Aiming to achieve an accurate evaluation of the circumferential position error of the V-shaped apex of double-helical gear, the definition of the V-shaped apex of double-helical gear and the evaluation method of the circumferential position error is studied based on the geometric characteristics of double-helical gear and the definition of shape error. First, the definition of the V-shaped apex of double-helical gear based on the helix and its circumferential position error is presented based on the (American Gear Manufacturers Association) AGMA940-A09 standard. Second, based on the basic parameters, the tooth profile characteristics, and the tooth flank forming principle of double-helical gear, the mathematical model of double-helical gear in a Cartesian space coordinate system is established, and the auxiliary tooth flank and auxiliary helix are constructed to generate some auxiliary measurement points. Finally, the auxiliary measurement points are fitted using the least-squares principle to calculate the position of the V-shaped apex of the double-helical gear in the actual meshing condition and its circumferential position error. The simulation and experimental results show that the simulation results verify the feasibility of the method, and the experimental results (the circumferential position error of the V-shaped apex is 0.0187 mm) are consistent with the results of the literature [Bohui et al., Metrol. Meas. Technol. 36, 33 (2016)]. This method can effectively realize the accurate evaluation of the double-helical gear V-shaped apex position error, providing some guidance for the design and manufacture of double-helical gear.

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