Construction of conical axoids on the basis of congruent spherical ellipses

Purpose: To carry out the transition from a cylindrical gear in which the centroids are congruent ellipses with centres of rotation in the foci, to a bevel gear on the basic of congruent spherical ellipses. Design/methodology/approach: Congruent ellipses with centres of rotation in the foci serve as centroids for the design of cylindrical gears with non-circular wheels. The article analytically shows that the analogues of ellipses on the plane - congruent spherical ellipses are the basis for the construction of the axoids of the corresponding bevel gears. An analogue of the centre-to-centre distance for ellipses in the plane is the angle between the axes of rotation of conical axoids. Findings: Based on the equality of the arcs of ellipses, the dependence of the angle of rotation of one axoid on the angle of rotation of another is found. Graphs of this dependence for separate cases are given. It is shown under what conditions the axes of axoids intersect at right angle. The parametric equations of spherical ellipses and corresponding axoids are given. They were used to construct spherical ellipses and corresponding conical axoids for different cases. For gears with right angle between the axes, separate positions of the axoids with different angles of their rotation around their axes are constructed. Practical implications: Spherical ellipses are directing curves for the construction of the corresponding conical axoids. Originality/value: The paper shows that congruent spherical ellipses act as centroids for the design of axoids of bevel gears. They roll one by one without sliding, rotating around axes that intersect in the centre of the sphere. To design such gears, it is important to know the interdependence between the geometric parameters, especially for common gears with a right angle between the axes.

Cutter Head Approximation Machining Method of Line Contact Spiral Bevel Gear Pairs Based On Controlling Topological Deviations

To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, the cutter head approximation machining method based on controlling topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be directly machined by cutter heads. First, the mathematical model of line contact conjugate flanks was established, and meshing equations and conjugate flank equations of bevel gear pairs were derived. Second, the gear tooth flank was set as the datum tooth flank for priority machining, and the pinion theoretical tooth flank which is fully conjugate with the gear tooth flank and the pinion machining tooth flank matching with the gear were solved. Then, the geometric topological deviations model of the comparison between the pinion machining tooth flank and its theoretical tooth flank can be established. Finally, with the pinion machining tooth flank approaching its theoretical tooth flank as the modification, the additional cutting motions and machining compensation parameters of cutter heads were obtained to control the pinion machining tooth flank deviations and reduce them to the allowable deviations of its theoretical tooth flank. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and feasibility of the cutter head approximation machining method.

Experimental Research on the Surface Quality of Milling Contour Bevel Gears

Contour bevel gears have the advantages of high coincidence, low noise and large bearing capacity, which are widely used in automobile manufacturing, shipbuilding and construction machinery. However, the quality of the tooth surface has a significant impact on the transmission accuracy of the gear, so it is of great significance to optimize the surface quality of the contour bevel gear. This paper firstly analyzes the formation process of machined surface roughness of contour bevel gears on the basis of generating machining method, and dry milling experiments of contour bevel gears are conducted to analyze the effects of cutting speed and feed rate on the machined surface roughness and surface topography of the workpiece. Then, the surface defects on the machined surface of the workpiece are studied by SEM, and the causes of the surface defects are analyzed by EDS. After that, XRD is used to compare the microscopic grains of the machined surface and the substrate material for diffraction peak analysis, and the effect of cutting parameters on the microhardness of the workpiece machined surface is investigated by work hardening experiment. The research results are of great significant for improving the machining accuracy of contour bevel gears, reducing friction losses and improving transmission efficiency.

5-axis double-flank CNC machining of spiral bevel gears via custom-shaped tools—Part II: physical validations and experiments

Recently, a new methodology for 5-axis flank computer numerically controlled (CNC) machining, called double-flank machining, has been introduced (see “5-axis double-flank CNC machining of spiral bevel gears via custom-shaped milling tools—Part I: Modeling and simulation”). Certain geometries, such as curved teeth of spiral bevel gear, admit this approach where the machining tool has tangential contact with the material block on two sides, yielding a more efficient variant of flank machining. To achieve high machining accuracy, the path-planning algorithm, however, does not look only for the path of the tool, but also for the shape of the tool itself. The proposed approach is validated by series of physical experiments using an abrasive custom-shaped tool specifically designed for a particular type of a spiral bevel gear. The potential of this new methodology is shown in the semifinishing stage of gear manufacturing, where it outperforms traditional ball end milling by an order of magnitude in terms of machining time, while keeping, or even improving, the machining error.

Modeling and analysis of transient lubrication characteristic of the helicopter main transmission spiral bevel gears in point contacts

An engineering calculation model is introduced for point-contact elastohydrodynamic lubrication analysis of spiral bevel gears. This model can analyze transient lubrication characteristics of spiral bevel gears. The influence of the angle between the lubricant entrainment and the minor axis of the contact ellipse is included in this model. The contact parameters of the spiral bevel gear are calculated, which will change with time during the meshing process. The variation of lubricant film thickness during the meshing process of spiral bevel gears is unraveled. Due to the influence of entrainment velocity, the oil film thickness at the out mesh side is smaller than that at the enter mesh side under the same contact force. It is evident that the higher the pressure is, the larger the contact area will be. Meanwhile, the thickness of the oil film is reduced, and the oil film distribution in the contact area is relatively uniform. Taking helicopter main transmission spiral bevel gears as an example, this study finally calculates the distribution characteristics of the oil film thickness of the spiral bevel gear, and solves the lubrication performance of the spiral bevel gear under different working conditions.