Principles of Gear Inspection

A summary of the principles of gear inspection as they apply to spur and helical gearing.


Over the next few editions of this column, I’d like to provide an understanding of the principles of gear inspection as they apply to spur and helical gearing, and the quirks that enter into the actual measuring and understanding of the data produced.
A gear tooth has three major elements to be inspected:

• Shape of the tooth profile (e.g. Involute)
• Position of the profile (index, spacing, etc)
• Shape and alignment of the tooth flank (lead) in respect to the axis of the gear

Prior to the 1970s, special machine tools were required for evaluating these elements—one for profile, a second for lead, and a third for spacing/index. These manual machines, still widely used today, require skilled trade personnel to set them up for each gear part number. Each machine takes about 20 minutes to complete its analysis, with the output presented on separate chart paper.

The gear checkers used today are, for the most part, made specifically to measure gears. They are computer-controlled and can determine average shapes of the teeth measured for profile and lead, analyzing the results to tell you whether the average complies with the tolerances entered by the operator. The output is produced by a computer and has many features to organize the results, such as color, tables showing history, comparison from green and hard charts, and tabular results of the values. Some machines are M&M, Klingelnberg, Hoffler, and Ziess. There are others, but these names supply 90+ percent of the gear checking machines to the gear industry.

In a perfectly finished gear tooth, with no discernable surface finish irregularities, the named elements are relatively simple to define and evaluate. In the real world, where surface finish errors are a given, features become confused. This is especially so in a pre-finished gear, such as one that is hobbed prior to shaving or grinding. (Figure 1)

Figure 1: A mechanical profile-checking machine and its output.

Even in teeth with no objectionable surface finish irregularities, modifications are made to the profile and the lead to accommodate working load stress, which bend the teeth during operating in its mounting. In the loaded “bent” condition, the tooth must realize its design shape and so, in the unloaded condition, as when being inspected, the tooth must be made to some other “non-standard” form. These modifications are made to the profile and to the lead. It is not usual to modify the index or spacing.

Additional modifications are required in roughed gears to accommodate the requirements of the finishing process and the effect of heat treatment. Over the next four columns, I will outline a brief summary of these modifications, starting with pre-finished gears—gear that will be finished after heat treatment.

Pre-finished gears


• Chamfer: As in finished gears, mainly incorporated to protect against nicks and burrs from handling.
• Undercut: This is a removal of material from the tooth flank below the start of active profile and is incorporated to provide clearance for finishing tools in those processes where such tools are not able to finish in the bottom of the tooth space.
Pressure Angle: This takes the form of a thickening of the tooth starting at the Start of Active Profile (SAP) and increasing to the tip. It leaves additional material on the tooth flank for a finishing operation and is an alternative to undercut.


• Slope: This is an increase in the spiral of the teeth or variation from the theoretical axis of the teeth around the gear and is incorporated to accommodate the amount of unwind or movement which takes place during heat treatment.
• Crowning: Required for the same purposes as in the finished gears, these modifications are usually a part of the finishing process. An exception to this would be gears of coarse pitches and large face widths where the amount of modification might exceed the removal capability of the finish process.
• Tooth Position: No modification is required.

Finished gears

Involute profile

• Tip Relief: This is the removal of a small amount of material from the tooth profile toward the tip.
• Pressure Angle: This is a slight change in the direction of “lean” of the gear tooth. May be in either the plus or minus direction depending on design requirements.
Chamfer: This is “ breaking “of the actual tip corner and denotes the end of the true involute profile.
Crown: This is a gradually increasing metal removal as measured toward the tip and the root from approximately mid tooth height. This could also be considered to be a rounding of the tooth in the profile direction. It is always a plus condition at the mid-height of the tooth.
• Hollow: This is the opposite of crown. This condition at the pitch diameter or middle of the tooth should be avoided. Involute profile hollows are the primary cause of noise.

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is retired from Eaton Corporation as a chief engineer. He has over 60 years of experience in the gear industry. Eaton is a power management company providing energy-efficient solutions that help customers effectively manage electrical, hydraulic, and mechanical power.