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<p>The pitch circle diameter, pitch deviations and eccentricity errors significantly influence the transmission accuracy, dynamic stability and load distribution in spur gear trains. In this work, a new flexible and accurate mathematical model and measurement approach for evaluating the actual pitch diameter, pitch deviations and eccentricity errors are established. The established work does not employ nominal or theoretical gear dimensions. Flank measurements are used to accurately determine the gear’s actual pitch diameter. A specially designed template determines the radii of the measured flank points. The developed model uses the measured radii to evaluate the template orientation from which the actual pitch diameter is obtained. Pitch deviations, at the actual pitch circle, and eccentricity error value and direction are then evaluated using the measured radii. The accuracy of the proposed approach was first verified using theoretical gear models. The models revealed no errors in template orientations nor measured radii required for pitch deviation evaluation. They revealed eccentricity deviations ranging from 0&#xa0;μm to 0.2&#xa0;μm at lower and higher assumed eccentricity values respectively. The developed approach was then applied to experimental measurements obtained using a Coordinate Measuring Machine and optical method. The pitch radius and eccentricity error of the gear measured by CMM are 13.646 and 0.052&#xa0;mm respectively. The standard error of the mean is 3 and 8&#xa0;μm for the left and right pitch flank deviations respectively. The developed work is applicable to gears with different dimensions and measurement techniques and can enhance the accuracy of reverse engineering applications.</p>

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A new developed methodology for the measurement of actual pitch circle diameter, corresponding pitch deviations and evaluation of eccentricity errors in spur gears

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月21日

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  • Mohamed Damir,
  • Abdallah Khalil

摘要

The pitch circle diameter, pitch deviations and eccentricity errors significantly influence the transmission accuracy, dynamic stability and load distribution in spur gear trains. In this work, a new flexible and accurate mathematical model and measurement approach for evaluating the actual pitch diameter, pitch deviations and eccentricity errors are established. The established work does not employ nominal or theoretical gear dimensions. Flank measurements are used to accurately determine the gear’s actual pitch diameter. A specially designed template determines the radii of the measured flank points. The developed model uses the measured radii to evaluate the template orientation from which the actual pitch diameter is obtained. Pitch deviations, at the actual pitch circle, and eccentricity error value and direction are then evaluated using the measured radii. The accuracy of the proposed approach was first verified using theoretical gear models. The models revealed no errors in template orientations nor measured radii required for pitch deviation evaluation. They revealed eccentricity deviations ranging from 0 μm to 0.2 μm at lower and higher assumed eccentricity values respectively. The developed approach was then applied to experimental measurements obtained using a Coordinate Measuring Machine and optical method. The pitch radius and eccentricity error of the gear measured by CMM are 13.646 and 0.052 mm respectively. The standard error of the mean is 3 and 8 μm for the left and right pitch flank deviations respectively. The developed work is applicable to gears with different dimensions and measurement techniques and can enhance the accuracy of reverse engineering applications.