Higher-Order Tooth Flank Form Error Correction for Face-Milled Spiral Bevel and Hypoid Gears

The increasing demand for low noise and high strength leads to higher quality requirements in manufacturing spiral bevel and hypoid gears. Due to heat treatment distortions, machine tolerances, variation of cutting forces, and other unpredictable factors, the real tooth flank form geometry may deviate from the theoretical or master target geometry. This will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In the hypoid gear development process, a corrective machine setting technique is usually employed to modify the machine settings, compensating for the tooth flank form errors. Existing published works described the corrective machine setting technique based on the use of mechanical hypoid gear generators, and the second-order approximation of error surfaces. Today, computer numerically controlled (CNC) hypoid gear generators have been widely employed by the gear industry. The universal motion concept has been implemented on most CNC hypoid generators, providing additional freedoms for the corrections of tooth flank form errors. Higher-order components of the error surfaces may be corrected by using the higher-order universal motions. This paper describes a new method of tooth flank form error correction utilizing the universal motions for spiral bevel and hypoid gears produced by the face-milling process. The sensitivity of the changes of tooth flank form geometry to the changes of universal motion coefficients is investigated. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth flank form errors. A numerical example of a face-mill completing process is presented. The developed new approach has been implemented with computer software. The new approach can also be applied to the face-hobbing process.