Surface Roughness Measurements of Cylindrical Gears and Bevel Gears on Gear Inspection Machines

Günter Mikoleizig

Alongside the macro test parameters on tooth flanks for profile and tooth traces, surface properties (roughness) play a decisive role in ensuring proper toothed gear function. This article addresses roughness measurement systems on tooth flanks. In addition to universal test equipment, modified test equipment based on the profile method for use on gears is addressed in particular. The equipment application here refers to cylindrical gear flanks and bevel gear flanks. The most important roughness parameters, as well as the implementation of the precise measurement procedure will also be described under consideration of the applicable DIN EN ISO standards as well as the current VDI/VDE Directive 2612 Sheet 5.

Introduction

Alongside the macro test parameters on tooth flanks for profile and tooth traces, surface properties (roughness) play a decisive role in ensuring proper toothed gear function. The generally increased load stresses on gear teeth can only be implemented by maintaining precisely defined roughness parameters. Roughness measurements are therefore conducted on the gearing flanks in all highly developed drives, in the automotive industry, aircraft industry, or the area of wind energy drives, for example.

This article addresses roughness measurement systems on tooth flanks. In addition to universal test equipment, modified test equipment based on the profile method for use on gears is addressed in particular. The equipment application here refers to cylindrical gear flanks and bevel gear flanks. The most important roughness parameters, as well as the implementation of the precise measurement procedure will also be described under consideration of the applicable DIN EN ISO standards as well as the current VDI/VDE Directive 2612 Sheet 5.

The Purpose of Roughness Measurement on Toothed Gear Flanks

Alongside the macro test parameters on tooth flanks for profile and flank lines, surface properties (roughness) play a decisive role in ensuring proper toothed gear function. Unlike general functional surfaces, the particular shape (curvature) and the slide-roll effect during meshing come into play with tooth flanks. Thus the surface roughness affects the following properties:

• Flank load capacity
• Tooth root load capacity
• Wear load capacity
• Load capacity involving heavy scoring
• Lubrication conditions
• Noise behavior
• Approach behavior

When determining the gearing quality according to DIN/AGMA/ISO standards via profile and tooth trace, an impression of the existing roughness is also obtained, but this is in no way comparable to roughness measurement performed according to the standard. The correlation is clear when the various probe elements for the measurement are taken into account, for example (Fig. 1). A standard gear measurement is performed with a 1.5 mm probe (radius 750 μm); for a roughness measurement, however, a diamond tip with a radius of 2 μm or 5 μm is used. A roughness measurement therefore measures significantly finer structures on the surfaces. Along with the macro test parameters on tooth flanks according to the gear standards for cylindrical gears, surface properties (roughness) plays an important role in ensuring a proper toothed gear function.

Overview of Roughness Parameters

The general roughness parameters are defined in the DIN EN ISO 4287 standard. An application of this standard for tooth flank measurements is described in the current VDI/VDE 2612 Sheet 5. In a general roughness measurement, the unfiltered P profile (Ref. 2) is obtained initially. Filtering then produces the longwave deviation (W profile) or the shortwave deviation (R profile). The shortwave deviations form the basis for the general roughness parameters used (Fig. 2).

During filtering of the recorded profiles, DIN ISO 16610-21 specifications apply, including measuring paths and cut-off wavelength (Fig. 3).

The profiles relevant for the roughness measurement are limited by the lambda C filter (waviness cut-off) and the lambda S filter (cut-off for even finer structures) (Fig. 4).

The most important roughness parameters for flank measurements are shown in Figure 5.

The arithmetic mean roughness value Ra is the ordinate value of the roughness profile within a single measurement path lr. The individual roughness depth Rz is the sum of the distance between the profile peak and profile valley within a single measurement path lr. Like Ra, the averaged roughness profile Rz is determined as an arithmetic mean from the individual measurement paths.

