While there has been a gradual convergence of generative gear metrology and 3-D or CMM type measurements, significant differences remain. This article explores the historical perspective and outlines the current technology.

Ever since the first CNC generative gear measuring systems for parallel axis gears were introduced to the marketplace in the late 1970s, efforts have been made to utilize coordinate measuring machines (CMMs) to check gears. Why not? After all, CMMs have three axes of measurement and can measure geometric shapes. Gears are geometric shapes, right?

Historical Perspective

Because the involute is easily generated by moving a point through space, generative motion was utilized for the purpose of evaluating the shape of gear teeth. The most direct and simple method is to mimic the generative method used to develop the gear tooth.

A fully equipped gear inspection lab needed at least three separate mechanical machines: an involute checker, a lead checker, and a pitch checker. Each needed to be maintained and calibrated on a regular basis, and operators needed to be trained in the use of each different machine. A note on nomenclature: current usage is profile (involute), helix (lead) and pitch. (Figure 1)

Figure 1

The earliest mechanical generative involute measuring machines utilized a simple disc of the exact base circle diameter of the subject gear mounted on the work spindle. The tangent slide pressed against it and moved as the disc rotated on the spindle. A measuring probe, mounted on the tangent slide, moves in the nominal path of the involute. The probe then would deviate either positively or negatively in response to any non-nominal conditions on the gear tooth.

A moving strip of paper (strip chart recorder) was arranged to move in sync with the rotation of the spindle, which ties the location on the strip chart with a specific position on the gear tooth.

This provided involute inspection of reasonable accuracy for the pre-CNC era. Every different gear base circle size required a very accurate disc of that exact size. A job shop might have needed hundreds of different discs to check their full range of gears. (Figure 2)

Figure 2

The next development eliminated the need for the separate base circle discs. A master disc was mounted below the work spindle of the gear checker, and a variable ratio base disc arrangement was used to position the tangent slide for any center distance within its adjustment range. This allowed any base circle size to be checked, but required additional skill for accurate operation.

The mechanical lead checker used similar mechanical motions to rotate the part and move the measuring probe in a coordinated manner in such a way as to generate the exact lead of the part. Again, the probe need only measure the deviation from nominal and record the deviation on a piece of moving chart paper.

If pitch was to be checked, a third machine would be needed.

The resulting charts, looking much like a seismograph or electrocardiogram, needed to be read and interpreted. This interpretation depended heavily on the experience of the person looking at the chart. Since the measurement and output were all analog, no numeric values were generated. Hard to believe, but this was all done without computers! This human-based interpretation was prone to variation and would sometimes lead to the gear lab developing a “guru” who would reign over all inspection charts. (Figure 3)

Figure 3: In the traditional gear-measuring technique before 1980, the plane of contact of a probe element was followed by a ruler (X), which is based on a circular disc with a diameter of the base circle while disc and gear turned firmly joined together (C). The strip chart recorder used to record the measurment diagrams moves in sync with the rolling path of the ruler. The measuring diagrams were indeed generating path-based.

Initial CMM efforts measured the pitch, helix and profile of the gear teeth by an X-Y-Z coordinate system, which calculated where the surface should be. The system would drive the probe to where the inspection point should be and take a measurement. The resulting deviations from the calculated nominal were reported. The ability to check pitch is made more difficult without a rotary table. The probe needs to be repositioned many times to reach the pitch diameter for each tooth all the way around the gear. This adds time and could reduce accuracy.

Most CMMs are capable of measuring objects from CAD data. However, gears are primarily manufactured using generative methods such as hobbing and shaping. Solid models and CAD data of gear teeth are not typically available or used for gear inspection. Arguing further against this is that a deviation table would be of little use to the operator of a hobber or gear grinder if corrections are necessary.

By comparison, the CNC generative gear inspection systems use interpolative two axis motions to create the nominal geometry by moving the probe in true involute and helical paths and measuring the deviation of the component from the theoretical. This motion directly creates the nominal geometry.

Because of the specific calculations required for gear geometry, early CMM inspection software often didn’t have the “horsepower” needed to check gears and supply information to the manufacturing people in a format that was familiar or useful. (Figure 4)

Figure 4

Compared to the mechanical gear inspection systems still in use at the time, as well as to the generative CNC systems just coming into wider use, the CMM approach was very slow. Since it utilized point-to-point measuring rather than the generative method, they also collected a relatively small amount of data. Probe tangency errors (often called I, J, K surface to normal vectors) also reduced accuracy. The lack of data density and industry acceptable analysis further prevented acceptance by the gear industry.

