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Aiming at the problem that most of the teeth root of straight bevel gears adopt fixed radius fillet transition with 0.3 times of modulus， which tends to to cause large bending stress on the tooth root and reduce the service life of bevel gears， a design method of variable radius tooth root fillet bevel gears is proposed. The general equation of the variable radius tooth root fillet under the standard tooth root bevel is established. Based on the fixed-radius non-standard planetary gear of an electric vehicle differential， the general equation of tooth root variable-radius fillet under different tooth root cones is derived， and the variable-radius non-standard planetary gear is optimally designed. Through finite element dynamics and fatigue life simulation analysis， it is concluded that the average tooth root bending stress of the bevel gear is reduced by 10.8% and the fatigue damage is reduced by 6.6% for the variable radius tooth root fillet compared with the fixed radius fillet with the largest radius. Therefore， the proposed design method improves the mechanical performance and fatigue life of the bevel gear.

A method of designing bevel gears is given, allowing to reduce the specific sliding ratio. Specific pressure coefficients are used as an additional evaluation criterion. The mathematical relationship between the criteria used is given. A distinguishing feature of the proposed methodology is the possibility of calculating the gears using an arbitrary coefficient of profile shift for each of the gears. In doing so, the value of the radial gap equal to 0.25 of the module is retained in the gears. The Bevel Gears x64 program is used for calculations. This program was written as part of the ongoing research. As an example, it is shown that a gear with number of pinion teeth z1 = 16 and number of wheel teeth z2 = 20, with the coefficient of profile shift for pinion x1 = 0.7 and for wheel x2 = 0.7, has relatively low and fairly close values of specific sliding ratio |λ1max| = 1.213 and |λ2max| = 1.214 as well as specific pressure ratio ϑ1 = 0.45 and ϑ2 = 0.347. In similar gears (z1 = 16, z2 = 20), designed according to the standard methodology (x1 = 0.17 and x2 = –0.17), the values of the studied indicators were |λ1max| = 3.165, |λ2max| = 2.512, ϑ1 = 0.942, and ϑ2 = 0.572. Reducing specific sliding ratios |λ1max| from 3.165 to 1.213 and |λ2max| from 2.512 to 1.214 will reduce the slippage of tooth dedendum on the pinion and wheel in proportion (2.6 and 2.1 times, respectively). The results show a significant increase of wear-resistance of the designed gears. [ABSTRACT FROM AUTHOR]

At present, most straight bevel gears use a root fillet transition surface with a radius of 0.3 modulus. This tends to cause excessive root bending stress and reduces the service life of bevel gears. In order to solve this problem, a root fillet transition surface controlled by a set of third-order Bezier curves is designed based on spherical involute tooth surface. In the common cone apex coordinate system of the bevel gear, the spherical involute tooth surface equations and the third-order Bezier curve equations controlling the root transition surface are established. The feasibility of gear manufacturing is verified by precision forging simulation. A Box–Behnken experiment was designed, and the response surface model was developed from the experimental results. The response surface model reflects the mathematical relationship between the four variables controlling the third-order Bezier curve and the maximum tooth root bending stress. Then, the nonlinear programming was used to optimize the four variables, and the optimal root transition surface was obtained. [ABSTRACT FROM AUTHOR]

The principle of tooth surface generating of skew bevel gear is analyzed about spherical involute， based on the theory that the line which in the plane that is tangent with the base cone of the skew bevel gear roll on the cone surface absolutely， a new milling method of gear surface is put forward. In this method， the alignment line obtained by the vertical intersection of the edge end circle and the base plane of the disk milling cutter is the tooth surface generation line， the relative motion between tool and workpiece is realized by using the relative motion relation generated by tooth surface. By analyzing the tooth surface generation motion， the machining motion process model of the tool and the workpiece is established. The tooth surface cutting is realized by the way of three-axis linkage of machine tool. The device for cutting test of skew bevel gear is designed and the correctness and feasibility of the method are verified by cutting test.

The parametric modeling of spiral bevel gear is of great significance to its further research on tooth contact analysis in its digitized design.From the precision of spiral bevel gear tooth with spherical involute tooth profile,the principle of forming the spherical involute is used to solve the parametric equations of all parts of tooth profile curve.Combining the unique advantages of Frenet frame in the SWEEP surface modeling,a modeling method of tooth surface of spiral bevel gear with the spherical involute is presented based on the SWEEP.Finally,the model is created by using the transverse tooth profiles through the SWEEP method.The numerical example verified that this method can finish fast and accurate parametric modeling process of the spiral bevel gear tooth surface,a new access to design of the spiral bevel gear is provided.

The involute profile is the most commonly used tooth profile for cylindrical gears. However, its counterpart for bevel gears is not commonly used because its generation is not compatible with the use of easy-to-manufacture cutting tools and market-oriented generation methods. Nowadays, with additive manufacturing technology growing across industries to manufacture parts and full-scale products, the spherical involute profile deserves to be given the possibility to become the reference profile for bevel gears generated by additive manufacturing, forging or plastic molding. In this work, both the spherical involute and the octoidal form systems for bevel gears are mathematically defined. The geometry of their respective crown-gears for generation is derived and the computerized modeling of the geometries of the generated bevel gears presented. The comparison between the obtained gear tooth geometries is performed from the point of view of the obtained geometric deviations, their behavior to the change of the shaft angle and the evolution of contact and bending stresses for different values of torque applied to the pinion. The results showed that the spherical involute profile can handle better with the changes in the shaft angle, although the octoidal profile presents lower contact and bending stresses. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a mathematical model of the spherical involute tooth surface of a spiral bevel gear whose generating curve is an arc of a circle is built. The parameters on the base cone of the gear are derived from those on the pitch cone of the gear. The algorithm derived can be used for designing the spherical involute surface of straight and spiral bevel gears. The curve of action, the paths of contact and the contact patterns of spiral bevel gears are obtained by the tooth contact analysis (TCA). The TCA results show that: 1) the curve of action is on a spherical surface; 2) the paths of contact do not change with the variation of the radii of the generating arcs of circles of the tooth surfaces of the pinion and the gear; 3) the length of the major semi axis of their contact ellipse is determined by the radii of the generating arcs of circles of the tooth surfaces of the pinion and the gear and it does not change during the transmission process. The 3-dimensional (3D) model of the gears is constructed in 3D modeling software based on the proposed method. [Copyright &y& Elsevier]

In this article, a new gear generating method for the spiral bevel gear with spherical involutes tooth curves was proposed. It was analysed that the tooth flank with cone-spiral involute surface could be formed by the space trajectory of a straight line. The straight line was named as a tracing line. In the method, three motions were demanded; those were the rotary motion of the workpiece, the rectilinear motion of the end of the tracing line along the dedendum, and the rotary motion of the tracing line in the plane. The motion equations were derived. The plate milling cutter with face cutting edges could be used to machine the spiral bevel gears and the chord line of the face circle worked as the tracing line. By the method, the spiral bevel gears without principle errors whose tooth flanks are exact spherical involute curves that could be achieved. [ABSTRACT FROM AUTHOR]