The total height of the roughness profile Rt is the sum of the height of the largest profile peak and the depth of the largest profile valley within the measurement path ln. The maximum individual roughness depth Rmax is the largest individual roughness depths Rz. The stock portion Rmr is the ratio of the sum of the stockfilled lengths Ml1-Mli for the total measuring path ln as a percent value.

The core roughness depth Rk is the depth of the roughness core profile. The reduced peak height Rpk is the height determined from the peaks projecting beyond the core area. The reduced peak depth Rvk is the height determined for the striations extending from the core area into the stock. The parameters Mr1and Mr2 of the stock percentage curve characterize the stock content at the limits of the roughness profile Mr.

Measuring Methods and Measuring Equipment for Roughness Measurement

In the VDI/VDE 2602 directive, and the DIN EN ISO 4287 and DIN EN ISO 16610-21 standard, these are profile methods that describe the properties of the profile equipment and the generalcase measurement conditions for roughness measurements of surfaces.

Skid-less probing systems and instruments with lateral skid (at the side off) are typically used to measure flank roughness (Ref. 1).

Figure 6 shows the tracing situation of a skid-less probing system in the tooth space. The profile here must be aligned as parallel as possible to the tracing direction of the test device. In the result, however, there is always a difference between the straight trace direction and the curved flank. The overall profile must therefore be corrected with a compensation arc, or residual errors must be eliminated with the lambda C profile filter. The possible trace path is limited due to the curved profile surface and the measuring range of the roughness probe

The probing conditions of a skid system are shown in Figure 7. The sidemounted probe skid follows the profile of the tooth flank. A deviation due to changing contact conditions during the roughness measurement must be taken into account here. The deviations are relatively small, however, and are largely eliminated due to profile filtering.

For roughness measurement on cylindrical gear flanks, measuring devices with an involute reference (Fig. 8) offer certain advantages. Logging of measured values in profile generation mode on the tooth flank (involute) ensures that the probe tip is always aligned perpendicular to the surface; thus the roughness can theoretically be scanned over the entire profile length. The disadvantage of this type of contact operation, however, is that the scanning speed for measured value logging is not constant, nor is a uniform measuring point distance ensured. But this is a minor disadvantage, resulting in measured value differences of up to 10%.

On current gear measuring centers, the involute reference is generated via CNC path control and can be used in principle in conjunction with skid-less systems and skid systems. For special profiles and bevel gear flanks with other profile forms, for instance, the CNC-guided path control can also execute reference profiles.

Roughness Measurement Procedure in Practice

The measuring conditions (Ref. 1) must first be defined in order to achieve generally comparable results. The following points must be taken into account to avoid measurement deviations:

• Probe system
• Profile filter
• Alignment of test specimen
• Environmental influences

Refer to Table 1 to select appropriate individual measurement paths and cutoff. As finish-machined surfaces on tooth flanks in particular must be tested, the highlighted values should be used preferentially. The measuring direction for the roughness measurement should be selected according to Table 2, based on the machining method and the resulting structures.

When selecting the appropriate parameters for the roughness measurement on tooth flanks, the stress on these surfaces due to compression and sliding must be taken into account. The parameter Rmax has little meaning for this stress, as individually projecting peaks, which are of little relevance for the load capacity, are taken into account here. The arithmetic mean raw value Ra is greatly distributed, but correlates the least with the function parameters and therefore should not be used. The preferred parameter for roughness on flank surfaces is Rz, as it provides a high degree of clarity and makes it possible to draw accurate conclusions about the height of the roughness profile.

In addition to the parameters that describe only the vertical expansion of the roughness profile, it is important to determine the roughness structure in order to determine the wear behavior or load capacity of a tooth flank. The stock percentage curve (Abbott-Firestone) and the resulting parameters Rk, Rpk and Rvk are appropriate for determining the structure of the roughness profile. A nearly S-shaped pattern in the stock percentage curve is ideal. Another appropriate parameter for the stock percentage is Rmr (c). See Table 3 for a comparison of roughness parameters and stock percentage curves.