Adding to the challenge for CMMs was the difficulty of programming. Since CMMs are typically general purpose systems, every move and measuring point needs to be painstakingly programmed by a skilled programmer. In contrast, dedicated gear inspection machine software has the programming for gear inspection already in the machine. The user need only enter basic gear data from the engineering drawing and the machine uses this data to measure the gear. The typical commodity level CMM of the time was never capable of the accuracy and repeatability necessary for gear inspection. Using the old toolmakers rule of thumb, typical gear tolerances in the .005mm (.0002”) range require inspection accuracy much greater than the tolerance. With the large volumetric inspection cube, standard accuracy CMMs are often not accurate or repeatable enough for the task of gear metrology.

Early CNC controllers didn’t have the speed needed for gear inspection. The axis drives created internal heat that effected accuracy as well. Bridge type CMMs, with scales mounted at the slides, made measurements by reading those scales which are far away from the gear. Without a rotary table, a CMM needs to be much larger than the subject gear to provide sufficient travel in all axes to reach the entire gear. This makes the footprint of the machine much larger, requiring a larger inspection facility, and further positioning the measuring scales even further from the gear tooth. All this meant that companies whose main endeavor was gear manufacturing almost always had dedicated, four axis, CNC, generative gear inspection machines. (Figure 5)

Figure 5

If a gear producing company was checking gears for their own products, the output from the CMM was often useful. However, if the gears produced were for outside customers, there were often correlation issues. The inability of most CMMs of that vintage to measure a certified and calibrated master artifact, and make adjustments to match the known values, made the CMM reports unacceptable to many customers.

The Need for Calibration

Most manufacturers have quality standards that require inspection to be traceable to a calibrated artifact. In the gear industry, it is an accepted practice to use a master artifact calibrated by an accredited laboratory and traceable to the N.I.S.T. (National Institute of Standards and Technology) or other standards authority. Therefore, one of the most important criteria for gear metrology is the ability to measure a recognized calibrated master artifact and to adjust the measuring machine to the calibrated measurement values.

Evolving Technology

Touch probes were almost universally used on CMMs, and these probes lacked the accuracy and repeatability required by the very small tolerances found on gear drawings. Further, it was not possible to lock out two axis of the 3-D touch probes to allow measuring in the transverse plane of a gear. Add the fact the inspection reports usually didn’t look like what the gear community was used to and expected, it is easy to see why CMMs were not favored for critical gear inspection.

Throughout the late 1980s and early 1990s, technological advancements allowed more sophisticated programming. The CMM manufacturers began putting rotary tables on CMMs to allow faster measurements, although the initial applications did not utilize generative inspection. Higher accuracy scanning probes increased data density. (Figure 6)

Figure 6: Involutes are generated in the transverse section. If you work in the axial direction, you only need two axes. This can either be two linear axes, (Method A) or an axis of rotation and a linear axis (Method B + D).Method A uses a path composed of XY stages, normally used on a CMM (X,Y,Z).Method B corresponds to the generation principle of a mechanical gearmeasuring machine by using rotary axis C and the tangential linear axis X. This generating principle is used in all 4-axis devices (C,X,Y,Z).Method D makes the tangential superfluous by the linear axis Y being driven with simultaneous rotation of C axis of the tooth base towards the tip circle. This principle is used in all three-axis (1 rotary + 2 linear axis C,Y,Z) GMM devices and is very sensitive to the deviations of the probe tip from the turnable center.Method C is used in cases where large modules require a larger than the maximum available X-Traverse. This process is called “skew rolling” and occasionally used for large gears, it combines Method B and D using four axes (C,X,Y,Z).

The generative inspection machine manufacturers also improved their products. The ability to use radial and axial references, like CMMs were always capable of, improved referencing and accuracy. Moving from 1D probes to 3-D probes with the ability to lock individual axes as needed made the generative machines more flexible and easier to use.

One factor exists when using CMMs or generative gear inspection systems for gear metrology, and that is the effect of temperature. However, because CMMs typically use the three axes for the measurement, and these axes are relatively long and far removed from the component, changes in temperature have an adverse effect on measurement.

Generative systems use the linear and rotary axes to create the motion needed to generate the theoretical geometry, and the measurement takes place at the probe, very near the part. In addition, motion control with closed loop servos constantly compensate for very small variations in the motion of the generating axes.

Temperature changes over time, and shorter fluctuations also influence measurement accuracy. Generative systems, with the measurement both closer to the gear, and shorter measurement times are less influenced by temperature changes and fluctuations.

