Using Master Gears

When Master Gears are designed properly, certain errors can be identified, and, with more discrimination, that type of error can be mapped out to indicate specific performance issues within the application itself.


In the design of generated and molded gears, it is common to specify a total composite error (TCE) tolerance for in-process inspection, especially for high volume production. TCE is defined as variation in center distance when rolled in tight mesh with a highly accurate master gear on a floating spring arbor. Highly accurate means that the errors in the master gear are negligible in comparative magnitude to the test gear. The purpose of roll testing is to assess attributes of gear quality in a production gear against a highly accurate master gage. The measurement itself is reflected back as composite error in the production or work gear. Even though composite error is an accumulation of diverse errors, the results can give indications as to whether the production gear is consistent with design intent. In some cases, the specific errors can be mapped to specific application performance issues. (See Figure 1)

Master Gear Design Questions

• For helical masters, given the total operating profile length and its location in degrees of roll: how is the number of teeth determined for the master gear?
• What is the effect of a helical overlap ratio on composite measurement?
• For helical masters, what is the right face width specification of the master relative to the production gear?
• For high-contact gears, where mating mesh contact ratio of the production gear with the master is greater than 2.0, how do you insure that the master will not span more than one tooth and will give a true double flank composite reading?
• Can a Gage R&R be done on double flank composite inspection equipment?

Master Gear Design Considerations

Master gears used in double flank composite measurements must meet the following design criteria in order to mesh properly with a test gear:
• The tip of the master gear must not contact the test gear below the form diameter of the test gear.  This applies to initial contact and to any type of secondary contact in the fillet zone due to inadequate clearance.
• The tip of the test gear must not contact the master gear below the form diameter of the master gear. This applies to initial contact and to any type of secondary contact in the fillet zone due to inadequate clearance.
• The minimum contact ratio of the double flank test must not be less than 1.0 when taking into account the maximum tooth thickness, minimum outside diameter, maximum root diameter, and maximum tip radius of the test gear. If the contact ratio drops below 1.0, then the meshing action of the gears on the test will generate an immediate jump in the double flank result for every tooth meshing cycle. This happens when the spring of the slide on the composite tester compensates for the loss of mesh force by abruptly pushing the gears together.
• The master gear and the test gear must have the same normal base pitch.  In most cases, this is when the normal module and normal pressure angle match between the master and the test gear. However, mathematically, it is possible to mesh a master gear with a different normal module and normal pressure angle than the test gear if the following equation is satisfied:

mnw is the normal module of the test gear, mm;
mn3 is the normal module of the master gear, mm;
αnw is the normal pressure angle of the test gear, degrees or radians;
αn3 is the normal pressure angle of the master gear, degrees or radians.

This may be useful in some special circumstances depending on product design.
• For parallel axis helical gear double flank arrangements, the master gear must have an equal helix angle to the test gear. However, it must be of opposite hand. (See Figure 2)

In addition, the following recommendations for good master gear practice may also be useful.
• The maximum contact ratio of the double flank test should be less than 2.0 when taking into account minimum tooth thickness, maximum outside diameter, minimum root diameter, and minimum tip radius of the test gear.  High contact ratios on the double flank tester promote more overlapping of the mesh and may hide errors in the test gear than may otherwise exist

Due to their face widths, helical gears may have an overall contact ratio greater than 2.0 when run against a master gear covering its full face width.  In such cases, a decision should be made to either accept the possible smoothing out of errors that would result with this high contact ratio or to possibly reduce the face width of the master gear and measure the helical gear in different contact zones along the test gears axis while maintaining an overall contact ratio of less than 2.0.

• In the case of when crossed axis helical double flank meshes where the driver is a worm, a worm can also be considered for the master gear. This may provide an advantage for the test gear in that only the functional zone is measured and other tooth errors that will not even be seen in the actual product mesh will be ignored.  In some cases, a narrow face width helical gear master may provide a similar result in a parallel axis arrangement.

In applications where a worm master is used, it may be necessary to add lubrication to the double flank mesh to assist sliding action in the mesh without causing reading errors.

• The extent of the master gear’s reach (i.e., the master gears outside diameter) into the test gear should be carefully chosen.  Although the mesh under test must have a minimum contact ratio of 1.0 and a maximum contact ratio of less than 2.0, there must also be no contact of the master beyond the form diameter of the test gear.  Therefore, there may be a wide range of choices in between those requirements when establishing the outside diameter of the master gear.

The decision on what master design to use may be based on the cost and availability of existing or commercially available master gears, or it may be based on measuring a test gear to at least its start of active profile location in the actual application. (See Figure 3)

• Every combination of master gear and test gear should be checked at all tolerance levels to make sure the mesh meets the criteria described here. Just because an off the shelf master gear is commercially available does not mean it will mesh properly with a specific test gear.
• In order to machine and produce high quality master gears by grinding, the bore on the master would need to be sufficiently large enough for a stable mandrel to hold the master gear during machining. Ground master gears with bores less than 6 mm should be carefully considered for the effect on master gear precision from a small diameter machining mandrel.

Answering the Questions

Considerations of the number of teeth in a master gear are determined by the tight mesh analysis of the master and work gear it is to be rolled with. An evaluation of profile contact between the master and work gear from the start to the end of the active profile is the first priority in order to error check the entire active flank. Secondly, total profile contact ratio and overlap in helical gears is a concern. The greater the contact ratio, the greater the amalgamation of error is blended, mixed, or fused into the composite result. The best design will optimally balance these considerations. Tight mesh contact ratios greater than 2.0 tend to hide errors that could be seen with lower contact ratios.

At a higher angle, helical gears overlap ratio can be a concern. In order to reduce the total contact ratio (and this is true for any spur or helical), a thinner master can be made at ¼ or ½ the face with of the work gear. However, in order to check the entire work gear face, the master must be rolled at more than one level to check error across the entire face width.

Gage R&R’s of double flank composite testing is very difficult due to the fact that composite rolling is a dynamic process rather than a static process. A Gage R&R done with double flank composite test process is rarely successful, and other methods are required to validate the accuracy and consistency of the measurement equipment.

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is a senior technical specialist in the development of gearing, drive motors, and power closure devices in the automotive industry. He currently serves on the AGMA Plastic and PM Gearing Committees. Eberle is a master six-sigma black belt and has authored many papers on gearing, measurement system analysis and process statistics. He can be reached at