# The accuracy of spur gearing

What values are measured to determine the accuracy of a spur gear?

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When deciding which spur gear to select for an application, there are several factors to consider. What is the anticipated torque? What is the desired life? What is the physical space available? What is the anticipated operating speed? These criteria help to size the gearing for the application. However, during production there are other factors to consider that will affect the performance of the gearing. The accuracy of the gear in regard to design standard can greatly impact a spur gear’s performance. As such, there are six criteria to which a spur gear is held in order to confirm that it is within tolerance of the accuracy grade desired. These include the Single Pitch Deviation (fpt), Total Cumulative Pitch Deviation (Fp), Total Profile Deviation (Fa), Total Helix Deviation (Fβ), Total Radial Composite Deviation (Fi”), and Runout Error of gear teeth (Fr).

Single pitch deviation is the deviation between actual measured pitch value between any adjacent tooth surface and theoretical circular pitch. Figure 1 details this deviation. Table 1 details the accepted values for this deviation based on the module, the reference diameter (also known as the pitch diameter) and the target accuracy grade.

Total cumulative pitch deviation is the difference between theoretical summation over any number of teeth interval, and summation of actual pitch measurement over the same interval. Figure 2 details this deviation. Table 2 details the accepted values for this deviation based on the Module, the Reference diameter (also known as the pitch diameter) and the target Accuracy grade.

Total profile deviation represents the distance (Fa) shown in Figure 3. The actual profile chart is lying in between upper design chart and lower design chart. Table 3 details the accepted values for this deviation based on the Module, the Reference diameter (also known as the pitch diameter), and the target Accuracy grade.

Total helix deviation represents the distance (Fβ) shown in Figure 4. The actual helix chart is lying in between upper helix chart and lower helix chart. Total helix deviation results in poor tooth contact, particularly concentrating contact to the tip area. Modifications, such as tooth crowning and end relief, can alleviate this deviation to some degree. Table 4 details the accepted values for this deviation based on the Module, the Reference diameter (also known as the pitch diameter) and the target Accuracy grade.

Total radial composite deviation represents variation in center distance when product gear is rotated one revolution in tight mesh with a master gear. Figure 5 details this deviation. Table 5 details the accepted values for this deviation based on the Module, the Reference diameter (also known as the pitch diameter) and the target Accuracy grade.

Runout error is typically measured by indicating the position of a pin or ball inserted in each tooth space around the gear and taking the largest difference. Runout causes a number of problems, one of which is noise. The source of this error is most often insufficient accuracy and ruggedness of the cutting arbor and tooling system. And, therefore, it is very important to pay attention to the cutting arbor and tooling system to reduce runout error. Shown in Figure 6 is the chart of runout. The values of runout include eccentricity. Table 6 details the accepted values for this deviation based on the Module, the Reference diameter (also known as the pitch diameter) and the target Accuracy grade.

As noted in all of the tables, the accepted value of deviation is dependent on the pitch of the gear (Module) and the reference diameter. As the pitch becomes coarser, the deviation standard reference value gets larger. As the pitch diameter increases, the deviation standard reference value also increases. Once a gear designer has selected the module and pitch diameter, they can select an appropriate accuracy grade for their application. With this information, the gear manufacturer can produce the perfect gear for the designer and the gear system will function as desired.

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is general manager of KHK USA Inc, a subsidiary of Kohara Gear Industry with a 24-year history of working in the industrial automation industry. He is skilled in assisting engineers with the selection of power-transmission components for use in industrial equipment and automation. Dengel is a member of PTDA and designated as an intern engineer by the state of New York. He is a graduate of Hofstra University with a Bachelor’s of Science in Structural Engineering.