A standard roughness testing device (Ref. 3) is shown in Figure 9. In addition to a feed mechanism with a microprobe system, the device also features a cross-slide to position and test the workpiece. An additional clamping fixture is generally needed to test toothed gears. According to the figure detail, compact reference area probe systems with an application range from module 0.5 can be used here. A PC computing system with high-performance software is available to control and evaluate the roughness measurements. The evaluation software takes into account a large number of established roughness measurement standards. A report printout of the measuring results can be custom-designed.

One advantage of the device presented is that general workpieces can also be tested, and a higher standard overall is provided for roughness measurement. It does, however, require more set-up for flank measurements and the device is not suitable for large and heavy workpieces (500 mm in diameter, for example).

Application example: cylindrical gear/ bevel gear measurement on gear measuring centers. Gear measuring centers are typically equipped with a rotary table for testing rotationally symmetrical workpieces and are suitable for measured value logging on small to very large workpieces, in conjunction with a model series. As previously described, the measuring method used here is the involute reference in combination with a skid system.

For roughness measurement a special probe system on the adapter plate of the measuring machine’s macro probe system is adapted (Fig. 10). An additional electrical connection is provided for transferring the measured values from the integrated micro-probe system for the roughness measurement. For measured value logging in the profile direction, the probe skid rests on the flank to be tested and executes a movement similar to a normal profile measurement for the macrostructure of the flank. As it does so, a diamond needle located in front of the probe skid logs the measured values for the roughness measurement. The probe system represented here is also suitable for measured value logging in the tooth trace direction. The roughness probe system also features an adjustment mechanism enabling the probe needle to be aligned perpendicular to the surface for helical cylindrical gears as well.

Thus in conjunction with an automatic probe change rack, a fully automatic process can be carried out for the roughness measurement in combination with other gear measurements. Because the measured value logging is controlled by the CNC-guided measuring axes, this results in highly precise positional accuracy and reproducibility for the measuring positions. The most important technical data for the integrated roughness test equipment are shown in Table 4.

To document the measuring results, the roughness parameters can also be documented on the standard measuring sheet for profile and reference tooth traces, or they can be printed as a separate measuring sheet including diagrams (Fig. 11).

Comparable to measured value logging on cylindrical gears, roughness measurements can also be conducted on bevel gears. The profile measurement here takes place based on the calculated nominal data, which are available in high resolution for measuring the macrostructure. Various probe systems are used for measured value logging, depending on the design of the bevel gears pinions/ ring gears. For pinion shafts a straight probe system is used — exactly like the probe system for cylindrical gears (Fig. 12) — and an angled system is used for ring gears.

A fully automatic test sequence can also be specified via the software operator guidance. Measuring positions, measuring paths, and the number of flanks to be tested, etc., can be programmed individually (Fig. 13). The measuring results are displayed numerically on the screen for the selected flanks (Fig. 14); measured values can also be printed out with diagrams (Fig. 15).

Thus the device presented here offers a reliable, convenient measuring method for roughness measurement on spiral bevel gears with spatially pronounced curves. Large-module bevel gears can also be tested in conjunction with suitable probe systems.

Concluding Remarks

These important measured values can be carried out quickly and easily in conjunction with conducting roughness measurements of tooth flanks on gear measuring centers using the equipment presented here.

Measurements on both smaller and larger gear teeth can be taken in a single clamping in conjunction with standard test parameters.

The measurement conditions for standardized roughness measurements are largely met by measured value logging in the profile direction with CNCcontrolled contouring in generation mode for each tooth profile.

References

1. VDI/VDE 2612; Sheet 5. Measurement and Testing of Gearings: Surface Roughness Measurement of Cylindrical Gears and Bevel Gears by Means of Stylus-Type Instruments (Release 2014/2015).
2. Jenoptik publication.
3. Mahr publication. “Mar Surf XR 20 Roughness Testing Device