virtual verification with SAM. (c) Manufacturing with ball end mill. (d) Virtual verification with ball end mill

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A qualitative comparison between double-flank machining using a custom-shaped tool and ball end milling, during the semifinishing stage, is presented. Moreover, a virtual comparison against single-flank milling using a barrel tool is also made. In particular, it is shown that surface roughness and manufacturing time are significantly reduced when using double-flank machining with custom-shaped tool.

5.1

Surface roughness

Surface roughness is one of the key parameters that influence a smooth movement between gears, their face-face contact, and consequently the life of the whole gear. Typically, the surface roughness is measured using a confocal microscope, however, due to the difficult accessibility of the faces of the gear, resin was applied in order to measure a negative of the tooth space.

The process for obtaining the negative of the face proceeds as follows: first, the area to be measured is degreased with the DN1 degreaser cleaner provided by PLASTIFORM’s own company (PLASTIFORM, Madrid, Spain). Once this is done, a closed area must be formed such that the fluid (liquid resin) covers both sides of the cavity, and then the fluid is applied to the measuring area using a dispensing gun. Finally, cca 6 min is needed for the solution to dry out, and then one can remove the negative of the cavity, see Fig. 8.

Curing process of the resin and its zoomed-in part after hardening

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It was selected a fluid type resin, so that it could flow through the entire gear cavity and thus adapt well to the surface of the faces. Specifically, the F65 product was used, which allows a semi-flexible geometry to be obtained, suitable for measurement by both contact measuring systems and optical measurement systems. The precision obtained with this resin is ± 1 μm.

A Leica DCM 3D confocal microscope was used to analyze the surface roughness of the resin. Both sides of the cavity were analyzed, as the amount of excess of material was slightly different on each side after roughing. The adjustment of the roughness measurement in this case was a cutting length of 0.8 mm and an evaluation length of 4 mm, according to ISO 4288 [32]. Figure 9 shows the topography and related data of both sides of the cavity.

Surface area and profile roughness parameters values of the left (top) and right (bottom) side of the gear tooth cavity

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Topography on both sides of the tooth cavity shows a perfectly recognizable grinding pattern, in which there are remarked peaks and valleys along the scanned surface caused by the random distribution of the abrasive grains. It is noticeable that slightly better results in term of roughness were obtained on the right face, as the roughing operation leaves that face smoother and stepless between passes, just the opposite of the left face, as it can be seen in Fig. 7(d). However, this fact is not a limitation of the proposed double-flank approach, but it is due to the fact that the roughing stage left the right face smoother.

The results are in accordance with “indicative surface roughness comparison” that many companies handle [33]. The roughness values obtained were acceptable for a semifinishing operation because they are close to those obtained with similar strategies considering them as finishing operations.

5.2

Machining time

Another aspect that was considered in this work was the analysis of machining time during semifinishing operations on gear teeth. To this end, machining time of ball end milling operation and double-flank SAM strategy with a custom-shaped tool was measured, and barrel flank milling virtual machining time was calculated. The conventional semifinishing operation using a ball end mill with 4 mm diameter was used with a stepover of 0.33 mm of depth of cut in 3 lateral steps in each face and a feed of 2800 mm/min. On the left face, 20 axial passes were repeated 3 times axially (60 passes total) while on the right face 20 passes were sufficient. In contrast, semifinishing using a custom-shaped tool was accomplished in a single sweep with the following parameters: a feed of 500 mm/min and a spindle speed of 16000 rpm. In the case of single-flank milling using a barrel-shaped tool with 12 mm of barrel diameter, in total 20 passes were done to cover the whole surface with a feed of 848 mm/min.

With the above-mentioned values of cutting parameters for the three manufacturing semifinishing operations, the following machining time results were obtained: (i) conventional ball end milling: 2 min and 7 s, (ii) double-flank SAM semifinishing with the custom-shaped tool: 24 s, and (iii) barrel flank milling: 1 min and 8 s. Double-flank SAM dominated in terms of machining time. When comparing with the other two, in the case of ball end milling, the semifinishing machining time was reduced by 81.1%, saving in total 43 min per gear. In the case of barrel flank milling, SAM double-flank machining was 2.83 times faster than barrel flank milling. See Fig. 4 for the summary of the machining times of each particular stage.

5.3

Dimensional deviation

Dimensional deviation of the three tested semi-finishing strategies: ball end mill operation, double-flank SAM with a custom-shaped tool, and barrel flank milling were qualitatively compared. Figure 10 shows simulation results of the three semifinishing operations using a commercial software.

Dimensional deviation of the three virtually simulated semi-finishing strategies: Ball end mill operation (top), double-flank SAM with a custom-shaped tool (middle), and barrel flank milling (bottom). The error distribution along the tooth space (left column) and the simulated paths (right column) are shown

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In the case of the root surface of the tooth, the results obtained by all methods were very similar, reaching a tooth surface excess of material of up to 0.8 mm. The results obtained on the tooth face surface show clear differences. In the case of ball finishing operation, a uniform finish was obtained along the entire surface with a stock around 0.23 mm. In the case of the SAM, there are two clearly differentiated zones. In the first zone, the right face, the values obtained in the semi-finishing are practically close to the final geometry of the piece. On the left side, an undercut of 0.1 mm was obtained along the tooth face. Comparing the above-mentioned results with barrel flank milling, it can be seen that the problem on the root surface is almost solved, except for the fillet radius, where is a stock of more than 0.3 mm. However, in the rest of the surface there is an undulation profile that goes from 0.03 mm in the bottom to 0.21 mm in the peak.

5.4

Discussion and limitations

The proposed approach significantly reduces the semifinishing time by using a properly designed custom-shaped tool. The tool has to be manufactured in advance, however, the custom-shaped tool costs are low, in particular: cylindrical steel bar F115 (85€ ) to create 4 SAM tools, i.e., 21.25€ per the steel core of the tool, and 45€ to add the abrasive grains. In total, the cost of the custom-shaped tool is 66.25€. In contrast, the on-market tool for ball end milling, VF4SVBR0200, costs 120€.

The surface roughness values range Sa = 2.59–3.87 mm using the SAM approach which is a slightly more than the numbers that can be obtained by means of conventional milling [33]. Nevertheless, these values are acceptable in the case of a workpiece which later undergoes finishing operations.

Another slight limitation is that the very bottom of the cavity is not accessible with the tool whose shape is designed to double-flank the two faces of the cavity. The bottom of the cavity has to be machined using ball end milling approach.

Comparing SAM double-flank machining with flank milling with barrel tools, both approaches offer similar accuracy, but double-flank machining is faster (factor of 2.83) due to the fact that only a single sweep of the tool is needed.

The presented results are promising, however, the double-flank methodology has been tested on one specific type of a spiral bevel gear, with parameters shown in Table 2. For gears with flat (planar) teeth, the double-flank approach is not challenging as the ideal motion boils down to a plane-plane bisector computation. The other extreme of small and even more curved reference geometry such as, e.g., pinions has not been experimented with, but can be a promising venue for future research.