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The alignment deviation of the V-vertex of two symmetrically arranged gears with different rotation directions is a unique geometric parameter of double helical gears, which has an important effect on the vibration, noise, and double helical gear service life. Aiming to more accurately represent the manufacturing accuracy of double helical gears and their transmission performance, this paper proposes the meaning of the v-vertex basis the contact line of tooth surface based on the apex characteristics of double helical gears. First, the mathematical model of tooth flank is established based on gear meshing theory. Secondly, a method for measuring and evaluating the alignment deviation of double helical gear v-vertex (full tooth contact line method) is proposed. Eventually, the validity and convenience of the proposed measurement method are verified by the experiment. Experimental results showed that the total alignment deviation of double helical gears evaluated by the full tooth contact line method is 0.0082 mm, which meets the design requirements in Reference 16. This paper provides a new measurement and evaluation method for the comprehensive and accurate evaluation of double helical gears, which has significant implications for the design and manufacture of high-precision double helical gears.

In order to realize the accurate assessment of the profile error of the crown of the bearing roller, according to the geometric characteristics and the definition of the shape error of the contour element of the logarithmic bus-type roller, based on the principle of least squares, the least squares piece-wise fitting and error evaluation method of the logarithmic bus-type (combined form of the two-segment logarithmic curve) bearing roller crown profile are studied. Firstly, the three-point method is used to determine the curvature of the discrete data points of the convexity curve, and the boundary point of the two logarithmic curves is determined by the curvature difference method. Secondly, the measuring points adjacent to both sides of the dividing point are selected as auxiliary dividing points; the auxiliary dividing points and the corresponding logarithmic curve segment measuring points are fitted together to fit a series of least squares curves and calculate the corresponding errors. Through comparison and judgment, the least square error of the logarithmic bus-type roller profile is finally determined. Finally, through comparison and judgment, the least square error of the logarithmic bus-type roller profile is finally determined. The example results show that the total error of the logarithmic bus-type roller crown profile curve is 0.0071mm. The method in this paper can effectively realize the fitting and error evaluation of the bearing crown profile error, and it also verifies that the logarithmic prime line can reduce the stress concentration and improve the service life of the bearing.

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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