In order to theoretically research the tooth surface maximum contact stress of a Cylindrical Gear with Variable Hyperbolic Circular-Arc-Tooth-Trace (VH-CATT), the computing formula of maximum contact stress of VH-CATT cylindrical gear is investigated according to Hertz formula in this paper. Insufficient contact fatigue strength will lead to pitting corrosion, plastic deformation of tooth surface and other damages. Therefore, the maximum contact stress of tooth surface must be carried out. The contact stress calculation formula is particularly considering the effect of normal force, total carrying length, synthetical curvature radius, and position angle. The present work establishes analytical solutions to research the effect of different parameters for the contact stress of VH-CATT cylindrical gear incorporating elastic deformation on the tooth surface, and which have shown that the different module, transmission ratio, pressure angle, tooth width, and the cutter head radius have a crucial effect on the contact stress and contact ellipse of VH-CATT cylindrical gear along the tooth width direction. Moreover, a finite element analysis is carried out to verify the correctness of the theoretical computing formula of contact stress of VH-CATT cylindrical gear. By contrast with the theoretical calculated value and the stress value of finite element analysis, its error is very small. It is indicated that the derived formula of contact fatigue strength of VH-CATT cylindrical gear has high accuracy and can accurately reflect the real contact stress value of tooth surface, which is beneficial for research on tooth break reduction, pitting, wear resistance and fatigue life improvement of the VH-CATT cylindrical gear. The study results also have a certain reference value for the design and check calculation of the VH-CATT cylindrical gear.

To reconstruct the tooth surface of a circular-arc-tooth-trace cylindrical gear (CATT cylindrical gear), a 3D model has been developed and the contact characteristics have been investigated. Based on the development principle and meshing theory, the tooth surface equation, tooth surface curvature equation and tooth surface contact ellipse equation of the CATT cylindrical gear were deduced, and it was proved that the contact was a point contact. Then, the tooth surface was reconstructed and a 3D model was developed. Next, by performing the finite element analysis and meshing impression experiment, it was proved again that the contact is the point contact, and the contact area became an ellipse under loading. Finally, the influences of the design parameters on the contact ellipse were investigated. The general tendency is that the elliptical contact area increases from the tooth root to the gear top; the elliptical contact area decreases when the modulus and the gear tooth number near the tooth root increase and it increases when the modulus and the gear tooth number near the tooth top increase; the elliptical contact area increases when the tooth line radius increases. The elliptical contact area decreases in a cliff-like manner near the tooth top. The research results provide a reference for the design, profile modification and lubrication of the CATT cylindrical gear.

As the most important working area of gear, teeth play the role of transmitting load and power. Tooth line and tooth profile are the two main characteristics of the tooth surface, which affect the shape of the tooth surface, tooth meshing characteristics and contact characteristics. Taking the elliptical cylinder gear pair in the reversing device of a new type of drum pumping unit as the research object, the dynamic meshing process of the gear is simulated by LS-PREPOST software based on loaded tooth contact analysis (LTCA) technology. The distribution law of the effective plastic strain, effective stress and tooth surface pressure in the direction of the tooth line and tooth profile as well as the tooth meshing force under different speed conditions are obtained. The results show that the effective plastic strain, effective stress and tooth surface pressure will decrease with the transition of the center position of the elliptical contact area on the tooth surface to both sides. The distribution of stress and strain in the direction of tooth line will change with the location of the teeth, and the rotational speed has a certain influence on the meshing force of the teeth. The results of this research can provide a theoretical basis for the subsequent analysis of the dynamic meshing characteristics and modification of non-circular gear.

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As an important parameter to distinguish noncircular gear from cylindrical gear, eccentricity is very important for the meshing characteristics and transmission error of noncircular gear. In order to study the transmission characteristics of the elliptic gear, a pair of elliptic gear in the reversing device of a new type of drum pumping was taken as the research object. Based on the analysis of the transmission pressure angle and instantaneous contact ratio of the elliptic gear, the eccentricity error was introduced into the analysis model of transmission error. The influences of the eccentricity on the transmission pressure angle, instantaneous contact ratio, and transmission error were analyzed, and the analysis accuracy is verified by the finite element method. The results show that the eccentricity has a great influence on the transmission pressure angle, instantaneous contact ratio, and transmission error of the elliptic gear, and the eccentricity error has a significant influence on the transmission error. In order to ensure the normal meshing condition of the elliptic gear, the eccentricity should be less than 0.7071, and the maximum instantaneous contact ratio is 1.809. The research results can provide some guidance for the following noncircular spur gear transmission test and transmission error research.