Speed of inspection is typically quite different between CMMs and generative inspection machines. In many cases, the CMM takes three or four times longer to measure a gear than a generative system. If manufacturing is waiting for the inspection results before going into production, this gets quite expensive.

CMM inspection of prismatic parts relies on a coordinate system and locates points within this 3-D space. Generative gear inspection does not utilize this coordinate system and uses either the measured datum surfaces or the center of rotation as the basis of all measurements. Since CMMs need to be able to measure planes, distances, locations, etc., they need the coordinate system. Since the dedicated gear checker need only measure the profile, helix and pitch of gears, it does not require the coordinate system to accomplish this.

Current Situation

From the above, it may be concluded that generative systems provide advantages for gear metrology. However, many companies have requirements for both gear and 3-D CMM metrology. The convergence of both methodologies have provided solutions for this with varying degrees of accuracy and success.

At the heart of generative gear inspection is the rotary table, and the ability to precisely synchronize the motion of the rotary table with a linear slide to create (generate) the nominal shape of the involute tooth and the helix. Measuring pitch error is relatively simple when using an integrated rotary table, since it allows each successive tooth to be accurately positioned in front of the measuring probe. Only the rotary and one linear axis are needed for any of the gear measurements. This eliminates the need for complicated probe reorientation needed if measuring pitch without a rotary table.

Measuring gears without a rotary table is possible, but it isn’t without difficulty. Pitch, in particular, requires the CMM probe to be reconfigured for different positions around the gear. When measuring the involute profile, the I, J, and K surface-to-normal vectors are changing with every change in roll angle. This can be compensated for, but if there a different deviation than the compensation was based on, inaccuracies result.

When a rotary table is integrated into the measurement system, additional options are available to measure involutes. The illustration below shows four approaches to involute measurement, three of which utilize rotary motion.

It is clear that the premium CMM manufacturers have continued to improve the accuracy and speed of their systems. This often comes at the cost of highly controlled lab environments and a high level of skill required for operators. In order to achieve the accuracy levels needed for gear inspection, some CMM manufacturers offer commodity (standard), medium and high accuracy models, with increasing cost as accuracy improves. The typical dedicated gear inspection system has the needed accuracy as part of the standard machine.

A case can be made that a very accurate generative gear inspection system is an advantageous platform for both gear inspection and CMM 3-D measurement. If it can be accepted that generative inspection is the fastest and most accurate way to check gears, then the former is obvious. Since generative systems, by definition, have high accuracy X, Y, and Z axes, then with the correct CNC controller and CMM software, they can excel at the latter. If the CMM tasks include rotationally symmetric components, the integrated rotary table can be utilized to enhance the accuracy and speed of measurement.


At the high end of metrology equipment, the convergence is taking place. Systems are now available that utilize granite construction, which minimizes thermal effects. Air bearings and linear motors for motion control are used for the highest accuracy. With I++ compatibility, many CMM software packages can be used regardless of the manufacturer of the measuring hardware. Industry accepted gear metrology software can operate on the same system as the CMM package, allowing each to be used to best advantage. At the heart of the system is a highly accurate rotary table.

The most successful implementations of CMM and generative gear inspection on one machine maintain separate software solutions. The standard CMM software is often CAD based and 3-D in its basic approach. Generative gear inspection uses the machine’s axes to create motion that moves the probe in a path that describes the gear tooth’s geometry. The other difference is in the analysis and reporting of the inspection results. The gear industry has evolved to have very specific standards, each with different analysis methods. AGMA 2000-A88, AGMA 2015, DIN, and ISO are just a few of the different methods required by gear manufacturers. In addition, customer specific custom standards exist for large companies such as GM, Ford and Caterpillar. The necessarily broader generic inspection approach of the CMM world precludes having these specific analysis and reporting options available due to the time and cost to develop and maintain them.

One system can do the job of the CMM and the gear checker without compromising either task if the tasks are considered as separate and different.

Previous articleExploring today’s heat-treating process involving furnaces, pumps
Next articleLubrication Engineers, Inc.
is vice president at Mitsubishi Heavy Industries America Inc. Machine Tool division. He has more than 25 years of experience in the gear manufacturing industry, including metrology, analysis, and project management. Smith serves as a committee chairman for AGMA, and he is an instructor for the AGMA Basic Gear School.
is the technical director of R&P Metrology GmbH. He has over 25 years of CMM and gear metrology experience working with Wenzel Präzision and Wenzel GearTec.